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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 and sensitivity in the amplitude regime. We describe the approximations that we applied to obtain the analytic expressions 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. Residual Doppler shifts are shown to limit sensitivity. An analytic expression for the amplitude regime of Rydberg atom-based sensing has not, to our knowledge, been obtained previously. The expressions, approximations and descriptions presented in the paper are important for maximizing the sensitivity of Rydberg atom-based sensors and for providing insight into the physics of multi-level interference phenomena.

Rydberg atom-based sensors are a new type of radio frequency sensor that is inherently quantum mechanical. Several configurations of the sensor use a local oscillator to determine the properties of the target radio frequency field. We explain how the physics of Rydberg atom-based sensors in two or more radio frequency fields can be precisely described by a multiply dressed Jaynes-Cummings model. Studying Rydberg atom-based sensors in two or more near resonant radio frequency fields is important for understanding how interfering signals as well as the local oscillator can affect measurements. Studies, so far, focus on a simplified approximation for the local oscillator-target field interaction that uses an analogy to radio frequency heterodyning. The atom acts as a medium for exchanging electromagnetic field excitations of the field modes whose spectrum is a ladder. The Jaynes-Cummings states and their avoided crossings can be used to determine the properties of the radio frequency fields. Radio frequency field sensitivity enhancement for non-resonant radio frequencies is achieved and self-calibrated measurements are recovered under specific conditions described by the theory.

We demonstrate Rydberg atom-based radio frequency sensing with a colinear three-photon scheme in a room temperature cesium vapor cell that minimizes residual Doppler broadening of the probe laser absorption feature. A sub-200 kHz spectral linewidth is observed and extends the self-calibrated Autler-Townes sensing regime to weaker fields by a factor of ~18 compared to the theoretical limit of the most commonly used two-photon scheme. The sensitivity of the method to microsecond pulses is shown to be sufficient to detect radio frequency Rabi frequencies of 2$\pi$ x 0.44 MHz using a 480 kHz bandwidth at 108.9 GHz, demonstrating the ability to sense time-dependent signals suitable for radar and communications.

Atom-based radio frequency electromagnetic field sensing using atomic Rydberg states is a promising technique that has recently attracted significant interest. Its unique advantages, such as extraordinary bandwidth, self-calibration and all-dielectric sensors, are a tangible improvement over antenna-based methods in applications such as test and measurement, and development of broad bandwidth receivers. Here, we demonstrate how an optical frequency comb can be used to acquire data in the Autler-Townes regime of Rydberg atom-based electrometry in a massively parallel fashion, eliminating the need for laser scanning. Two-photon electromagnetically induced transparency read-out and preparation of cesium is used for the demonstration. A flat, quasi-continuous optical comb is generated with the probe laser at 852 nm using an electro-optic modulator and arbitrary waveform generator. A single frequency coupling laser at 509 nm is tuned to the Rydberg launch state. An enhanced transmission signal is obtained using self-heterodyne spectroscopy. The comb signal is beat against a local oscillator derived from the single frequency probe laser on a fast photodiode. The transmission of each probe laser comb tooth is observed. We resolve electromagnetically induced transparency peaks with linewidths below 5 MHz, with and without laser locking. Radio frequency electromagnetic fields as low as 66 $\mu$Vcm$^{-1}$ are detected with sensitivities of 2.3 $\mu$Vcm$^{-1}$Hz$^{-1/2}$. The method offers a significant advantage for reading-out electromagnetically induced transparency and Autler-Townes splitting as neither laser needs to be scanned and slow frequency drifts can be tolerated in some applications. The method enables the detection of the amplitude of a pulsed radio frequency electromagnetic field when the incoming pulse Autler-Townes splits the electromagnetically induced transparency peak., Comment: 18 pages. 5 figures. Submitted to Physical Review Applied

Rydberg atoms have shown significant promise as the basis for highly sensitive detectors of continuous radio-frequency (RF) E-fields. Here, we study their time-dependent response to pulse-modulated RF E-fields at 19.4 GHz using a cesium vapour cell at room temperature. We use density matrix simulations to explain the time scales that shape the transient atomic response under different laser conditions, finding them to be limited by dephasing mechanisms including transit time broadening, Rydberg-Rydberg collisions, and ionization. Using a matched filter, we demonstrate the detection of individual pulses with durations from 10 $\mu$s down to 50 ns and amplitudes from 15000 $\mu$V cm$^{-1}$ down to ~170 $\mu$V cm$^{-1}$, corresponding to a sensitivity of ~240 nV cm$^{-1}$ Hz$^{-1/2}$. Finally, we highlight the potential of a Rydberg vapour cell as a receiver by detecting pulse trains from a rotating emitter on a simulated passing aircraft.

We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective $C_3$ dipole-dipole and $C_6$ van der Waals coefficients. We compare the $C_3$ and $C_6$ with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole-dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in $50S_{1/2}$ states in the blockade regime. For internuclear distances close to the blockade radius, $R_{bl} \approx 4 - 6\,\mu$m, molecular calculations are in much better agreement with experimental results than those based on the properties of single atoms and independent calculations of $C_3$ and $C_6$ which were used to analyze the original experiment. We find that the calculated $C_6$ coefficient is within $8\%$ of the experimental value while the $C_3$ coefficient is within $20\%$ of the experimental value., Comment: 16 pages, 6 figures

We investigate the phenomenon of bistability in a thermal gas of cesium atoms excited to Rydberg states. We present both measurements and a numerical model of the phenomena based on collisions. By directly measuring the plasma frequency, we show that the origin of the bistable behavior lies in the creation of a plasma formed by ionized Rydberg atoms. Recombination of ions and electrons manifests as fluorescence which allows us to characterize the plasma properties and study the transient dynamics of the hysteresis that occurs. We determine scaling parameters for the point of plasma formation, and verify our numerical model by comparing measured and simulated spectra. These measurements yield a detailed microscopic picture of ionization and avalanche processes occurring in thermal Rydberg gases. From this set of measurements, we conclude that plasma formation is a fundamental ingredient in the optical bistability taking place in thermal Rydberg gases and imposes a limit on usable Rydberg densities for many applications., Comment: 13 pages, 10 figures

Ultralong-range Rydberg trimer molecules are spectroscopically observed in an ultracold gas of Cs($nd_{3/2}$) atoms. The atomic Rydberg state anisotropy allows for the formation of angular trimer states, whose energies may not be obtained from integer multiples of dimer energies. These nonadditive trimers are predicted to coexist with Rydberg dimer lines. The existence of such effective three-body interactions is confirmed with observation of asymmetric line profiles and interpreted by a theoretical approach which includes relativistic spin interactions. Simulations of the observed spectra with and without angular trimer lines lends convincing support to the existence of effective three-body interactions., Comment: 10 pages, 7 figures

We present an experimental study of cavity assisted Rydberg atom electromagnetically induced transparency (EIT) using a high-finesse optical cavity ($F \sim 28000$). Rydberg atoms are excited via a two-photon transition in a ladder-type EIT configuration. A three-peak structure of the cavity transmission spectrum is observed when Rydberg EIT is generated inside the cavity. The two symmetrically spaced side peaks are caused by bright-state polaritons, while the central peak corresponds to a dark-state polariton. Anti-crossing phenomenon and the effects of mirror adsorbate electric fields are studied under different experimental conditions. We determine a lower bound on the coherence time for the system of $7.26 \pm 0.06 \,\mu$s, most likely limited by laser dephasing. The cavity-Rydberg EIT system can be useful for single photon generation using the Rydberg blockade effect, studying many-body physics, and generating novel quantum states amongst many other applications., Comment: 8 pages, 7 figures

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, $\sim 3 \mu V cm^{-1}Hz^{-1/2}$ sensitivity is achieved and is found to be photon shot noise limited., Comment: 18 Pages, 6 Figures

We utilize a homodyne detection technique to achieve a new sensitivity limit for atom-based, absolute radio-frequency electric field sensing of $\mathrm{5 \mu V cm^{-1} Hz^{-1/2} }$. 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., Comment: 20 pages, 6 figures

We calculate vibrational spectra of ultralong-range Cs(32p) Rydberg molecules which form in an ultracold gas of Cs atoms. We account for the partial-wave scattering of the Rydberg electrons from the ground Cs perturber atoms by including the full set of spin-resolved ${}^{1,3}S_J$ and ${}^{1,3}P_J$ scattering phase shifts, and allow for the mixing of singlet (S=0) and triplet (S=1) spin states through Rydberg electron spin-orbit and ground electron hyperfine interactions. Excellent agreement with observed data in Sa{\ss}mannshausen et al. [Phys. Rev. Lett. 113, 133201(2015)] in line positions and profiles is obtained. We also determine the spin-dependent permanent electric dipole moments for these molecules. This is the first such calculation of ultralong-range Rydberg molecules in which all of the relativistic contributions are accounted for., Comment: 9 pages, 6 figures

We propose a hybrid quantum system where the strong coupling regime can be achieved between a Rydberg atomic ensemble and propagating surface phonon polaritons on a piezoelectric superlattice. By exploiting the large electric dipole moment and long lifetime of Rydberg atoms as well as tightly confined surface phonon polariton modes, it is possible to achieve a coupling constant far exceeding the relevant decay rates. The frequency of the surface mode can be selected so it is resonant with a Rydberg transition by engineering the piezoelectric superlattice. We describe a way to observe the Rabi splitting associated with the strong coupling regime under realistic experimental conditions. The system can be viewed as a new type of optomechanical system.

We investigate the coherent manipulation of interacting Rydberg atoms placed inside a high-finesse optical cavity for the deterministic preparation of strongly coupled light-matter systems. We consider a four-level diamond scheme with one common Rydberg level for N interacting atoms. One side of the diamond is used to excite the atoms into a collective `superatom' Rydberg state using either {\pi}-pulses or stimulated Raman adiabatic passage (STIRAP) pulses. The upper transition on the other side of the diamond is used to transfer the collective state to one that is coupled to a field mode of an optical cavity. Due to the strong interaction between the atoms in the Rydberg level, the Rydberg blockade mechanism plays a key role in the deterministic quantum state synthesis of the atoms in the cavity. We use numerical simulation to show that non-classical states of light can be generated and that the state that is coupled to the cavity field is a collective one. We also investigate how different decay mechanisms affect this interacting many-body system. We also analyze our system in the case of two Rydberg excitations within the blockade volume. The simulations are carried out with parameters corresponding to realizable high-finesse optical cavities and alkali atoms like rubidium., Comment: 38 pages, 12 figures

We observe that when an ultracold ground state cesium (Cs) atom becomes bound within the electronic cloud of an extended Cs electronic orbit, ultralong-range molecules with giant (kilo-Debye) permanent electric dipole moments form. Large molecular permanent electric dipole moments are challenging to experimentally realize. Meeting this challenge has garnered significant interest because permanent electric dipole moments are important for understanding symmetry breaking in molecular physics, control of chemical reactions and realization of strongly correlated many-body quantum systems. These new hybrid class of `trilobite' molecules are predominated with degenerate Rydberg manifolds, making them difficult to produce with conventional optical association. Their behavior is quantitatively reproduced with detailed coupled-channel calculations., Comment: 18 pages, 3 figures, submitted to Science on 2014-09-03; v2: "One-sentence summary" removed from title

We report the observation of cold Cs Rydberg atom molecules bound at internuclear separations of R~3-9 um. The bound states result from avoided crossings between Rydberg atom pair interaction potentials in an applied electric field. The molecular states can be modified by changing the applied electric field. The molecules are observed by mapping the radial separation of the two Rydberg atoms as a function of time delay between excitation and detection using the Coulomb repulsion of the ions after pulsed field ionization. Measurements were performed for 63D+65D, 64D+66D, 65D+67D, and 66D+68D pairs. The experiment is in good agreement with calculations of the pair interactions for these states., Comment: 6 pages, 5 figures, submitted to Nature Physics