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Prethermalization after a sudden quench in a weakly interacting Bose system

Giuseppe Menegoz

Published Oct 30, 2014• 0 citations
OpenAlex

Abstract

We calculate the dynamics of local and non-local correlation functions of one and threedimensional weakly interacting Bose gas after an interaction quench. Within the Bogoliubov approximation we discuss the resulting quasi-steady prethermal state and relaxation to it. We discuss the deacay rates of Bogoliubov quasi-particles characterizing the expected departure from the prethermal state towards a fully thermalized one. We conclude that prethermalization in this situation manifest as a crossover.

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We calculate the dynamics of local and non-local correlation functions of one and threedimensional weakly interacting Bose gas after an interaction quench. Within the Bogoliubov approximation we discuss the resulting quasi-steady prethermal state and relaxation to it. We discuss the deacay rates of Bogoliubov quasi-particles characterizing the expected departure from the prethermal state towards a fully thermalized one. We conclude that prethermalization in this situation manifest as a crossover.
The dynamics of a weakly interacting Bose gas at low temperatures is close to integrable due to the approximate quadratic nature of the many-body Hamiltonian. While the short-time physics after an abrupt ramp of the interaction constant is dominated by integrable dynamics, integrability is broken at longer times by higher-order interaction terms in the Bogoliubov Hamiltonian, in particular, by Beliaev-Landau scatterings involving three quasiparticles. The two-stage relaxation process is highlighted in the evolution of local observables such as the density-density correlation function: an integrable dephasing mechanism leads the system to a prethermal stage, followed by true thermalization conveyed by quasiparticle collisions. Our results bring the crossover from prethermalization to thermalization within reach of current experiments with ultracold atomic gases.
Understanding nonequilibrium dynamics of strongly interacting quantum systems represents one of the most challenging problems in many-body physics. Here, quantum thermalization dynamics are explored in real-time in an ultracold Fermi gas suddenly quenched to the BEC-BCS crossover. When quenched to unitarity, it is observed that the cloud size remains unchanged in the early evolution while the momentum distribution emerges two prethermal states with a lifetime difference of two orders of magnitude in the early and intermediate stage before very slowly evolving to the final stationary state. It is revealed that a crossover momentum, at which the momentum distribution remains nearly unchanged, is determined by the thermal wavelength at high temperatures and the Fermi momentum while at low temperatures. It is identified that the universal prethermal dynamics scaling where momentum distributions with different temperatures collapse onto one curve. When quenched to the BEC side, the thermalization rapidly relaxes into a prethermal state and exhibits the low energy oscillation related to the molecular bound states. This work provides benchmarks for the study of quantum thermalization in strongly interacting fermionic many-body systems.
Abstract. 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.
We explore the dynamics of a resonant Bose gas following its quench to a strongly interacting regime near a Feshbach resonance. For such deep quenches, we utilize a self-consistent dynamic field approximation and find that after an initial regime of many-body Rabi-type oscillations between the condensate and finite-momentum quasiparticle pairs, at long times, the gas reaches a prethermalized nonequilibrium steady state. We explore the resulting state through its broad stationary momentum distribution function, that exhibits a power-law high-momentum tail. We study the dynamics and steady-state form of the associated enhanced depletion, quench-rate-dependent excitation energy, Tan's contact, structure function, and radio-frequency spectroscopy. We find these predictions to be in a qualitative agreement with recent experiments.
We calculate the dynamics of one- and two-body correlation functions in a homogeneous Bose gas at zero temperature following a sudden change in the interaction strength, in the continuum and in a lattice. By choosing suitable examples, we highlight features in the correlation functions that emerge due to the interactions and the band structure. We find that interactions dramatically change the way correlations build up and subsequently decay following a quench. For example, the Bogoliubov dispersion induces a crossover from diffusive spreading of short-range correlations to ballistic spreading of longer-range correlations. In the lattice, the correlation functions develop additional features absent in the continuum. Most strikingly, the lattice induces an additional velocity scale and some features propagate with that velocity. Finally, we discuss the ultra-short-range properties of the density-density correlation function following a quench, and the implications for experiments using this quantity to probe the ``contact.'' Our calculations, which can be readily tested in current experiments, suggest that the dynamics of correlations may be a useful tool for extracting many-body parameters.