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Physical Review Applied

Rydberg-Atom Sensors in Bichromatic Radio-Frequency Fields

Mohammad Noaman, Donald W. Booth, James P. Shaffer

Published Aug 28, 2023• 12 citations
Publisher

Abstract

Rydberg-atom-based sensors are a type of radio-frequency sensor that is inherently quantum mechanical. Several configurations of the sensor use a local oscillator to determine the properties of the target radio-frequency field. We explain how the physics of Rydberg-atom-based sensors in two or more radio-frequency fields can be precisely described by a multiply dressed Jaynes-Cummings model. Studying Rydberg-atom-based sensors in two or more near-resonant radio-frequency fields is important for understanding how interfering signals as well as the local oscillator can affect measurements. Studies, so far, focus on a simplified approximation for the local oscillator-target field interaction that uses an analogy to radio-frequency heterodyning. The atom acts as a medium for exchanging electromagnetic field excitations of the field modes whose spectrum is a ladder. The Jaynes-Cummings states and their avoided crossings can be used to determine the properties of the radio-frequency fields. Radio-frequency field sensitivity enhancement for nonresonant radio frequencies is achieved and self-calibrated measurements are recovered under specific conditions described by the theory.

DOI
10.1103/physrevapplied.20.024068

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Rydberg-atom-based sensors are a type of radio-frequency sensor that is inherently quantum mechanical. Several configurations of the sensor use a local oscillator to determine the properties of the target radio-frequency field. We explain how the physics of Rydberg-atom-based sensors in two or more radio-frequency fields can be precisely described by a multiply dressed Jaynes-Cummings model. Studying Rydberg-atom-based sensors in two or more near-resonant radio-frequency fields is important for understanding how interfering signals as well as the local oscillator can affect measurements. Studies, so far, focus on a simplified approximation for the local oscillator-target field interaction that uses an analogy to radio-frequency heterodyning. The atom acts as a medium for exchanging electromagnetic field excitations of the field modes whose spectrum is a ladder. The Jaynes-Cummings states and their avoided crossings can be used to determine the properties of the radio-frequency fields. Radio-frequency field sensitivity enhancement for nonresonant radio frequencies is achieved and self-calibrated measurements are recovered under specific conditions described by the theory.
Rydberg atom-based sensors are a new type of radio frequency sensor that is inherently quantum mechanical. Several configurations of the sensor use a local oscillator to determine the properties of the target radio frequency field. We explain how the physics of Rydberg atom-based sensors in two or more radio frequency fields can be precisely described by a multiply dressed Jaynes-Cummings model. Studying Rydberg atom-based sensors in two or more near resonant radio frequency fields is important for understanding how interfering signals as well as the local oscillator can affect measurements. Studies, so far, focus on a simplified approximation for the local oscillator-target field interaction that uses an analogy to radio frequency heterodyning. The atom acts as a medium for exchanging electromagnetic field excitations of the field modes whose spectrum is a ladder. The Jaynes-Cummings states and their avoided crossings can be used to determine the properties of the radio frequency fields. Radio frequency field sensitivity enhancement for non-resonant radio frequencies is achieved and self-calibrated measurements are recovered under specific conditions described by the theory.
Rydberg atom radio-frequency sensors are a unique platform for precision electromagnetic field measurement; e.g., they have extraordinary carrier bandwidth spanning MHz to THz and can be self-calibrated. These photonic sensors use lasers to prepare and read out the atomic response to a radio-frequency electromagnetic field. Most work on Rydberg atom sensors centers on radio-frequency electric field strength because the sensor functions as a square law detector, unless an external radio-frequency heterodyning field is used. A heterodyning field acts as a local oscillator and enables phase readout at the expense of the radio-frequency equipment necessary to generate it. In order to overcome the disadvantages of a radio-frequency local oscillator, we investigate all-optical phase-sensitive detection using a five-level closed-loop excitation scheme. We show that under finite detuning of the loop fields, the atomic response oscillates at the frequency of the detuning. The oscillation is transferred to a probe laser absorption signal. The phase, frequency, and amplitude of the radio-frequency signal are imprinted on the oscillatory dynamics and can be determined using demodulation and matched filter techniques applied to the probe laser transmission signal.
Rydberg atom-based radio frequency electromagnetic field sensors are drawing wide-spread interest because of their unique properties, such as small size, dielectric construction, and self-calibration. These photonic sensors use lasers to prepare atoms and read out the atomic response to a radio frequency electromagnetic field based on electromagnetically induced transparency, or related phenomena. Much of the theoretical work has focused on the Autler-Townes splitting induced by the radio frequency wave. The amplitude regime, where the change in transmission observed on resonance is measured to determine electric field strength, has received less attention. In this paper, we deliver analytic expressions that are useful for calculating the absorption coefficient in the amplitude regime. Our main goal is to describe the analytic expressions for the absorption coefficient and demonstrate their validity over a large range of the interesting parameter space. The effect of the thermal motion of the atoms is explicitly addressed. The analytic formulas for the absorption coefficient for different types of Doppler broadening are compared to estimate the sensitivity under conditions where it is limited by the laser shot noise. Residual Doppler shifts are shown to limit sensitivity. The expressions, approximations and descriptions presented in the paper are important for understanding the absorption of Rydberg atom-based sensors in the amplitude regime. This provides insight into the physics of multi-level interference phenomena.
Multi-photon dressing and interference in atomic systems is a key to several cutting edge technologies like Rydberg atom radio frequency sensors, clocks and magnetometers because it enables the engineering of atomic properties. Rydberg atom sensors are attracting significant interest because they can be used for applications where it is difficult or impossible to use conventional antennas, opening a number of new opportunities in fields like communications, test and measurement and radar. To date, radio frequency field amplitude detection is well-established in Rydberg electrometry. Phase detection, which is crucial for encoding radio frequency signals, typically requires an external heterodyning field or an atomic closed-loop interferometer. The heterodyne method compromises the intrinsic transparency of the sensor to the radio frequency wave and its inherently broad carrier bandwidth, in addition to increasing its complexity by introducing a local oscillator. In prior theoretical work, aimed at overcoming the disadvantages of the heterodyne method, we theoretically investigated the possibility of using the oscillatory dynamics of an all-optical five-level closed loop to sense the phase and amplitude of the target radio frequency fields. In this work, we experimentally demonstrate the scheme. We determine the coherence time of the loop to be on the order of ms and show that in-phase and quadrature signals can be extracted from a radio frequency signal.
We present enhanced sensing of a radio frequency (RF) electric field (E-field) by the combined polarizability of Rydberg atoms and the optimized local oscillator (LO) field of a superheterodyne receiver. Our modified theoretical model reveals the dependencies of the sensitivity of E-field amplitude measurement on the polarizability of Rydberg states and the strength of the LO field. The enhanced sensitivities of the megahertz (MHz) E-field are demonstrated at the optimal LO field for three different Rydberg states 43D5/2{\rm 43D}_{5/2}43D5/2​, 60S1/2{\rm 60S}_{1/2}60S1/2​, and 90S1/2{\rm 90S}_{1/2}90S1/2​. The sensitivity of 63 MHz for the 90S1/2{\rm 90S}_{1/2}90S1/2​ state reaches 9.6 ×10−5 V/m/Hz\times 10^{-5}\rm \,V/m/\sqrt {Hz}×10−5V/m/Hz​, which is approximately an order of magnitude higher than those already published. This result closely approaches the sensitivity limit of a 1 cm passive dipole antenna without using an impedance matching network. This atomic sensor based on the Rydberg Stark effect with heterodyne technique is expected to boost an alternative solution to electric dipole antennas.
Abstract Rydberg atom-based sensors using the atomic heterodyne technique demonstrate prominent performance on sensing sensitivity and thus have significant potential for radar, electronic reconnaissance, and communication applications. Here, we propose a local oscillator (LO) embedded field enhancement resonator to improve the sensitivity and integration of Rydberg atomic heterodyne sensors. In this approach, a vapor cell filled with cesium atoms is placed into the resonance structure for electric (E) field measurements. By integrating parallel-plate waveguide (PPWG) antennas and the resonator, the LO signal can be directly guided to the resonator using coaxial cable instead of the use of external antennas radiating through free space, allowing for a more flexible and practical Rydberg atom-based heterodyne technique. Based on the off-resonant Rydberg atomic heterodyne approach, for a radio frequency (RF) signal at 638 MHz, it is found that the sensitivity is 43 μ V/cm Hz\sqrt{\text{Hz}}Hz​ Hz in the absence of the resonator, while in the presence of our resonator, the sensitivity is down to 854.36 nV/cm Hz\sqrt{\text{Hz}}Hz​ Hz , indicating 50 times or 34 dB improvement capacity of the proposed resonator. This type of enhancement resonator is expected to benefit Rydberg atomic heterodyne applications in practical environments.