Removing exactly one photon from an arbitrary input pulse is an elementary operation in quantum optics and enables applications in quantum information processing and quantum simulation. Here we demonstrate a deterministic single-photon absorber based on the saturation of an optically thick free-space medium by a single photon due to Rydberg blockade. Single-photon subtraction adds a new component to the Rydberg quantum optics toolbox, which already contains photonic logic building-blocks such as single-photon sources, switches, transistors, and conditional $π$-phase shifts. Our approach is scalable to multiple cascaded absorbers, essential for preparation of non-classical light states for quantum information and metrology applications, and, in combination with the single-photon transistor, high-fidelity number-resolved photon detection.
The preparation of light pulses with well-defined quantum properties requires precise control at the individual photon level. Here, we demonstrate exact and controlled multi-photon subtraction from incoming light pulses. We employ a cascaded system of tightly confined cold atom ensembles with strong, collectively enhanced coupling of photons to Rydberg states. The excitation blockade resulting from interactions between Rydberg atoms limits photon absorption to one per ensemble and engineered dephasing of the collective excitation suppresses stimulated re-emission of the photon. We experimental…
We study electromagnetically induced transparency (EIT) of a weakly interacting cold Rydberg gas. We show that the onset of interactions is manifest as a depopulation of the Rydberg state and numerically model this effect by adding a density-dependent non-linear term to the optical Bloch equations. In the limit of a weak probe where the depopulation effect is negligible, we observe no evidence of interaction induced decoherence and obtain a narrow Rydberg dark resonance with a linewidth of <600 kHz, limited by the Rabi frequency of the coupling beam
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 theoretically investigate the effect of dissipation on multi-photon excitation of Rydberg atoms. The steady states and the dynamics are compared via two types of four-level excitation schemes with different dissipative paths of spontaneous emission. We find that in the case of strong Rydberg-Rydberg interaction, the schemes will settle in several different non-equilibrium steady states. The interesting aspect is that there exists the multi-stable steady states, which reveals the competition between interaction-induced nonlinearity and dissipation caused by spontaneous emission. A numerical …
The combination of high optical nonlinearity in the electromagnetically induced transparency (EIT) effect and strong electric dipole-dipole interaction (DDI) among the Rydberg-state atoms can lead to important applications in quantum information processing and many-body physics. One can utilize the Rydberg-EIT system in the strongly-interacting regime to mediate photon-photon interaction or qubit-qubit operation. One can also employ the Rydberg-EIT system in the weaklyinteracting regime to study the Bose-Einstein condensation of Rydberg polaritons. Most of the present theoretical models dealt …
We proposed utilizing a medium with a high optical depth (OD) and a Rydberg state of low principal quantum number, $n$, to create a weakly-interacting many-body system of Rydberg polaritons, based on the effect of electromagnetically induced transparency (EIT). We experimentally verified the mean field approach to weakly-interacting Rydberg polaritons, and observed the phase shift and attenuation induced by the dipole-dipole interaction (DDI). The DDI-induced phase shift or attenuation can be viewed as a consequence of the elastic or inelastic collisions among the Rydberg polaritons. Using a w…
We present an extension of our recent paper [Bienias et al., Phys. Rev. A 90, 053804 (2014)] in which we demonstrated the scattering properties and bound-state structure of two Rydberg polaritons, as well as the derivation of the effective low-energy many-body Hamiltonian. Here, we derive a microscopic Hamiltonian describing the propagation of Rydberg slow light polaritons in one dimension. We describe possible decoherence processes within a Master equation approach, and derive equations of motion in a Schroedinger picture by using an effective non-Hermitian Hamiltonian. We illustrate diagramm…
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 prop…
We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical p…
We report the creation of an interacting cold Rydberg gas of strontium atoms. We show that the excitation spectrum of the inner valence electron is sensitive to the interactions in the Rydberg gas, even though they are mediated by the outer Rydberg electron. By studying the evolution of this spectrum we observe density-dependent population transfer to a state of higher angular momentum l. We determine the fraction of Rydberg atoms transferred, and identify the dominant transfer mechanism to be l-changing electron-Rydberg collisions associated with the formation of a cold plasma.
Finite-range interacting spin models are the simplest models to study the effect of beyond nearest-neighbour interactions and access new effects caused by the range of the interactions. Recent experiments have reached the regime of dominant interactions in Ising quantum magnets via optical coupling of trapped neutral atoms to Rydberg states. This approach allows for the tunability of all relevant terms in an Ising Hamiltonian with $1/r^6$ interactions in a transverse and longitudinal field. This review summarizes the recent progress of these implementations in Rydberg lattices with site-resolv…
We show that the dipole-dipole interaction between three identical Rydberg atoms can give rise to bound trimer states. The microscopic origin of these states is fundamentally different from Efimov physics. Two stable trimer configurations exist where the atoms form the vertices of an equilateral triangle in a plane perpendicular to a static electric field. The triangle edge length typically exceeds $R\approx 2\,μ\text{m}$, and each configuration is two-fold degenerate due to Kramers' degeneracy. The depth of the potential wells and the triangle edge length can be controlled by external paramet…
We theoretically investigate the dynamics of a gas of strongly interacting Rydberg atoms subject to a time-domain Ramsey interferometry protocol. The many-body dynamics is governed by an Ising-type Hamiltonian with long range interactions of tunable strength. We analyze and model the contrast degradation and phase accumulation of the Ramsey signal and identify scaling laws for varying interrogation times, ensemble densities, and ensemble dimensionalities.
We investigate the effect of degenerate atomic states on the exciton delocalization of dipole-dipole interacting Rydberg assemblies. Using a frozen gas and regular one-, two-, and three-dimensional lattice arrangements as examples, we see that degeneracies can enhance the delocalization compared to the situation when there is no degeneracy. Using the Zeeman splitting provided by a magnetic field, we controllably lift the degeneracy to study in detail the transition between degenerate and non-degenerate regimes.
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 …
We show that the dipole-dipole interaction between two Rydberg atoms can lead to substantial Abelian and non-Abelian gauge fields acting on the relative motion of the two atoms. We demonstrate how the gauge fields can be evaluated by numerical techniques. In the case of adiabatic motion in a single internal state, we show that the gauge fields give rise to a magnetic field that results in a Zeeman splitting of the rotational states. In particular, the ground state of a molecular potential well is given by the first excited rotational state. We find that our system realises a synthetic spin-orb…
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…
Mean-field Pulse Adaptation for the Circularization of Interacting Rydberg Atoms
Forschungszentrum Jülich GmbH（于利希研究中心）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文系）；OIST Graduate University（冲绳科学技术大学院大学）
Abstract Far-from equilibrium dynamics that lead to self-organization are highly relevant to complex dynamical systems not only in physics, but also in life-, earth-, and social sciences. It is challenging however to find systems with sufficiently controllable parameters that allow quantitatively modelling of emergent properties. Here, we study a non-equilibrium phase transition and observe signatures of self-organized criticality in a dilute thermal vapour of atoms optically excited to strongly interacting Rydberg states. Electromagnetically induced transparency (EIT) provides excellent contr…
We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transi…
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…
We show that the resonant dipole-dipole interaction can give rise to bound states between two and three Rydberg atoms with non-overlapping electron clouds. The dimer and trimer states arise from avoided level crossings between states converging to different fine structure manifolds in the limit of separated atoms. We analyze the angular dependence of the potential wells, characterize the quantum dynamics in these potentials and discuss methods for their production and detection. Typical distances between the atoms are of the order of several micrometers which can be resolved in state-of-the-ar…
We explore the fluorescence signals from a pair of atoms driven towards Rydberg states on a three-level ladder transition. The dipole--dipole interactions between Rydberg excited atoms significantly distort the dark state and electromagnetically induced transparency behavior observed with independent atoms and, thus, their steady state light emission. We calculate and analyze the temporal correlations between intensities and amplitudes of the signals emitted by the atoms and explain their origin in the atomic Rydberg state interactions.
We provide a detailed theoretical and conceptual study of a planned experiment to excite Rydberg states of ions trapped in a Paul trap. The ultimate goal is to exploit the strong state dependent interactions between Rydberg ions to implement quantum information processing protocols and to simulate the dynamics of strongly interacting spin systems. We highlight the promises of this approach when combining the high degree of control and readout of quantum states in trapped ion crystals with the novel and fast gate schemes based on interacting giant Rydberg atomic dipole moments. We discuss antic…
This review summarizes experimental works performed over the last decade by several groups on the manipulation of a few individual interacting Rydberg atoms. These studies establish arrays of single Rydberg atoms as a promising platform for quantum state engineering, with potential applications to quantum metrology, quantum simulation and quantum information.
We show that Jaynes-Cummings dynamics can be observed in mesoscopic atomic ensembles interacting with a classical electromagnetic field in the regime of Rydberg blockade, where the time dynamics of the average number of Rydberg excitations in mesoscopic ensembles displays collapses and revivals typical of this model. As the frequency of Rabi oscillations between collective states of Rydberg blockaded ensembles depends on the number of interacting atoms, for randomly loaded optical dipole traps we predict collapses and revivals of Rabi oscillations. We have studied the effects of finite interac…
Three-body Förster resonances at long-range interactions of Rydberg atoms were first predicted and observed in Cs Rydberg atoms by R.Faoro et al., Nature Comm. 6, 8173 (2015). In these resonances, one of the atoms carries away an energy excess preventing the two-body resonance, leading thus to a Borromean type of Förster energy transfer. But they were in fact observed as the average signal for the large number of atoms $N\gg1$. In this Letter we report on the first experimental observation of the three-body Förster resonances ${\rm 3}\times nP_{3/2} (|{\rm M}|)\to nS_{1/2} +(n+1)S_{1/2} +nP_{3…
Assembled arrays of individual atoms with Rydberg-mediated interactions provide a powerful platform for the simulation of many-body spin Hamiltonians as well as the implementation of universal gate-based quantum information processing. We demonstrate the first realization of Rydberg excitations and controlled interactions in microlens-generated multisite trap arrays of reconfigurable geometry. We utilize atom-by-atom assembly for the deterministic preparation of pre-defined 2D structures of rubidium Rydberg atoms with exactly known mutual separations and selectable interaction strength. By ada…
Interfacing light and matter at the quantum level is at the heart of modern atomic and optical physics and enables new quantum technologies involving the manipulation of single photons and atoms. A prototypical atom-light interface is electromagnetically induced transparency, in which quantum interference gives rise to hybrid states of photons and atoms called dark-state polaritons. We have observed individual dark-state polaritons as they propagate through an ultracold atomic gas involving Rydberg states. Strong long-range interactions between Rydberg atoms give rise to an effective interacti…
We study a system of atoms that are laser-driven to $nD_{3/2}$ Rydberg states and assess how accurately they can be mapped onto spin-$1/2$ particles for the quantum simulation of anisotropic Ising magnets. Using non-perturbative calculations of the pair interaction potentials between two atoms in the presence of both electric and magnetic fields, we emphasize the importance of a careful selection of the experimental parameters in order to maintain the Rydberg blockade and avoid excitation of unwanted Rydberg states. We then benchmark these theoretical observations against experiments using two…
Studying the complex quantum dynamics of interacting many-body systems is one of the most challenging areas in modern physics. Here, we use machine learning (ML) models to identify the symmetrized base states of interacting Rydberg atoms of various atom numbers (up to six) and geometric configurations. To obtain the data set for training the ML classifiers, we generate Rydberg excitation probability profiles that simulate experimental data by utilizing Lindblad equations that incorporate laser intensities and phase noise. Then, we classify the data sets using support vector machines (SVMs) and…
The understanding of dynamical evolutions of interacting photon pulses in Rydberg atomic ensemble is the prerequisite for realizing quantum devices with such system. We present an approach that efficiently simulates the dynamical processes, using a set of local functions we construct to reflect the profiles of narrowband pulses. For two counter-propagating photon pulses, our approach predicts the distinct phenomena from the widely concerned Rydberg blockade to the previously less noticed significant absorption in the anomalous dispersion regime, which can occur by respectively setting the puls…
The concept of topological phases is a powerful framework to characterize ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. While a few topological phases appear in condensed matter systems, a current challenge is the implementation and study of such quantum many-body ground states in artificial matter. Here, we report the experimental realization of a symmetry protected topological phase of interacting bosons in a one-dimensional lattice, and demonstrate a robust ground state degeneracy attributed to protected edge states. The setup is based on ato…
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 loss…
When ground state atoms are excited to a Rydberg state, van der Waals interactions among them can lead to a strong suppression of the excitation. Despite the strong interactions the evolution can still be reversed by a simple phase shift in the excitation laser field. We experimentally prove the coherence of the excitation in the strong blockade regime by applying an `optical rotary echo' technique to a sample of magnetically trapped ultracold atoms, analogous to a method known from nuclear magnetic resonance. We additionally measured the dephasing time due to the interaction between the Rydbe…
Arrays of optically trapped atoms excited to Rydberg states have recently emerged as a competitive physical platform for quantum simulation and computing, where high-fidelity state preparation and readout, quantum logic gates and controlled quantum dynamics of more than 100 qubits have all been demonstrated. These systems are now approaching the point where reliable quantum computations with hundreds of qubits and realistically thousands of multiqubit gates with low error rates should be within reach for the first time. In this article we give an overview of the Rydberg quantum toolbox, emphas…
We study a gas of ultracold atoms resonantly driven into a strongly interacting Rydberg state. The long distance behavior of the spatially frozen effective pseudospin system is determined by a set of dimensionless parameters, and we find that the experimental data exhibits algebraic scaling laws for the excitation dynamics and the saturation of Rydberg excitation. Mean field calculations as well as numerical simulations provide an excellent agreement with the experimental finding, and are evidence for universality in a strongly interacting frozen Rydberg gas.
A defining property of particles is their behavior under exchange. In two dimensions anyons can exist which, opposed to fermions and bosons, gain arbitrary relative phase factors or even undergo a change of their type. In the latter case one speaks of non-Abelian anyons - a particularly simple and aesthetic example of which are Fibonacci anyons. They have been studied in the context of fractional quantum Hall physics where they occur as quasiparticles in the $k=3$ Read-Rezayi state, which is conjectured to describe a fractional quantum Hall state at filling fraction $ν=12/5$. Here we show that…
We propose a scheme for rapid generation of high fidelity steady state entanglement between a pair of atoms. A two-photon excitation process towards long-lived Rydberg states with finite pairwise interaction, a dark state interference effect in the individual atoms, and spontaneous emission from their short-lived excited states lead to rapid, dissipative formation of an entangled steady state. We show that for a wide range of physical parameters, this entangled state is formed on a time scale given by the strengths of coherent Raman and Rabi fields applied to the atoms, while it is only weakly…
We demonstrate finite range binding potentials between pairs of Rydberg atoms interacting with each other via attractive and repulsive van der Waals potentials and driven by a microwave field. We show that, using destructive quantum interference to cancel single-atom Rydberg excitation, the Rydberg-dimer states can be selectively and coherently populated from the two-atom ground state. This can be used to realize a two-qubit interaction gate which is not susceptible to mechanical forces between the atoms and is therefore immune to motional decoherence.
We study the appearance of correlated many-body phenomena in an ensemble of atoms driven resonantly into a strongly interacting Rydberg state. The ground state of the Hamiltonian describing the driven system exhibits a second order quantum phase transition. We derive the critical theory for the quantum phase transition and show that it describes the properties of the driven Rydberg system in the saturated regime. We find that the suppression of Rydberg excitations known as blockade phenomena exhibits an algebraic scaling law with a universal exponent.
We study resonant optical excitations of strongly-interacting Rydberg states of atoms in the presence of relaxations. We employ the quantum stochastic (Monte Carlo) wavefunctions to simulate the dissipative dynamics of tens of atoms in two-dimensional lattices. We show that under typical experimental conditions involving slow Rydberg state decay and sizable relaxation of atomic coherences, on the time scale of several microseconds the atomic ensemble approaches a stationary state in which much of the quantum correlations between the atoms have decayed away. The steady state, however, exhibits …
We consider the dynamics of intracavity electromagnetically induced transparency (EIT) in an ensemble of strongly interacting Rydberg atoms. By combining the advantage of variable cavity lifetimes with intracavity EIT and strongly interacting Rydberg dark-state polaritons, we show that such intracavity EIT system could exhibit very strong photon blockade effect.
Fast Pulses for High-Fidelity Circularization of Interacting Rydberg atoms
Forschungszentrum Jülich GmbH（于利希研究中心）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université（卡斯特尔布罗塞尔实验室，法兰西学院，法国国家科学研究中心，巴黎文理研究大学，索邦大学）；Institut Universitaire de France（法兰西学院研究院）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文学系）
How do isolated quantum systems approach an equilibrium state? We experimentally and theoretically address this question for a prototypical spin system formed by ultracold atoms prepared in two Rydberg states with different orbital angular momenta. By coupling these states with a resonant microwave driving we realize a dipolar XY spin-1/2 model in an external field. Starting from a spin-polarized state we suddenly switch on the external field and monitor the subsequent many-body dynamics. Our key observation is density dependent relaxation of the total magnetization much faster than typical de…
We present the experimental demonstration of interaction induced enhancement in Rydberg excitation or Rydberg anti-blockade in thermal atomic vapor. We have used optical heterodyne detection technique to measure Rydberg population due to two-photon excitation to the Rydberg state. The anti-blockade peak which doesn't satisfy the two-photon resonant condition is observed along with the usual two-photon resonant peak which can't be explained using the model with non-interacting three-level atomic system. A model involving two interacting atoms is formulated for thermal atomic vapor using the dre…
We experimentally and theoretically investigate the dephasing rates of the coherent evolution of a resonantly driven pseudo spin emersed in a reservoir of pseudo spins. The pseudo spin is realized by optically exciting 87 Rb atoms to a Rydberg state. Hence, the upper spin states are coupled via the strong van der Waals interaction. Two different experimental techniques to measure the dephasing rates are shown: the 'rotary echo' technique known from nuclear magnetic resonance physics and electromagnetically induced transparency. The experiments are performed in a dense frozen Rydberg gas, eithe…
Fundamental error bound for entanglement generation between interacting Rydberg atoms
Institute of Electronic Structure and Laser and Center for Quantum Science and Technologies, FORTH（电子结构与激光研究所及量子科学与技术中心，FORTH）；University of Crete（克里特大学）；A. Alikhanyan National Laboratory (YerPhI)（阿·阿里哈尼扬国家实验室（耶尔皮））
Coupling light to Rydberg states of atoms under conditions of electromagnetically induced transparency (EIT) leads to the formation of strongly interacting quasi-particles, termed Rydberg polaritons. We derive a one-dimensional model describing the time evolution of these polaritons under paraxial propagation conditions, which we verify by numerical two-excitation simulations. We determine conditions allowing for a description by an effective Hamiltonian of a single-species polariton, and calculate ground-state correlations by use of the density matrix renormalization group (DMRG). Under typic…
