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Rydberg atoms are used in a wide range of applications due to their peculiar properties like strong dipolar and van der Waals interactions. The choice of Rydberg state has a huge impact on the strength and angular dependence of the interactions, and so a detailed understanding of the underlying processes and resulting properties of the interactions is therefore key to select the most suitable states for experiments. We study the van der Waals interactions in alkali atoms in detail and highlight the structures which allow an understanding and exploitation of the various interaction properties. A particular theme is the identification of F\"orster resonances with $n_1 \neq n_2$, which offer interaction potentials with a wide range of properties that make them particularly interesting for experimental applications. A second theme is a focus on the underlying structures that shape the angular dependency and sign of the interactions. This understanding -- instead of brute-force calculations -- allows for a much simpler and more systematic search for suitable pair states. These insights can be used for the selection of tailored interaction potentials subject to experimental constraints and requirements. We use rubidium as an example species in this work and also provide data for cesium and pair states that are coupled via two- or three-photon transitions, i.e. up to F states, in the appendix., Comment: 6 pages (5 figures) plus appendix (16 pages, 33 figures)

We report on the coherent creation, control and read-out of a single photonic qutrit in a Rydberg ensemble. In each measurement, an optical photon is stored as a Rydberg polariton through electromagnetically induced transparency. Employing two microwave fields, the polariton is driven into an arbitrary superposition of three collective states, each encoded in a Rydberg state. The collective state is mapped into a photonic time-bin qutrit with the microwave field and read out sequentially. The complete sequence, including preparation, control, and read-out, is less than 1.8~$\mu$s, which mitigates decoherence significantly. We measure the coherence of the qutrit with non-destructive Ramsey interferometry, which is preferable for quantum information processing, and find good quantitative agreement with the theoretical model. The ability to write, process and read out the single photonic qutrit on microsecond time scales with microwave coupled Rydberg states demonstrates the coherent connectivity among the high Hilbert space of the qutrit.Our study is an important step in exploring qutrit based quantum information processes and quantum simulation of topological physics with microwave coupled Rydberg atom ensembles., Comment: 7 pages, 4 figures

Floquet systems are periodically driven systems. In this framework, the system Hamiltonian and associated spectra of interest are modified, giving rise to new quantum phases of matter and nonequilibrium dynamics without static counterparts. Here we experimentally demonstrate a self-induced Floquet system in the interacting Rydberg gas. This originates from the photoionization of thermal Rydberg gases in a static magnetic field. Importantly, by leveraging the Rydberg electromagnetically induced transparency spectrum, we probe the nonequilibrium dynamics in the bistable regime and identify the emergence of a discrete time crystalline phase. Our work fills the experimental gap in the understanding the relation of multistability and dissipative discrete time crystalline phase. In this regard, it constitutes a highly controlled platform for exploring exotic nonequilibrium physics in dissipative interacting systems., Comment: 6 pages, 4 figures

Maintaining the coherence in quantum systems is interesting in both fundamental physics and quantum information processing. In particular, suppressing the dephasing caused by thermal fluctuations in quantum systems can potentially enable functional quantum devices. Techniques to reduce motional dephasing of quantum superpositions include spin echo and bang-bang. In this paper, we demonstrate the effectiveness of a novel protocol on a collective quantum superposition state known as a Rydberg polariton. These collective states are potentially important in the context of single photon sources, optical transistor, all-optical quantum gates and fast read-out of quantum information. However progress in Rydberg polariton quantum technology has been hindered by fast motional dephasing on which no effective methods exist for undoing it. Here, we show how our protocol via optical dressing using Raman lasers cancels dephasing and enhances coherence times by more than an order of magnitude., Comment: 9 pages, 7 figures

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

The identification of tipping points is essential for prediction of collapses or other sudden changes in complex systems. Applications include studies of ecology, thermodynamics, climatology, and epidemiology. However, detecting early signs of proximity to a tipping is made challenging by complexity and non-linearity. Strongly interacting Rydberg atom gases offer model systems that offer both complexity and non-linearity, including phase transition and critical slowing down. Here, via an external probe we observe prior warning of the proximity of a phase transition of Rydberg thermal gases. This warning signal is manifested as a deviation from linear growth of the variance with increasing probe intensity. We also observed the dynamics of the critical slowing down behavior versus different time scales, and atomic densities, thus providing insights into the study of a Rydberg atom system's critical behavior. Our experiment suggests that the full critical slowing down dynamics of strongly-interacting Rydberg atoms can be probed systematically, thus providing a benchmark with which to identify critical phenomena in quantum many-body systems.

Microwave-optical conversion is key to future networks of quantum devices, such as those based on superconducting technology. Conversion at the single quantum level requires strong nonlinearity, high bandwidth, and compatibility with a millikelvin environment. A large nonlinearity is observed in Rydberg atoms, but combining atomic gases with dilution refrigerators is technically challenging. Here we demonstrate that a strong microwave-optical nonlinearity in a cryogenic, solid-state system by exploiting Rydberg states of excitons in \cuprite. We measure a microwave-optical cross-Kerr coefficient of $B_0 = 0.022 \pm 0.008 $ m V$^{-2}$ at 4~K, which is several orders of magnitude larger than other solid-state systems. Our results highlight the potential of Rydberg excitons for nonlinear optics, and form the basis for a microwave-optical frequency converter based on Cu$_2$O., Comment: 5 pages, 3 figures

We demonstrate simultaneous detection of radio-frequency (RF) fields ranging from the very high-frequency (VHF) band (128 MHz) to terahertz frequencies (0.61 THz) using a caesium Rydberg-atom receiver. The RF fields are concurrently applied to a series of atomic transitions involving states of increasing orbital angular momentum, where the energy separations become progressively smaller, allowing access to a very wide range of radio frequencies. We show that the optical response of the system in the presence of the RF fields can be reproduced theoretically using a simple Lindblad-master-equation approach. Furthermore, we demonstrate experimentally that a series of amplitude-modulated tones can be detected simultaneously using multiple carrier frequencies. This demonstration opens the way for RF communications across multiple bands simultaneously using a single optical receiver.

We observe synchronisation in a thermal (35-60 {\deg}C) atomic (Rb) ensemble driven to a highly-excited Rydberg state (principle quantum number n ranging from 43 to 79). Synchronisation in this system is unexpected due to the atomic motion, however, we show theoretically that sufficiently strong interactions via a global Rydberg density mean field causes frequency and phase entrainment. The emergent oscillations in the vapor's bulk quantities are detected in the transmission of the probe laser for a two-photon excitation scheme., Comment: 6 pages main document (including 4 figures) and 4 pages Supplementary Material (including 3 figures). Updated version, including additional appendix E

It is challenging to probe ergodicity breaking trends of a quantum many-body system when dissipation inevitably damages quantum coherence originated from coherent coupling and dispersive two-body interactions. Rydberg atoms provide a test bed to detect emergent exotic many-body phases and non-ergodic dynamics where the strong Rydberg atom interaction competes with and overtakes dissipative effects even at room temperature. Here we report experimental evidence of a transition from ergodic towards ergodic breaking dynamics in driven-dissipative Rydberg atomic gases. The broken ergodicity is featured by the long-time phase oscillation, which is attributed from the formation of Rydberg excitation clusters in limit cycle phases. The broken symmetry in the limit cycle is a direct manifestation of many-body interactions, which is verified by tuning atomic densities in our experiment. The reported result reveals that Rydberg many-body systems are a promising candidate to probe ergodicity breaking dynamics, such as limit cycles, and enable the benchmark of non-equilibrium phase transition.