Interacting Rydberg Gases Research Articles

Dissipative time crystal in a strongly interacting Rydberg gas

Dissipative time crystal in a strongly interacting Rydberg gas

Driven-Dissipative Rydberg Blockade in Optical Lattices.

While dissipative Rydberg gases exhibit unique possibilities to tune dissipation and interaction properties, very little is known about the quantum many-body physics of such long-range interacting open quantum systems. We theoretically analyze the steady state of a van der Waals interacting Rydberg gas in an optical lattice based on a variational treatment that also includes long-range correlations necessary to describe the physics of the Rydberg blockade, i.e., the inhibition of neighboring Rydberg excitations by strong interactions. In contrast to the ground state phase diagram, we find that the steady state undergoes a single first order phase transition from a blockaded Rydberg gas to a facilitation phase where the blockade is lifted. The first order line terminates in a critical point when including sufficiently strong dephasing, enabling a highly promising route to study dissipative criticality in these systems. In some regimes, we also find good quantitative agreement of the phase boundaries with previously employed short-range models, however, with the actual steady states exhibiting strikingly different behavior.

Photon bound state dynamics from a single artificial atom

The interaction between photons and a single two-level atom constitutes a fundamental paradigm in quantum physics. The nonlinearity provided by the atom leads to a strong dependence of the light–matter interface on the number of photons interacting with the two-level system within its emission lifetime. This nonlinearity unveils strongly correlated quasiparticles known as photon bound states, giving rise to key physical processes such as stimulated emission and soliton propagation. Although signatures consistent with the existence of photon bound states have been measured in strongly interacting Rydberg gases, their hallmark excitation-number-dependent dispersion and propagation velocity have not yet been observed. Here we report the direct observation of a photon-number-dependent time delay in the scattering off a single artificial atom—a semiconductor quantum dot coupled to an optical cavity. By scattering a weak coherent pulse off the cavity–quantum electrodynamics system and measuring the time-dependent output power and correlation functions, we show that single photons and two- and three-photon bound states incur different time delays, becoming shorter for higher photon numbers. This reduced time delay is a fingerprint of stimulated emission, where the arrival of two photons within the lifetime of an emitter causes one photon to stimulate the emission of another.

Self-Induced Transparency in Warm and Strongly Interacting Rydberg Gases.

We study dispersive optical nonlinearities of short pulses propagating in high number density, warm atomic vapors where the laser resonantly excites atoms to Rydberg P states via a single-photon transition. Three different regimes of the light-atom interaction, dominated by either Doppler broadening, Rydberg atom interactions, or decay due to thermal collisions between ground state and Rydberg atoms, are found. We show that using fast Rabi flopping and strong Rydberg atom interactions, both in the order of gigahertz, can overcome the Doppler effect as well as collisional decay, leading to a sizable dispersive optical nonlinearity on nanosecond timescales. In this regime, self-induced transparency (SIT) emerges when areas of the nanosecond pulse are determined primarily by the Rydberg atom interaction, rather than the area theorem of interaction-free SIT. We identify, both numerically and analytically, the condition to realize Rydberg SIT. Our study contributes to efforts in achieving quantum information processing using glass cell technologies.

Blockade-induced resonant enhancement of the optical nonlinearity in a Rydberg medium

We predict a resonant enhancement of the nonlinear optical response of an interacting Rydberg gas under conditions of electromagnetically induced transparency. The enhancement originates from a two-photon process which resonantly couples electronic states of a pair of atoms dressed by a strong control field. We calculate the optical response for the three-level system by explicitly including the dynamics of the intermediate state. We find an analytical expression for the third order susceptibility for a weak classical probe field. The nonlinear absorption displays the strongest resonant behavior on two-photon resonance where the detuning of the probe field equals the Rabi frequency of the control field. The nonlinear dispersion of the medium exhibits various spatial shapes depending on the interaction strength. Based on the developed model, we propose a realistic experimental scenario to observe the resonance by performing transmission measurements.

Emergence of spatial order in highly interacting Rydberg gases

We describe the emergence of strong spatial correlations, akin to liquid-like behavior and crystallization effects, in low (one and two) dimensional gases of cold Rydberg atoms. The presence of an external electric field permanently polarizes the atoms, which became highly correlated due to the long-range dipole-dipole interaction. We describe a theoretical approach particularly suited for strongly coupled systems and numerically obtain both the two-particle distribution function and the static structure factor. The experimental implementation of such highly interacting systems is discussed, including detailed calculations of the interaction strength for different Rydberg states. The results provide new insights into many-body effects associated with strongly interacting Rydberg atoms, including the possibility of observing novel highly ordered phases.

Deexcitation spectroscopy of strongly interacting Rydberg gases

We present experimental results on the controlled de-excitation of Rydberg states in a cold gas of Rb atoms. The effect of the van der Waals interactions between the Rydberg atoms is clearly seen in the de-excitation spectrum and dynamics. Our observations are confirmed by numerical simulations. In particular, for off-resonant (facilitated) excitation we find that the de-excitation spectrum reflects the spatial arrangement of the atoms in the quasi one-dimensional geometry of our experiment. We discuss future applications of this technique and implications for detection and controlled dissipation schemes.

Lévy statistics of interacting Rydberg gases

A statistical analysis of the laser excitation of cold and randomly distributed atoms to Rydberg states is developed. We first demonstrate with a hard ball model that the distribution of energy level shifts in an interacting gas obeys L\'evy statistics, in any dimension $d$ and for any interaction $-C_p/R^p$ under the condition $d/p<1$. This result is confirmed with a Monte Carlo rate equations simulation of the actual laser excitation in the particular case $p=6$ and $d=3$. With this finding, we develop a statistical approach for the modeling of probe light transmission through a cold atom gas driven under conditions of electromagnetically induced transparency involving a Rydberg state. The simulated results are in good agreement with experiment.

Spectral shift and dephasing of electromagnetically induced transparency in an interacting Rydberg gas

We perform spectroscopic measurements of electromagnetically induced transparency (EIT) in a strongly interacting Rydberg gas, and observe a significant spectral shift of the transparency from the single-atom EIT resonance as well as a spectral dephasing of the same order. We characterize the shift and dephasing as a function of atomic density, probe Rabi frequency, and principal quantum number of Rydberg states, and demonstrate that the observed spectral shift and dephasing are reduced if the size of a Gaussian atomic cloud is increased. We simulate our experiment with a semi-analytical model, which gives results in good agreement with our experimental data.

Experimental observation of controllable kinetic constraints in a cold atomic gas

Many-body systems relaxing to equilibrium can exhibit complex dynamics even if their steady state is trivial. At low temperatures or high densities their evolution is often dominated by steric hindrances affecting particle motion [1,2,3]. Local rearrangements are highly constrained, giving rise to collective - and often slow - relaxation.This dynamics can be difficult to analyse from first principles, but the essential physical ingredients are captured by idealized lattice models with so- called kinetic constraints [4]. Here we experimentally realize a many-body system exhibiting manifest kinetic constraints and measure its dynamical properties. In the cold Rydberg gas used in our experiments, the nature of the constraints can be tailored through the detuning of the excitation lasers from resonance [5,6,7,8], which controls whether the system undergoes correlated or anti- correlated dynamics. Our results confirm recent theoretical predictions [5,6], and highlight the analogy between the dynamics of interacting Rydberg gases and that of soft-matter systems.

Variational analysis of driven-dissipative Rydberg gases

We study the nonequilibrium steady state arising from the interplay between coherent and dissipative dynamics in strongly interacting Rydberg gases using a recently introduced variational method [H. Weimer, Phys. Rev. Lett. 114, 040402 (2015)]. We give a detailed discussion of the properties of this approach and we provide a comparison with methods related to the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. We find that the variational approach offers some intrinsic advantages and we also show that it is able to explain the experimental results obtained in an ultracold Rydberg gas on a quantitative level.

Effective dynamics of strongly dissipative Rydberg gases

We investigate the evolution of interacting Rydberg gases in the limit of strong noise and dissipation. Starting from a description in terms of a Markovian quantum master equation we derive effective equations of motion that govern the dynamics on a ‘coarse-grained’ timescale where fast dissipative degrees of freedom have been adiabatically eliminated. Specifically, we consider two scenarios which are of relevance for current theoretical and experimental studies—Rydberg atoms in a two-level (spin) approximation subject to strong dephasing noise as well as Rydberg atoms under so-called electromagnetically induced transparency (EIT) conditions and fast radiative decay. In the former case we find that the effective dynamics is described by classical rate equations up to second order in an appropriate perturbative expansion. This drastically reduces the computational complexity of numerical simulations in comparison to the full quantum master equation. When accounting for the fourth order correction in this expansion, however, we find that the resulting equation breaks the preservation of positivity and thus cannot be interpreted as a proper classical master rate equation. In the EIT system we find that the expansion up to second order retains information not only on the ‘classical’ observables, but also on some quantum coherences. Nevertheless, this perturbative treatment still achieves a non-trivial reduction of complexity with respect to the original problem.

Out-of-equilibrium evolution of kinetically constrained many-body quantum systems under purely dissipative dynamics.

We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system.

Out-of-equilibrium structures in strongly interacting Rydberg gases with dissipation

The non-equilibrium dynamics of a gas of cold atoms in which Rydberg states are off-resonantly excited is studied in the presence of noise. The interplay between interaction and off-resonant excitation leads to an initial dynamics where aggregates of excited Rydberg atoms slowly nucleate and grow, eventually reaching long-lived meta-stable arrangements which then relax further on much longer timescales. This growth dynamics is governed by an effective Master equation which permits a transparent and largely analytical understanding of the underlying physics. By means of extensive numerical simulations we study the many-body dynamics and the correlations of the resulting non-equilibrium states in various dimensions. Our results provide insight into the dynamical richness of strongly interacting Rydberg gases in noisy environments, and highlight the usefulness of these kind of systems for the exploration of soft-matter-type collective behaviour.

Semianalytical model for nonlinear absorption in strongly interacting Rydberg gases

Rate equation models are extensively used to describe the many-body states of laser driven atomic gases. We show that the properties of the rate equation model used to describe nonlinear optical effects arising in interacting Rydberg gases can be understood by considering the excitation of individual super-atoms. From this we deduce a simple semi-analytic model that accurately describes the Rydberg density and optical susceptibility for different dimensionalities. We identify the previously reported universal dependence of the susceptibility on the Rydberg excited fraction as an intrinsic property of the rate equation model that is rooted in one-body properties. Benchmarking against exact master equation calculations, we identify regimes in which the semi-analytic model is particularly reliable. The performance of the model improves in the presence of dephasing which destroys higher order atomic coherences.

Kinetic Constraints, Hierarchical Relaxation, and Onset of Glassiness in Strongly Interacting and Dissipative Rydberg Gases

We show that the dynamics of a laser driven Rydberg gas in the limit of strong dephasing is described by a master equation with manifest kinetic constraints. The equilibrium state of the system is uncorrelated but the constraints in the dynamics lead to spatially correlated collective relaxation reminiscent of glasses. We study and quantify the evolution towards equilibrium in one and two dimensions, and analyze how the degree of glassiness and the relaxation time are controlled by the interaction strength between Rydberg atoms. We also find that spontaneous decay of Rydberg excitations leads to an interruption of glassy relaxation that takes the system to a highly correlated nonequilibrium stationary state. The results presented here, which are in principle also applicable to other systems such as polar molecules and atoms with large magnetic dipole moments, show that the collective behavior of cold atomic and molecular ensembles can be similar to that found in soft condensed-matter systems.

Driven-dissipative dynamics of a strongly interacting Rydberg gas

We study the non-equilibrium many-body dynamics of a cold gas of ground state alkali atoms weakly admixed by Rydberg states with laser light. On a timescale shorter than the lifetime of the dressed states, effective dipole-dipole or van der Waals interactions between atoms can lead to the formation of strongly correlated phases, such as atomic crystals. Using a semiclassical approach, we study the long-time dynamics where decoherence and dissipative processes due to spontaneous emission and blackbody radiation dominate, leading to heating and melting of atomic crystals as well as particle losses. These effects can be substantially mitigated by performing active laser cooling in the presence of atomic dressing.

Finite-size effects in strongly interacting Rydberg gases

The scaling of the number of Rydberg excitations in a laser-driven cloud of atoms with the interaction strength is found to be affected by the finite size of the system. The scaling predicted by a theoretical model is compared with results extracted from a numerical many-body simulation. We find that the numerically obtained scaling exponent in general does not agree with the analytical prediction. By individually testing the assumptions leading to the theoretical prediction using the results from the numerical analysis, we identify the origin of the deviations, and explain it as arising from the finite size of the system. Furthermore, finite-size effects in the pair correlation function $g^{(2)}$ are predicted. Finally, in larger ensembles, we find that the theoretical predictions and the numerical results agree, provided that the system is sufficiently homogeneous.

Universal time evolution of a Rydberg lattice gas with perfect blockade

We investigate the dynamics of a strongly interacting spin system that is motivated by current experimental realizations of strongly interacting Rydberg gases in lattices. In particular, we are interested in the temporal evolution of quantities such as the density of Rydberg atoms and density–density correlations when the system is initialized in a fully polarized state without Rydberg excitations. We show that in the thermodynamic limit the expectation values of these observables converge at least logarithmically to universal functions and outline a method to obtain these functions. We prove that a finite one-dimensional system follows this universal behavior up to a given time. The length of this universal time period depends on the actual system size. This shows that the study of small systems allows us to make precise predictions about the thermodynamic limit provided that the observation time is sufficiently short. We discuss this for various observables and for systems with different dimensions, interaction ranges and boundary conditions.

Nonlocal Nonlinear Optics in Cold Rydberg Gases

We present an analytical theory for the nonlinear optical response of a strongly interacting Rydberg gas under conditions of electromagnetically induced transparency. Simple formulas for the third-order optical susceptibility are derived and shown to be in excellent agreement with recent experiments. The obtained expressions reveal strong nonlinearities, which in addition are of highly nonlocal character. This property together with the enormous strength of the Rydberg-induced nonlinearities is shown to yield a unique laboratory platform for nonlinear wave phenomena, such as collapse-arrested modulational instabilities in a self-defocusing medium.