Spin-motion coupling in a circular Rydberg state quantum simulator: case of two atoms

Rydberg atoms are remarkable tools for the quantum simulation of spin arrays. Circular Rydberg atoms open the way to simulations over very long time scales, using a combination of laser trapping of the atoms and spontaneous-emission inhibition, as shown in the proposal of a XXZ spin-array simulator based on chains of trapped circular atoms [T.L. Nguyen $\textit{et al.}$, Phys. Rev. X 8, 011032 (2018)]. Such simulators could reach regimes (thermalization, glassy dynamics) that are out of the reach of those based on ordinary, low-angular-momentum short-lived Rydberg atoms. Over the promised long time scales, the unavoidable coupling of the spin dynamics with the atomic motion in the traps may play an important role. We study here the interplay between the spin exchange and motional dynamics in the simple case of two interacting circular Rydberg atoms confined in harmonic traps. The time evolution is solved exactly when the position dependence of the dipole-dipole interaction terms can be linearized over the extension of the atomic motion. We present numerical simulations in more complex cases, using the realistic parameters of the simulator proposal. We discuss three applications. First, we show that realistic experimental parameters lead to a regime in which atomic and spin dynamics become fully entangled, generating interesting non-classical motional states. We also show that, in other parameter regions, the spin dynamics notably depends on the initial temperature of the atoms in the trap, providing a sensitive motional thermometry method. Last, and most importantly, we discuss the range of parameters in which the motion has negligible influence over the spin dynamics.Comment: 18 pages, 12 figure

Real-time quantum feedback prepares and stabilizes photon number states

Feedback loops are at the heart of most classical control procedures. A controller compares the signal measured by a sensor with the target value. It adjusts then an actuator in order to stabilize the signal towards its target. Generalizing this scheme to stabilize a micro-system's quantum state relies on quantum feedback, which must overcome a fundamental difficulty: the measurements by the sensor have a random back-action on the system. An optimal compromise employs weak measurements providing partial information with minimal perturbation. The controller should include the effect of this perturbation in the computation of the actuator's unitary operation bringing the incrementally perturbed state closer to the target. While some aspects of this scenario have been experimentally demonstrated for the control of quantum or classical micro-system variables, continuous feedback loop operations permanently stabilizing quantum systems around a target state have not yet been realized. We have implemented such a real-time stabilizing quantum feedback scheme. It prepares on demand photon number states (Fock states) of a microwave field in a superconducting cavity and subsequently reverses the effects of decoherence-induced field quantum jumps. The sensor is a beam of atoms crossing the cavity which repeatedly performs weak quantum non-demolition measurements of the photon number. The controller is implemented in a real-time computer commanding the injection, between measurements, of adjusted small classical fields in the cavity. The microwave field is a quantum oscillator usable as a quantum memory or as a quantum bus swapping information between atoms. By demonstrating that active control can generate non-classical states of this oscillator and combat their decoherence, this experiment is a significant step towards the implementation of complex quantum information operations.Comment: 12 pages, 4 figure

Towards quantum simulation with circular Rydberg atoms

The main objective of quantum simulation is an in-depth understanding of many-body physics. It is important for fundamental issues (quantum phase transitions, transport, . . . ) and for the development of innovative materials. Analytic approaches to many-body systems are limited and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1/2 arrays providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultra-cold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the individual detection of arbitrary spin observables. The proposed simulator realizes an XXZ spin-1/2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kHz. All the model parameters can be tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder or Floquet time crystals. This platform presents unrivaled features for quantum simulation

Array of Individual Circular Rydberg Atoms Trapped in Optical Tweezers

Circular Rydberg atoms (CRAs), i.e., Rydberg atoms with maximal orbital momentum, are highly promising for quantum computation, simulation and sensing. They combine long natural lifetimes with strong inter-atomic interactions and coupling to electromagnetic fields. Trapping individual CRAs is essential to harness these unique features. We report the first demonstration of CRAs laser-trapping in a programmable array of optical bottle beams. We observe the decay of a trapped Rubidium circular level over 5ms using a novel optical detection method. This first optical detection of alkali CRAs is both spatially- and level selective. We finally observe the mechanical oscillations of the CRAs in the traps. This work opens the route to the use of circular levels in quantum devices. It is also promising for quantum simulation and information processing using the full extent of Rydberg manifolds

Préparation et stabilisation d'un champ non classique en cavité par rétroaction quantique

Feedback loops are central to most classical control procedures. A controller compares the signal measured by a sensor with the target value or set-point. It then adjusts an actuator to stabilize the signal around the target value. Generalizing this scheme to the quantum world must overcome a fundamental difficulty: the sensor measurement causes a random back-action on the system. In this manuscript, we demonstrate the first continuously operated quantum feedback loop. The system to be controlled is a mode of the electromagnetic field trapped in a very high finesse microwave Fabry-Perot cavity. Circular Rydberg atoms achieve a quantum non-demolition measurement of the photon number in the mode by the succession of weak measurements. Knowing the outcome of these measurements, and knowing all the experimental imperfections of the system, a classical computer estimates in real-time the density matrix of the field. It then calculates the amplitude of small classical microwave fields injected into the cavity in order to stabilize the field around a target state. In this thesis, we have been able to prepare on demand and stabilize Fock states containing from 1 to 4 photons.L'utilisation de boucles de rétroaction est au cœur de nombreux systèmes de contrôle classiques. Un contrôleur compare le signal mesuré par une sonde à la valeur de consigne. Il dirige alors un actionneur pour stabiliser le signal autour de la valeur ciblée. Étendre ces concepts au monde quantique se heurte à une difficulté fondamentale : le processus de mesure modifie inévitablement par une action en retour le système à contrôler. Dans ce mémoire, nous présentons la première réalisation d'une boucle de rétroaction quantique utilisée en continu. Le système contrôlé est un mode du champ électromagnétique piégé dans une cavité Fabry-Pérot micro-onde de très haute finesse. Des atomes de Rydberg circulaires réalisent par une succession de mesures dites faibles une mesure quantique non-destructive du nombre de photons dans le mode. Étant donnés les résultats de ces mesures, et connaissant toutes les imperfections expérimentales du système, un ordinateur de contrôle estime en temps réel la matrice densité du champ piégé dont il déduit l'amplitude de champs micro-ondes classiques à injecter permettant de stabiliser l'état du champ autour d'un état cible. Dans ce mémoire, nous montrons comment nous avons été capables de préparer sur demande et de stabiliser les états de Fock du champ contenant de 1 à 4 photons

Simulation quantique avec des atomes froids. Comment manipuler et sonder des systèmes quantiques à l’échelle de l’atome individuel

Les systèmes physiques à grand nombre de particules, d’une importance capitale en physique, sont incroyablement complexes. Leur comportement, en effet, « ne doit pas être compris à travers une simple extrapolation des propriétés de quelques particules. Au contraire, à chaque niveau de complexité, des propriétés entièrement nouvelles émergent (…) » (P.W. Anderson [1]). L’avènement des technologies quantiques, et tout particulièrement de la simulation quantique, permet aujourd’hui d’aborder d’une façon nouvelle et prometteuse la physique de ces systèmes à N corps en interaction. Nous présentons ici l’apport des dispositifs à atomes froids, à travers deux exemples d’expériences aujourd’hui en construction au Laboratoire Kastler Brossel

Feedback stabilization of discrete-time quantum systems subject to non-demolition measurements with imperfections and delays

International audienceWe consider a controlled quantum system whose finite dimensional state is governed by a discrete-time nonlinear Markov process. In open-loop, the measurements are assumed to be quantum non-demolition (QND). The eigenstates of the measured observable are thus the open-loop stationary states: they are used to construct a closed-loop supermartingale playing the role of a strict control Lyapunov function. The parameters of this supermartingale are calculated by inverting a Metzler matrix that characterizes the impact of the control input on the Kraus operators defining the Markov process. The resulting state feedback scheme, taking into account a known constant delay, provides the almost sure convergence of the controlled system to the target state. This convergence is ensured even in the case where the filter equation results from imperfect measurements corrupted by random errors with conditional probabilities given as a left stochastic matrix. Closed-loop simulations corroborated by experimental data illustrate the interest of such nonlinear feedback scheme for the photon box, a cavity quantum electrodynamics system

Progressive field-state collapse and quantum non-demolition photon counting

The irreversible evolution of a microscopic system under measurement is a central feature of quantum theory. From an initial state generally exhibiting quantum uncertainty in the measured observable, the system is projected into a state in which this observable becomes precisely known. Its value is random, with a probability determined by the initial system's state. The evolution induced by measurement (known as 'state collapse') can be progressive, accumulating the effects of elementary state changes. Here we report the observation of such a step-by-step collapse by non-destructively measuring the photon number of a field stored in a cavity. Atoms behaving as microscopic clocks cross the cavity successively. By measuring the light-induced alterations of the clock rate, information is progressively extracted, until the initially uncertain photon number converges to an integer. The suppression of the photon number spread is demonstrated by correlations between repeated measurements. The procedure illustrates all the postulates of quantum measurement (state collapse, statistical results and repeatability) and should facilitate studies of non-classical fields trapped in cavities