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Physical systems that display competitive non-linear dynamics have played a key role in the development of mathematical models of Nature. Important examples include predator-prey models in ecology, biology, consumer-resource models in economics, and reaction-diffusion equations in chemical reactions. However, as real world systems are embedded in complex environments, where it is difficult or even impossible to control external parameters, quantitative comparison between measurements and simple models remains challenging. This motivates the search for competitive dynamics in isolated physical systems, with precise control. An ideal candidate is laser excitation in dilute atomic ensembles. For example, atoms in highly-excited Rydberg states display rich many-body dynamics including ergodicity breaking, synchronisation and time crystals. Here, we demonstrate predator-prey dynamics by laser excitation and ionisation of Rydberg atoms in a room temperature vapour cell. Ionisation of excited atoms produce electric fields that suppress further excitation. This starves the ionisation process of resource, giving rise to predator-prey dynamics. By comparing our results to the Lotka-Volterra model, we demonstrate that as well applications in non-linear dynamics, our experiment has applications in metrology, and remote sensing of localised plasmas., Comment: 16 pages, 7 figures

Recent years have witnessed the use of pervasive wireless signals (e.g., Wi-Fi, RFID, and mmWave) for sensing purposes. Due to its non-intrusive characteristic, wireless sensing plays an important role in various intelligent sensing applications. However, limited by the inherent thermal noise of RF transceivers, the sensing granularity of existing wireless sensing systems are still coarse, limiting their adoption for fine-grained sensing applications. In this paper, we introduce the quantum receiver, which does not contain traditional electronic components such as mixers, amplifiers, and analog-to-digital converters (ADCs) to wireless sensing systems, significantly reducing the source of thermal noise. By taking non-intrusive liquid recognition as an application example, we show the superior performance of quantum wireless sensing. By leveraging the unique property of quantum receiver, we propose a novel double-ratio method to address several well-known challenges in liquid recognition, eliminating the effect of liquid volume, device-target distance and container. We implement the quantum sensing prototype and evaluate the liquid recognition performance comprehensively. The results show that our system is able to recognize 17 commonly seen liquids, including very similar ones~(e.g., Pepsi and Coke) at an accuracy higher than 99.9\%. For milk expiration monitoring, our system is able to achieve an accuracy of 99.0\% for pH value measurements at a granularity of 0.1, which is much finer than that required for expiration monitoring., Comment: 7 pages, 6 figures

We demonstrate the continuous broadband microwave receivers based on AC Stark shifts and Floquet States of Rydberg levels in a cesium atomic vapor cell. The resonant transition frequency of two adjacent Rydberg states 78$S_{1/2}$ and 78$P_{1/2}$ is tuned based on AC Stark effect of 70~MHz Radio frequency (RF) field that is applied outside the vapor cell. Meanwhile, the Rydberg states also exhibit Floquet even-order sidebands that are used to extend the bandwidths further. We achieve microwave electric field measurements over 1.172~GHz of continuous frequency range. The sensitivity of the Rydberg receiver with heterodyne technique in the absence of RF field is 280.2~nVcm$^{-1}$Hz$^{-1/2}$, while it is dramatically decreased with tuning the resonant transition frequency in the presence of RF field. Surprisingly, the sensitivity can be greatly improved if the microwave field couples the Floquet sideband transition. The achieving of continuous frequency and high sensitivity microwave detection will promote the application of Rydberg receiver in the radar technique and wireless communication., Comment: 5 pages, 4 figures

Time crystals, as temporal analogs of space crystals, manifest as stable and periodic behavior that breaks time translation symmetry. In an open quantum system, many-body interaction subjected to dissipation allows one to develop the time crystalline order in an unprecedented way, as refer to dissipative time crystal. Here we report the observation of a time crystal comb in the continuously driven-dissipative and strongly interacting Rydberg thermal gas, in which continuous time crystal and sub-harmonics of limit cycles as well as the high-order harmonic oscillation phases are observed in the same system by manipulating the Rydberg excitation. Our work provides new ways to explore the nonequilibrium phases of matter in open systems. Such time crystals with persistent oscillation rooted in emergent quantum correlations, may emerge as a ubiquitous tool in quantum metrology, for instance, continuous sensing and parameter estimation surpassing the standard quantum limit., Comment: 17 pages, 5 figures

Long-range $(n+2)D_{5/2} \, nF_J$ Rydberg macro-dimers are observed in an ultracold cesium Rydberg gas for $39\leq n\leq48$. Strong dipolar "flip" ($\langle D_{5/2} F_{5/2} \vert \hat{V}_{dd} \vert F_{5/2} D_{5/2} \rangle$, $\langle D_{5/2} F_{7/2} \vert \hat{V}_{dd} \vert F_{7/2} D_{5/2} \rangle$) and "cross" ($\langle D_{5/2} F_{7/2} \vert \hat{V}_{dd} \vert F_{5/2} D_{5/2} \rangle$) couplings lead to bound, fine-structure-mixed $(n+2)D_{5/2}nF_J$ macro-dimers at energies between the $F_J$ fine-structure levels. The $DF$ macro-dimers are measured by microwave photo-association from optically prepared $[(n+2)D_{5/2}]_2$ Rydberg pair states. Calculated adiabatic potential curves are used to elucidate the underlying physics and to model the $DF$ macro-dimer spectra, with good overall agreement. Microwave photo-association allows Franck-Condon tuning, which we have studied by varying the detuning of a Rydberg-atom excitation laser. Further, in Stark spectroscopy we have measured molecular DC electric polarizabilities that are considerably larger than those of the atomic states. The large molecular polarizabilities may be caused by high-$\ell$ mixing. The observed linewidths of the Stark-shifted molecular lines provide initial evidence for intra-molecular induced-dipole-dipole interaction.

We report on high-resolution microwave spectroscopy of cesium Rydberg $(n+2)D_{5/2}\rightarrow nF_{J}$ transitions in a cold atomic gas. Atoms laser-cooled and trapped in a magnetic-optical trap are prepared in the $D$ Rydberg state using a two-photon laser excitation scheme. A microwave field transmitted into the chamber with a microwave horn drives the Rydberg transitions, which are probed via state selective field ionization. Varying duration and power of the microwave pulse, we observe Fourier side-band spectra as well as damped, on-resonant Rabi oscillations with pulse areas up to $\gtrsim 3 \pi$. Furthermore, we investigate the Zeeman effect of the clearly resolved $nF_J$ fine-structure levels in fields up to 120~mG, where the transition into $nF_{7/2}$ displays a thee-peak Zeeman pattern, while $nF_{5/2}$ shows a two-peak pattern. Our theoretical models explain all observed spectral characteristics, showing good agreement with the experiment. Our measurements provide a pathway for the study of high-angular-momentum Rydberg states, initialization and coherent manipulation of such states, Rydberg-atom macrodimers, and other Rydberg-atom interactions. Furthermore, the presented methods are suitable for calibration of microwave radiation as well as for nulling and calibration of DC magnetic fields in experimental chambers for cold atoms.

We present precise measurements of the quantum defects of cesium $n$F$_J$ Rydberg levels. We employ high-precision microwave spectroscopy of $(n+2)\mathrm{D}_{5/2}\rightarrow n\mathrm{F}_{5/2,7/2}$ transitions for $n=45$ to 50 in a cold-atom setup. Cold cesium $(n+2)$D$_{5/2}$ atoms, prepared via two-photon laser excitation, are probed by scanning weak microwave fields interacting with the atoms across the $n\mathrm{F}_{5/2,7/2}$ resonances. Transition spectra are acquired using state-selective electric-field ionization and time-gated ion detection. Transition-frequency intervals are obtained by Lorentzian fits to the measured spectral lines, which have linewidths ranging between 70~kHz and 190~kHz, corresponding to about one to three times the Fourier limit. A comprehensive analysis of relevant line-shift uncertainties and line-broadening effects is conducted. We find quantum defect parameters $\delta_{0}(\mathrm{F}_{5/2})=0.03341537(70)$ and $\delta_{2}(\mathrm{F}_{5/2})=-0.2014(16)$, as well as $\delta_{0}(\mathrm{F}_{7/2})=0.0335646(13)$ and $\delta_{2}(\mathrm{F}_{7/2})=-0.2052(29)$, for $J=5/2$ and $J=7/2$, respectively. Fine structure parameters $A_{FS}$ and $B_{FS}$ for Cs $n{\rm{F}}_J$ are also obtained. Results are discussed in context with previous works, and the significance of the results is discussed.

We study Rydberg electromagnetically induced transparency (EIT) of a cascade three-level atom involving 80$D_{5/2}$ state in a strong interaction regime employing a cesium ultracold cloud. In our experiment, a strong coupling laser couples 6$P_{3/2}$ to 80$D_{5/2}$ transition, while a weak probe, driving 6$S_{1/2}$ to 6$P_{3/2}$ transition, probes the coupling induced EIT signal. At the two-photon resonance, we observe that the EIT transmission decreases slowly with time, which is a signature of interaction induced metastability. The dephasing rate $\gamma_{\rm OD}$ is extracted with optical depth OD = $\gamma_{\rm OD}t$. We find that the optical depth linearly increases with time at onset for a fixed probe incident photon number $R_{\rm in}$ before saturation. The dephasing rate shows a nonlinear dependence on $R_{\rm in}$. The dephasing mechanism is mainly attributed to the strong dipole-dipole interactions, which leads to state transfer from $nD_{5/2}$ to other Rydberg states. We demonstrate that the typical transfer time $\tau_{0(80D)}$ obtained by the state selective field ionization technique is comparable with the decay time of EIT transmission $\tau_{0({\rm EIT})}$. The presented experiment provides a useful tool for investigating the strong nonlinear optical effects and metastable state in Rydberg many-body systems., Comment: 7 pages, 5 figures

We demonstrate a continuous frequency electric field measurement based on the far off-resonant AC stark effect in a Rydberg atomic vapor cell. In this configuration, a strong far off-resonant field, denoted as a local oscillator (LO) field, acts as a gain shifting the Rydberg level to a high sensitivity region. An incident weak signal field with a few hundreds of kHz difference from the LO field is mixed with the LO field in Rydberg system to generate an intermediate frequency (IF) signal, which is read out by the Rydberg electromagnetically induced transparency (Rydberg-EIT) spectroscopy. Not like resonant EIT-AT spectra, we realize the electric field measurement of the signal frequency from 2 GHz to 5 GHz using a single Rydberg state. A minimum detectable filed strength is down to 2.31~$\mu$V/cm and a linear dynamic range is over 65~dB. The minimum detectable filed is comparable with a resonant microwave-dressed Rydberg heterodyne receiver using the same system, which is 1.45~$\mu$V/cm. We also show the system has an inherent polarization selectivity feature. Our method can provide a high sensitivity of electric field measurement and be extended to arbitrary frequency measurements., Comment: 5 pages, 4 figures

An ensemble of excited atoms can synchronize emission of light collectively in a process known as superradiance when its characteristic size is smaller than the wavelength of emitted photons. The underlying superradiance depends strongly on electromagnetic (photon) fields surrounding the atomic ensemble. High mode densities of microwave photons from $300\,$K blackbody radiation (BBR) significantly enhance decay rates of Rydberg states to neighbouring states, enabling superradiance that is not possible with bare vacuum induced spontaneous decay. Here we report observations of the superradiance of ultracold Rydberg atoms embedded in a bath of room-temperature photons. The temporal evolution of the Rydberg $|nD\rangle$ to $|(n+1)P\rangle$ superradiant decay of Cs atoms ($n$ the principal quantum number) is measured directly in free space. Theoretical simulations confirm the BBR enhanced superradiance in large Rydberg ensembles. We demonstrate that the van der Waals interactions between Rydberg atoms change the superradiant dynamics and modify the scaling of the superradiance. In the presence of static electric fields, we find that the superradiance becomes slow, potentially due to many-body interaction induced dephasing. Our study provides insights into many-body dynamics of interacting atoms coupled to thermal BBR, and might open a route to the design of blackbody thermometry at microwave frequencies via collective, dissipative photon-atom interactions.

Cs$_2$ Rydberg-ground molecules consisting of a Rydberg, $nD_{J}$ (33 $\leq$ $n$ $\leq$ 39), and a ground state atom, 6$S_{1/2} (F=$3 or 4$)$, are investigated by photo-association spectroscopy in a cold atomic gas. We observe vibrational spectra that correspond to triplet $^T\Sigma$ and mixed $^{S,T}\Sigma$ molecular states. We establish scaling laws for the energies of the lowest vibrational states vs principal quantum number and obtain zero-energy singlet and triplet $s$-wave scattering lengths from experimental data and a Fermi model. Line broadening in electric fields reveals the permanent molecular electric-dipole moments; measured values agree well with calculations. We discuss the negative polarity of the dipole moments, which differs from previously reported cases., Comment: 5 pages, 4 figures