Atom-Based Sensing of Weak Radio Frequency Electric Fields Using Homodyne Readout

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.

Broadband and robust Mach-Zehnder interferometer for Rydberg atomic system

We present a broadband and robust Mach-Zehnder interferometer (MZI) with meter-scale arm length, aiming to acquire the full information of an atomic system. We utilize a pre-loading phase shifter as servo actuator, broadening the servo bandwidth to 108 kHz without sacrificing the size of the piezoelectric transducer (PZT) and mirror. An auxiliary laser at 780 nm, counter-propagating with the probe laser, is employed to achieve arbitrary phase locking of the MZI, boosting a phase accuracy of 0.45 degrees and an Allan deviation of 0.015 degrees, which breaks the current record. By utilizing our robust MZI, the measurement accuracy of atomic system can be theoretically predicted to improve by 2.3 times compared to the most stable MZI in other literatures. In addition, we also demonstrate the sensitivity improvement in imaginary part and real part of the susceptibility in virtue of the completed interferometer, which exhibits tremendous potential in atom-based measurement system.

Stable, narrow-linewidth laser system with a broad frequency tunability and a fast switching time

For a Rydberg atom-based sensor to change its sensing frequency, the wavelength of the Rydberg state excitation laser must be altered. The wavelength shifts required can be on the order of 10 nm. A fast-tunable narrow-linewidth laser with broadband tuning capability is required. Here, we present a demonstration of a laser system that can rapidly switch a coupling laser as much as 8 nm in less than 50 μs. The laser system comprises a frequency-stabilized continuous wave laser and an electro-optic frequency comb. A filter enables selection of individual comb lines. A high-speed electro-optic modulator is used to tune the selected comb line to a specific frequency, i.e., an atomic transition. Through Rydberg atom-based sensing experiments, we demonstrate frequency hopping between two Rydberg states and a fast switching time of 400 μs, which we show can be reduced to ∼50 μs with a ping-pong scheme. If updating the RF frequency is not required during frequency hopping, a 200 ns switching time can be achieved. These results showcase the potential of the laser system for advanced Rydberg atom-based radio frequency sensing applications, like communications and radar.

Magnetic-field-induced splitting of Rydberg Electromagnetically Induced Transparency and Autler-Townes spectra in 87Rb vapor cell

We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each mF state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the theoretical calculations agree qualitatively with experimental results. The Rydberg atom microwave electric field sensor performance was enhanced by making use of the splitting interval between the two maximum absolute mF states separated by the static magnetic field, which was attributed to the stronger Clebsch-Gordon coefficients between the extreme mF states and the frequency detuning of the microwave electric field under the static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.

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.

Three-dimensional location system based on an L-shaped array of Rydberg atomic receivers

The Rydberg atomic receiver, sensing microwave electric field with high sensitivity and broad bandwidth, possesses the potential to be the staple for precise navigation and remote sensing. In this Letter, a Ku-band three-dimensional location system using an L-shaped array of Rydberg atomic receivers is theoretically proposed and experimentally demonstrated, and the proof of principle results show excellent consistency between the location-derived and the setting coordinates. The novel L-shaped array, together with the triangulation method, gives both phase difference and angle of arrival, achieving location of the horn for a signal microwave field in three-dimensional space. The concluded validity of this location system in the testing scene remains at approximately 90% with a theoretical maximum location tolerance of 5.7 mm. Furthermore, the estimation of two different spatiotemporal coordinates for the moving target confirms the velocity measurement capability of the system with errors less than 0.5 mm/s. The proposed location system using a Rydberg atomic receiver array is a verification for the most basic element and can be extended through repetition or nesting to a multi-input-multi-output system as well as multi-channel information processing.

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.

Polarization Spectroscopy Applied to Electromagnetically Induced Transparency in Hot Rydberg Atoms Using a Laguerre–Gaussian Beam

In this work, we have applied polarization spectroscopy to study electromagnetically induced transparency involving hot Rb85 Rydberg state in a vapor cell using a Laguerre–Gaussian mode beam. Such spectroscopy technique generates a dispersive signal, which allows a direct measurement of the transition linewidth. Our results show that the measured transition linewidth for a Laguerre–Gaussian mode control beam is narrower than for a Gaussian mode. Besides, it can be well reproduced by a simplified Lindblad master equation model.

Sensitivity Improvement and Determination of Rydberg Atom-Based Microwave Sensor

We present a theoretical and experimental investigation of the improvement and determination of the sensitivity of Rydberg atom-based microwave RF sensor. An optical Bloch equation has been set up based on the configuration that two-color cascading lasers exciting atom to highly Rydberg state and a microwave RF coupling this Rydberg state to its adjacent neighbor. The numerical simulation shows that the sensitivity of the atomic RF sensor is correlated with the amplitude strengths of the applied two lasers and the RF itself. It also depends on the frequency detuning of the coupling laser, which induces an asymmetrically optical splitting. The coupling laser frequency fixing at the shoulder of the stronger one is more favorable for a higher sensitivity. Accordingly, we perform an experimental demonstration for the optimization of all these parameters and the sensitivity is improved to 12.50(04) nVcm−1·Hz−1/2.

A Molecular Approach to Quantum Sensing

The second quantum revolution hinges on the creation of materials that unite atomic structural precision with electronic and structural tunability. A molecular approach to quantum information science (QIS) promises to enable the bottom-up creation of quantum systems. Within the broad reach of QIS, which spans fields ranging from quantum computation to quantum communication, we will focus on quantum sensing. Quantum sensing harnesses quantum control to interrogate the world around us. A broadly applicable class of quantum sensors would feature adaptable environmental compatibility, control over distance from the target analyte, and a tunable energy range of interaction. Molecules enable customizable "designer" quantum sensors with tunable functionality and compatibility across a range of environments. These capabilities offer the potential to bring unmatched sensitivity and spatial resolution to address a wide range of sensing tasks from the characterization of dynamic biological processes to the detection of emergent phenomena in condensed matter. In this Outlook, we outline the concepts and design criteria central to quantum sensors and look toward the next generation of designer quantum sensors based on new classes of molecular sensors.

A Condensed Excited (Rydberg) Matter: Perspective and Applications

A condensed excited matter called Rydberg Matter (RM) have been studied experimentally for 30 years, but have not sparked widespread attention yet, unlike ordinary Rydberg atoms. RM formed by clusters of Rydberg atoms at a solid surface have a longer lifetime compared to Rydberg atoms, and is liquid-like. This review describes how the RM state is generated, and its potential applications. These include using RM for research into catalysis, space phenomena and sensor applications, or for producing environmentally friendly energy. A background on RM is presented, with its structure and special properties, and the working principle of RM generation. The experimental set-ups, materials, and detectors used are discussed, together with methods to improve the amount of RM produced. The materials used for the catalysts are of special interest, as this should have a large influence on the energy of the RM, and therefore also on the applications. Currently most of the catalysts used are potassium doped iron oxide designed for styrene production, which should give the possibility of improvements. And as there is little knowledge on the exact mechanisms for RM formation, suggestions are given as to where research should start.

Improvement of Microwave Electric Field Measurement Sensitivity via Multi-Carrier Modulation in Rydberg Atoms

The microwave electric field intensity is precisely measured by the Autler–Townes splitting of electromagnetically induced transparency spectrum in a 5S1/2−5P3/2−57D5/2−58P3/2 four-level ladder-type 85Rb atomic system. A robust multi-carrier modulation scheme is employed to improve the spectral signal-to-noise ratio, which determines the optical readout of Rydberg atom-based microwave electrometry. As a result, a factor of 2 measurement sensitivity improvement is clearly achieved compared with the on resonant Autler–Townes splitting case credit to the advantage of matched filtering. This research paves the way for building a high sensitivity, portable sensor and offers a platform for achieving compact and sensitive receiver.

Phase-Sensitive Vector Terahertz Electrometry from Precision Spectroscopy of Molecular Ions

This article proposes a new method for sensing THz waves that can allow electric field measurements traceable to the International System of Units and to the fundamental physical constants by using the comparison between precision measurements with cold trapped HD+ ions and accurate predictions of molecular ion theory. The approach exploits the lightshifts induced on the two-photon rovibrational transition at 55.9 THz by a THz wave around 1.3 THz, which is off-resonantly coupled to the HD+ fundamental rotational transition. First, the direction and the magnitude of the static magnetic field applied to the ion trap is calibrated using Zeeman spectroscopy of HD+. Then, a set of lightshifts are converted into the amplitudes and the phases of the THz electric field components in an orthogonal laboratory frame by exploiting the sensitivity of the lightshifts to the intensity, the polarization and the detuning of the THz wave to the HD+ energy levels. The THz electric field measurement uncertainties are estimated for quantum projection noise-limited molecular ion frequency measurements with the current accuracy of molecular ion theory. The method has the potential to improve the sensitivity and accuracy of electric field metrology and may be extended to THz magnetic fields and to optical fields.

Dispersive microwave electrometry using Zeeman frequency modulation spectroscopy of electromagnetically induced transparency in Rydberg atoms

We herein developed and demonstrated a Zeeman frequency modulation scheme for improving the signal-to-noise ratio of microwave electric field measurement using Rydberg atoms. The spectra of the electromagnetically induced transparency (EIT) and Autler-Townes splitting of Rydberg atoms is frequency modulated by an alternating current magnetic field. The signal-to-noise ratio of the corresponding dispersive error signal is enhanced more than 10 times than that of the original spectrum. Furthermore, we show that the slope of the dispersive error signal near the resonance of the Rydberg EIT can be used to characterize the weak microwave electric field amplitudes. The more intuitive and simpler structure compared with other existing frequency modulation technologies greatly reduces the difficulties of experiments and experimental data analysis.

Rydberg Level Shift due to the Electric Field Generated by Rydberg Atom Collision Induced Ionization in Cesium Atomic Ensemble

We experimentally studied the Rydberg level shift caused by the electric field, which is generated by Rydberg atom collision induced ionization in a cesium atomic ensemble. The density of charged particles caused by collisions between Rydberg atoms is changed by controlling the ground-state atomic density and optical excitation process. We measured the Rydberg level shift using Rydberg electromagnetically-induced-transparency (EIT) spectroscopy, and interpreted the physical origin using a semi-classical model. The experimental results are in good agreement with the numerical simulation. These energy shifts are important for the self-calibrated sensing of microwave field by the employing of Rydberg EIT. Moreover, in contrast to the resonant excitation case, narrow-linewidth spectroscopy with high signal-to-noise ratio would be useful for high-precision measurements.

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.

Nonlinearity of Microwave Electric Field Coupled Rydberg Electromagnetically Induced Transparency and Autler-Townes Splitting

An electromagnetically induced transparency (EIT) of a cascade-three-level atom involving Rydberg level in a room-temperature cell, formed with a cesium 6 S 1 / 2 -6 P 3 / 2 -66 S 1 / 2 scheme, is employed to detect the Autler-Townes (AT) splitting resulted with a 15.21-GHz microwave field coupling the 66 S 1 / 2 →65 P 1 / 2 transition. Microwave field induced AT splitting, f A T , is characterized by the distance of peak-to-peak of an EIT-AT spectrum. The f A T dependence on the microwave Rabi frequency, Ω M W , demonstrates two regions, the strong-coupling linear region, f A T ≈ Ω M W and the weak-coupling nonlinear region, f A T ≲ Ω M W . The f A T dependencies on the probe and coupling Rabi frequency are also investigated. Using small probe- and coupling-laser, the Rabi frequency is found to enlarge the linear regime and decrease the uncertainty of the microwave field measurements. The measurements agree with the calculations based on a four-level atomic model.

Rydberg-atom-based digital communication using a continuously tunable radio-frequency carrier

Up to now, the measurement of radio-frequency (RF) electric field achieved using the electromagnetically-induced transparency (EIT) of Rydberg atoms has proved to be of high-sensitivity and shows a potential to produce a promising atomic RF receiver at resonance between two chosen Rydberg states. In this paper, we study the extension of the feasibility of digital communication via this quantum-based antenna over a continuously tunable RF-carrier at off-resonance. Our experiment shows that the digital communication at a rate of 500 kbps can be performed reliably within a tunable bandwidth of 200 MHz near a 10.22 GHz carrier. Outside of this range, the bit error rate (BER) increases, rising to, for example, 15% at an RF-detuning of ±150 MHz. In the measurement, the time-varying RF field is retrieved by detecting the optical power of the probe laser at the center frequency of RF-induced symmetric or asymmetric Autler-Townes splitting in EIT. Prior to the digital test, we studied the RF-reception quality as a function of various parameters including the RF detuning and found that a choice of linear gain response to the RF-amplitude can suppress the signal distortion. The modulating signal can be decoded at speeds up to 500 kHz in the tunable bandwidth. Our test consolidates the physical basis for reliable communication and spectral sensing over a wider broadband RF-carrier, which paves a way for the concurrent multi-channel communications founded on the same pair of Rydberg states.

Realization of a Rydberg-Dressed Ramsey Interferometer and Electrometer

We present the experimental realization and characterization of a Ramsey interferometer based on optically trapped ultracold potassium atoms, where one state is continuously coupled by an off-resonant laser field to a highly excited Rydberg state. We show that the observed interference signals can be used to precisely measure the Rydberg atom-light coupling strength as well as the population and coherence decay rates of the Rydberg-dressed states with subkilohertz accuracy and for Rydberg state fractions as small as one part in 10^{6}. We also demonstrate an application for measuring small, static electric fields with high sensitivity. This provides the means to combine the outstanding coherence properties of Ramsey interferometers based on atomic ground states with a controllable coupling to strongly interacting states, thus expanding the number of systems suitable for metrological applications and many-body physics studies.

Field Distortion and Optimization of a Vapor Cell in Rydberg Atom-Based Radio-Frequency Electric Field Measurement

Highly excited Rydberg atoms in a room-temperature vapor cell are promising for developing a radio-frequency (RF) electric field (E-field) sensor and relevant measurement standards with high accuracy and sensitivity. The all-optical sensing approach is based on electromagnetically-induced transparency and Autler-Townes splitting induced by the RF E-field. Systematic investigation of measurement uncertainty is of great importance for developing a national measurement standard. The presence of a dielectric vapor cell containing alkali atoms changes the magnitude, polarization, and spatial distribution of the incident RF field. In this paper, the field distortion of rubidium vapor cells is investigated, in terms of both field strength distortion and depolarization. Full-wave numerical simulation and analysis are employed to determine general optimization solutions for minimizing such distortion and validated by measuring the E-field vector distribution inside different vapor cells. This work can improve the accuracy of atom-based RF E-field measurements and contributes to the development of related RF quantum sensors.

A terahertz-driven non-equilibrium phase transition in a room temperature atomic vapour

There are few demonstrated examples of phase transitions that may be driven directly by terahertz frequency electric fields, and those that are known require field strengths exceeding 1 MV cm-1. Here we report a non-equilibrium phase transition driven by a weak (≪1 V cm-1), continuous-wave terahertz electric field. The system consists of room temperature caesium vapour under continuous optical excitation to a high-lying Rydberg state, which is resonantly coupled to a nearby level by the terahertz electric field. We use a simple model to understand the underlying physical behaviour, and we demonstrate two protocols to exploit the phase transition as a narrowband terahertz detector: the first with a fast (20 μs) non-linear response to nano-Watts of incident radiation, and the second with a linearised response and effective noise equivalent power ≤1 pW Hz-1/2. The work opens the door to a class of terahertz devices controlled with low-field intensities and operating in a room temperature environment.

Fiber-coupled vapor cell for a portable Rydberg atom-based radio frequency electric field sensor

We demonstrate a movable, Rydberg atom-based radio frequency (RF) electric (E) field probe. The technique is based on electromagnetically induced transparency and Autler-Townes splitting. Two fibers attached to a 10 mm cubic Cs133 vapor cell are used to couple counter-propagating probe and control lasers through the cell. This all-dielectric fiber-coupled sensor can be moved from the optics table to locations more suitable for RF (gigahertz to sub-terahertz) E-field measurements and calibrations.

Rydberg-atom based radio-frequency electrometry using frequency modulation spectroscopy in room temperature vapor cells

Rydberg atom-based electrometry enables traceable electric field measurements with high sensitivity over a large frequency range, from gigahertz to terahertz. Such measurements are particularly useful for the calibration of radio frequency and terahertz devices, as well as other applications like near field imaging of electric fields. We utilize frequency modulated spectroscopy with active control of residual amplitude modulation to improve the signal to noise ratio of the optical readout of Rydberg atom-based radio frequency electrometry. Matched filtering of the signal is also implemented. Although we have reached similarly, high sensitivity with other read-out methods, frequency modulated spectroscopy is advantageous because it is well-suited for building a compact, portable sensor. In the current experiment, ∼3 µV cm^-1 Hz^-1/2 sensitivity is achieved and is found to be photon shot noise limited.