We demonstrate a nonequilibrium phase transition in a dilute thermal atomic gas. The phase transition, between states of low and high Rydberg occupancy, is induced by resonant dipole-dipole interactions between Rydberg atoms. The gas can be considered as dilute as the atoms are separated by distances much greater than the wavelength of the optical transitions used to excite them. In the frequency domain, we observe a mean-field shift of the Rydberg state which results in intrinsic optical bistability above a critical Rydberg number density. In the time domain, we observe critical slowing down where the recovery time to system perturbations diverges with critical exponent α=-0.53±0.10. The atomic emission spectrum of the phase with high Rydberg occupancy provides evidence for a superradiant cascade.

Nonequilibrium Phase Transition in a Dilute Rydberg Ensemble

We study electromagnetically induced transparency (EIT) of a weakly interacting cold Rydberg gas. We show that the onset of interactions is manifest as a depopulation of the Rydberg state and numerically model this effect by adding a density-dependent non-linear term to the optical Bloch equations. In the limit of a weak probe where the depopulation effect is negligible, we observe no evidence of interaction induced decoherence and obtain a narrow Rydberg dark resonance with a linewidth of <600 kHz, limited by the Rabi frequency of the coupling beam

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Electromagnetically induced transparency of an interacting cold Rydberg ensemble

The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)--traceable and self-calibrated method for measuring a microwave-electric-field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between the microwave Rabi frequency and Autler-Townes splitting is more valid and is even more robust against the experimental parameters in the EIA's linear region. Furthermore, a narrower linewidth of cold Rydberg EIA enables us to realize a direct SI-traceable microwave-electric-field measurement as small as $\ensuremath{\sim}100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$.

Microwave electrometry via electromagnetically induced absorption in cold Rydberg atoms

A comprehensive study of three-photon electromagnetically induced transparency (EIT) and absorption (EIA) on the rubidium cascade $5{S}_{1/2}\ensuremath{\rightarrow}5{P}_{3/2}$ (laser wavelength 780 nm), $5{P}_{3/2}\ensuremath{\rightarrow}5{D}_{5/2}$ (776 nm), and $5{D}_{5/2}\ensuremath{\rightarrow}28{F}_{7/2}$ (1260 nm) is performed. The 780-nm probe and 776-nm dressing beams are counteraligned through a Rb room-temperature vapor cell, and the 1260-nm coupler beam is co- or counteraligned with the probe beam. Several cases of EIT and EIA, measured over a range of detunings of the 776-nm beam, are studied. The observed phenomena are modeled by numerically solving the Lindblad equation, and the results are interpreted in terms of the probe-beam absorption behavior of velocity- and detuning-dependent dressed states. Interaction-time effects are discussed. To explore the utility of three-photon Rydberg EIA and EIT for microwave electric-field diagnostics, a sub-THz field generated by a signal source and a frequency quadrupler is applied to the Rb cell. The 100.633-GHz field resonantly drives the $28{F}_{7/2}\ensuremath{\leftrightarrow}29{D}_{5/2}$ transition and causes Autler-Townes splittings in the Rydberg EIA and EIT spectra, which are measured and employed to characterize the performance of the microwave quadrupler.

Electromagnetically induced transparency, absorption, and microwave-field sensing in a Rb vapor cell with a three-color all-infrared laser system

In this paper we demonstrate the detection of millimeter waves via Autler-Townes splitting in 85Rb Rydberg atoms. This method may provide an independent, atom-based, SI-traceable method for measuring mm-wave electric fields, which addresses a gap in current calibration techniques in the mm-wave regime. The electric- field amplitude within a rubidium vapor cell in the WR-10 waveguide band is measured for frequencies of 93 GHz, and 104 GHz. Relevant aspects of Autler-Townes splitting originating from a four-level electromagnetically induced transparency scheme are discussed. We measure the E-field generated by an open-ended waveguide using this technique. Experimental results are compared to a full-wave finite element simulation.

Millimeter Wave Detection via Autler-Townes Splitting in Rubidium Rydberg Atoms

Electromagnetically induced transparency (EIT) and Aulter-Townes splitting (ATS) are two similar yet distinct phenomena that modify the transmission of a weak probe field through an absorption medium in the presence of a coupling field, featured in a variety of three-level atomic systems. In many applications it is important to distinguish EIT from ATS splitting. We present EIT and ATS spectra in a cold-atom three-level cascade system, involving the 35$S_{1/2}$ Rydberg state of cesium. The EIT linewidth, $\gamma_{EIT}$, defined as the full width at half maximum (FWHM), and the ATS splitting, $\gamma_{ATS}$, defined as the peak-to-peak distance between AT peak pairs, are used to delineate the EIT and ATS regimes and to characterize the transition between the regimes. In the cold-atom medium, in the weak-coupler (EIT) regime $\gamma_{EIT}$ $\approx$ A + B($\Omega_{c}^2$ + $\Omega_{p}^2)/\Gamma_{eg}$, where $\Omega_{c}$ and $\Omega_{p}$ are the coupler and probe Rabi frequencies, $\Gamma_{eg}$ is the spontaneous decay rate of the intermediate 6P$_{3/2}$ level, and parameters $A$ and $B$ that depend on the laser linewidth. We explore the transition into the strong-coupler (ATS) regime, which is characterized by the linear relation $\gamma_{ATS}$ $\approx$ $\Omega_{c}$. The experiments are in agreement with numerical solutions of the Master equation.

https://iopscience.iop.org/article/10.1088/1367-2630/aad153/pdf

Transition from electromagnetically induced transparency to Autler–Townes splitting in cold cesium atoms

Long-range macrodimers formed by $D$-state cesium Rydberg atoms are studied in experiments and calculations. Cesium ${[62{D}_{J}]}_{2}$ Rydberg-atom macrodimers, bonded via long-range multipole interaction, are prepared by two-color photoassociation in a cesium atom trap. The first color (pulse A) resonantly excites seed Rydberg atoms, while the second (pulse B, detuned by the molecular binding energy) resonantly excites the Rydberg-atom macrodimers below the ${[62{D}_{J}]}_{2}$ asymptotes. The molecules are measured by extraction of autoionization products and Rydberg-atom electric-field ionization, and ion detection. Molecular spectra are compared with calculations of adiabatic molecular potentials. From the dependence of the molecular signal on the detection delay time, the lifetime of the molecules is estimated to be $3--6\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{s}$.

Cs 62 D J Rydberg-atom macrodimers formed by long-range multipole interaction

Precise measurement of a weak radio frequency electric field using a resonant atomic probe

We study Rydberg electromagnetically induced transparency (EIT) of cesium atoms in a magnetic field. The ladder level scheme consists of ground ($6{S}_{1/2}$), excited ($6{P}_{3/2}$), and Rydberg ($48{D}_{5/2}$) levels. The relevant 96 relevant magnetic sublevels are coupled to each other via coherent coupling and decay. A quantum Monte Carlo wave-function (QMCWF) approach is employed to solve the quantum master equation. The simulated EIT probe-absorption spectra and their magnetic-field dependence are compared with results of a cold-atom experiment, in which we perform an in situ, atom-based measurement of a rapidly decaying eddy-current magnetic field. The EIT spectrum in the magnetic field has two dominant lines with a Zeeman splitting of 5.6 MHz per gauss, which are employed to measure the magnetic field. The QMCWF results show good agreement with the experiment, exhibit additional spectroscopic features, and provide insights into the optical-pumping dynamics, radiation-pressure effects, and the relation of these phenomena with the EIT behavior.

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Rydberg electromagnetically induced transparency in a large Hilbert space

We utilize an electromagnetically induced transparency (EIT) of a three-level cascade system involving Rydberg state in a room-temperature cell, formed with a cesium 6S1/2–6P3/2–66S1/2 scheme, to investigate the Autler–Townes (AT) splitting resulting from a 15.21-GHz radio-frequency (RF) field that couples the Rydberg transition. The radio-frequency electric field induced AT splitting, γ AT, is defined as the peak-to-peak distance of an EIT-AT spectrum. The dependence of AT splitting γ AT on the probe and coupling Rabi frequency, Ωp and Ωc, is investigated. It is found that the EIT-AT splitting strongly depends on the EIT linewidth that is related to the probe and coupling Rabi frequency in a weak RF-field regime. Using a narrow linewidth EIT spectrum would decrease the uncertainty of the RF field measurements. This work provides new experimental evidence for the theoretical framework in [J. Appl. Phys. 121, 233106 (2017)].

Yongmei Xue

Papers

Transition from electromagnetically induced transparency to Autler–Townes splitting in cold cesium atoms

Cs 62 D J Rydberg-atom macrodimers formed by long-range multipole interaction

Precise measurement of a weak radio frequency electric field using a resonant atomic probe

Rydberg electromagnetically induced transparency in a large Hilbert space

Rydberg electromagnetically induced transparency and Autler–Townes splitting in a weak radio-frequency electric field*