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Rydberg states of alkali atoms are highly sensitive to electromagnetic radiation in the GHz-to-THz regime because their transitions have large electric dipole moments. Consequently, environmental blackbody radiation (BBR) can couple Rydberg states together at $\mu$s timescales. Here, we track the BBR-induced transfer of a prepared Rydberg state to its neighbors and use the evolution of these state populations to characterize the BBR field at the relevant wavelengths, primarily at 130 GHz. We use selective field ionization readout of Rydberg states with principal quantum number $n\sim30$ in $^{85}$Rb and substantiate our ionization signal with a theoretical model. With this detection method, we measure the associated blackbody-radiation-induced time dynamics of these states, reproduce the results with a simple semi-classical population transfer model, and demonstrate that this measurement is temperature sensitive with a statistical sensitivity to the fractional temperature uncertainty of 0.09 Hz$^{-1/2}$, corresponding to 26 K$\cdot$Hz$^{-1/2}$ at room temperature. This represents a calibration-free SI-traceable temperature measurement, for which we calculate a systematic fractional temperature uncertainty of 0.006, corresponding to 2 K at room temperature when used as a primary temperature standard.

Electrometry based on electromagnetically induced transparency (EIT) in alkali Rydberg vapor cells may suffer reduced sensitivity due to spurious line broadening effects, caused by surface charges, contaminant gases, or other manufacturing defects. In order to draw conclusions about the deleterious effects of potential contaminant gases inside Rydberg electrometry vapor cells, we revisit collisional broadening and shifts of both the D$_2$ line and Rydberg levels of rubidium. Specifically, we measure the broadening and shifts of the $5{\rm S}_{1/2}\rightarrow 5{\rm P}_{3/2}$ (i.e., the D$_2$ line) and $5{\rm S}_{1/2}\rightarrow 5{\rm P}_{3/2}\rightarrow (25{\rm D},27{\rm S},30{\rm D},32{\rm S},35{\rm D},37{\rm S})$ transitions of $^{85}$Rb due to He, Ne, N$_2$ and Ar. By combining these measurements with observations of velocity changing collisions in the sub-Doppler spectrum of the D$_2$ line, we conclude the following: (1) that contaminant gases are most likely not the cause of irregular line shapes or shifts of Rydberg transitions due to the high pressures required, and (2) the sub-Doppler spectrum of the D$_2$ line, through its accompanying loss of contrast at high pressures, can validate that a vapor cell is sufficiently free of contaminant gas for EIT electrometry. We use the theory of Omont, J. Phys. France 38, 1343 (1977), to extend our results to a wide variety of possible contaminant gases and further derive scaling laws applicable to all gases., Comment: 10 pages, 6 figures, 3 tables

Improving the bandwidth of Rydberg atom-based receivers is an ongoing challenge owing to the long-lived Rydberg state lifetimes that limit the refresh rate of ground state atoms. In particular, the LO-based Rydberg mixer approach allows for bandwidths into the few-MHz range. Here, we use heterodyne detection of the Rydberg atom receiver probe laser to separate the negative and positive sidebands that originate from distinct six wave mixing processes, in order to investigate their individual bandwidths. We experimentally confirm the prediction that the negative sideband exhibits a higher bandwidth than the positive sideband. We further explore the effect of coupling and probe laser Rabi frequency on the bandwidth, which we find to be in good agreement with our model. We achieved a maximum experimental (and theoretical) bandwidth of about 11 (11) MHz and 3.5 (5) MHz for the negative and positive sidebands, respectively, from the -3dB roll-off point for optimized field parameters. This work provides insight into the bandwidth-limiting features of Rydberg atom receivers and points the way towards further optimization of their response.

We show that the use of an optical frequency comb probe leads to dramatically improved bandwidth (as high as 12+/-1 MHz) for the detection of modulated radio frequencies in Rydberg atom-based electrometry.

Rydberg atom-based electric field sensing can provide all-optical readout of radio frequency fields in a dielectric environment. However, because a single set of optical fields is typically used to prepare the Rydberg state and read out its response to RF fields, it is challenging to perform simultaneous and independent measurements of the RF field(s). Here we show that using two independent schemes to prepare and read out the same Rydberg state can be used to perform independent measurements in general, which we demonstrate specifically by resolving the the RF polarization. We expect this work will be useful for fiber-coupled sensor heads where spatial multiplexing is challenging, as well as for complex multi-level sensing schemes.

We present a three-photon based fluorescence readout method where the strength of the fluorescence scales with the strength of the radio-frequency (RF) field being applied. We compare this method to conventional three-photon electromagnetically-induced transparency (EIT) and electromagnetically-induced absorption (EIA). Our demonstrated EIA/EIT sensitivity in the collinear three-photon Cesium system is the best reported to date at roughly 30 uVm^{-1}Hz^{-1/2}. The fluorescence is nearly 4 fold better in sensitivity compared to EIA/EIT readout., Comment: 9 figure, quantum optics, rydberg electrometry

Applying a magnetic field as a method for tuning the frequency of Autler-Townes splitting for Rydberg electrometry has recently been demonstrated. In this paper we provide a theoretical understanding of EIT signals in the presence of a large magnetic field, as well as demonstrate some advantages of this technique over traditional Autler-Townes based electrometry. We show that a strong magnetic field provides a well-defined quantization axis regardless of the optical field polarizations, we demonstrate that by separating the $m_J$ levels of the Rydberg state we can perform an Autler-Townes splitting with a single participating dipole moment, and we demonstrate recovery of signal strength by populating a single $m_J$ level using circularly polarized light.

Recent advances in Rydberg atom electrometry detail promising applications in radio frequency (RF) communications. Presently, most applications use carrier frequencies greater than 1~GHz where resonant Autler-Townes splitting provides the highest sensitivity. This letter documents a series of experiments with Rydberg atomic sensors to collect and process waveforms from the automated identification system (AIS) used in maritime navigation in the Very High Frequency (VHF) band. Detection in this band is difficult with conventional resonant Autler-Townes based Rydberg sensing and requires a new approach. We show the results from a new method called High Angular Momentum Matching Excited Raman (HAMMER), which enhances low frequency detection and exhibits superior sensitivity compared to the traditional AC Stark effect. From measurements of electromagnetically induced transparency (EIT) in rubidium and cesium vapor cells, we show the relationship between incident electric field strength and observed signal-to-noise ratio and find that the sensitivity of the HAMMER scheme in rubidium achieved an equivalent single VHF tone sensitivity of $\mathrm{100~\mu V/m/\sqrt{Hz}}$. With these results, we estimate the usable range of the atomic vapor cell antenna for AIS waveforms given current technology and detection techniques., Comment: 9 figure, 8 pages

We examine spectral signatures of Rydberg atoms driven with near-resonant dual-tone radio-frequency (RF) fields in the regime of strong driving. We experimentally demonstrate and theoretically model a variety of nonlinear and multiphoton phenomena in the atomic Rydberg response that manifest in the EIT spectra. Our results echo previous studies of two-level atoms driven with bichromatic optical fields. In comparison to the optical studies, the RF-driven Rydberg system utilizes a more complex excitation pathway, and electromagnetic fields from two different spectral regimes: a two-photon optical excitation continuously creates highly excited Rydberg atoms, while RF fields drive resonant coupling between the Rydberg levels and generate strong mixing. Yet, our spectra reflect nearly identical effects of the dual-tone RF fields on the atomic Rydberg observables, showing detuning-dependent splittings and Rabi frequency dependent peak numbers and relative strengths, and avoided crossings at subharmonic resonances. We thus validate previous two-state models in this more complex physical system. In the context of Rydberg electrometry, we use these investigations to explore a technique where we tune a known RF field to observe spectra which give frequency and power of an unknown RF field using the complex dual-tone spectra.

We present a thermal velocity sampling method for calculating Doppler-broadened atomic spectra, which more efficiently reaches a smooth limit than regular velocity weighted sampling. The method uses equal-population sampling of the 1-D thermal distribution, sampling the 'inverse transform' of the cumulative distribution function, and is broadly applicable to normal distributions. We also discuss efficiencies from eliminating velocity classes which don't significantly contribute to observed atomic lines, and comment on the application of this method in 2- and 3-dimensions., Comment: 8 pages, 7 figures. Code and data will be available with final publication

Radio frequencies in the HF and VHF (3 MHz to 300 MHz) bands are challenging for Rydberg atom-based detection schemes, as resonant detection requires exciting the atoms to extremely high energy states. We demonstrate a method for detecting and measuring radio frequency (RF) carriers in the HF and VHF bands via a controlled Autler-Townes line splitting. Using a resonant, high-frequency (GHz) RF field, the absorption signal from Townes-Merrit sidebands created by a low frequency, non-resonant RF field can be enhanced. Notably, this technique uses a measurement of the optical frequency separation of an avoided crossing to determine the amplitude of a non-resonant, low frequency RF field. This technique also provides frequency-selective measurements of low frequency RF electric fields. To show this, we demonstrate amplitude modulated signal transduction on a low frequency VHF carrier. We further demonstrate reception of multiple tones simultaneously, creating a Rydberg `spectrum analyzer' over the VHF range., Comment: Data for figures can be found at: https://datapub.nist.gov/od/id/mds2-2852

Although Rydberg atom-based electric field sensing provides key advantages over traditional antenna-based detection, it remains limited by the need for a local oscillator (LO) for low-field and phase resolved detection. In this work, we demonstrate that closed-loop quantum interferometric schemes can be used to generate a system-internal reference that can directly replace an external LO for Rydberg field sensing. We reveal that this quantum-interferometrically defined internal reference phase and frequency can be used analogously to a traditional LO for atom-based down-mixing to an intermediate frequency for lock-in phase detection. We demonstrate that this LO-equivalent functionality provides analogous benefits to an LO, including full 360$^\circ$ phase resolution as well as improved sensitivity. The general applicability of this approach is confirmed by demodulating a four phase-state signal broadcast on the atoms. Our approach opens up new sensing schemes and provides a clear path towards all-optical Rydberg atom sensing implementations.

We investigate the sensitivity of three-photon EIT in Rydberg atoms to radio frequency detection and compare it against conventional two-photon systems. Specifically, we model the 4-level and 5-level atomic system and compare how the transmission of the probe changes with different powers of the lasers used and strengths of the RF field. In this model, we also define a sensitivity metric to best relate to the operation of the current best experimental implementation based on shot noise limited detection. We find that the three-photon system boasts much narrower line widths compared to the conventional two-photon EIT. However, these narrow line features do not align with the regions of the best sensitivity. In addition to this, we calculate the expected sensitivity for the two-photon Rydberg sensor and find that the best achievable sensitivity is over an order of magnitude better than the current measured values of 5 uV/m/Hz. However, by accounting for the additional noise sources in the experiment and the quantum efficiency of the photo-detectors, the values are in good agreement., Comment: 9 pages, 6 figures

On-resonance Rydberg atom-based radio-frequency (RF) electric field sensing methods remain limited by the narrow frequency signal detection bands available by resonant transitions. The use of an additional RF tuner field to dress or shift a target Rydberg state can be used to return a detuned signal field to resonance and thus dramatically extend the frequency range available for resonant sensing. Here we investigate three distinct tuning level schemes based on adjacent Rydberg transitions, which are shown to have distinct characteristics and can be controlled with mechanisms based on the tuning field frequency or field strength. We further show that a two-photon Raman feature can be used as an effective tuning mechanism separate from conventional Autler-Townes splitting. We compare our tuning schemes to AC Stark effect-based broadband RF field sensing and show that although the sensitivity is diminished as we tune away from a resonant state, it nevertheless can be used in configurations where there is a low density of Rydberg states, which would result in a weak AC Stark effect.

We investigate the Stark shift in Rydberg rubidium atoms through electromagnetically induced transparency for the measurement of direct current (dc) and 60~Hz alternating current (ac) voltages. This technique has direct applications to atom-based measurements of dc and ac voltage and the calibration of voltage instrumentation. We present experimental results for different atomic states that allow for dc and ac voltage measurements ranging from 0~V to 12~V. A Rydberg atom-based voltage standard could become an alternative calibration method with more favorable size, weight, power consumption, and cost compared to the more precise Josephson voltage standard. In this study, we also demonstrate how the voltage measurements can be utilized to determine the atomic polarizability for the Rydberg states. The Rydberg atom-based voltage measurement technology would become a complimentary method for dissemination of the voltage scale directly to the end user., Comment: 13 pages, 14 figures, 3 tables

We demonstrate improved sensitivity of Rydberg electrometry based on electromagnetically induced transparency (EIT) with a ground state repumping laser. Though there are many factors that limit the sensitivity of radio frequency field measurements, we show that repumping can enhance the interaction strength while avoiding additional Doppler or power broadening. Through this method, we nearly double the EIT amplitude without an increase in the width of the peak. A similar increase in amplitude without the repumping field is not possible through simple optimization.We also establish that one of the key limits to detection is the photon shot noise of the probe laser. We show an improvement on the sensitivity of the device by a factor of nearly 2 in the presence of the repump field., Comment: 5 pages, 6 figures

We demonstrate the use of multiple atomic-level Rydberg-atom schemes for continuous frequency detection of radio frequency (RF) fields. Resonant detection of RF fields by electromagnetically-induced transparency and Autler-Townes (AT) in Rydberg atoms is typically limited to frequencies within the narrow bandwidth of a Rydberg transition. By applying a second field resonant with an adjacent Rydberg transition, far-detuned fields can be detected through a two-photon resonance AT splitting. This two-photon AT splitting method is several orders of magnitude more sensitive than off-resonant detection using the Stark shift. We present the results of various experimental configurations and a theoretical analysis to illustrate the effectiveness of this multiple level scheme. These results show that this approach allows for the detection of frequencies in continuous band between resonances with adjacent Rydberg states.

In this work, we demonstrate the use of a Rydberg atom-based sensor for determining the angle-of-arrival of an incident radio-frequency (RF) wave or signal. The technique uses electromagnetically induced transparency in Rydberg atomic vapor in conjunction with a heterodyne Rydberg atom-based mixer. The Rydberg atom mixer measures the phase of the incident RF wave at two different locations inside an atomic vapor cell. The phase difference at these two locations is related to the direction of arrival of the incident RF wave. To demonstrate this approach, we measure phase differences of an incident 19.18 GHz wave at two locations inside a vapor cell filled with cesium atoms for various incident angles. Comparisons of these measurements to both full-wave simulation and to a plane-wave theoretical model show that these atom-based sub-wavelength phase measurements can be used to determine the angle-of-arrival of an RF field., Comment: 4 pages, 5 figures

We investigate electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in Rydberg rubidium atoms for a six-level excitation scheme. In this six-level system, one radio-frequency field simultaneously couples to two high-laying Rydberg states and results in interesting atomic spectra observed in the EIT lines. We present experimental results for several excitation parameters. We also present two theoretical models for this atomic system, where these two models capture different aspects of the observed spectra. One is a six-level model used to predict dominant spectral features and the other a more complex eight-level model used to predict the full characteristics of this system. Both models shows very good agreement with the experimental data., Comment: 13 pages, 11 figures

We demonstrate how Rydberg atoms and the phenomena of electromagnetically induced transparency can be used to aid in the recording of a musical instrument in real time as it is played. Also, by using two different atomic species (cesium and rubidium) in the same vapor cell, we demonstrate the ability to record two guitars simultaneously, where each atomic species detects and allows for the recording of each guitar separately. The approach shows how audio data (the musical composition) can be detected with a quantum system, illustrating how we can control ensembles of atoms to such an extent that we can use them in this "entertaining" example of recording a musical instrument., Comment: 5 page, 4 figures. arXiv admin note: substantial text overlap with arXiv:1903.00786

Recently, we introduced a Rydberg-atom based mixer capable of detecting and measuring the phase of a radio-frequency field through the electromagnetically induced transparency (EIT) and Autler-Townes (AT) effect. The ability to measure phase with this mixer allows for an atom-based receiver to detect digital modulated communication signals. In this paper, we demonstrate detection and reception of digital modulated signals based on various phase-shift keying approaches. We demonstrate Rydberg atom-based digital reception of binary phase-shift keying (BPSK), quadrature phase-shift keying (QPSK), and quadrature amplitude (QAM) modulated signals over a 19.626~GHz carrier to transmit and receive a bit stream in cesium vapor. We present measured values of Error Vector Magnitude (EVM, a common communication metric used to assess how accurate a symbol or bit stream is received) as a function of symbol rate for BPSK, QPSK, 16QAM, 32QAM, and 64QAM modulation schemes. These results allow us to discuss the bandwidth of a Rydberg-atom based receiver system., Comment: 5 pages, 6 figures

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

With the re-definition of the International System of Units (SI) that occurred in October of 2018, there has recently been a great deal of attention on the development of atom-based sensors for metrology applications. In particular, great progress has been made in using Rydberg-atom based techniques for electric (E) field metrology. These Rydberg-atom based E-field sensors have made it possible to develop atom-based receivers and antennas, which potentially have many benefits over conventional technologies in detecting and receiving modulated signals. In this paper, we demonstrate the ``first'' multi-channel atom-based reception of both amplitude (AM) and frequency (FM) modulation signals. We demonstrate this by using two different atomic species in order to detect and receive AM and FM modulated signals in stereo. Also, in this paper we investigate the effect of Gaussian noise on the ability to receive AM/FM signals. These results illustrate the multi-band (or multi-channel) receiving capability of a atom-based receiver/antenna to produce high fidelity stereo reception from both AM and FM signals. This paper shows an interesting way of applying the relatively newer (and something esoteric) field of quantum-optics and atomic-physics to the century old topic of radio reception., Comment: 10 pages, 9 figures, 1 Table, and 32 references

In this work we demonstrate an approach for the measurement of radio-frequency (RF) power using electromagnetically induced transparency (EIT) in a Rydberg atomic vapor. This is accomplished by placing alkali atomic vapor in a rectangular waveguide and measuring the electric (E) field strength (utilizing EIT and Autler-Townes splitting) for a wave propagating down the waveguide. The RF power carried by the wave is then related to this measured E-field, which leads to a new direct International System of Units (SI) measurement of RF power. To demonstrate this approach, we first measure the field distribution of the fundamental mode in the waveguide and then measure the power carried by the wave at both 19.629 GHz and 26.526 GHz. We obtain good agreement between the power measurements obtained with this new technique and those obtained with a conventional power meter., Comment: 4 page, 7 figures

We investigate the effect of band-limited white Gaussian noise (BLWGN) on electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, when performing atom-based continuous-wave (CW) radio-frequency (RF) electric (E) field strength measurements with Rydberg atoms in an atomic vapor. This EIT/AT-based E-field measurement approach is currently being investigated by several groups around the world as a means to develop a new SI traceable RF E-field measurement technique. For this to be a useful technique, it is important to understand the influence of BLWGN. We perform EIT/AT based E-field experiments with BLWGN centered on the RF transition frequency and for the BLWGN blue-shifted and red-shifted relative to the RF transition frequency. The EIT signal can be severely distorted for certain noise conditions (band-width, center-frequency, and noise power), hence altering the ability to accurately measure a CW RF E-field strength. We present a model to predict the changes in the EIT signal in the presence of noise. This model includes AC Stark shifts and on resonance transitions associated with the noise source. The results of this model are compared to the experimental data and we find very good agreement between the two., Comment: 14 page, 15 figures, 1 table