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

A photonic crystal receiver for Rydberg atom-based sensing

Rydberg atom-based sensors use atoms dressed by lasers to detect and measure radio frequency electromagnetic fields. The absorptive properties of the atomic gas, configured as a Rydberg atom-based sensor, change in the presence of a radio frequency electromagnetic field. While these sensors are reasonably sensitive, the best conventional radio frequency sensors still outperform Rydberg atom-based sensors with respect to sensitivity. One approach to increase the sensitivity of Rydberg atom-based sensors is to engineer the vapor cell that contains the atomic gas. In this work, we introduce a passive, all-dielectric amplifier integrated into a Rydberg atom-based sensor vapor cell. The vapor cell is a combination of a slot waveguide and a photonic crystal. The structural features of the vapor cell yield a power amplification of ~24 dB. The radio frequency electromagnetic field is coupled adiabatically into the slot waveguide and slowed to increase the interaction between the radio frequency field and the atoms to effectively amplify the incoming signal, i.e., increase the Rabi frequency on the radio frequency transition. The work shows the utility of vapor cell engineering for atom-based quantum technologies and paves the way for other such devices.

Analytical model for transient evolution of an EIT-AT spectrum with Rydberg atoms

An analytical model of an electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting spectrum with a four-level Rydberg atom was presented, and equations were derived to explain the dependence of the transient absorption for a probe laser on light and microwave (MW) fields. The analytical solution of absorption for the probe laser Im[χ(t)] shows that it depends on the spontaneous decay rate from level |2〉 to level |1〉, Rabi frequencies of the control and MW fields. For 87Rb atoms, a stronger control laser shortens the steady-state time window and a stronger MW field will lead to a higher oscillation frequency shown in analytical and numerical results. The time-dependent EIT-AT splitting spectrum is also investigated, and the stable splitting distance shows a linear dependence on the continuous MW E-field strength.

Rydberg electromagnetically induced transparency based laser lock to Zeeman sublevels with 0.6 GHz scanning range

We propose a technique for frequency locking a laser to the Zeeman sublevel transitions between the 5P3/2 intermediate and 32D5/2 Rydberg states in 87Rb. This method allows for continuous frequency tuning over 0.6 GHz by varying an applied external magnetic field. In the presence of the applied field, the electromagnetically induced transparency (EIT) spectrum of an atomic vapor splits via the Zeeman effect according to the strength of the magnetic field and the polarization of the pump and probe lasers. We show that the 480 nm pump laser, responsible for transitions between the Zeeman sublevels of the intermediate state and the Rydberg state, can be locked to the Zeeman-split EIT peaks. The short-term frequency stability of the laser lock is 0.15 MHz, and the long-term stability is within 0.5 MHz. The linewidth of the laser lock is ∼0.8 and ∼1.8 MHz in the presence and absence of the external magnetic field, respectively. In addition, we show that in the absence of an applied magnetic field and adequate shielding, the frequency shift of the lock point has a peak-to-peak variation of 1.6 MHz depending on the polarization of the pump field, while when locked to Zeeman sublevels, this variation is reduced to 0.6 MHz. The proposed technique is useful for research involving Rydberg atoms, where large continuous tuning of the laser frequency with stable locking is required.

Key Technologies in Developing Chip-Scale Hot Atomic Devices for Precision Quantum Metrology

Chip-scale devices harnessing the interaction between hot atomic ensembles and light are pushing the boundaries of precision measurement techniques into unprecedented territory. These advancements enable the realization of super-sensitive, miniaturized sensing instruments for measuring various physical parameters. The evolution of this field is propelled by a suite of sophisticated components, including miniaturized single-mode lasers, microfabricated alkali atom vapor cells, compact coil systems, scaled-down heating systems, and the application of cutting-edge micro-electro-mechanical system (MEMS) technologies. This review delves into the essential technologies needed to develop chip-scale hot atomic devices for quantum metrology, providing a comparative analysis of each technology's features. Concluding with a forward-looking perspective, this review discusses the future potential of chip-scale hot atomic devices and the critical technologies that will drive their advancement.

Rydberg-atom-based radio-frequency sensors: amplitude-regime sensing

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.

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.

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.

Tunable frequency of a microwave mixed receiver based on Rydberg atoms under the Zeeman effect

Researchers are interested in the sensor based on Rydberg atoms because of its broad testing frequency range and outstanding sensitivity. However, the discrete frequency detection limits its further employment. We expand the frequency range of microwaves using Rydberg atoms under the Zeeman effect. In such a scheme, the magnetic field is employed as a tool to split and modify adjacent Rydberg level intervals to realize tunable frequency measurement over 100 MHz under 0-31.5 Gauss magnetic field. In this frequency range, the microwave has a linear dynamic variation range of 63 dB, and has achieved a sensitivity of 11.72 µV cm-1Hz-1/2 with the minimum detectable field strength of 17.2 µV/cm.. Compared to the no magnetic field scenario, the sensitivity would not decrease. By theoretical analysis, in a strong magnetic field, the tunable frequency range can be much larger than 100 MHz. The proposed method for achieving tunable frequency measurement provides a crucial tool in radars and communication.

Enhanced microwave metrology using an optical grating in Rydberg atoms

An enhanced measurement of the microwave (MW) electric (E) field is proposed using an optical grating in Rydberg atoms. Electromagnetically induced transparency (EIT) of Rydberg atoms appears driven by a probe field and a control field. The EIT transmission spectrum is modulated by an optical grating. When a MW field drives the Rydberg transition, the central principal maximum of the grating spectrum splits. It is interesting to find that the magnitude of the sharp grating spectrum changes linearly with the MW E-field strength, which can be used to measure the MW E-field. The simulation result shows that the minimum detectable E-field strength is nearly 1/8 of that without gratings, and its measurement accuracy could be enhanced by about 60 times. Other discussion of MW metrology based on a grating spectrum is also presented.

Precise measurement of microwave polarization using a Rydberg atom-based mixer

A Rydberg atom-based mixer has opened up a new method to characterize microwave electric fields such as the precise measurement of their phase and strength. This study further demonstrates, theoretically and experimentally, a method to accurately measure the polarization of a microwave electric field based on a Rydberg atom-based mixer. The results show that the amplitude of the beat note changes with the polarization of the microwave electric field in a period of 180 degrees, and in the linear region a polarization resolution better than 0.5 degree can be easily obtained which reaches the best level by a Rydberg atomic sensor. More interestingly, the mixer-based measurements are immune to the polarization of the light field that forms the Rydberg EIT. This method considerably simplifies theoretical analysis and the experimental system required for measuring microwave polarization using Rydberg atoms and is of interest in microwave sensing.

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.

Real-time imaging of electromagnetic fields

The measurement and diagnosis of electromagnetic fields are important foundations for various electronic and optical systems. This paper presents an innovative optically controlled plasma scattering technique for imaging electromagnetic fields. On a silicon wafer, the plasma induced by the photoconductive effect is exploited as an optically controlled scattering probe to image the amplitude and phase of electromagnetic fields. A prototype is built and realizes the imaging of electromagnetic fields radiated from antennas from 870MHz to 0.2 terahertz within one second. Measured results show good agreement with the simulations. It is demonstrated that this new technology improves the efficiency of electromagnetic imaging to a real-time level, while combining various advantages of ultrafast speed, super-resolution, ultra-wideband response, low-cost and vectorial wave mapping ability. This method may initiate a new avenue in the measurement and diagnosis of electromagnetic fields.

Autler-Townes splitting of three-photon excitation of cesium cold Rydberg gases

We demonstrate the three-photon Autler-Townes (AT) spectroscopy in a cold cesium Rydberg four-level atom by detecting the field ionized Rydberg population. The ground state |6S_1/2〉, two intermediate states |6P_3/2〉 and |7S_1/2〉 and Rydberg state |60P_3/2〉 form a cascade four-level atomic system. The three-photon AT spectra and AT splittings are characterized by the Rabi frequency Ω₈₅₂ and Ω₁₄₇₀ and detuning δ₈₅₂ of the coupling lasers. Due to the interaction of two coupling lasers with the atoms, the AT spectrum has three peaks denoted with the letters A, B and C. Positions of the peaks and relative AT splittings, γ_AB and γ_BC, strongly depend on two coupling lasers. The dependence of the AT splitting, γ_AB and γ_BC, on the coupling laser detuning, δ₈₅₂, and Rabi frequency, Ω₈₅₂ and Ω₁₄₇₀ are investigated. It is found that the AT splitting γ_AB mainly comes from the first photon coupling, whereas the γ_BC mainly comes from the second photon coupling with the atom. The three-photon AT spectra and relevant AT splittings are simulated with the four-level density matrix equation and show good agreement with the theoretical simulations considering the spectral line broadening. Our work is of great significance both for further understanding the interaction between the laser and the atom, and for the application of the Rydberg atom based field measurement.

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.

Measuring the phase noise of Raman lasers with an atom-based method

Phase noise of Raman lasers is a major source of noise for a Raman-type cold atom interferometer, which is traditionally measured using the signal source analyzer. We report here an atom-based method to measure the phase noise performance between two Raman lasers. By analyzing and calibrating the system noise sources, we can characterize the contribution of phase noise from the total deviation of the relative atom population at the middle of the interference fringe. Knowing the transfer function specified by the operation sequence of the interferometer, we can obtain the transfer function and power spectrum density of the phase noise term. By varying the time sequences of the interferometer, we can measure the white phase noise floor and the phase noise performance over a large range of Fourier frequencies from 1 to 100 000 Hz with a minor difference of 1 dB compared with results from the traditional method using a signal analyzer, which proves the validity of the atom-based method. Compared with the traditional measurement method, the atom-based method can have higher accuracy and have the ability of self-calibrating.

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.

DC electric fields in electrode-free glass vapor cell by photoillumination

We demonstrate laser induced DC electric fields in an all-glass vapor cell without bulk or thin film electrodes. The spatial field distribution is mapped by Rydberg electromagnetically induced transparency (EIT) spectroscopy. The fields are generated by a photoelectric effect and allow DC electric field tuning of up to 0.8 V/cm within the Rydberg EIT probe region. We explain the measured with a boundary-value electrostatic model. This work may inspire new approaches for DC electric field control in designing miniaturized atomic vapor cell devices. Limitations and other charge effects are also discussed.

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.

Quantum-Limited Atomic Receiver in the Electrically Small Regime

We use a quantum sensor based on thermal Rydberg atoms to receive data encoded in electromagnetic fields in the extreme electrically small regime, with a sensing volume over 10^{7} times smaller than the cube of the electric field wavelength. We introduce the standard quantum limit for data capacity, and experimentally observe quantum-limited data reception for bandwidths from 10 kHz up to 30 MHz. In doing this, we provide a useful alternative to classical communication antennas, which become increasingly ineffective when the size of the antenna is significantly smaller than the wavelength of the electromagnetic field.

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.

Highly sensitive atomic based MW interferometry

We theoretically study a scheme to develop an atomic based micro-wave (MW) interferometry using the Rydberg states in Rb. Unlike the traditional MW interferometry, this scheme is not based upon the electrical circuits, hence the sensitivity of the phase and the amplitude/strength of the MW field is not limited by the Nyquist thermal noise. Further, this system has great advantage due to its much higher frequency range in comparision to the electrical circuit, ranging from radio frequency (RF), MW to terahertz regime. In addition, this is two orders of magnitude more sensitive to field strength as compared to the prior demonstrations on the MW electrometry using the Rydberg atomic states. Further, previously studied atomic systems are only sensitive to the field strength but not to the phase and hence this scheme provides a great opportunity to characterize the MW completely including the propagation direction and the wavefront. The atomic based MW interferometry is based upon a six-level loopy ladder system involving the Rydberg states in which two sub-systems interfere constructively or destructively depending upon the phase between the MW electric fields closing the loop. This work opens up a new field i.e. atomic based MW interferometry replacing the conventional electrical circuit in much superior fashion.