Atom-based vector microwave electrometry using rubidium Rydberg atoms in a vapor cell

Fast simulation for interacting four-level Rydberg atoms: electromagnetically induced transparency and Autler-Townes splitting

Quantum sensing using Rydberg atoms is an emerging technology for precise measurement of electric fields. However, most existing computational methods are all based on a single-particle model and neglect Rydberg-Rydberg interaction between atoms. In this study, we introduce the interaction term into the conventional four-level optical Bloch equations. By incorporating fast iterations and solving for the steady-state solution efficiently, we avoid the computation of a massive 4N × 4N dimensional matrix. Additionally, we apply the Doppler frequency shift to each atom used in the calculation, eliminating the requirement for an additional Doppler iteration. These schemes allow for the calculation of the interaction between 7000 atoms around one minute. Based on the many-body model, we investigate the Rydberg-Rydberg interaction of Rydberg atoms under different atomic densities. Furthermore, we compare our results with the literature data of a three-level system and the experimental results of our own four-level system. The results demonstrate the validity of our model, with an effective error of 4.59% compared to the experimental data. Finally, we discover that the many-body model better predicts the linear range for measuring electric fields than the single-particle model, making it highly applicable in precise electric field measurements.

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.

Measurement of relative transition strengths of 133Cs Rydberg D states using electromagnetically induced transparency

Transition strengths between states are fundamental physical properties of atomic spectra. The differences in fine structure splitting of certain states are mainly attributed to the angular momentum parts of transition dipole matrix elements. These can be calculated by integrating the wave-functions theoretically and can be accessed by selecting corresponding polarizations of the exciting lasers experimentally. We measured the transition strengths ratios of nD5 / 2 /nD3 / 2 via Rydberg electromagnetically induced transparency (EIT) by changing the powers and polarizations of probing and coupling lasers in a room temperature cesium vapor cell. The variation of the ratios on the principal quantum number n which ranges from 40 to 62 is also investigated. Theoretical and experimental results agreed with each other.

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.

Interaction of a four-level atom with a quantized field in the presence of a nonlinear Kerr medium

Quantum entanglement and atomic coherence are examined for a system consisting of a four-level atom (FLA) interacted with a nonlinear quantum field. We assume that the FLA-field coupling, Kerr medium and quantified field are all [Formula: see text]-deformed with full nonlinear formalism. We consider N-configuration and cascade (C)-configuration of the FLA. We explore the impact of field deformation and Kerr medium on the dynamics of the quantumness measures when the quantized field is initially prepared in a deformed coherent state without and with Kerr medium effect. Moreover, we examine the statistical properties of the radiation field using the second order correlation function. The results indicate how the considered quantumness measures in the FLA-field system can be manipulated and controlled through the parameters of the quantum model.

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.

Optimal Generators for Quantum Sensing

We propose a computationally efficient method to derive the unitary evolution that a quantum state is most sensitive to. This allows one to determine the optimal use of an entangled state for quantum sensing, even in complex systems where intuition from canonical squeezing examples breaks down. In this paper we show that the maximal obtainable sensitivity using a given quantum state is determined by the largest eigenvalue of the quantum Fisher information matrix (QFIM) and the corresponding evolution is uniquely determined by the coinciding eigenvector. Since we optimize the process of parameter encoding rather than focusing on state preparation protocols, our scheme is relevant for any quantum sensor. This procedure naturally optimizes multiparameter estimation by determining, through the eigenvectors of the QFIM, the maximal set of commuting observables with optimal sensitivity.

Super low-frequency electric field measurement based on Rydberg atoms

We demonstrate the measurement of super low-frequency electric field using Rydberg atoms in an atomic vapor cell with inside parallel electrodes, thus overcoming the low-frequency electric-field-screening effect at frequencies below a few kHz. Rydberg electromagnetically induced transparency (EIT) spectra involving 52D5/2 state is employed to measure the signal electric field. An auxiliary DC field is applied to improve the sensitivity. A DC Stark map is demonstrated, where the utilized 52D5/2 exhibits mj = 1/2, 3/2, 5/2 Stark shifts and splittings. The mj = 1/2 state is employed to detect the signal field because of its larger polarizability than that of mj = 3/2, 5/2. Also, we show that the strength of the spectrum is dependent on the angle between the laser polarizations and the electric field. With optimization of the applied DC field to shift the mj = 1/2 Rydberg energy level to a high sensitivity region and the laser polarizations to obtain the maximum mj = 1/2 signal, we achieve the detection of the signal electric field with a frequency of 100 Hz down to 214.8 µV/cm with a sensitivity of 67.9 µV cm-1Hz-1/2, and the linear dynamic range is over 37 dB. Our work extends the measurement frequency of Rydberg sensors to super low frequency with high sensitivity, which has the advantages of high sensitivity and miniaturization for receiving super low frequency.

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.

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.

Atom-based sensing technique of microwave electric and magnetic fields via a single rubidium vapor cell

We present an atom-based approach for determining microwave electric and magnetic fields by using a single rubidium vapor cell in a microwave waveguide. For a ⁸⁷Rb cascade three-level system employed in our experiment, a weak probe laser driving the lower transition, 5S_1/2→5P_3/2, is first used to measure the microwave magnetic field based on the atomic Rabi resonance. When a counter-propagating strong coupling laser is subsequently turned on to drive the Rydberg transition, 5P_3/2→67D_5/2, the same probe laser is then used as a Rydberg electromagnetically induced transparency (EIT) probe to measure the microwave electric field by investigating the resonant microwave dressed Autler-Townes splitting (ATS). By tuning the hyperfine transition frequency of the ground state using an experimentally feasible static magnetic field, we first achieved a measurement of the microwave electric and magnetic field strength at the same microwave frequency of 6.916 GHz. Based on the ideal relationship between the electric and magnetic field components, we obtained the equivalent microwave magnetic fields by fitting the inversion to the measured microwave electric fields, which demonstrated that the results were in agreement with the experimental measurement of the microwave magnetic fields in the same microwave power range. This study provides new experimental evidence for quantum-based microwave measurements of electric and magnetic fields by a single sensor in the same system.

Theoretical study of a four-level EIT-type system in the presence of structured coupling light for microwave field detection

In this work, we have theoretically studied the four-level atomic system for the measurement of a microwave (MW) field. We employed the electromagnetically induced transparency (EIT) technique for finding the MW field in the presence of a Laguerre-Gaussian (LG) beam as a coupling light. We have shown that, by the application of LG modes, narrower dips for the probe absorption spectrum can be generated, which can be easily identified and gives better resolution compared with the Gaussian mode. An exact location of dips in the probe absorption spectrum is found, and it is useful in the measurement of MW fields. We have estimated the FWHM of the probe absorption spectrum for Gaussian and LG coupling cases as 3.74×10⁵ H z and 1.07×10⁵ H z, respectively. Based on FWHM, we have found that minimum change in MW electric field in the order of 3.32µV c m ^-1 will be detectable in the case of the LG mode as a coupling beam.

Sensitivity enhancement of far-detuned RF field sensing based on Rydberg atoms dressed by a near-resonant RF field

Rydberg-atom electrometers promise traceable standards for RF electrometry by enabling stable and uniform measurement. In this Letter, we propose an approach to increase the sensitivity of the Rydberg-atom electrometer for far-detuned RF field sensing. The key physical mechanism is the addition of a new ingredient-a local RF field near-resonant with a Rydberg transition-so that the far-detuned field can be detected by the shift of an Autler-Townes (AT) splitting peak, which can be dozens of times larger than the AC Stark shift of the electromagnetic induced transparency (EIT) signal without the near-resonant field. The method enables us to measure far-detuned fields with higher sensitivities, including sub-GHz RF fields (even DC electric fields) which are rarely involved in the existing sensitivity enhancement methods.

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.

Microwave-field sensing via electromagnetically induced absorption of Rb irradiated by three-color infrared lasers

A microwave electric field sensing has been set up based on a three-color electromagnetically induced absorption in rubidium vapor cell via cascading transitions. All transitions are irradiated by infrared lasers: a 780 nm laser servers as probe to monitor the optical transmittancy via transition 5S_1/2→P_3/2;, a 776 nm laser and a 1260 nm laser are used to couple the states 5P_3/2 and 5D_5/2 and states 5D_5/2 and 44F_7/2, respectively. We find that a frequency detuning ∼2π × ( - 40) MHz of the 776 nm dressing beam prefers to a better signal-to-noise ratio for the probe beam. The off-resonance greatly depresses the double resonance pumping effect. A demonstration measurement for the electric field of microwave 1.18988 GHz, corresponding to the coupling resonance between two adjacent Rydberg states 44F_7/2 and 44F_9/2, gives a sensitivity of 55.79(23)nVcm^-1/Hz and a smallest discernible electric field of 78.9(33) nVcm^-1 in time scale of 500 ms.

Rydberg atom-based AM receiver with a weak continuous frequency carrier

We demonstrate an atom-based amplitude-modulation (AM) receiver for digital communication with a weak continuous frequency carrier using a Rydberg AC Stark effect in a vapor cell and achieve the operating carrier frequency continuously from 0.1 GHz to 5 GHz at a single Rydberg state. A strong local oscillator (LO) field E_LO acts as a gain to shift the Rydberg level to a high sensitivity region, and a weak carrier field E_Carr keeps the same frequency with the LO field. The digital baseband signals are encoded onto the E_Carr using the amplitude modulation technique with the different modulation frequency. The response of Rydberg atom to the baseband signal is probed via a Rydberg electromagnetically induced transparency (EIT). The measured instantaneous bandwidth of the system is about 230 kHz. To demonstrate the performance of our system for an actual communication, we consider a color image as an example, the received image displays that the bit error rate (BER) is less than 5% when the maximum data transfer rate is about 238 kbps. Meanwhile, our system shows the weak carrier field of E_Carr ≥ 13.52 μV/cm can be used for the practical communication with BER less than 5%. Our works break the limitation that EIT-AT based atomic receivers only operate at the near resonant frequencies of the Rydberg transitions, making this emerging of quantum technology close to the practical application with high sensitivity and broad bandwidth.

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.

Pole analysis of EIT-AT spectrum with Rydberg atoms

We investigate the electromagnetically induced transparency (EIT) and Autler Townes (AT) splitting spectrum with a four-level Rydberg atom by pole analysis of the probe coherence. A pair of poles corresponding to the two peaks of the spectral splitting is observed. The spectral split or the pole positions are affected by the microwave intensity (MW) and the detuning between the probe and the coupling laser. In the absence of any detuning, the two poles coincide and separate again on the imaginary axis of the complex detuning plane at weak MW field. The two poles do not coincide when the probe (coupling) laser is detuned for scanning the coupling (probe) laser frequency. However, under finite detuning, the two poles approach the nearest distance in the absence of any splitting and are separated again in the direction parallel to the imaginary axis. The spectral analysis of the poles provides an alternate way to establish the relationship between the splitting and the intensity of MW, which may play a role in the application of atomic-based MW measurements.

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.

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.

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.

Robust Coherent Transport of Light in Multilevel Hot Atomic Vapors

Using a model system, we demonstrate both experimentally and theoretically that coherent scattering of light can be robust in hot atomic vapors despite a significant Doppler effect. By operating in a linear regime of far-detuned light scattering, we also unveil the emergence of interference triggered by inelastic Stokes and anti-Stokes transitions involving the atomic hyperfine structure.

Interplay between optical pumping and Rydberg EIT in magnetic fields

We perform Zeeman spectroscopy on a Rydberg electromagnetically induced transparency (EIT) system in a room-temperature Cs vapor cell, in magnetic fields up to 50 Gauss. The magnetic interactions of the |6S1/2 Fg = 4> ground, |6P3/2 Fe = 5> intermediate, and |33S1/2> Rydberg states that form the ladder-type EIT system are in the linear Zeeman, quadratic Zeeman, and the Paschen-Back regimes, respectively. We explain the dependence of Rydberg EIT spectra on the magnetic field and polarization. The asymmetry of the EIT spectra, which is caused by the quadratic Zeeman effect of the intermediate state, becomes paramount in magnetic fields ≥40 Gauss. We investigate the interplay between Rydberg EIT, which reduces photon scattering, and optical pumping, which relies on photon scattering. We employ a quantum Monte Carlo wave-function approach to quantitatively model the spectra and their asymmetry behavior. Simulated spectra are in good agreement with the experimental data.

A Quantum-Based Microwave Magnetic Field Sensor

In this paper, a quantum-based method for measuring the microwave magnetic field in free space is presented by exploring atomic Rabi resonance in the clock transition of ¹³³Cs. A compact cesium glass cell serving as the microwave magnetic field sensing head was used to measure the spatial distribution of microwave radiation from an open-ended waveguide antenna. The measured microwave magnetic field was not restricted by other microwave devices. The longitudinal distribution of the magnetic field was measured. The experimental results measured by the sensor were in agreement with the simulation. In addition, a slightly electromagnetic perturbation caused by the glass cell was investigated through simulation calculations.

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.

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.

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.

Microwave-assisted Rydberg electromagnetically induced transparency

We demonstrate electromagnetically induced transparency (EIT) in a four-level cascade-like system, where the two upper levels are Rydberg states coupled by a microwave field. A two-photon transition consisting of an off-resonant microwave field and an off-resonant optical field forms an effective coupling field to induce transparency of the probe light. We characterize the Rabi frequency of the effective coupling field, as well as the EIT microwave spectra. The results show that microwave-assisted EIT allows us to efficiently access Rydberg states with relatively high orbital angular momentum ℓ=3, which is promising for the study of exotic Rydberg molecular states.

Single-photon cesium Rydberg excitation spectroscopy using 318.6-nm UV laser and room-temperature vapor cell

We demonstrate a single-photon Rydberg excitation spectroscopy of cesium (Cs) atoms in a room-temperature vapor cell. Cs atoms are excited directly from 6S_1/2 ground state to nP_3/2 (n = 70 - 100) Rydberg states with a 318.6 nm ultraviolet (UV) laser, and Rydberg excitation spectra are obtained by transmission enhancement of a probe beam resonant to Cs 6S_1/2, F = 4 - 6P_3/2, F' = 5 transition as partial population on F = 4 ground state are transferred to Rydberg state. Analysis reveals that the observed spectra are velocity-selective spectroscopy of Rydberg state, from which the amplitude and linewidth influenced by lasers' Rabi frequency have been investigated. Fitting to energies of Cs nP_3/2 (n = 70 -100) states, the determined quantum defect is 3.56671(42). The demodulated spectra can also be employed as frequency references to stabilize the UV laser frequency to specific Cs Rydberg transition.

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.

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

We utilize a homodyne detection technique to achieve a new sensitivity limit for atom-based, absolute radio-frequency electric field sensing of 5 μV cm⁻¹ Hz^−1/2. A Mach-Zehnder interferometer is used for the homodyne detection. With the increased sensitivity, we investigate the dominant dephasing mechanisms that affect the performance of the sensor. In particular, we present data on power broadening, collisional broadening and transit time broadening. Our results are compared to density matrix calculations. We show that photon shot noise in the signal readout is currently a limiting factor. We suggest that new approaches with superior readout with respect to photon shot noise are needed to increase the sensitivity further.

High-resolution vector microwave magnetometry based on solid-state spins in diamond

The measurement of the microwave field is crucial for many developments in microwave technology and related applications. However, measuring microwave fields with high sensitivity and spatial resolution under ambient conditions remains elusive. In this work, we propose and experimentally demonstrate a scheme to measure both the strength and orientation of the microwave magnetic field by utilizing the quantum coherent dynamics of nitrogen vacancy centres in diamond. An angular resolution of 5.7 mrad and a sensitivity of 1.0 μT Hz^−1/2 are achieved at a microwave frequency of 2.6000 GHz, and the microwave magnetic field vectors generated by a copper wire are precisely reconstructed. The solid-state microwave magnetometry with high resolution and wide frequency range that can work under ambient conditions proposed here enables unique potential applications over other state-of-art microwave magnetometry.

Microwave technology is crucial for communications and high-speed electronics. Wang et al. now use nitrogen-vacancy defects in diamond to measure the strength and orientation of the magnetic component of a microwave electromagnetic field on the nanoscale.

Proposal for an optomechanical microwave sensor at the subphoton level

Because of their low energy content, microwave signals at the single-photon level are extremely challenging to measure. Guided by recent progress in single-photon optomechanics and hybrid optomechanical systems, we propose a multimode optomechanical transducer that can detect intensities significantly below the single-photon level via adiabatic transfer of the microwave signal to the optical frequency domain where the measurement is then performed. The influence of intrinsic quantum and thermal fluctuations is also discussed.

Subwavelength microwave electric-field imaging using Rydberg atoms inside atomic vapor cells

We have recently shown [Nat. Phys.8, 819 (2012)] that Alkali atoms contained in a vapor cell can serve as a highly accurate standard for microwave (MW) electric field strength as well as polarization. Here we show for the first time that Rydberg atom electromagnetically induced transparency can be used to image MW electric fields with unprecedented precision. The spatial resolution of the method is far into the subwavelength regime ∼λ/650 or 66 μm at 6.9 GHz. The electric field resolutions are similar to those we have already demonstrated ∼50  μV cm(-1). Our experimental results agree with finite element calculations of test electric-field patterns.