Quantum-Limited Atomic Receiver in the Electrically Small Regime

Approaching the standard quantum limit of a Rydberg-atom microwave electrometer

The development of a microwave electrometer with inherent uncertainty approaching its ultimate limit carries both fundamental and technological significance. However, because of the thermal motion of atoms, the state-of-art Rydberg electrometer falls considerably short of the standard quantum limit by about three orders of magnitude. Here, we use an optically thin medium with approximately 5.2 × 105 laser-cooled atoms to implement the microwave heterodyne detection. By mitigating various noises and strategically optimizing the electrometer parameters, our study reduces the equivalent noise temperature by a factor of 20 and achieves an electric field sensitivity of 10.0 nV cm-1 Hz-1/2, lastly reaching a factor of 2.6 above the standard quantum limit. Our work also provides valuable insights into the inherent capabilities and limitations of Rydberg electrometers, offering superior sensitivity in detecting weak microwave signals for numerous applications.

Remote sensing of soil moisture using Rydberg atoms and satellite signals of opportunity

Spaceborne radar remote sensing of the earth system is essential to study natural and man-made changes in the ecosystem, water and energy cycles, weather and air quality, sea level, and surface dynamics. A major challenge with current approaches is the lack of broad spectrum tunability due to narrow band microwave electronics, that limit systems to specific science variable retrievals. This results in a significant limitation in studying dynamic coupled earth system processes such as surface and subsurface hydrology from a single compact instrument, where co-located broad spectrum radar remote sensing is needed to sense multiple variables simultaneously or over a short duration. Rydberg atomic sensors are highly sensitive broad-spectrum quantum detectors that can be dynamically tuned to cover micro-to-millimeter waves with no requirement for RF band-specific electronics. Rydberg atomic sensors can use existing transmitted signals such as from navigation and communication satellites to enable remote sensing. We demonstrate remote sensing of soil moisture, an important earth system variable, via ground-based radar reflectometry with Rydberg atomic systems. To do this, we sensitize the atoms to XM satellite radio signals and use signal correlations to demonstrate use of these satellite signals for remote sensing of soil moisture.

Radio frequency electric field-enhanced sensing based on the Rydberg atom-based superheterodyne receiver

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 ${\rm 43D}_{5/2}$, ${\rm 60S}_{1/2}$, and ${\rm 90S}_{1/2}$. The sensitivity of 63 MHz for the ${\rm 90S}_{1/2}$ state reaches 9.6 $\times 10^{-5}\rm \,V/m/\sqrt {Hz}$, 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.

Rydberg atom electric field sensing for metrology, communication and hybrid quantum systems

Rydberg atoms-based electric field sensing has developed rapidly over the past decade. A variety of theoretical proposals and experiment configurations are suggested and realized to improve the measurement metrics, such as intensity sensitivity, bandwidth, phase, and accuracy. The Stark effect and electromagnetically induced transparency (EIT) or electromagnetically induced absorption (EIA) are fundamental physics principles behind the stage. Furthermore, various techniques such as amplitude- or frequency-modulation, optical homodyne read-out, microwave superheterodyne and frequency conversion based on multi-wave mixing in atoms are utilized to push the metrics into higher levels. In this review, different technologies and the corresponding metrics they had achieved were presented, hoping to inspire more possibilities in the improvement of metrics of Rydberg atom-based electric field sensing and broadness of application scenarios.

Accurate measurement of the frequency offset of the laser based on electromagnetically induced transparency

We propose a method using electromagnetically induced transparency (EIT) to measure the frequency offset of the laser relative to a cavity's resonance frequency, thereby reducing the laser detuning when preparing Rydberg atoms. Laser reflection by the vapor cell enables observation of two EIT peaks corresponding to the co-propagating and counter-propagating beams, and the peaks' position is related to laser detuning, allowing us to estimate the frequency offset of the probe and coupling lasers. The method reduces the measurement uncertainty compared to directly observing saturated absorption spectroscopy (SAS) and EIT, making it suitable for applications that require strict control over laser detuning.

Array of Individual Circular Rydberg Atoms Trapped in Optical Tweezers

Circular Rydberg atoms (CRAs), i.e., Rydberg atoms with maximal orbital momentum, are highly promising for quantum computation, simulation, and sensing. They combine long natural lifetimes with strong interatomic interactions and coupling to electromagnetic fields. Trapping individual CRAs is essential to harness these unique features. We report the first demonstration of CRAs laser trapping in a programmable array of optical bottle beams. We observe the decay of a trapped rubidium circular level over 5 ms using a novel optical detection method. This first optical detection of alkali CRAs is both spatially and level selective. We finally observe the mechanical oscillations of the CRAs in the traps. This work opens the route to the use of circular levels in quantum devices. It is also promising for quantum simulation and information processing using the full extent of Rydberg manifolds.

Near-field antenna measurement based on Rydberg-atom probe

Current near-field antenna measurement methods are commonly based on metal probes, with the accuracy limited and hard to be optimized due to the drawbacks they suffered, such as large volume, severe metal reflection/interference and complex circuit signal processing in parameter extracting. In this work, a novel method is proposed based on Rydberg atom in the near-field antenna measurement, which can offer a higher accuracy due to its intrinsic character of traceability to electric field. Replacing the metal probe in near-field measurement system by Rydberg atoms contained in a vapor cell (probe), amplitude- and phase- measurements on a 2.389 GHz signal launched out from a standard gain horn antenna are conducted on a near-field plane. They are transformed to far-field pattern and agree well with simulated results and measured results by using a traditional metal probe method. A high precision in longitudinal phase testing with an error below 1.7% can be achieved.

Intra-cavity frequency-doubled VECSEL system for narrow linewidth Rydberg EIT spectroscopy

High-power, narrow-linewidth light sources in the visible and UV spectra are in growing demand, particularly as quantum information and sensing research proliferates. Vertical external-cavity surface-emitting lasers (VECSELs) with intra-cavity frequency conversion are emerging as an attractive platform to fill these needs. Using such a device, we demonstrate 3.5 MHz full-width half-maximum Rydberg-state spectroscopy via electromagnetically induced transparency (EIT). The laser's 690 mW of output power at a wavelength of 475 nm enables large Rabi frequencies and strong signal-to-noise ratio in shorter measurement times. In addition, we characterize the frequency stability of the VECSEL using the delayed self-heterodyne technique and direct comparison with a commercial external-cavity diode laser (ECDL). We measure the pre-doubled light's Lorentzian linewidth to be 2π × 5.3(2) kHz, and the total linewidth to be 2π × 23(2) kHz. These measurements provide evidence that intra-cavity frequency-doubled VECSELs can perform precision spectroscopy at and below the MHz level, and are a promising tool for contemporary, and future, quantum technologies.

Sensitivity of a Rydberg-atom receiver to frequency and amplitude modulation of microwaves

Electromagnetically induced transparency in atomic systems involving Rydberg states is known to be a sensitive probe of incident microwave (MW) fields, in particular those resonant with Rydberg-to-Rydberg transitions. Here we propose an intelligible analytical model of a Rydberg atomic receiver's response to amplitude- (AM) and frequency-modulated (FM) signals and compare it with experimental results, presenting a setup that allows sending signals with either AM or FM and evaluating their efficiency with demodulation. Additionally, the setup reveals a detection configuration using all circular polarizations for optical fields and allowing detection of a circularly polarized MW field, propagating colinearly with optical beams. In our measurements, we systematically show that several parameters exhibit local optimum characteristics and then estimate these optimal parameters and working ranges, addressing the need to devise a robust Rydberg MW sensor and its operational protocol.

Deep learning enhanced Rydberg multifrequency microwave recognition

Recognition of multifrequency microwave (MW) electric fields is challenging because of the complex interference of multifrequency fields in practical applications. Rydberg atom-based measurements for multifrequency MW electric fields is promising in MW radar and MW communications. However, Rydberg atoms are sensitive not only to the MW signal but also to noise from atomic collisions and the environment, meaning that solution of the governing Lindblad master equation of light-atom interactions is complicated by the inclusion of noise and high-order terms. Here, we solve these problems by combining Rydberg atoms with deep learning model, demonstrating that this model uses the sensitivity of the Rydberg atoms while also reducing the impact of noise without solving the master equation. As a proof-of-principle demonstration, the deep learning enhanced Rydberg receiver allows direct decoding of the frequency-division multiplexed signal. This type of sensing technology is expected to benefit Rydberg-based MW fields sensing and communication.

Laser-frequency stabilization with differential single-beam saturated absorption spectroscopy of 4He atoms

Differential single-beam saturated-absorption spectroscopy (DSSAS) is proposed to stabilize lasing frequency and suppress Doppler-broadened background and common-mode optical noise. The spectral first-derivative demodulated signal of metastable He4 atoms is used as an error signal to stabilize a fiber laser around 1083 nm. Experimental results show that, compared with existing non-DSSAS frequency stabilization, DSSAS stabilization produces better stability and lower fluctuations, especially for frequency-noise-corrupted lasers. In DSSAS stabilization, for data acquired over 7000 s, the root mean square frequency fluctuation of the fiber laser is 16.4 kHz, and the frequency stability described by the modified Allan deviation is 4.1 × 10^-12 at 100 s. Even for a defective laser with poor frequency stability, the proposed scheme demonstrates experimentally high capability of noise suppression and reduces the frequency fluctuations by two orders of magnitude. Given its simplicity and compact design, frequency stabilization by DSSAS is promising for quantum-sensor applications, such as atomic magnetometers, atomic gyroscopes, and atomic clocks.

Bench-Top Cooling of a Microwave Mode Using an Optically Pumped Spin Refrigerator

We experimentally demonstrate the temporary removal of thermal photons from a microwave mode at 1.45 GHz through its interaction with the spin-polarized triplet states of photo-excited pentacene molecules doped within a p-terphenyl crystal at room temperature. The crystal functions electromagnetically as a narrowband cryogenic load, removing photons from the otherwise room-temperature mode via stimulated absorption. The noise temperature of the microwave mode dropped to 50_{-32}^{+18}  K (as directly inferred by noise-power measurements), while the metal walls of the cavity enclosing the mode remained at room temperature. Simulations based on the same system's behavior as a maser (which could be characterized more accurately) indicate the possibility of the mode's temperature sinking to ∼10  K (corresponding to ∼140 microwave photons). These observations, when combined with engineering improvements to deepen the cooling, identify the system as a narrowband yet extremely convenient platform-free of cryogenics, vacuum chambers, and strong magnets-for realizing low-noise detectors, quantum memory, and quantum-enhanced machines (such as heat engines) based on strong spin-photon coupling and entanglement at microwave frequencies.

Radiative lifetime measurement of ultracold cesium Rydberg states by a simplified optical pumping method

We demonstrate one simplified all-optical method to measure the radiative lifetime of ultracold cesium (Cs) Rydberg atoms. This method is based on photodetection of one ground state atomic absorption in a ladder-type electromagnetic induced transparency (EIT), which contains one ground state, one intermediate state, and one Rydberg state. In the presence and absence of optical pumping between the Rydberg state and the intermediate state, the absorption difference with varying delay time can reconstruct the population evolution of target Rydberg atoms. By using this method, the radiative lifetimes of 50S_1/2 and 50D_5/2 of Cs atoms are measured to be 53(9)µs and 42(9)µs, respectively, which are consistent with theoretical calculations. The agreements show the reliability of our presented method, which can provide a route for researching light-matter interaction behavior without the need to quantify absorption characteristic.

Proposal of Rydberg atomic receiver for amplitude-modulated microwave signals with active Raman gain

An efficient scheme for a microwave (MW) receiver is proposed based on the active Raman gain (ARG) in Rydberg atoms. The ⁸⁷Rb atoms are excited to the Rydberg state (53D_5/2), and the gain spectrum has a single gain peak. The MW field is resonant with the Rydberg transition (53D_5/2→54P_3/2), resulting in a split in the gain spectrum. The frequency splitting of two peaks depends linearly on the MW field strength. The distortion and attenuation of the probe field are reduced, due to the system's operating in the stimulated Raman emission mode. Simulation results show that the fidelity of MW communication based on the Rydberg atomic ARG scheme is improved by at least 10 times compared to that based on an electromagnetically induced transparency scheme, and the system seems more robust to amplitude modulation signals with different modulation depths.

Laser Trapping of Circular Rydberg Atoms

Rydberg atoms are remarkable tools for quantum simulation and computation. They are the focus of an intense experimental activity, mainly based on low-angular-momentum Rydberg states. Unfortunately, atomic motion and levels lifetime limit the experimental timescale to about 100  μs. Here, we demonstrate two-dimensional laser trapping of long-lived circular Rydberg states for up to 10 ms. Our method is very general and opens many opportunities for quantum technologies with Rydberg atoms. The 10 ms trapping time corresponds to thousands of interaction cycles in a circular-state-based quantum simulator. It is also promising for quantum metrology and quantum information with Rydberg atoms, by bringing atom-field interaction times into unprecedented regimes.

Waveguide-integrated Rydberg Atom-based RF Field Detector for Near-field Antenna Measurements

We demonstrate simultaneous amplitude and phase measurements of a radio-frequency (RF) field through the use of a Rydberg atom-based sensor embedded inside a waveguiding structure. This measurement uses the Rydberg atom-based sensor in a mixer configuration, which requires the presence of a local oscillator (LO) RF field. The waveguiding structure supplies the LO field. The combined waveguide and Rydberg atom system is used to measure phase and amplitude in the near-field of a horn antenna to extract the far-field pattern.

Measurement of the Near Field Distribution of a Microwave Horn Using a Resonant Atomic Probe

We measure the near field distribution of a microwave horn with a resonant atomic probe. The microwave field emitted by a standard microwave horn is investigated utilizing Rydberg electromagnetically inducted transparency (EIT), an all-optical Rydberg detection, in a room temperature caesium vapor cell. The ground 6 S 1 / 2 , excited 6 P 3 / 2 , and Rydberg 56 D 5 / 2 states constitute a three-level system, used as an atomic probe to detect microwave electric fields by analyzing microwave dressed Autler–Townes (AT) splitting. We present a measurement of the electric field distribution of the microwave horn operating at 3.99 GHz in the near field, coupling the transition 56 D 5 / 2 → 57 P 3 / 2 . The microwave dressed AT spectrum reveals information on both the strength and polarization of the field emitted from the microwave horn simultaneously. The measurements are compared with field measurements obtained using a dipole metal probe, and with simulations of the electromagnetic simulated software (EMSS). The atomic probe measurement is in better agreement with the simulations than the metal probe. The deviation from the simulation of measurements taken with the atomic probe is smaller than the metal probe, improving by 1.6 dB. The symmetry of the amplitude distribution of the measured field is studied by comparing the measurements taken on either side of the field maxima.

Weak electric-field detection with sub-1 Hz resolution at radio frequencies using a Rydberg atom-based mixer

Rydberg atoms have been used for measuring radio-frequency (RF) electric (E)-fields due to their strong dipole moments over the frequency range of 500 MHz-1 THz. For this, electromagnetically induced transparency (EIT) within the Autler-Townes (AT) regime is used such that the detected E-field is proportional to AT splitting. However, for weak E-fields AT peak separation becomes unresolvable thus limiting the minimum detectable E-field. Here, we demonstrate using the Rydberg atoms as an RF mixer for weak E-field detection well below the AT regime with frequency discrimination better than 1 Hz resolution. A heterodyne detection scenario with two E-fields incident on a vapor cell filled with cesium atoms is used. One E-field at 19.626000 GHz drives the 34 D 5 / 2 → 35 P 3 / 2 Rydberg transition and acts as a local oscillator (LO) and a second signal E-field (Sig) of interest is at 19.626090 GHz. In the presence of the LO, the Rydberg atoms naturally down convert the Sig field to a 90 kHz intermediate frequency (IF) signal. This IF signal manifests as an oscillation in the probe laser intensity through the Rydberg vapor and is easily detected with a photodiode and lock-in amplifier. In the configuration used here, E-field strength down to ≈ 46 μ V / m ± 2 μ V / m were detected with a sensitivity of ≈ 79 μ Vm - 1 Hz - 1 / 2 . Furthermore, neighboring fields 0.1 Hz away and equal in strength to Sig could be discriminated without any leakage into the lock-in signal. For signals 1 Hz away and as high as +60 dB above Sig, leakage into the lock-in signal could be kept below -3 dB.