We study Rydberg atoms modulated by strong radio-frequency (RF) fields with a frequency of 70 MHz. The Rydberg atoms are prepared in a room temperature cesium cell, and their level structure is probed using electromagnetically induced transparency (EIT). As the RF field increases from the weak-into the strong-field regime, the range of observed RF-induced phenomena progresses from AC level shifts through increasingly pronounced and numerous RF-modulation sidebands to complex state-mixing and level-crossings with high-l hydrogen-like states. Weak anharmonic admixtures in the RF field generate clearly visible modifications in the Rydberg-EIT spectra. A Floquet analysis is employed to model the Rydberg spectra, and good agreement with the experimental observations is found. Our results show that all-optical spectroscopy of Rydberg atoms in vapor cells can serve as an antenna-free, atom-based and calibration-free technique to measure and map RF electric fields and to analyze their higher-harmonic contents.

Electromagnetically induced transparency (EIT) and Autler-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 three-level cascade system, involving cold cesium atoms in the S 35 1 2 Rydberg state. The EIT linewidth, γ EIT , defined as the full width at half maximum of the transparency window, and the ATS splitting, γ ATS , defined as the peak-to-peak distance between AT absorption peaks, are used to delineate the EIT and ATS regimes and to characterize the transition between the regimes. In the coldatom medium, in the weak-coupler (EIT) regime γ EIT ≈A + B( cwhere Ω c and Ω p are the coupler and probe Rabi frequencies, Γ 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 relation γ ATS ≈Ω c . The experiments are in agreement with numerical solutions of the Master equation. Our analysis accounts for non-ideal conditions that exist in typical realizations of Rydberg-EIT, including laser-frequency jitter, Doppler mismatch of the utilized two-color Rydberg EIT system, and strong probe fields. The obtained criteria to distinguish cold-atom EIT from ATS are readily accessible and applicable in practical implementations.

Long-range macrodimers formed by D-state cesium Rydberg atoms are studied in experiments and calculations. Cesium [62DJ ]2 Rydberg-atom macrodimers, bonded via long-range multipole interaction, are prepared by two-color photo-association 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 [62DJ ]2 asymptotes. The molecules are measured by extraction of auto-ionization products and Rydberg-atom electricfield 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 µs.

An optical probe of cesium Rydberg atoms generated in a thermal vapor cell is used to retrieve a baseband signal modulated onto a 16.98-GHz carrier wave in real-time, demonstrating an atombased quantum receiver suitable for microwave communication. The 60S 1/2 Rydberg level of cesium atoms in the cell is tracked via electromagnetically induced transparency (EIT), an established laser-spectroscopic method. The microwave carrier is resonant with the 60S 1/2 → 60P 1/2 Rydberg transition, resulting in an Autler-Townes (AT) splitting of the EIT signal. Amplitude modulation of the carrier wave results in a corresponding modulation in the optically retrieved AT splitting. Frequency modulation causes a change in relative height of the two AT peaks, which can be optically detected and processed to retrieve the modulation signal. The optical retrieval of the baseband signal does not require electronic demodulation. The method is suitable for carrier frequencies within a range from ∼ 1 GHz to hundreds of GHz. The baseband bandwidth, which is ∼ 20 Hz in the present demonstration, can be increased by faster spectroscopic sampling.1 THz [7], including measurements of microwave (MW) fields [8] and their polarizations [9], and millimeter waves [10]. Small Rydberg-atom field sensors that employ µm-length vapor cells and hollow-core fibers [11] offer significant potential for miniaturization. Recently, Rydberg atoms have also been explored as sensitive, high bandwidth, atomic communications receivers for digital communication [12]. Rydberg atoms have many electronic states with a large number of electric-dipole transitions between them [2], leading to a strong electromagnetic response of these atoms at a dense set of frequencies within the MHz-to THz-range. Rydberg-atom-based field detectors can have a higher sensitivity than detectors with traditional dipole antennas [13], making them suitable for long-distance communication with potential for high-speed parallel operation. In addition, Rydberg atomic receivers can be used for subwavelength imaging of microwave electric-field distributions [14,15].

We investigate atom-based electric-field calibration and polarization measurement of a 100-MHz linearly polarized radio-frequency (RF) field using cesium Rydberg-atom electromagnetically induced transparency (EIT) in a room-temperature vapor cell. The calibration method is based on matching experimental data with the results of a theoretical Floquet model. The utilized 60DJ fine structure Floquet levels exhibit J-and mj-dependent AC Stark shifts and splittings, and develop even-order RF-modulation sidebands. The Floquet map of cesium 60DJ fine structure states exhibits a series of exact crossings between states of different mj, which are not RF-coupled. These exact level crossings are employed to perform a rapid and precise (±0.5%) calibration of the RF electric field. We also map out three series of narrow avoided crossings between fine structure Floquet levels of equal mj and different J, which are weakly coupled by the RF field via a Raman process. The coupling leads to narrow avoided crossings that can also be applied as spectroscopic markers for RF field calibration. We further find that the line-strength ratio of intersecting Floquet levels with different mj provides a fast and robust measurement of the RF field's polarization.