We review experimental and theoretical tools to excite, study and understand strongly interacting Rydberg gases. The focus lies on the excitation of dense ultracold atomic samples close to, or within quantum degeneracy, to high lying Rydberg states. The major part is dedicated to highly excited S-states of Rubidium, which feature an isotropic van-der-Waals potential. Nevertheless, the setup and the methods presented are also applicable to other atomic species used in the field of laser cooling and atom trapping.
We show that cold Rydberg gases enable an efficient six-wave mixing process where terahertz or microwave fields are coherently converted into optical fields and vice versa. This process is made possible by the long lifetime of Rydberg states, the strong coupling of millimeter waves to Rydberg transitions and by a quantum interference effect related to electromagnetically induced transparency (EIT). Our frequency conversion scheme applies to a broad spectrum of millimeter waves due to the abundance of transitions within the Rydberg manifold, and we discuss two possible implementations based on …
We theoretically study trapped ions that are immersed in an ultracold gas of Rydberg-dressed atoms. By off-resonant coupling on a dipole-forbidden transition, the adiabatic atom-ion potential can be made repulsive. We study the energy exchange between the atoms and a single trapped ion and find that Langevin collisions are inhibited in the ultracold regime for these repulsive interactions. Therefore, the proposed system avoids recently observed ion heating in hybrid atom-ion systems caused by coupling to the ion's radio frequency trapping field and retains ultracold temperatures even in the pr…
We measure nonlocal third-order spatial correlations in non-degenerate ultracold gases of bosonic ($^{84}$Sr) and spin-polarized fermionic ($^{87}$Sr) strontium through studies of the formation rates for ultralong-range trimer Rydberg molecules. The trimer production rate is observed to be very sensitive to the effects of quantum statistics with a strong enhancement of up to a factor of six (3!) in the case of bosonic $^{84}$Sr due to bunching, and a marked reduction for spin-polarized fermionic $^{87}$Sr due to anti-bunching. The experimental results are compared to theoretical predictions an…
Variational analysis of driven-dissipative Rydberg gases
本文用最近引进的变分方法研究了强相互作用里德伯气体中相干动力学和耗散动力学相互作用引起的非平衡定态[H。Weimer，Phys. Rev. Lett. 114，040402（2015）]。我们给出了一个详细的讨论，这种新的方法的属性，我们提供了一个比较与Bogoliubov Born-Green-Kirkwood-Yvon层次结构相关的方法。我们发现，变分的方法提供了一些内在的优势，我们也表明，它是能够解释实验结果在一个前所未有的定量水平上的超冷里德伯气体。
We study steady state phases of a one-dimensional array of Rydberg atoms coupled by a microwave (MW) field where the higher energy Rydberg state decays to the lower energy one via single-body and collective (superradiant) decay. Using mean-field approaches, we examine the interplay among the MW coupling, intra-state van der Waals (vdW) interaction, and single-body and collective dissipation between Rydberg states. A linear stability analysis reveals that a series of phases, including uniform, antiferromagnetic, oscillatory, and bistable and multistable phases can be obtained. Without the vdW i…
We have investigated formation of structures of Rydberg atoms excited from a disordered gas of ultracold atoms, using rate equations for two-photon Rydberg excitation in a single atom without eliminating the intermediate state. We have explored the validity range of these rate equations and defined a simple measure to determine, whether our model is applicable for a given set of laser parameters. We have applied these rate equations in Monte Carlo simulations of ultracold gases, for different laser beam profiles, and compared these simulations to experimental observations and find a general ag…
Atoms excited into high-lying Rydberg states and under strong dipole-dipole interactions exhibit phenomena associated with highly correlated and complex systems. We perform first principles numerical simulations on the dynamics of such systems. The emergence of a roton minimum in the excitation spectrum, as expected in strongly correlated gases and accurately described by Feynman's theory of liquid helium, is shown to significantly inhibit particle transport, with a strong suppression of the diffusion coefficient, due to the emerging spatial order. We also demonstrate how the ability to tempor…
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 groundstate and Rydberg atoms, are described. 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…
When atomic gases are laser driven to Rydberg states in an off resonant way, a single Rydberg atom may enhance the excitation rate of surrounding atoms. This leads to a facilitated excitation referred to as Rydberg anti-blockade. In the usual facilitation scenario, the detuning of the laser from resonance compensates the interaction shift. Here, we discuss a different excitation mechanism, which we call anomalous facilitation. This occurs on the "wrong side" of the resonance and originates from inhomogeneous broadening. The anomalous facilitation may be seen in experiments of attractively inte…
We calculate pair potential curves for interacting Rydberg atoms in a constant electric field and use them to determine the effective $C_3$ dipole-dipole and $C_6$ van der Waals coefficients. We compare the $C_3$ and $C_6$ with experiments where the angle of a polarizing electric field is varied with respect to the axis of a quasi-1-dimensional trap at ultracold temperatures. The dipoles produced via polarization of the atoms have an angular dependent dipole-dipole interaction. We focus on the interaction potential of two rubidium Rydberg atoms in $50S_{1/2}$ states in the blockade regime. For…
Dense Rydberg gases are out-of-equilibrium systems where strong density-density interactions give rise to effective kinetic constraints. They cause dynamic arrest associated with highly-constrained many-body configurations, leading to slow relaxation and glassy behavior. Multi-component Rydberg gases feature additional long-range interactions such as excitation-exchange. These are analogous to particle swaps used to artificially accelerate relaxation in simulations of atomistic models of classical glass formers. In Rydberg gases, however, swaps are real physical processes, which provide dynami…
Mean-field energy-level shifts arising as a result of strong electrostatic dipole interactions within dilute gases of polarized helium Rydberg atoms have been probed by microwave spectroscopy. The Rydberg states studied had principal quantum numbers $n=70$ and 72, and electric dipole moments of up to 14050 D, and were prepared in pulsed supersonic beams at particle number densities on the order of $10^{8}$ cm$^{-3}$. Comparisons of the experimental data with the results of Monte Carlo calculations highlight effects of the distribution of nearest-neighbor spacings in the pulsed supersonic beams…
We investigate the phenomenon of bistability in a thermal gas of cesium atoms excited to Rydberg states. We present both measurements and a numerical model of the phenomena based on collisions. By directly measuring the plasma frequency, we show that the origin of the bistable behavior lies in the creation of a plasma formed by ionized Rydberg atoms. Recombination of ions and electrons manifests as fluorescence which allows us to characterize the plasma properties and study the transient dynamics of the hysteresis that occurs. We determine scaling parameters for the point of plasma formation, …
We report an experimental investigation of the facilitated excitation dynamics in off-resonantly driven Rydberg gases by separating the initial off-resonant excitation phase from the facilitation phase, in which successive facilitation events lead to excitation avalanches. We achieve this by creating a controlled number of initial seed excitations. Greater insight into the avalanche mechanism is obtained from an analysis of the full counting distributions. We also present simple mathematical models and numerical simulations of the excitation avalanches that agree well with our experimental res…
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 dissipat…
Assemblies of highly excited Rydberg atoms in an ultracold gas can be set into motion by a combination of van-der-Waals and resonant dipole-dipole interactions. Thereby, the collective electronic Rydberg state might change due to non-adiabatic transitions, in particular if the configuration encounters a conical interaction. For the experimentally most accessible scenario, in which the Rydberg atoms are initially randomly excited in a three-dimensional bulk gas under blockade conditions, we numerically show that non-adiabatic transitions can be common when starting from the most energetic repul…
Photoexcitation rates for creation of ultralong-range Rydberg molecules (ULRM) with 31$\lesssim n \lesssim41$ in both ground and excited vibrational levels in cold ($T\sim900$~nK) gases of polarized and unpolarized $^{87}$Sr are presented. The measured production rates of the $ν=0, 1$ and 2 vibrational levels reveal rather different $n$ dependences which are analyzed by evaluating the Franck-Condon factors associated with excitation of the different vibrational levels and molecular rotational states. In particular, for gases of spin-polarized fermions, only Rydberg dimers with odd rotational q…
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 Lévy 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 …
In the presence of strong dephasing noise the dynamics of Rydberg gases becomes effectively classical, due to the rapid decay of quantum superpositions between atomic levels. Recently a great deal of attention has been devoted to the stochastic dynamics that emerges in that limit, revealing several interesting features, including kinetically-constrained glassy behaviour, self-similarity and aggregation effects. However, the non-equilibrium physics of these systems, in particular in the regime where coherent and dissipative processes contribute on equal footing, is yet far from being understood…
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 …
We present a comprehensive study of the diverse properties of heteronuclear Rydberg molecules, placing a special emphasis on those composed of the light alkali atoms, Li, Na, and K. Electron-atom scattering phase shifts, which determine the strength of the molecular bond, are calculated at very low energy and then used in a spin-dependent theoretical model to calculate accurate Rydberg molecule potential energy curves. The wide parameter range accessible by combining the various properties of different alkali atoms often leads to hybridized electronic states accessible via one or two photon ex…
We present photo-excitation of ultra-long-range Rydberg molecules as a probe of spatial correlations in quantum gases. Rydberg molecules can be created with well-defined internuclear spacing, set by the radius of the outer lobe of the Rydberg electron wavefunction $R_n$. By varying the principal quantum number $n$ of the target Rydberg state, the molecular excitation rate can be used to map the pair-correlation function of the trapped gas $g^{(2)}(R_n)$. We demonstrate this with ultracold Sr gases and probe pair-separation length scales ranging from $R_n = 1400 - 3200$ $a_0$, which are on the …
Simulating neural network criticality and resource dynamics with Rydberg gases
RPTU University Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道分校）；State Research Center OPTIMAS（OPTIMAS州立研究中心）；Max Planck Graduate Center with Johannes Gutenberg University Mainz (MPGC)（美因茨约翰内斯·古腾堡大学马克斯·普朗克研究生院）
We investigate the possibility of a bistable phase in an open many-body system. To this end we discuss the microscopic dynamics of a continuously off-resonantly driven Rydberg lattice gas in the regime of strong decoherence. Our experimental results reveal a prolongation of the temporal correlations with respect to the lifetime of a single Rydberg excitation and show strong evidence for the formation of finite-sized Rydberg excitation clusters in the steady state. We simulate our data using a simplified and a full many-body rate-equation model. The results are compatible with the formation of …
We propose a novel scheme to efficiently tune the scattering length of two colliding ground-state atoms by off-resonantly coupling the scattering-state to an excited Rydberg-molecular state using laser light. For the s-wave scattering of two colliding ${^{87}}\mathrm{Rb}$ atoms, we demonstrate that the effective optical length and pole strength of this Rydberg optical Feshbach resonance can be tuned over several orders of magnitude, while incoherent processes and losses are minimised. Given the ubiquity of Rydberg molecular states, this technique should be generally applicable to homo-nuclear …
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, i…
Two-dimensional (2D) spectroscopy uses multiple electromagnetic pulses to infer the properties of a complex system. A paradigmatic class of target systems are molecular aggregates, for which one can obtain information on the eigenstates, various types of static and dynamic disorder and on relaxation processes. However, two-dimensional spectra can be difficult to interpret without precise knowledge of how the signal components relate to microscopic Hamiltonian parameters and system-bath interactions. Here we show that two-dimensional spectroscopy can be mapped in the microwave domain to highly …
We discuss the density shift and broadening of Rydberg spectra measured in cold, dense atom clouds in the context of Rydberg atom spectroscopy done at room temperature, dating back to the experiments of Amaldi and Segrè in 1934. We discuss the theory first developed in 1934 by Fermi to model the mean-field density shift and subsequent developments of the theoretical understanding since then. In particular, we present a model whereby the density shift is calculated using a microscopic model in which the configurations of the perturber atoms within the Rydberg orbit are considered. We present sp…
We study the out-of-equilibrium dynamics of dissipative gases of atoms excited to two or more high-lying Rydberg states. This situation bears interesting similarities to classical binary (in general $p$-ary) mixtures of particles. The effective forces between the components are determined by the inter-level and intra-level interactions of Rydberg atoms. These systems permit to explore new parameter regimes which are physically inaccessible in a classical setting, for example one in which the mixtures exhibit non-additive interactions. In this situation the out-of-equilibrium evolution is chara…
Cold atomic gases resonantly excited to Rydberg states can exhibit strong optical nonlinearity at the single photon level. We observe that in such samples radiation trapping leads to an additional mechanism for Rydberg excitation. Conversely we demonstrate that Rydberg excitation provides a novel in situ probe of the spectral, statistical, temporal and spatial properties of the trapped re-scattered light. We also show that absorption can lead to an excitation saturation that mimics the Rydberg blockade effect. Collective effects due to multiple scattering may co-exist with co-operative effects…
As was recently shown in Ref. 1, many eigenstates of a random Rydberg gas with resonant dipole-dipole interactions are highly delocalized. Although the high degree of delocalization is generic to various types of power-law interactions and to both two and three-dimensional systems, in their detailed aspects the coherence distributions are sensitive to these parameters and vary dramatically between different systems. We calculate the eigenstates of both two and three-dimensional gases and quantify their delocalization throughout the atoms in the gas using a coherence measure. By contrasting the…
Guiding of Rydberg atoms in a high-gradient magnetic guide
本文研究了$^{87}$ Rb 59 D $_{5/2}$里德伯原子在高梯度直线双线磁波导中的导向作用。采用延时微波电离和离子探测技术探测里德伯原子的运动。我们观察到引导的里德伯原子在一段时间内的5毫秒以下的激发。被引导原子信号的衰减时间约为初始状态的5倍。我们将寿命的增加归因于初始阶段的$l$变化碰撞和热诱导的里德伯-里德伯跃迁。对里德伯原子引导的详细模拟再现了大多数实验观察，并提供了对内部状态演化的洞察。
Disordered systems provide paradigmatic instances of ergodicity breaking and localization phenomena. Here we explore the dynamics of excitations in a system of Rydberg atoms held in optical tweezers. The finite temperature produces an intrinsic uncertainty in the atomic positions, which translates into quenched correlated disorder in the interatomic interaction strengths. In a simple approach, the dynamics in the many-body Hilbert space can be understood in terms of a one-dimensional Anderson-like model with disorder on every other site, featuring both localized and delocalized states. We cond…
