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arXiv:2405.14928 · New Journal of Physics

Unbounded entropy production and violent fragmentation for repulsive-to-attractive interaction quench in long-range interacting systems

Paolo Molignini, Barnali Chakrabarti

Published Sep 27, 2024• 9 citations
arXivHTMLPDF

Abstract

Abstract We study the non-equilibrium dynamics of a one-dimensional Bose gas with long-range interactions that decay as ( 1 r α ) ( 0.5 < α < 4.0 ). We investigate exotic dynamics when the interactions are suddenly switched from strongly repulsive to strongly attractive, a procedure known to generate super-Tonks-Girardeau gases in systems with contact interactions. We find that relaxation is achieved through a complex intermediate dynamics demonstrated by violent fragmentation and chaotic delocalization. We establish that the relaxed state exhibits classical gaseous characteristics and an asymptotic state associated with unbounded entropy production. The phase diagram shows an exponential boundary between the coherent (quantum) gas and the chaotic (classical) gas. We show the universality of the dynamics by also presenting analogous results for spinless fermions. Weaker quench protocols give a certain degree of control over the relaxation process and induce a slower initial entropy growth. Our study showcases the complex relaxation behavior of tunable long-range interacting systems that could be engineered in state-of-the-art experiments, e.g. in trapped ions or Rydberg atoms.

DOI
10.1088/1367-2630/ad80b8

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Abstract We study the non-equilibrium dynamics of a one-dimensional Bose gas with long-range interactions that decay as ( 1 r α ) ( 0.5 < α < 4.0 ). We investigate exotic dynamics when the interactions are suddenly switched from strongly repulsive to strongly attractive, a procedure known to generate super-Tonks-Girardeau gases in systems with contact interactions. We find that relaxation is achieved through a complex intermediate dynamics demonstrated by violent fragmentation and chaotic delocalization. We establish that the relaxed state exhibits classical gaseous characteristics and an asymptotic state associated with unbounded entropy production. The phase diagram shows an exponential boundary between the coherent (quantum) gas and the chaotic (classical) gas. We show the universality of the dynamics by also presenting analogous results for spinless fermions. Weaker quench protocols give a certain degree of control over the relaxation process and induce a slower initial entropy growth. Our study showcases the complex relaxation behavior of tunable long-range interacting systems that could be engineered in state-of-the-art experiments, e.g. in trapped ions or Rydberg atoms.
We analyze the dynamics of one-dimensional quantum gases with strongly attractive contact interactions. We specify a class of initial states for which attractive forces effectively act as strongly repulsive ones during the time evolution. Our findings extend the theoretical results on the super-Tonks-Girardeau gas to a highly nonequilibrium dynamics. The mechanism is illustrated on the prototypical problem of the domain stability in a two-component Fermi gas. We also discuss finite-range interactions and analyze the universality of the presented results. Moreover, we use our conclusions to argue for the existence of metastable quantum droplets in the regime of strongly attractive contact and attractive dipolar interactions.
We study the out-of-equilibrium dynamics of dipolar bosons and fermions after a sudden change in the interaction strength from zero to a finite repulsive value. We simulate the interaction quench on the initial state which is the ground state of harmonic potential with noninteracting bosons and fermions. We solve the time-dependent many-boson Schrödinger equation exactly using numerical methods. To understand the many-body dynamics we analyze several measures of many-body information entropy, monitoring their time evolution and assessing their dependence on interaction strength. We establish that for weak interaction quench the dynamics is statistics independent, both dipolar bosons and fermions do not relax, whereas it is significantly different for dipolar bosons from that of dipolar fermions in the stronger interaction quench. While dipolar bosons exhibit concurrent signature of relaxation in all entropy measures, dipolar fermions fail to relax, exhibiting modulated oscillation in all entropy dynamics. For dipolar bosons and larger interaction quench, the many-body information entropy measures dynamically approach the value predicted for the Gaussian orthogonal ensemble of random matrices, implying statistical relaxation and ergodicity. The entire relaxation process and signature of ergodicity are established by three unique features: dynamical delocalization in Hilbert space, violent orbital fragmentation, and saturation of all entropy measures to the maximum entropy states in the long-time dynamics. It highlights the importance of many-body effects with a possible exploration in quantum simulation with ultracold atoms.
A Tonks-Girardeau (TG) gas is a highly correlated quantum state of strongly interacting bosons confined to one dimension, where repulsive interactions make the particles behave like impenetrable fermions. By suddenly tuning these interactions to the attractive regime, it is possible to realize a super-Tonks-Girardeau (sTG) gas—a highly excited, metastable state of strongly attractive bosons with unique stability properties. Inspired by the sTG quench scenario, we investigate a similar setup but with the inclusion of long-range dipolar interactions, which modify the system away from the TG Mott insulating limit. We simulate an interaction quench on dipolar bosons initially prepared in various states and fillings, using real-space densities, orbital occupations, Glauber correlation functions, and autocorrelation functions to probe postquench stability. Our results reveal that stability is maintained only at very weak dipolar interaction strengths when starting from a unit-filled TG Mott state. In contrast, all cluster states—whether unit-filled or doubly-filled—eventually collapse under attractive interactions. This collapse is not always visible in the density profile but becomes apparent in the autocorrelation function, indicating complex many-body restructuring of the quantum state. Our findings underscore the potential of dipolar interactions to drive novel quantum dynamics and highlight the delicate balance required to stabilize excited states in long-range interacting systems.
We consider a 1D Bose gas with attractive interactions in a highly excited state containing no bound states. We show that in this so-called super Tonks-Girardeau gas, relaxation processes are suppressed, making the system metastable over long time scales. We compute dynamical correlation functions, revealing the structure of excitations, an enhancement of umklapp correlations and new branches due to intermediate bound states. These features give a clear signature of the super Tonks-Girardeau regime and can be used to experimentally identify it. We demonstrate that, despite its off-equilibrium nature, the system displays critical behavior: correlation functions are characterized by asymptotic power-law decay described by the Luttinger liquid framework.
We study the complex quantum dynamics of a system of many interacting atoms in an elongated anharmonic trap. The system is initially in a Bose–Einstein condensed state, well described by Thomas–Fermi profile in the elongated direction and the ground state in the transverse directions. After a sudden quench to a coherent superposition of the ground and lowest energy transverse modes, quantum dynamics starts. We describe this process employing a three-mode many-body model. The experimental realization of this system displays decaying oscillations of the atomic density distribution. While a mean-field description predicts perpetual oscillations of the atomic density distribution, our quantum many-body model exhibits a decay of the oscillations for sufficiently strong atomic interactions. We associate this decay with the fragmentation of the condensate during the evolution. The decay and fragmentation are also linked with the approach of the many-body model to the chaotic regime. The approach to chaos lifts degeneracies and increases the complexity of the eigenstates, enabling the relaxation to equilibrium and the onset of thermalization. We verify that the damping time and quantum signatures of chaos show similar dependences on the interaction strength and on the number of atoms.
We obtain an exact expression for the time evolution of the interacting Bose gas following a quench from a generic initial state using the Yudson representation for integrable systems. We study the time evolution of the density and noise correlation for a small number of bosons and their asymptotic behavior for any number. We show that for any value of the coupling, as long as it is repulsive, the system asymptotes towards a strongly repulsive gas, while for any value of an attractive coupling the long time behavior is dominated by the maximal bound state. This occurs independently of the initial state and can be viewed as an emerging "dynamic universality."