U.S. patent application number 15/183010 was filed with the patent office on 2016-12-15 for atom-based electromagnetic radiation electric-field sensor.
The applicant listed for this patent is THE REGENTS OF THE UNIVERSITY OF MICHIGAN. Invention is credited to David A. ANDERSON, Joshua GORDON, Christopher HOLLOWAY, Steven JEFFERTS, Stephanie A. MILLER, Georg A. RAITHEL, Andrew SCHWARZKOPF, Nithiwadee THAICHAROEN.
Application Number | 20160363617 15/183010 |
Document ID | / |
Family ID | 57516925 |
Filed Date | 2016-12-15 |
United States Patent
Application |
20160363617 |
Kind Code |
A1 |
ANDERSON; David A. ; et
al. |
December 15, 2016 |
Atom-Based Electromagnetic Radiation Electric-Field Sensor
Abstract
A method is presented for measuring the electric field of
electromagnetic radiation using the spectroscopic responses of
Rydberg atoms to the electromagnetic radiation field. The method
entails implementing quantitative models of the Rydberg atom
response to the electromagnetic radiation field to provide
predetermined atomic properties or spectra for field amplitudes and
or frequencies of interest, spectroscopically measuring the
response (spectrum) of Rydberg atoms exposed to an unknown
electromagnetic radiation field, and obtaining the electric field
amplitude and/or frequency of the unknown electromagnetic radiation
by using features extracted from the measured spectrum and
comparing them to features in a predetermined spectrum among the
set of predetermined spectra.
Inventors: |
ANDERSON; David A.; (Ann
Arbor, MI) ; RAITHEL; Georg A.; (Ann Arbor, MI)
; HOLLOWAY; Christopher; (Boulder, CO) ; GORDON;
Joshua; (Lafayette, CO) ; SCHWARZKOPF; Andrew;
(Gaithersburg, MD) ; THAICHAROEN; Nithiwadee; (Ann
Arbor, MI) ; MILLER; Stephanie A.; (Ann Arbor,
MI) ; JEFFERTS; Steven; (Boulder, CO) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
THE REGENTS OF THE UNIVERSITY OF MICHIGAN |
Ann Arbor |
MI |
US |
|
|
Family ID: |
57516925 |
Appl. No.: |
15/183010 |
Filed: |
June 15, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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62175805 |
Jun 15, 2015 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01R 29/0885
20130101 |
International
Class: |
G01R 29/08 20060101
G01R029/08 |
Claims
1. A method for measuring the electric field of electromagnetic
radiation using the spectroscopic responses of Rydberg atoms to the
radiation to be measured, comprising: providing predetermined
atomic spectra for atoms of a known type; placing the atoms within
the unknown electromagnetic radiation field to be measured, where
the atoms are in a gaseous state and contained in a vacuum
enclosure; propagating one or more light beams through the atoms,
where at least one light beam is coupled to a Rydberg state;
measuring an atomic spectrum using the one or more light beams
while the unknown electromagnetic radiation is interacting with or
has interacted with the atoms; analyzing the measured atomic
spectrum to extract spectral features; comparing the spectral
features from the measured atomic spectrum to spectral features of
the predetermined atomic spectra; matching the measured atomic
spectrum to a given spectrum in the predetermined atomic spectra;
and quantifying at least one of field strength or frequency of the
unknown electromagnetic radiation field using the given spectrum
and the predetermined atomic spectra.
2. The method of claim 1 wherein providing predetermined atomic
spectra for atoms further comprises determining a model of atomic
response in presence of the electromagnetic radiation.
3. The method of claim 1 wherein providing predetermined atomic
spectra for atoms further comprises calculating the predetermined
atomic spectra at a fixed frequency for a range of electric field
values.
4. The method of claim 1 wherein providing predetermined atomic
spectra for atoms further comprises calculating the predetermined
atomic spectra at a fixed electric field for a range of
frequencies.
5. The method of claim 1 wherein providing predetermined atomic
spectra for atoms further comprises calculating the predetermined
atomic spectra using Floquet theory.
6. The method of claim 1 wherein the atoms contained in the vacuum
enclosure are maintained at a fixed temperature and density.
7. The method of claim 1 wherein measuring an atomic spectrum using
electromagnetically induced transparency.
8. The method of claim 5 wherein measuring an atomic spectrum of
the atoms further comprises propagating a probing light beam
through the atoms, where the probing light beam has a frequency
resonant with transition of the atoms from a first quantum state to
a second quantum state; propagating a coupling light beam through
the atoms simultaneously with the probing light beam, where the
coupling light beam is overlapped spatially with the probing light
beam, frequency of the coupling light beam is scanned across a
range in which atoms transition from the second quantum state to a
Rydberg state; and detecting the probing light beam passing though
the atoms using a light detector.
9. The method of claim 7 wherein measuring an atomic spectrum of
the atoms further comprises propagating a probing light beam
through the atoms, where frequency of the probing light beam is
scanned across a range in which atoms transition from a first
quantum state to a second quantum state; and propagating a coupling
light beam through the atoms concurrently with the probing light
beam, where the coupling light beam is overlapped spatially with
the probing light beam, frequency of the coupling light beam is
resonant with transition of the atoms from the second quantum state
to a Rydberg state; and detecting the probing light beam passing
though the atoms using a light detector.
10. The method of claim 1 wherein the spectral features extracted
from the measured atomic spectrum are defined as the frequency
difference between two split peak pairs in the measured atomic
spectrum.
11. The method of claim 10 wherein comparing the spectral features
from the measured atomic spectrum further comprises overlaying the
predetermined atomic spectra onto the measured atomic spectrum and
shifting the predetermined atomic spectra such that the
predetermined atomic spectra aligns with the measured atomic
spectrum.
12. The method of claim 11 wherein quantifying field strength of
the unknown electromagnetic radiation field further comprises
determining Rabi frequency from a splitting of a Rydberg line in
the measured atomic spectrum, calculating dipole moment of the
relevant Rydberg transition, and computing magnitude of field
strength of the unknown electromagnetic radiation field from the
Rabi frequency and the dipole moment.
13. The method of claim 1 wherein the spectral features extracted
from the measured atomic spectrum are defined as one or more of
peak heights, peak widths and relative peak positions in a Floquet
map.
14. The method of claim 13 wherein comparing the spectral features
from the measured atomic spectrum further comprises overlaying the
predetermined atomic spectra onto the measured atomic spectrum,
shifting the predetermined atomic spectra in relation to the
measured atomic spectrum so that the spectral features are in
agreement, thereby yielding the field strength or frequency of the
unknown electromagnetic field.
15. The method of claim 1 further comprises measuring the atomic
spectrum without the necessity of metal or conductive material in
the vacuum enclosure.
16. A method for measuring the electric field of electromagnetic
radiation using the spectroscopic responses of Rydberg atoms to the
radiation to be measured, comprising: calculating predetermined
atomic spectra for atoms of a known type using Floquet theory;
propagating an unknown electromagnetic radiation field towards the
atoms, where the atoms are in a gas state and contained in a vacuum
enclosure; propagating one or more light beams through the atoms,
where at least one light beam is coupled to a Rydberg state of the
atoms; measuring an atomic spectrum using the one or more light
beams while the unknown electromagnetic radiation is interacting
with or has interacted with the atoms; analyzing the measured
atomic spectrum to extract spectral features; comparing the
spectral features from the measured atomic spectrum to spectral
features of the predetermined atomic spectra; and matching the
measured atomic spectrum to a given spectrum in the predetermined
atomic spectra, thereby quantifying one of field strength or
frequency of the unknown electromagnetic radiation field.
17. The method of claim 16 further comprises measuring an atomic
spectrum using electromagnetically induced transparency.
18. The method of claim 16 further comprises measuring an atomic
spectrum using electromagnetically induced transparency.
19. The method of claim 16 further comprises analyzing the measured
atomic spectrum to extract peak positions and comparing the peak
positions from the measured atomic spectrum to peak positions of
the predetermined atomic spectra by overlaying the predetermined
atomic spectra onto the measured atomic spectrum and shifting the
predetermined atomic spectra in relation to the measured atomic
spectrum until the peak positions in the predetermined atomic
spectra fall within full width half maximum of the peak positions
in the measured atomic spectrum.
20. A system for measuring the electric field of electromagnetic
radiation using spectroscopic responses of Rydberg atoms,
comprising: a vapor cell containing atoms of a known type; a source
of electromagnetic radiation arranged to emit electromagnetic
radiation towards the vapor cell; a probing light source configured
to propagate a probing light beam through the vapor cell, where
frequency of the probing light beam is scanned across a range in
which the atoms transition from a first quantum state to a second
quantum state; a coupling light source configured to propagate a
coupling light beam through the vapor cell concurrently with the
probing light beam, where the coupling light beam is
counterpropagating to and overlapped spatially with the probing
light beam, and frequency of the coupling light beam is resonant
with transition of the atoms from the second quantum state to a
Rydberg state; a light detector configured to receive the probing
light beam after passing through the vapor cell; a data store that
stores predetermined atomic spectra for the atoms in the presence
of the electromagnetic radiation; and a data processor in data
communication with the light detector and the data store, and
operates to measure an atomic spectrum for the atoms from the
probing light beam received from the light detector and analyze the
measured atomic spectrum to extract spectral features, wherein the
data processor compares the spectral features from the measured
atomic spectrum to spectral features of the predetermined atomic
spectra; and matches the measured atomic spectrum to a given
spectrum in the predetermined atomic spectra, thereby quantifying
one of field strength or frequency of the unknown electromagnetic
radiation field.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. Provisional
Application No. 62/175,805, filed on Jun. 15, 2016. The entire
disclosure of the above application is incorporated herein by
reference.
FIELD
[0002] The present disclosure relates to a technique for measuring
the electric field (or frequency) of electromagnetic radiation
using the response of Rydberg atoms.
BACKGROUND
[0003] Significant progress has been made in recent years towards
establishing atomic measurement standards for field quantities.
Rydberg atoms hold particular appeal for applications in
electrometry due to their large transition electric dipole moments,
which lead to a strong atomic response to electric (E) fields.
Rydberg electromagnetically induced transparency (EIT) in atomic
vapors has recently been demonstrated by applicants as a practical
approach to absolute measurements of radio-frequency (RF) E fields
over a broad frequency range (10 MHz to 500 GHz) and dynamic range
(.about.100 mV/m to >1 kV/m) suitable for the development of
calibration-free broadband RF sensors. The utility of the Rydberg
EIT technique in characterizing RF E fields has been demonstrated
in a number of applications. These include microwave polarization
measurements, millimeter-wave (mm-wave) sensing, and subwavelength
imaging. The approach has also been employed in room-temperature
studies of multiphoton transitions in Rydberg atoms, as well as in
measurements of static E fields for precise determinations of
quantum defects.
[0004] The Rydberg EIT measurement technique has been employed in
measurements of weak RF fields. In the weak-field regime, the
atom-field interaction strength is small compared to the Rydberg
energy-level structure, and the level shifts of the relevant
coupled atom-field states are well described using perturbation
theory. By exploiting near-resonant and resonant dipole transitions
between high-lying Rydberg levels, which elicit a maximal atomic
response, RF fields from as small as approximately 100 mV/m to a
few tens of V/m have been measured. For measurements of strong RF E
fields, the atom-field interaction cannot be modeled using
perturbative methods and requires a non-perturbative method to
accurately describe the response of the atomic system. Extending
the atom-based measurement approach to a high-power regime could
enable, for example, subwavelength characterizations of antennas
radiating high-power microwaves among other applications.
[0005] This section provides background information related to the
present disclosure which is not necessarily prior art.
SUMMARY
[0006] This section provides a general summary of the disclosure,
and is not a comprehensive disclosure of its full scope or all of
its features.
[0007] A method is presented for measuring the electric field of
electromagnetic radiation using the spectroscopic responses of
Rydberg atoms. The method includes: providing predetermined atomic
spectra for atoms of a known type; placing the atoms within the
unknown electromagnetic radiation field to be measured, where the
atoms are in a gaseous state and contained in a vacuum enclosure;
propagating one or more light beams through the atoms, where at
least one light beam is coupled to a Rydberg state; measuring an
atomic spectrum using the one or more light beams while the unknown
electromagnetic radiation is interacting with or has interacted
with the atoms; analyzing the measured atomic spectrum to extract
spectral features; comparing the spectral features from the
measured atomic spectrum to spectral features of the predetermined
atomic spectra; matching the measured atomic spectrum to a given
spectrum in the predetermined atomic spectra; and quantifying at
least one of field strength or frequency of the unknown
electromagnetic radiation field using the given spectrum and the
predetermined atomic spectra.
[0008] Predetermined atomic spectra for the atoms are models of
atomic responses in presence of the electromagnetic radiation. In
one embodiment, the predetermined atomic spectra are calculated at
a fixed frequency for a range of electric field values. In another
embodiment, the predetermined atomic spectra are calculated at a
fixed electric field for a range of frequencies. In some
embodiments, the predetermined atomic spectra are calculated using
Floquet theory.
[0009] In some embodiments, the atomic spectrum can be measured
using electromagnetically induced transparency. For example, a
probing light beam is propagated through the atoms, where the
probing light beam has a frequency resonant with transition of the
atoms from a first quantum state to a second quantum state; a
coupling light beam is propagated through the atoms simultaneously
with the probing light beam, where the coupling light beam is
overlapped spatially with the probing light beam, frequency of the
coupling light beam is scanned across a range in which atoms
transition from the second quantum state to a Rydberg state; and
the probing light beam passing though the atoms is detected using a
light detector. In another example, a probing light beam is
propagated through the atoms, where frequency of the probing light
beam is scanned across a range in which atoms transition from a
first quantum state to a second quantum state; a coupling light
beam is propagated through the atoms concurrently with the probing
light beam, where the coupling light beam is overlapped spatially
with the probing light beam, frequency of the coupling light beam
is resonant with transition of the atoms from the second quantum
state to a Rydberg state; and the probing light beam passing though
the atoms is detected using a light detector.
[0010] In one aspect of this disclosure, spectral features
extracted from the measured atomic spectrum are further defined as
the frequency difference between two split peak pairs in the
measured atomic spectrum. These spectral features can be compared
by overlaying the predetermined atomic spectra onto the measured
atomic spectrum and shifting the predetermined atomic spectra such
that the predetermined atomic spectra aligns with the measured
atomic spectrum. In this case, field strength of the unknown
electromagnetic radiation field can be quantified by determining
Rabi frequency from a splitting of a Rydberg line in the measured
atomic spectrum, calculating dipole moment of the relevant Rydberg
transition, and computing magnitude of field strength of the
unknown electromagnetic radiation field from the Rabi frequency and
the dipole moment.
[0011] In another aspect of this disclosure, the spectral features
extracted from the measured atomic spectrum are further defined as
one or more of peak heights, peak widths and relative peak
positions in a Floquet map. These spectral features can be compared
by overlaying the predetermined atomic spectra onto the measured
atomic spectrum, shifting the predetermined atomic spectra in
relation to the measured atomic spectrum so that the spectral
features are in agreement, thereby yielding the field strength or
frequency of the unknown electromagnetic field.
[0012] A system is also presented for measuring the electric field
of electromagnetic radiation using spectroscopic responses of
Rydberg atoms. The system includes: a vapor cell containing atoms
of a known type; a source of electromagnetic radiation arranged to
emit electromagnetic radiation towards the vapor cell; a probing
light source configured to propagate a probing light beam through
the vapor cell, where frequency of the probing light beam is
scanned across a range in which the atoms transition from a first
quantum state to a second quantum state; a coupling light source
configured to propagate a coupling light beam through the vapor
cell concurrently with the probing light beam, where the coupling
light beam is counterpropagating to and overlapped spatially with
the probing light beam, and frequency of the coupling light beam is
resonant with transition of the atoms from the second quantum state
to a Rydberg state; a light detector configured to receive the
probing light beam after passing through the vapor cell; a data
store that stores predetermined atomic spectra for the atoms in the
presence of the electromagnetic radiation; and a data processor in
data communication with the light detector and the data store. The
data processor measures an atomic spectrum for the atoms from the
probing light beam received from the light detector and analyzes
the measured atomic spectrum to extract spectral features. The data
processor also compares the spectral features from the measured
atomic spectrum to spectral features of the predetermined atomic
spectra; and matches the measured atomic spectrum to a given
spectrum in the predetermined atomic spectra, thereby quantifying
one of field strength or frequency of the unknown electromagnetic
radiation field.
[0013] Further areas of applicability will become apparent from the
description provided herein. The description and specific examples
in this summary are intended for purposes of illustration only and
are not intended to limit the scope of the present disclosure.
DRAWINGS
[0014] The drawings described herein are for illustrative purposes
only of selected embodiments and not all possible implementations,
and are not intended to limit the scope of the present
disclosure.
[0015] FIG. 1 is a diagram depicting an example measurement
system;
[0016] FIGS. 2A and 2B are diagrams illustrating 3-level and
4-level atomic systems, respectively;
[0017] FIG. 3 is a flowchart illustrating a technique for measuring
the electric field and/or frequency of electromagnetic
radiation;
[0018] FIG. 4 is a block diagram of an experimental set up for the
proposed electric field measurement technique;
[0019] FIG. 5 is a graph showing a probe transmission as a function
of .DELTA..sub.p for the three-level EIT system;
5 S 1 / 2 - 5 P 3 2 - 50 D ##EQU00001##
[0020] FIG. 6 is a graph showing an EIT-signal as a function of
.DELTA..sub.p for the EIT system 5S.sub.1/2-5P.sub.3/2-28D.sub.5/2,
and a signal when the 28D.sub.5/2 level is coupled to the
29P.sub.3/2 level by a 104.77 GHz RF field;
[0021] FIG. 7 is a graph showing experimental data for the
measurement for .DELTA.f at 17.04 GHz;
[0022] FIG. 8 is a graph showing a comparison of experimental data
to both numerical simulations and to far-field calculations for
15.59 GHz, 17.04 GHz, and 104.77 GHz;
[0023] FIGS. 9A and 9B show weak-field measurement of 132.6495 GHz
mm waves on the 26D.sub.5/2-27P.sub.3/2 one-photon transition
versus {square root over (power)}; and a strong-field measurement
of 12.461 154 8 GHz microwaves on the 65D-66D two-photon transition
versus power, respectively;
[0024] FIG. 10 is a graph showing the calculated |m.sub.j|=1/2
(black circles) and 3/2 (red circles) Floquet quasienergies and
their relative excitation rates (circle area) from 5P.sub.3/2;
[0025] FIG. 11A shows an experimental spectra of the 65D-66D
two-photon transition versus microwave power; and
[0026] FIG. 11B shows a composite Floquet map model of FIG.
11A.
[0027] Corresponding reference numerals indicate corresponding
parts throughout the several views of the drawings.
DETAILED DESCRIPTION
[0028] Example embodiments will now be described more fully with
reference to the accompanying drawings.
[0029] With reference to FIGS. 1 and 2, the basic concept for
measuring the electric field of electromagnetic radiation is
presented. FIG. 1 depicts an example measurement system 10. The
measurement system 10 is comprised generally of a source of
electromagnetic radiation 12, one or more light sources 13, a light
detector 14 and atoms of a known type contained in a vacuum
enclosure 15. In this example, a probing light beam is provided
from a probing light source 13A and a coupling light beam is
provided from a coupling light beam 13B. The atoms serve as the
active medium for the measurement probe. In this example,
rubidium-85 (.sup.85Rb) atoms are chosen as the active medium
although other types of atoms fall within the scope of this
disclosure, especially alkali atoms and those having a sufficiently
high vapor pressure at room temperature.
[0030] The measurement method is demonstrated using
electromagnetically transparency (EIT) in an atomic vapor or gas as
an optical readout of atomic structure that is representative of
the electric field or frequency of the electromagnetic radiation
field of interest. Generally, an atom can be in different states
with associated energies (levels). This is illustrated in FIG. 2
where the states of an atom are designated by |i>, where "i" is
a given state. FIG. 2A shows the three levels of an atom relevant
to the optical EIT readout of atomic structure. Here, the probe
laser is resonant with the |1> to |2> transition (transition
from a ground state to a first excited state) and a strong coupler
laser is resonant with the |2> to |3> transition (transition
from a first excited state to a Rydberg state). If the coupler
laser is off, the probe laser gets scattered (absorbed and
reemitted) by the atom. However, when the coupler laser is on,
there is an increased transmission of the probe laser due to
quantum interference of excitation pathways when both the probe is
resonant with the |1> to |2> transition and the coupler is
resonant with the |2> to |3> transition. This is the
phenomenon of EIT. This provides a way to optically detect state
|3> by measuring a change in the transmission of the probe
through the atomic medium when, for example, the coupler laser is
scanned in frequency through |2> to |3> resonance. Thus,
state |3> is detected as a narrow (EIT) transmission peak in the
probe absorption. With the appropriate choice of optical fields for
the EIT, different atomic states (like |3> in this case) can be
optically interrogated.
[0031] When an electromagnetic radiation field interacts with an
atom, the atomic structure, or its energy levels, can change. How
the atomic structure changes in this interaction depends on the
nature (e.g. frequency and amplitude) of the electromagnetic
radiation. FIG. 2B illustrates a special case of an interaction of
the atom with an electromagnetic radio-frequency (RF) field that is
weak and resonant between two Rydberg levels |3> and |4>. In
the case that the applied RF field is weak, the interaction of the
RF field with the atom leads to a change in the structure of the
atomic energy levels (|3> and |4>) such that two dressed
states are formed whose separation is proportional to the electric
field amplitude of the RF source. In this case, one observes a
splitting of the original EIT peak into two peaks. This splitting
is known as Autler-Townes (AT) splitting which is related to the
Rabi frequency .OMEGA..sub.RF of the |.beta.-|4 transition and
applied field amplitude, and allows for a measurement of the
E-field strength. In more general cases, for different RF
frequencies and amplitudes, the structure of the atomic energy
levels changes in different ways (not just a splitting) and more
than just one or two energy levels may change. These changes in the
atomic structure are also detected optically using EIT, providing a
measured spectrum with different spectral features. The electric
field or frequency of the electromagnetic radiation is then
determined by matching the measured spectrum to a calculated
spectrum in a set of predetermined spectra (previously calculated
for the RF field frequency and amplitude range of interest) that
uniquely corresponds to the electric field and frequency of the RF
field. The match is achieved by comparing the spectral features
(such as relative peak positions, peak heights, peak widths) of the
measured spectrum to those of the calculated spectra in the set.
The matched predetermined spectrum, which was calculated for a
specific electric field amplitude and frequency, then provides the
electric field amplitude and frequency of interest.
[0032] To measure the field strength (or amplitude) for different
RF field frequencies, different states |3 and |4 can be chosen.
State |3, with a state |4 to which the RF radiation field can
couple, is selected by tuning the wavelength of the coupling laser.
A large range of atomic transitions can be selected, allowing
measurements of RF fields over a correspondingly wide selection of
frequencies. In essence, the atoms act as a highly tunable,
resonant, frequency selective RF detectors. This is a significant
benefit of using Rydberg atoms as field probes. The wide range of
states |3 selectable by the coupling laser and of states |4
available for RF measurement translates to the broadband nature of
the probe, which allows RF measurements ranging from 10 MHz to 500
GHz.
[0033] FIG. 3 depicts a proposed method for measuring the electric
field (or frequency) of electromagnetic radiation using the
response of Rydberg atoms. To obtain a measurement of the EM
radiation E-field strength it is critical that the atomic response
be accurately modeled over the desired range of EM radiation field
frequencies and amplitudes. This is necessary so that a comparison
of the experimentally observed spectra can be made and information
on the nature of the EM radiation field can be obtained. The atomic
response over a broad range of EM radiation field frequencies and
field strengths varies from linear regimes (where there is a linear
response of the atomic level shifts to the incident EM radiation
field) to highly non-linear regimes. Measurement of an arbitrary
(unknown) EM radiation field therefore requires a complete model of
a broad range of atom-field interactions. As a starting point, a
set of predetermined atomic spectra are provided at 31 for atoms of
a known type, where each of the predetermined atomic spectra models
the response of the atoms to an electromagnetic radiation field.
Techniques for calculating the predetermined atomic spectra are
further described below.
[0034] Electromagnetic radiation is propagated at 32 from a source
towards the atoms residing in an active measurement region. In one
embodiment, the atoms are in a gas state contained in a vacuum
enclosure, such as a vapor cell, which defines the active
measurement region. Concurrently, light from one or more light
sources is propagated at 33 through the atoms residing in the
active measurement region, where the light includes at least one
light field that is coupled to a Rydberg state of the atoms for
measuring the atomic spectrum.
[0035] While the electromagnetic radiation is interacting with the
atoms (or has interacted with the atoms), an atomic spectrum is
measured at 34 using the light from the one or more light sources.
In the example embodiment, the atomic spectrum is measured using
electromagnetically induced transparency as is further described
below. In other embodiments, the atomic spectrum can be measured by
(1) absorption spectroscopy, wherein the spectrum is obtained by
monitoring the absorption of a light beam through the medium of
atoms, (2) Rydberg-atom counting via charged particle detectors or
current measurement devices, wherein the Rydberg atoms are ionized
and resulting charges are detected by a measurement device. Other
techniques for measuring an atomic spectrum also fall within the
scope of this disclosure.
[0036] Next, the measured atomic spectrum is analyzed at 35 to
extract spectral features. In one example, the peaks in the
measured spectrum are numerically fit to Gaussians to extract
features including relative peak positions, peak heights, and peak
widths. Other techniques for extracting spectral features from the
measured atomic spectrum are also contemplated by this
disclosure.
[0037] Extracted spectral features from the measured spectrum are
then compared at 36 to the spectral features of the predetermined
atomic spectra. For example, the predetermined spectra shown as
dots in FIGS. 9A and 9B contain information on the relative peak
positions (signal positions along the vertical axes) and relative
peak heights (size of blue dot) for two fixed electromagnetic
radiation field frequencies (i.e., 132.6495 GHz in FIG. 9A and and
12.461 GHz in FIG. 9B) and different electric field amplitudes for
each (top axes). Measured spectra are represented in gray scale in
FIGS. 9A and 9B for different output powers of the electromagnetic
radiation source. Note a single measured spectrum for a specific
output power is a vertical trace in the respective plot, with
signal strength represented on a gray scale. The relative positions
of the signal peaks in each measured spectrum are matched at 37 to
the calculated spectrum with the closest relative peak positions.
It is envisioned that other spectral features in the measured
spectrum, such as peak height or peak width, can be used to
determine the best match with a calculated spectrum. From the
matched calculated spectrum, the electric field (or frequency) of
the electromagnetic radiation is quantified as indicated at 38. In
this example, the field strength is read from the scale above the
plot. It is to be understood that only the relevant steps of the
methodology are discussed in relation to FIG. 3, but that other
steps, including software-implemented instructions, may be needed
to control and manage the overall operation of the measurement
system 10.
[0038] In the example embodiment, the measurement system 10 further
includes a data processor (e.g. computer) and a data store (e.g.,
non-transitory computer memory). The data processor is in data
communication with the light detector and configured to receive a
measure of the atomic spectrum from the light detector. The steps
of analyzing the measures atomic spectrum, comparing the spectral
features from the measured atomic spectrum to the spectral features
of the predetermined atomic spectra, and matching the measured
atomic spectrum to a given spectrum in the predetermined atomic
spectra can be implemented by the data processor. The predetermined
atomic spectra are stored in the data store for use by the
processor.
[0039] Alternatively, within the limit of weak and resonant
electromagnetic radiation fields, the electric field can be
obtained by a direct measurement of the splitting between two
peaks. The splitting is proportional to the electric field and the
predetermined dipole moment of the transition between the
resonantly coupled states. In this way, the electric field can be
computed from the Rabi frequency as further described below.
[0040] The method to determine the properties of an electromagnetic
radiation field from an optically measured atomic spectrum relies
on having accurate models of the atomic response (spectra) over the
field amplitude and frequency range of interest. Two models of the
atomic response to electromagnetic radiation fields are described
and validated experimentally. First, a perturbative model of the
atomic response is implemented that is valid for the special case
of weak electromagnetic radiation fields that are resonant or
near-resonant with an atomic transition. Second, a complete
non-perturbative model based on Floquet theory is described that is
valid over the full range from weak to strong electromagnetic
fields that are either on resonance or off-resonance with any
atomic transition.
[0041] First, a simple model is implemented for use within the
limit of weak EM fields resonant with an electric-dipole transition
between the optically excited Rydberg level |3 with another Rydberg
level |4. Here, the EM field splits the Rydberg-atom spectrum into
two lines, known as the Autler-Townes effect. An example of such a
splitting is seen in FIG. 6. In the limit of weak fields where
higher-order effects can be neglected, the splitting between the
line pair, .DELTA.f, is identical with the Rabi frequency
(.OMEGA..sub.RF=27.pi..DELTA.f) of the transition from level |3 to
level |4, and the electric field of the EM radiation is given
by
E RF = RF .OMEGA. RF = RF 2 .pi..DELTA. f ( 1 ) ##EQU00002##
[0042] where the unknown field, E.sub.RF, is proportional to the
splitting, Planck's constant, and inversely proportional to the
transition dipole moment .sub.RF, which quantifies the atomic
response to the resonant field within this weak-field limit. The
unknown field strength is calculated using first principles, for
example with the method given by T. F. Gallagher in "Rydberg
Atoms", Cambridge University Press, 1994. For embodiments based on
rubidium atoms, in the calculation of the dipole moment .sub.RF,
one can use quantum defects described by W. Li et al in
"Millimeter-wave spectroscopy of cold Rb Rydberg atoms in a
magneto-optical trap: Quantum defects of the ns, np and nd series"
and by M. Mack et al in "Measurement of absolute transition
frequencies of 85 Rb to nS and nD Rydberg states by means of
electromagnetically induced transparency".
[0043] When using room-temperature vapor cells and scanning the
probe laser frequency, differential Doppler shifts between the
probe and coupling beams alter the frequency separations between
EIT peaks in the probe transmission spectrum. Splittings of
5P.sub.3/2 hyperfine states are scaled by
1-.lamda..sub.c/.lamda..sub.p while splittings of Rydberg states
are scaled by .lamda..sub.c/.lamda..sub.p. The latter factor is
relevant to measurements of RF-induced splittings of EIT peaks and
therefore is modified. With reference to FIG. 6, the frequency
splitting of the EIT peaks in the probe spectrum, .DELTA.f, is
measured and the E-field amplitude is then given by
E RF = 2 .pi. RF .lamda. p .lamda. c .DELTA. f ( 2 )
##EQU00003##
[0044] In the weak-field regime, predetermined spectra can be
calculated with this model for a fixed electromagnetic radiation
frequency, associated dipole moment, and range of electric field
amplitudes. A measured spectrum, like the one shown in FIG. 6
(labeled "RF on"), is fit with a double Gaussian fitting function
to extract spectral features of the measured spectrum including the
splitting of the peaks. Here, the predetermined spectra can then be
searched for the predetermined spectrum with a splitting that most
closely matches the spitting of the measured spectrum. The matched
predetermined spectrum then provides the electric field amplitude
value corresponding to the measured splitting. Further, in the
weak-field regime of the atom-field interaction, where Equations
(1) or (2) are valid, the electric field amplitude can be obtained
from the splitting of the peaks of the measured spectrum. In the
weak-field regime, the search and match process amounts to
dividing/multiplying with the predetermined dipole moment, Planck's
constant, and any Doppler correction factors.
[0045] In an example embodiment, the measurement system relies upon
on rubidium-85 (.sup.85Rb) atoms as the active medium. As such, the
probe light is a 780 nm ("red") laser and the |1 to |2 atomic
resonance corresponds to the 5S.sub.1/2-5P.sub.3/2 transition. To
ensure that the |3 to |4 atomic resonance in .sup.85Rb is an RF
transition, the |2 to |3 transition will correspond to a .about.480
nm ("blue") laser. Inset of FIG. 7 depicts a four-level atomic
system. FIG. 7 shows the measured .DELTA.f as a function of the
square root of the RF signal generator (labeled as {square root
over (P)}.sub.SG). It can be seen that the measured .DELTA.f is
linear with respect to {square root over (P)}.sub.SG (noting
|E|.varies. {square root over (P)}.sub.SG), as predicted for the
case of weak fields. With the measured splitting .DELTA.f, and the
calculated electric-dipole matrix element, the absolute field
strength at the location for the lasers is obtained. Examples for
three different RF fields, of different frequencies, are shown in
FIG. 8 with a calculation of the expected electric field amplitude
following Equation 2, validating this model of the atom-field
interaction in this weak-field regime and its implementation in
measuring the electric field amplitude.
[0046] An experimental setup used to demonstrate this optical
measurement approach is shown in FIG. 4. The experimental setup
included a vapor cell 41, a horn antenna 42 (and a waveguide
antenna is used for the higher frequency measurements), a probe
laser 43, and a coupling laser 44, a lock-in amplifier 45, and a
photo diode detector 46. In this example, the vapor cell is a glass
cylinder with a length 75 mm and a diameter 25 mm containing
(.sup.85Rb) atoms. The levels |1, |2, |3, and |4 correspond,
respectively, to the .sup.85Rb 5S.sub.1/2 ground state, 5P.sub.3/2
excited state, and two Rydberg states. The probe laser is a 780 nm
laser which is scanned across the 5S.sub.1/2-5P.sub.3/2 transition.
The probe beam is focused to a full-width at half-maximum (FWHM) of
80 .mu.m, with a power of order 100 nW to keep the intensity below
the saturation intensity of the transition. FIG. 5 shows a typical
transmission signal as a function of relative probe detuning
.DELTA..sub.p. The global shape of the curve is the Doppler
absorption spectrum of .sup.85Rb at room temperature. To produce an
EIT signal, a counterpropagating coupling laser (wavelength
.lamda..sub.c.apprxeq.480 nm, "blue") is applied with a power of 22
mW, focused to a FWHM of 100 .mu.m. As an example, tuning the
coupling laser near the 5P.sub.3/2-50D.sub.5/2 Rydberg transition
results in distinct EIT transmission peaks as seen in FIG. 5. The
strongest peak at .DELTA..sub.p=0 is labeled as "EIT signal".
[0047] In order to improve the signal-to-noise ratio, heterodyne
detection can be used. The blue laser amplitude is modulated with a
30 kHz square wave and any resulting modulation of the probe
transmission is detected with a lock-in amplifier. This removes the
Doppler background and isolates the EIT signal as shown in the
black curve of FIG. 6 (labeled as "RF off"). Here, the coupling
laser is tuned near the 5P.sub.3/2-28D.sub.5/2 transition ("blue"
with .DELTA..sub.c.apprxeq.482.63 nm). Application of a RF field at
104.77 GHz to couple states 28D.sub.5/2 and 29P.sub.3/2 splits the
EIT peak as shown in the gray curve (labeled as "RF on"). Using
this heterodyne detection technique in the experimental data
presented below results in measured EIT-signals with improved
signal-to-noise ratio.
[0048] In weak RF-fields, the Rydberg levels are dynamically (ac)
Stark-shifted and, in the case of a near- or on-resonant drive of a
Rydberg transition, exhibit Autler-Townes splittings. For
single-photon transitions in the weak-field limit, the RF E-field
strength is directly proportional to the Autler-Townes splitting of
the Rydberg EIT line, which is given by the Rabi frequency
.OMEGA..sub.RF=.sub.RFE.sub.RF/ , where here again .sub.RF is the
Rydberg transition dipole moment and E.sub.RF is the RF radiation
E-field vector.
[0049] FIG. 9A shows, as another example, experimental spectra for
the on-resonant one-photon 26D.sub.5/2-27P.sub.3/2 mm-wave
(132.6495 GHz) transition as a function of the square root of
mm-wave power. This is similar to the previous example but for a
higher frequency electromagnetic radiation field. Here, the EIT
coupling-laser frequency is resonant with the mm-wave-free
.sup.85Rb 5P.sub.3/2(F'=4)-26D.sub.5/2 transition, where F' denotes
the intermediate-state hyperfine component. As expected in weak RF
fields, .OMEGA..sub.RF is a linear function of the square root of
power (which is proportional to E.sub.RF), making the splitting an
excellent marker for an electric field value associated with that
splitting. The faint level pairs centered at about -70 and -110 MHz
correspond to spectra associated with the intermediate
5P.sub.3/2(F'=2, 3) hyperfine components. From the measured
spitting, using .OMEGA.=.sub.RF,zE.sub.z/ and the predetermined
values of the dipole moments for a z-polarized field d.sub.z
(405ea.sub.0 for magnetic quantum number m.sub.j=1/2 and this
transition), the E.sub.RF fields obtained from the EIT spectra are
in excellent agreement with the predetermined spectra calculated
following Equation 2 (blue dots in FIG. 9). It is found that the
maximum field amplitude measured in the experiment shown in FIG. 9A
is 16 V/m, about 0.02% of the microwave-ionization field of these
atoms and well within the weak-field limit.
[0050] In FIG. 9A, the predetermined spectra (shown in blue)
contains the information on the relative peak positions for
132.6495 GHz mm-waves over a range of electric field amplitudes
(top axis). Measured spectra are represented in gray scale in FIGS.
9A and 9B for different output powers of the electromagnetic
radiation source. Note a single measured spectrum for a specific
output power is a vertical trace in the respective plot, with
signal strength represented on a gray scale. The measured spectra
are plotted as a function of the square root of the output power,
which is proportional to the electric field in this linear regime
as described previously. Here, both the frequency axis and
electric-field/root-power axis for the measured and calculated
spectra have the same, fixed relative step sizes.
[0051] To search the calculated spectra for a match with the
measured spectra, the calculated spectra are overlaid on the
measured spectra. The calculated spectra are first shifted
vertically until the symmetry points between the measured and
calculated splittings are equal. The calculated spectra are then
shifted horizontally until the splittings of the measured and
calculated spectra are equal. A match is obtained between the
measured and calculated spectra under the criterion that the
splitting of a calculated spectrum is equal to the measured
spectrum within a fraction of the linewidth of the measured
spectrum. Once the match is obtained, the measured spectrum is now
linked to the electric field associated with the matched
predetermined spectrum, thereby quantifying the electromagnetic
radiation electric field for that measured spectrum. In FIG. 9A,
all of the measured spectra were matched simultaneously. However,
it is envisioned that individual or a select number of measured
spectra can be matched following the same approach.
[0052] In an alternative approach, a more general model is set
forth to determine the atomic response to electromagnetic radiation
fields. This more robust model can be used in the strong field
regime, but it also applies to the weak field regime as well, and
for on-resonance and off-resonance fields. To illustrate the atomic
response in strong fields, measured and calculated atomic spectra
for Rydberg atoms that have been strongly driven at the zero-field
65D.sub.5/2-66D.sub.5/2 two-photon resonance frequency (12.461 154
8 GHz) have been studied. This two-photon Rydberg transition is
chosen to accommodate high-power microwaves in the K.sub.u band.
FIG. 9B shows experimental EIT spectra centered on the 65D level
for injected microwave powers ranging from 13 to 24 dBm in steps of
1 dBm. The 12 data sets are plotted as a function of power. For
this high-power measurement, the microwave-induced shifts are in
the range of several hundred MHz, i.e., about a factor of 10 larger
than the shifts of the low-power measurement in FIG. 9A. As
detailed below, the maximum field reached in FIG. 9B is 230 V/m,
about 20% of the microwave-field-ionization limit for that case. It
is noted that the field-free fine structure of the 65D and 66D
states (approximately 40 MHz) is broken up in the strong-field
regime because it is small compared to the microwave-induced
shifts. This aspect heralds the greater complexity of high-power
Rydberg EIT spectra compared to low-power spectra, as evidenced by
the comparison of FIG. 9A with FIG. 9B.
[0053] At the lowest microwave power in FIG. 9B, the microwave
interaction broadens the 65D EIT resonance to a FWHM width of
2.pi..times.50.+-.1 MHz, which is a factor of 2 larger than that of
the microwave-free EIT resonance (not-shown). For increasing
microwave power, the EIT signal splits into multiple
distinguishable spectral lines. For two-photon transitions, the
two-photon Rabi frequency .OMEGA..sub.RF.about.E.sub.RF.sup.2.
Hence, the lines are expected to shift linearly as a function of RF
power. Most levels in FIG. 9B exhibit linear shifts up to microwave
powers of approximately 70 mW.
[0054] In strong fields, higher-order couplings lead to a
redistribution of oscillator strength between many field-perturbed
Rydberg states, resulting in smaller signal strengths compared to
those in weak fields. This is reflected in FIG. 9B, where one
observes a rapid initial decrease in the signal strength; over the
first 30-mW increase in microwave power, the peak signal strengths
of the individual spectral lines reduce by more than an order of
magnitude. As the microwave power is increased further, the shifts
of the spectral lines become nonlinear in power, reflecting
substantial state mixing and higher-order couplings. The transition
from linear to nonlinear behavior occurs gradually as a function of
power, also, the details of this transition varies from level to
level. As seen by close inspection of FIG. 9B, even at the lowest
powers most levels exhibit some degree of nonlinearity. A
quantitative model of the complex level structure in the
strong-field regime is described below.
[0055] Inhomogeneous fields within the measurement volume
contribute to the background and additional spectral lines, which
are observed in FIG. 9B. The field inhomogeneity is attributed in
part to the presence of the dielectric cell, and to the fact that
the measurement is done in the near-field of the microwave horn.
The effects of the field inhomogeneity are also discussed in detail
in sections below.
[0056] In strong fields, where typical Rabi frequencies approach or
exceed atomic transition frequencies, high-order couplings become
significant and perturbative approaches are no longer valid. To
model the strong-field experimental spectra, a (non-perturbative)
Floquet method is adequate. Following the Floquet theorem, the
solutions to Schrodinger's equation for a time-periodic Hamiltonian
H(t)=H(t+T), where T is the period of the rf field, are of the
form
.PSI..sub.v(t)=e.sup.-iW.sup.v.sup.t/ (13)
Here, .PSI..sub.v(t)=.PSI..sub.w(t+T) are the periodic Floquet
modes and W.sub.v their quasienergies, with an arbitrary model
label v. For the atom-field interaction strength of interest here,
the Floquet modes can be represented using standard basis states
|n,l,j,m.sub.j=|k, i.e.,
.PSI..sub.v(t)=e.sup.iW.sup.v.sup.t/ .SIGMA..sub.kC.sub.v,k(t)|k)
(14)
with time-periodic (complex) coefficient functions that satisfy
C.sub.v,k(t)=C.sub.v,k(t+T). The Floquet energies W.sub.v and
states .PSI..sub.v(t=0) are determined by finding the eigenvalues
and vectors of the time-evolution operator (t,T+t). The coefficient
functions C.sub.v,k(t) are then obtained by integrating
.PSI..sub.v(t) over one period of the RF field, t.di-elect
cons.[0,T].
[0057] In the laser excitation of Floquet states from the
intermediate 5P.sub.3/2 state, multiphoton processes are important
because the atom may emit or absorb a number of microwave photons
together with an optical photon. To compute excitation line
strengths, the above functions C.sub.v,k(t) are
Fourier-expanded:
.PSI. v ( t ) = - W v t / .SIGMA. k .SIGMA. N = - .infin. .infin. C
~ v , k , N - Nw rf t k , C ~ v , k , N = 1 T .intg. 0 T C v , k (
t ) Nw rf t t . ( 15 ) ##EQU00004##
The integer N is interpreted as a number of microwave photons with
frequency .omega..sub.rf associated with the bare atomic state. The
laser frequencies .omega..sub.L, where Floquet levels are
resonantly excited from the 5P.sub.3/2 level, and the corresponding
line strengths S.sub.v,N are then given by:
w.sub.L=W.sub.v+N w.sub.rf,
S.sub.v,N=(eE.sub.L/ ).sup.2|.SIGMA..sub.k{tilde over
(C)}.sub.v,k,N{circumflex over (.di-elect cons.)}k|{circumflex over
(r)}|5P.sub.3/2,m.sub.j|.sup.2 (16)
where E.sub.L is the amplitude of the laser E field, {circumflex
over (.di-elect cons.)} is the laser-field polarization vector, and
k|{circumflex over (r)}|5P.sub.3/2,m.sub.j are the electric-dipole
matrix elements of the basis states with |5P.sub.3/2,m.sub.j. Each
Floquet level W.sub.v leads to multiple resonances, which are
associated with the microwave photon number N. Because of parity,
in the absence of additional static fields, a Floquet level W.sub.v
may generate resonances for either even N or odd N but not
both.
[0058] In FIG. 10, calculated Floquet energies and excitation rates
S.sub.v,N are shown in the vicinity of the 65D Rydberg level for a
microwave frequency of 12.461 154 8 GHz and field strengths ranging
from 0 to 350 V/m. The field is displayed on a quadratic scale to
show the dependence of the atomic-level shifts on power and for
direct comparison with FIG. 9B. Over the limited frequency range
displayed in FIG. 10, it is always N=0. Further inspection of the
calculated Floquet energies and excitation rates, not presented in
detail here, shows that for fields above approximately 150 V/m
several Floquet levels W.sub.v visible in FIG. 10 have copies with
high excitation rates for even values of N between about -8 and
+8.
[0059] The Floquet modes in strong fields exhibit nontrivial
wave-packet motion, and their optical excitation rates have to be
calculated according to Eq. (16). Low-field approximations along
the lines of Equations (1) and (2) are not valid. It would, for
instance, be incorrect to associate the excitation rates of the
Floquet modes in FIGS. 10 and 11, with the 65D probabilities the
modes carry. To qualitatively explain this, it is noted that in
weak fields the dressed-state coefficients and dipole moments have
fixed amplitudes and phases relative to the field (in the field
picture and using the rotating-wave approximation). In strong
fields, wave-function coefficients and dipole moments vary
significantly throughout the microwave-field cycle. Specifically,
the Floquet modes are time-periodic wave packets that are
synchronized with the driving rf field.
[0060] In FIG. 9B, one finds an excellent overall agreement between
dominant features in the experimental and theoretical Floquet maps.
Additional features evident in the experimental map are due to
E-field inhomogeneities, which are discussed below. Both
experimental and theoretical maps exhibit several arched lines at
positive frequencies and, at negative frequencies, several lines
that shift approximately linearly in power. The dominant
downshifting line suddenly terminates at close to -400 MHz. It is
evident from FIG. 10 that the sudden termination of the
downshifting lines is due to a wide Floquet avoided crossing.
Avoided crossings in Floquet maps, such as those in FIG. 10,
provide convenient markers for spectroscopic determination of the
rf E field on an absolute scale. In the present case, the prominent
avoided crossing at 165 V/m (see label 2 in FIG. 10) has several
matching locations in the experimental spectrum shown in FIG. 19B.
These are seen more clearly in FIG. 11A, which shows the
experimental data on a dBm scale. The appearance of multiple copies
of the calculated avoided crossing in the experiment points to the
fact that the microwave field within the cell had multiple dominant
domains, each of which produced its own rendering of the avoided
crossing. The rendering at the lowest injected microwave power
corresponds to the E field domain with the highest field at a given
injected power [calculation and E field axis shown in FIG. 9B]. In
FIG. 9B, the avoided crossing is observed first at 130 mW, at which
point the domain that has the highest field reaches 165 V/m. It
follows that at a microwave power of 250 mW a maximum RF E field of
230.+-.14 V/m is reached. The uncertainty of this value is given by
half the experimental power step size (.+-.0.5 dB, corresponding to
.+-.6% in field).
[0061] Using Floquet models, a method for measuring the electric
field (or frequency) of electromagnetic radiation proceeds as
follows. First, the Floquet model is used to calculate
predetermined spectra for the electromagnetic radiation over the
electric field and frequency ranges of interest. A measured
spectrum, like any of the ones shown in FIG. 9B, is analyzed to
extract spectral features of the measured spectrum including
relative peak positions, peak heights, and peak widths. The
predetermined spectra can then be searched for the predetermined
spectrum with the features that most closely match those of the
measured spectrum. For example, due to the complex non-linear
features of the spectra, the search entails first shifting the
overlaid calculated spectra vertically over the measured spectra so
that the zero-field (RF off) calculated spectrum and measured
spectrum are both at the same frequency (zero in the plot). The
calculated spectrum is then shifted horizontally until the
positions of the various peaks in the measured and calculated
spectra overlap. In this example, the predetermined spectra are
calculated at a fixed frequency over a range of field strengths. By
matching the measured spectrum to the calculated predetermined
spectra, one can quantify the electric field of the electromagnetic
radiation field associated with each of the measured spectra. The
quality of the overlap and match is determined by how well the peak
positions of the calculated spectra fall within the measured peak
positions. Different criteria for this match will result in
different uncertainties in the final field value. In one example,
the criterion is that the calculated peak should fall within the
full width half maximum of the measured signal. In this example,
the uncertainty is dominated by the experimental step size, not the
matching criteria. There are also considerations of unaccounted for
peaks in the spectra due to, for example, field inhomogeneities,
which can also be modelled. It is emphasized that the matching
process is necessary to obtain the electric field for atomic
spectra in a medium to strong field regime where simple models like
Equations 1 and 2 do not apply. The proposed approach provides a
more general way to measure such properties of the electromagnetic
radiation field of interest. As before, the described process is
for matching a series of measured spectra at the same time. A
single measured spectrum can be matched to a predetermined spectrum
following a similar procedure.
[0062] Furthermore, a measurement of the frequency of the
electromagnetic radiation field can be achieved by calculating
predetermined spectra at a fixed electric field value for a range
of electromagnetic field frequencies. This results in predetermined
spectra that are linked to the frequency for the radiation field
that can then be search and matched with a measured atomic spectra
as described above to obtain a value for the electromagnetic field
frequency. A simultaneous measurement of electric field and
frequency can also be achieved by calculating a series of
predetermined calculated spectral maps like the ones shown in FIG.
9 for a range of frequencies. This would result in a larger set of
predetermined spectra that can be searched in both frequency and
field amplitude for a match with the measured spectrum.
[0063] In the following sections, an explanation is provided of the
analysis used to model the experimental spectra plotted in FIGS. 9B
and 11A. The spectra contain information on the continuous
distribution of the microwave E field strength along the length of
the EIT probe and coupling beams passing through the spectroscopic
cell. The microwave boundary conditions are symmetric about the xy
plane, with the incident microwave E field being z polarized and
the optical beams propagating along the x axis. Since the microwave
field is primarily z polarized along the optical beams, it drives
.DELTA.m.sub.j=0 Rydberg transitions with the m.sub.j=.+-.1/2 and
m.sub.j=.+-.3/2 manifolds of states. The field distribution is a
result of superpositions of reflections from the cell walls. Also,
the cell is placed within the near field of the source, leading to
additional variability of the microwave field along the probe beam.
Hence, one may picture the RF field as a speckle pattern, akin to
speckle patterns seen for general, nonideal coherent fields. Here,
one should expect the number of speckles to be on the order of the
cell length divided by the wavelength, which in this case is 3.
Also, since there are no structures within the cell that are very
close to the optical probe beam path, one would not expect any
sharp spatial features in the microwave E field (features which
might otherwise arise from sharp metallic or dielectric edges and
the like). Therefore, for each theoretical line in FIG. 10, the
measured EIT spectra are expected to exhibit a small number of
spectral features that correspond to the local maxima and minima of
the microwave field along the length of the probe beam.
[0064] Based on the observation of five downward spectral lines
[labeled in FIG. 11A] and the fact that the calculated spectrum has
only one corresponding downward line (feature 1 in FIG. 10), the
spectrum is modeled considering populations of atoms located within
a set of five dominant microwave E field regions. In the model, the
probability distribution for intensity on a decibel scale is given
by
P.sub.dBi(s)=.SIGMA..sub.|m.sub.j.sub.|=1/2.sup.3/2.SIGMA..sub.k=1.sup.5-
w.sub.m.sub.j(|m.sub.j|)w.sub.k(k)P.sub.dBi0(s+.DELTA.s.sub.k).
(17)
[0065] Here, k is an index for the five microwave field domains,
w.sub.k(k) is the probability that an atom contributing to the
signal resides within domain k, w.sub.mj (|m.sub.j|) is the
probability that an atom contributing to the signal has a magnetic
quantum number |m.sub.j|, and P.sub.dBi0 is a Gaussian point-spread
function that accounts for inhomogeneous spectral broadening within
the five domains. The values .DELTA.s.sub.k indicate by what amount
(in decibels) the central microwave intensity within the kth
microwave field region is shifted relative to the intensity in the
highest-intensity (k=1) domain. For P.sub.dBi0, it is assumed a
Gaussian that is the same for all k. The fit parameters in the
model are .DELTA.s.sub.k, w.sub.m.sub.j,w.sub.k, and the standard
deviation d.sub.dBi0 for P.sub.dBi0. One can account for the
optical EIT line broadening and laser line drifts by a Gaussian
spread function in frequency, P.sub.v(v), which has a standard
deviation .sigma..sub.y. From the theoretical spectrum
S.sub.T(s,v), the model spectrum S.sub.E(s.sub.0s.sub.v) is then
given by the convolution
S.sub.E(s.sub.0,v.sub.0)=.intg.S.sub.T(s.sub.0-s',v.sub.0+v')P.sub.v(v')-
P.sub.dBi(s')dv'ds', (18)
where the intensities in the arguments of S.sub.E and S.sub.T are
measured in dBi, defined as 10 log.sub.10 [I/(W/m.sup.2)], where I
is the RF field intensity.
[0066] FIG. 11B shows the model spectrum S.sub.E(s.sub.0,v.sub.0)
in dBi for the data in FIG. 11A. In the model spectrum, the field
domains have empirically fitted intensity shifts of
.lamda..sub.S.sub.k=0.0, -2.0, -4.17, -6.0, and -8.0 db for k=1, .
. . , 5. The corresponding fitted weighting factors are
w.sub.k=0.39, 0.21, 0.27, 0.09, and 0.04. The intensity shifts are
significant to better than about 0.5 dB, while the weighting
factors are significant to better than about .+-.0.04. The
weighting factors w.sub.m.sub.j for the |m.sub.j|=1/2 and 3/2
states are 0.7 and 0.3, respectively (significance level better
than about 0.1). The larger |m.sub.j|=1/2 weight likely results
from optical pumping by the EIT probe field. Furthermore,
.sigma..sub.dBi=1 dBi and .sigma..sub.v=30 MHz.
[0067] A comparison of the measured spectrum and the model spectrum
in FIG. 11 shows that a strong-field Floquet analysis of the atomic
physics of Rydberg atoms in microwave fields, combined with a
straightforward empirical model of the microwave intensity
distribution and the weighting in the sample, leads to remarkably
good agreement between spectra with rather complex features.
Utilizing a combination of resonant, strong electric-dipole
transitions as in FIG. 9A and higher-order transitions such as the
two-photon transition in FIG. 9B, it is possible to observe level
shifts in Rydberg EIT spectra over a wide dynamic range of the
applied RF intensity.
[0068] The models of the atom-field interactions described herein
(Autler-Towns model and Floquet model) depend only on invariable
atomic parameters such as quantum defects and dipole moments, and
fundamental constants, such as Planck's constant. The method to
determine the electric field or frequency of an unknown
electromagnetic radiation field using these models therefore
provides a measurement that is directly SI traceable in which the
uncertainty of each step in the computation is well-characterized
and documented. The uncertainty of the dipole moment calculation is
considered to be less than 0.1%, so the overall traceability to SI
units has a correspondingly small uncertainty, compared to previous
E-field measurement techniques.
[0069] Since the spectroscopic response is well described by the
Floquet theory laid out above, predetermined spectra for a chosen
RF frequency and field amplitude range, and measured spectrum can
be used together as described above to quantify the RF E field
causing the observed spectral features in a calibration-free
manner. Specifically, there are no antenna systems and readout
instruments that need to be calibrated to translate a reading into
a field, because spectral features such as line shifts and avoided
crossings follow from the invariable nature of the underlying
atomic physics. The field measurement precision is given by how
well the spectral features are resolved. For instance, in the
present disclosure, the avoided crossing pointed out by the arrows
in FIGS. 10 and 11 can be resolved to within .+-.0.5 dBi
uncertainty, corresponding to an absolute field uncertainty of
.+-.0.6%.
[0070] While in the experimental examples shown here a cell on the
order of 25 mm to 75 mm is used, the vapor cell can be made smaller
and hence allow a compact probe (or sensor head).
[0071] Regardless of the size of the vapor cell, this technique
allows for sub-wavelength imaging of an RF field over a large
frequency range. This has been demonstrated where field
distributions inside a glass cell were imaged at both 17.04 GHz and
104.77 GHz. The unique feature of this imaging approach is that the
spatial resolution is not governed by the size of the vapor cell
that holds the atoms. The RF field will only interact with the
atoms that are exposed to the two laser beams. As such, the spatial
resolution of this approach is based on beam widths of the two
lasers used in this experiment, which can be in principle on the
order of the diffraction limit, i.e., 10's of mircometers. The
applications of such a small spatial imaging capability are
numerous. For example, the sensing volume could be scanned over a
printed-circuit-board (PCB) or a metasurface in order to map their
fields, as well as other applications where E-field measurements on
a small spatial resolution are desired.
[0072] The techniques described herein may be implemented in part
by one or more computer programs executed by one or more
processors. The computer programs include processor-executable
instructions that are stored on a non-transitory tangible computer
readable medium. The computer programs may also include stored
data. Non-limiting examples of the non-transitory tangible computer
readable medium are nonvolatile memory, magnetic storage, and
optical storage.
[0073] Some portions of the above description present the
techniques described herein in terms of algorithms and symbolic
representations of operations on information. These algorithmic
descriptions and representations are the means used by those
skilled in the data processing arts to most effectively convey the
substance of their work to others skilled in the art. These
operations, while described functionally or logically, are
understood to be implemented by computer programs. Furthermore, it
has also proven convenient at times to refer to these arrangements
of operations as modules or by functional names, without loss of
generality.
[0074] Unless specifically stated otherwise as apparent from the
above discussion, it is appreciated that throughout the
description, discussions utilizing terms such as "processing" or
"computing" or "calculating" or "determining" or "displaying" or
the like, refer to the action and processes of a computer system,
or similar electronic computing device, that manipulates and
transforms data represented as physical (electronic) quantities
within the computer system memories or registers or other such
information storage, transmission or display devices.
[0075] Certain aspects of the described techniques include process
steps and instructions described herein in the form of an
algorithm. It should be noted that the described process steps and
instructions could be embodied in software, firmware or hardware,
and when embodied in software, could be downloaded to reside on and
be operated from different platforms used by real time network
operating systems.
[0076] The present disclosure also relates to an apparatus for
performing the operations herein. This apparatus may be specially
constructed for the required purposes, or it may comprise a
general-purpose computer selectively activated or reconfigured by a
computer program stored on a computer readable medium that can be
accessed by the computer. Such a computer program may be stored in
a tangible computer readable storage medium, such as, but is not
limited to, any type of disk including floppy disks, optical disks,
CD-ROMs, magnetic-optical disks, read-only memories (ROMs), random
access memories (RAMs), EPROMs, EEPROMs, magnetic or optical cards,
application specific integrated circuits (ASICs), or any type of
media suitable for storing electronic instructions, and each
coupled to a computer system bus. Furthermore, the computers
referred to in the specification may include a single processor or
may be architectures employing multiple processor designs for
increased computing capability.
[0077] The algorithms and operations presented herein are not
inherently related to any particular computer or other apparatus.
Various general-purpose systems may also be used with programs in
accordance with the teachings herein, or it may prove convenient to
construct more specialized apparatuses to perform the required
method steps. The required structure for a variety of these systems
will be apparent to those of skill in the art, along with
equivalent variations. In addition, the present disclosure is not
described with reference to any particular programming language. It
is appreciated that a variety of programming languages may be used
to implement the teachings of the present disclosure as described
herein.
[0078] The foregoing description of the embodiments has been
provided for purposes of illustration and description. It is not
intended to be exhaustive or to limit the disclosure. Individual
elements or features of a particular embodiment are generally not
limited to that particular embodiment, but, where applicable, are
interchangeable and can be used in a selected embodiment, even if
not specifically shown or described. The same may also be varied in
many ways. Such variations are not to be regarded as a departure
from the disclosure, and all such modifications are intended to be
included within the scope of the disclosure.
* * * * *