Remi Geiger

Experimental Observation of a Generalized Gibbs Ensemble

Detecting multiple temperatures Most people have an intuitive understanding of temperature. In the context of statistical mechanics, the higher the temperature, the more a system is removed from its lowest energy state. Things become more complicated in a nonequilibrium system governed by quantum mechanics and constrained by several conserved quantities. Langen et al. showed that as many as 10 temperature-like parameters are necessary to describe the steady state of a one-dimensional gas of Rb atoms that was split into two in a particular way (see the Perspective by Spielman). Science, this issue p. 207; see also p. 185 Interferometry suggests that as many as 10 parameters are needed to describe the steady state of an integrable system. [Also see Perspective by Spielman] The description of the non-equilibrium dynamics of isolated quantum many-body systems within the framework of statistical mechanics is a fundamental open question. Conventional thermodynamical ensembles fail to describe the large class of systems that exhibit nontrivial conserved quantities, and generalized ensembles have been predicted to maximize entropy in these systems. We show experimentally that a degenerate one-dimensional Bose gas relaxes to a state that can be described by such a generalized ensemble. This is verified through a detailed study of correlation functions up to 10th order. The applicability of the generalized ensemble description for isolated quantum many-body systems points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution.

Local emergence of thermal correlations in an isolated quantum many-body system

The relaxation mechanisms of isolated quantum many-body systems are insufficiently understood, but a one-dimensional quantum gas experiment uncovers the local emergence of thermal correlations and their cone-like propagation through the system.

Ultracold Atoms Out of Equilibrium

The relaxation of isolated quantum many-body systems is a major unsolved problem connecting statistical and quantum physics. Studying such relaxation processes remains a challenge despite considerable efforts. Experimentally, it requires the creation and manipulation of well-controlled and truly isolated quantum systems. In this context, ultracold neutral atoms provide unique opportunities to understand nonequilibrium phenomena because of the large set of available methods to isolate, manipulate, and probe these systems. Here, we give an overview of the rapid experimental progress that has been made in the field over the past few years and highlight some of the questions that may be explored in the future.

Prethermalization revealed by the relaxation dynamics of full distribution functions

We detail the experimental observation of the non-equilibrium many-body phenomenon prethermalization. We study the dynamics of a rapidly and coherently split one-dimensional Bose gas. An analysis based on the use of full quantum mechanical probability distributions of matter wave interference contrast reveals that the system evolves towards a quasi-steady state. This state, which can be characterized by an effective temperature, is not the final thermal equilibrium state. We compare the evolution of the system to an integrable Tomonaga-Luttinger liquid model and show that the system dephases to a prethermalized state rather than undergoing thermalization towards a final thermal equilibrium state.

Multimode Dynamics and Emergence of a Characteristic Length Scale in a One-Dimensional Quantum System

We study the nonequilibrium dynamics of a coherently split one-dimensional Bose gas by measuring the full probability distribution functions of matter-wave interference. Observing the system on different length scales allows us to probe the dynamics of excitations on different energy scales, revealing two distinct length-scale-dependent regimes of relaxation. We measure the crossover length scale separating these two regimes and identify it with the prethermalized phase-correlation length of the system. Our approach enables a direct observation of the multimode dynamics characterizing one-dimensional quantum systems.

How to estimate the differential acceleration in a two-species atom interferometer to test the equivalence principle

We propose a scheme for testing the weak equivalence principle (universality of free-fall (UFF)) using an atom-interferometric measurement of the local differential acceleration between two atomic species with a large mass ratio as test masses. An apparatus in free fall can be used to track atomic free-fall trajectories over large distances. We show how the differential acceleration can be extracted from the interferometric signal using Bayesian statistical estimation, even in the case of a large mass and laser wavelength difference. We show that this statistical estimation method does not suffer from acceleration noise of the platform and does not require repeatable experimental conditions. We specialize our discussion to a dual potassium/rubidium interferometer and extend our protocol with other atomic mixtures. Finally, we discuss the performance of the UFF test developed for the free-fall (zero-gravity) airplane in the ICE project (http://www.ice-space.fr).

Local relaxation and light-cone-like propagation of correlations in a trapped one-dimensional Bose gas

We describe the relaxation dynamics of a coherently split one-dimensional (1D) Bose gas in the harmonic approximation. A dephased, prethermalized state emerges in a light-cone-like evolution which is connected to the spreading of correlations with a characteristic velocity. In our description we put special emphasis on the influence of the longitudinal trapping potential and the finite size of the system, both of which are highly relevant in experiments. In particular, we quantify their influence on the phase correlation properties and the characteristic velocity with which the prethermalized state is established. Finally, we show that the trapping potential has an important effect on the recurrences of coherence which are expected to appear in a finite size system.

Prethermalization in one-dimensional Bose gases: Description by a stochastic Ornstein-Uhlenbeck process

We experimentally study the relaxation dynamics of a coherently split one-dimensional Bose gas using matterwave interference. Measuring the full probability distributions of interference contrast reveals the prethermalization of the system to a non-thermal steady state. To describe the evolution of noise and correlations we develop a semiclassical effective description that allows us to model the dynamics as a stochastic Ornstein-Uhlenbeck process.

Cooling of a One-Dimensional Bose Gas.

We experimentally study the dynamics of a degenerate one-dimensional Bose gas that is subject to a continuous outcoupling of atoms. Although standard evaporative cooling is rendered ineffective by the absence of thermalizing collisions in this system, we observe substantial cooling. This cooling proceeds through homogeneous particle dissipation and many-body dephasing, enabling the preparation of otherwise unexpectedly low temperatures. Our observations establish a scaling relation between temperature and particle number, and provide insights into equilibration in the quantum world.

Improving the phase response of an atom interferometer by means of temporal pulse shaping

We study theoretically and experimentally the influence of temporally shaping the light pulses in an atom interferometer, with a focus on the phase response of the interferometer. We show that smooth light pulse shapes allow rejecting high frequency phase fluctuations (above the Rabi frequency) and thus relax the requirements on the phase noise or frequency noise of the interrogation lasers driving the interferometer. The light pulse shape is also shown to modify the scale factor of the interferometer, which has to be taken into account in the evaluation of its accuracy budget. We discuss the trade-offs to operate when choosing a particular pulse shape, by taking into account phase noise rejection, velocity selectivity, and applicability to large momentum transfer atom interferometry.