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arXiv:2010.13657 · Physical Review Applied

Optical Radio-Frequency Phase Measurement With an Internal-State Rydberg Atom Interferometer

David Alexander Anderson, Rachel Sapiro, Luís F. Gonçalves, Ryan Cardman, Georg A. Raithel

Published Apr 11, 2022• 49 citations
arXivHTMLPDF

Abstract

We realize and model an internal-state Rydberg atom interferometer for measurement of phase and intensity of radio-frequency (rf) electromagnetic waves. A phase reference is supplied to the atoms via a modulated laser beam, enabling atomic measurement of the rf wave's phase without a rf reference wave. The rf and optical fields give rise to closed interferometric loops within the atoms' internal Hilbert space. In our experiment, we construct interferometric loops in the state space ${6{P}_{3/2},90{S}_{1/2},91{S}_{1/2},90{P}_{3/2}}$ of cesium and employ them to measure phase and intensity of a 5-GHz rf wave in a room-temperature vapor cell. Electromagnetically induced transparency on the $6{S}_{1/2}$ to $6{P}_{3/2}$ transition serves as an all-optical interferometer probe. The rf phase is measured over a range of $\ensuremath{\pi}$, and a sensitivity of 2 mrad is achieved. Measurements of rf phase and amplitude at submillimeter optical spatial resolution are demonstrated.

DOI
10.1103/physrevapplied.17.044020

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We realize and model an internal-state Rydberg atom interferometer for measurement of phase and intensity of radio-frequency (rf) electromagnetic waves. A phase reference is supplied to the atoms via a modulated laser beam, enabling atomic measurement of the rf wave's phase without a rf reference wave. The rf and optical fields give rise to closed interferometric loops within the atoms' internal Hilbert space. In our experiment, we construct interferometric loops in the state space 6P3/2,90S1/2,91S1/2,90P3/2{6{P}_{3/2},90{S}_{1/2},91{S}_{1/2},90{P}_{3/2}}6P3/2​,90S1/2​,91S1/2​,90P3/2​ of cesium and employ them to measure phase and intensity of a 5-GHz rf wave in a room-temperature vapor cell. Electromagnetically induced transparency on the 6S1/26{S}_{1/2}6S1/2​ to 6P3/26{P}_{3/2}6P3/2​ transition serves as an all-optical interferometer probe. The rf phase is measured over a range of \ensuremathπ\ensuremath{\pi}\ensuremathπ, and a sensitivity of 2 mrad is achieved. Measurements of rf phase and amplitude at submillimeter optical spatial resolution are demonstrated.
We design phase-sensitive Rydberg-atom interferometry by implementing Floquet electromagnetically induced transparency (FEIT). The FEIT mixes the sidebands of a Rydberg state induced by a megahertz radio frequency (rf) field and recombines them into FEIT bands. The FEIT bands act as screens to present the interference between paths with different phases, which are transitions between the sidebands and excited states. This interferometry can measure the phase of a megahertz rf field without a local rf reference field. A phase reference is supplied to the atoms via a periodic electrical signal in the FEIT. We demonstrate that the megahertz rf phase can be resolved over the full $2\ensuremath{\pi}$ range with a theoretical accuracy of ${10}^{\ensuremath{-}4}$ rad. Moreover, the rf amplitude can also be resolved with higher accuracy than with the traditional EIT-based scheme.
We study Rydberg atoms modulated by strong radio-frequency (rf) fields with a frequency of 70 MHz. The Rydberg atoms are prepared in a room-temperature cesium cell, and their level structure is probed using electromagnetically induced transparency (EIT). As the rf field increases from the weak- into the strong-field regime, the range of observed rf-induced phenomena progresses from ac level shifts through increasingly pronounced and numerous rf modulation sidebands to complex state mixing and level crossings with $\mathrm{high}\ensuremath{-}l$ hydrogenlike states. Weak anharmonic admixtures in the rf field generate clearly visible modifications in the Rydberg EIT spectra. A Floquet analysis is employed to model the Rydberg spectra, and good agreement with the experimental observations is found. Our results show that all-optical spectroscopy of Rydberg atoms in vapor cells can serve as an antenna-free, atom-based, and calibration-free technique to measure rf electric fields and to analyze their higher-harmonic contents.
We investigate and employ optical Rydberg resonances in an atomic vapor cell for measurements of high-intensity VHF-band radio frequency (rf) electric fields. An atomic vapor cell with integrated electrodes is used to generate high-intensity 50--500 MHz rf electric fields reaching $\ensuremath{\sim}5$ kV/m in a submillimeter gap. The fields are measured using Rydberg electromagnetically induced transparency as an optical readout of field-sensitive 30DJ30{D}_{J}30DJ​ and 35DJ35{D}_{J}35DJ​ Rydberg states of atoms within the gap. The rf electric field is determined by matching observed spectroscopic markers, including ac level shifts, even-harmonic rf sidebands, and rf-induced avoided crossings in the Rydberg manifold to calculated spectra derived from a nonperturbative Floquet theory. In our measurements, rf field frequencies and electric-field amplitudes are determined to an accuracy of 1.01.0%1.0 and 1.51.5%1.5, respectively. In the atom-field interaction, we observe a transition from a quantum regime, characterized by discrete even-harmonic Floquet states separated by an even multiple of the rf field frequency, into a semiclassical regime at very strong fields, in which the spectrum exhibits unresolved resonances whose strengths are smoothly modulated at a frequency of approximately five times the rf frequency. The underlying physics is explored.
In this work, theoretical and experimental works on Rydberg-atom based radio-frequency (RF) sensors are presented. The results were obtained in close collaboration with the Quantum Valley Ideas Lab, whose goal is the miniaturization and prototyping of these sensors. The Rydberg-atom based RF sensors utilize lasers to coherently excite an atomic vapor in a vapor cell at room temperature to a highly excited Rydberg state, which is extremely sensitive to external environmental influences. In this work, Rydberg-atom based RF sensing is described as coherent multi-photon interference in the atom-light coupled system by introducing atom-light coherences. The presence of the RF wave influences the absorption of a probe laser propagating through the atomic medium. The atomic response of the Rydberg-atoms can be engineered by changing the atom-light coherences through laser power and frequency. Analytic expressions for the atomic response to the incident RF wave are derived in the weak probe limit and provide a deeper understanding of the underlying coherent multi-photon interference processes, which help to further tailor the Rydberg-atom for the purpose of the application. Good agreement with full numerical simulations of the Lindblad-master equation is found. An analysis of the various Doppler limits strongly motivates an excitation scheme where the effective wave vector mismatch on the Rydberg transition vanishes, as a promising candidate to achieve narrower spectral linewidths and, consequently, a higher sensitivity. The level structure of cesium presents a unique three-photon excitation scheme where residual Doppler shifts become comparable to the spectral linewidth of the coupling lasers. The experimental realization of this excitation scheme is demonstrated. A spectral linewidth of the Rydberg transition of 190 kHz is achieved. The measurements present the world record sensitivity, 45 nV/cm/Hz^1/2, for all-optical RF sensing with room temperature operation. These results make the three-photon excitation scheme a prime candidate for the next generation of Rydberg-atom based RF sensor prototypes. Finally, all-optical phase-sensitive RF detection is theoretically investigated in a closed-loop excitation scheme. An analytic expression is derived that intuitively describes the atomic response. Furthermore, it provides insights into the probe intensity dynamics that occur when the system is operated under finite detuning. These oscillatory dynamics allow for the extraction of the in- (I) and out- (Q) of-phase response to the RF wave, thereby enabling the simultaneous detection of the RF E-field amplitude and phase. A blueprint for the experimental realization is presented, and angle-of-arrival tolerances for the RF wave are estimated. A quadrature amplitude modulation (QAM) sequence was modelled and the simultaneous extraction of the phase and amplitude of the RF wave of interest was successfully demonstrated.
Although Rydberg-atom-based electric field sensing provides key advantages over traditional antenna-based detection, it remains limited by the need for a local oscillator (LO) for low-field and phase-resolved detection. In this work, we demonstrate that closed-loop quantum interferometric schemes can be used to generate a system-internal reference that can directly replace an external LO for Rydberg field sensing. We reveal that this quantum interferometrically defined internal reference phase and frequency can be used analogously to a traditional LO for atom-based down-mixing to an intermediate frequency for lock-in phase detection. We demonstrate that this LO-equivalent functionality provides analogous benefits to an LO, including full ${360}^{\ensuremath{\circ}}$ phase resolution as well as improved sensitivity. The general applicability of this approach is confirmed by demodulating a four-phase-state signal broadcast on the atoms. Our approach may open up new sensing schemes and although the present implementation still uses an auxiliary rf field, we provide a clear path toward all-optical Rydberg-atom sensing implementations by discussing several schemes that allow for all-optical rf phase detection without the need for an external rf LO field.
We show experimentally obtained frequency- and power-dependent optical response of a room-temperature cesium vapor cell used as a Rydberg microwave receiver based on electromagnetically induced transparency. An applied microwave field couples the 70S1/2{70S_{1/2}}70S1/2​ Rydberg state to the nearby 70P1/2{70P_{1/2}}70P1/2​, 70P3/2{70P_{3/2}}70P3/2​, 69P1/2{69P_{1/2}}69P1/2​, and 69P3/2{69P_{3/2}}69P3/2​ states, modifying the probe-transmission spectrum. Probe transmission is recorded over a 800 MHz range of coupling laser detunings. These EIT spectra are measured for RF frequencies from 9 to 13.5 GHz and over a 40 dB range of RF power. We analyze the RF induced splittings in the recorded EIT spectra. We observe both limiting cases, where the EIT peak separation is either dominated by the RF detuning or by the RF power. At higher powers we are also able to observe complex features due to coupling of multiple nearby Rydberg states. We further analyze the probe-transmission signal at zero coupling-laser detuning. Sigmoidal fits to the power-response curves are used to determine the midpoint power and the 10-90% transition interval as functions of RF frequency.