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arXiv:2205.02166 · Physical review. B./Physical review. B

Fate of the quasicondensed state for bias-driven hard-core bosons in one dimension

Tharnier O. Puel, Stefano Chesi, Stefan Kirchner, Pedro Ribeiro

Published Mar 9, 2023• 1 citation
arXivHTMLPDF

Abstract

Bosons in one dimension display a phenomenon called quasicondensation where correlations decay in a power-law fashion. We study the fate of this quasicondensed state in an open-system setup where two macroscopic leads, held at different chemical potentials, drive the system far away from equilibrium. For generic leads, we find that a finite bias destroys the quasicondensed state and the system exhibits exponential-decay correlations and subleading power-law corrections that are bias dependent. Near the equilibrium, we found a diverging correlation length and determine the critical properties, including the critical scaling form of the correlations. Also, we contrast our findings against the fate of quasicondensation in thermal equilibrium and discuss the special case of reflectionless coupling where the quasicondensation survives out of equilibrium. This exactly solvable interacting nonequilibrium system has the remarkable property that the near-equilibrium state cannot be obtained within linear response. These results aid in unraveling the enigmatic properties spawned by strong interactions once liberated from equilibrium constraints.

DOI
10.1103/physrevb.107.125122

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Bosons in one dimension display a phenomenon called quasicondensation where correlations decay in a power-law fashion. We study the fate of this quasicondensed state in an open-system setup where two macroscopic leads, held at different chemical potentials, drive the system far away from equilibrium. For generic leads, we find that a finite bias destroys the quasicondensed state and the system exhibits exponential-decay correlations and subleading power-law corrections that are bias dependent. Near the equilibrium, we found a diverging correlation length and determine the critical properties, including the critical scaling form of the correlations. Also, we contrast our findings against the fate of quasicondensation in thermal equilibrium and discuss the special case of reflectionless coupling where the quasicondensation survives out of equilibrium. This exactly solvable interacting nonequilibrium system has the remarkable property that the near-equilibrium state cannot be obtained within linear response. These results aid in unraveling the enigmatic properties spawned by strong interactions once liberated from equilibrium constraints.
Abstract Quasicondensation in one dimension is known to occur for equilibrium systems of hard-core bosons (HCBs) at zero temperature. This phenomenon arises due to the off-diagonal long-range order in the ground state, characterized by a power-law decay of the one-particle density matrix g 1 ( x , y ) ∼ | x − y | − 1 / 2 —a well-known outcome of Luttinger liquid theory. Remarkably, HCBs, when allowed to freely expand from an initial product state (i.e. characterized by initial zero correlation), exhibit quasicondensation and demonstrate the emergence of off-diagonal long-range order during nonequilibrium dynamics. This phenomenon has been substantiated by numerical and experimental investigations in the early 2000s. In this work, we revisit the dynamical quasicondensation of HCBs, providing a fully analytical treatment of the issue. In particular, we derive an exact asymptotic formula for the equal-time one-particle density matrix by borrowing ideas from the framework of quantum Generalized Hydrodynamics. Our findings elucidate the phenomenology of quasicondensation and of dynamical fermionization occurring at different stages of the time evolution, as well as the crossover between the two.
Long-range order in quantum many-body systems is usually associated with equilibrium situations. Here, we experimentally investigate the quasicondensation of strongly interacting bosons at finite momenta in a far-from-equilibrium case. We prepare an inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant d. After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice. Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta ±(π/2)(ℏ/d) in the momentum distribution function.
The singularities of the dynamical response function are one of the most remarkable effects in many-body interacting systems. However in one dimension these divergences only exist strictly at zero temperature, making their observation very difficult in most cold atomic experimental settings. Moreover the presence of a finite temperature destroys another feature of one-dimensional quantum liquids: the real space quasilong-range order in which the spatial correlation functions exhibit power-law decay. We consider a nonequilibrium protocol where two interacting Bose gases are prepared either at different temperatures or chemical potentials and then joined. We show that the nonequilibrium steady state emerging at large times around the junction displays edge singularities in the response function and quasilong-range order.
We unveil a mechanism for quasicondensation of hard-core bosons in the presence of quasiperiodicity-induced multifractal single-particle states. The observed phase, here dubbed a fractal quasicondensate, is characterized by natural orbitals with multifractal properties and by an occupancy of the lowest natural orbital, ${\ensuremath{\lambda}}_{0}\ensuremath{\simeq}{L}^{\ensuremath{\gamma}}$, which grows with system size but with a nonuniversal scaling exponent, $\ensuremath{\gamma}<1/2$. In contrast to fractal quasicondensates obtained when the chemical potential lies in a region of multifractal single-particle states, placing the chemical potential in regions of localized or delocalized states yields, respectively, no condensation or the usual 1D quasicondensation with $\ensuremath{\gamma}=1/2$. Our findings are established by studying one-dimensional hard-core bosons subjected to various quasiperiodic potentials, including the well-known Aubry-Andr\'e model, employing a mapping to noninteracting fermions that allows for numerically exact results. We discuss how to test our findings in state-of-the-art ultracold atom experiments.
We study the nonequilibrium dynamics of two tunnel-coupled one-dimensional quasicondensates following a quench of the coupling strength from zero to a fixed finite value. More specifically, starting from two independent quasicondensates in thermal equilibrium, with initial temperature and chemical potential imbalance, we suddenly switch on the tunnel-coupling and analyze the postquench equilibration in terms of particle number and energy imbalances. We find that, in certain parameter regimes, the net energy can flow from the colder quasicondensate to the hotter one and is governed by the surplus of low-energy particles flowing from the cold to the hot system relative to the high-energy particles flowing in the reverse direction. In all cases, the approach to the new thermal equilibrium occurs through transient, damped oscillations. We also find that, for a balanced initial state, the coupled quasicondensates can relax into a final thermal equilibrium state in which they display a thermal phase coherence length that is larger than their initial phase coherence length, even though the new equilibrium temperature is higher. The increase in the phase coherence length occurs due to phase locking which manifests itself via an increased degree of correlation between the local relative phases of the quasicondensates at two arbitrary points.