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arXiv:2106.08092 · SciPost Physics

The one-dimensional Bose gas with strong two-body losses: the effect of the harmonic confinement

Lorenzo Rosso, Alberto Biella, Leonardo Mazza

Published Jan 28, 2022• 32 citations
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Abstract

We study the dynamics of a one-dimensional Bose gas in presence of strong two-body losses. In this dissipative quantum Zeno regime, the gas fermionises and its dynamics can be described with a simple set of rate equations. Employing the local density approximation and a Boltzmann-like dynamical equation, the description is extended to take into account an external potential. We show that in the absence of confinement the population is depleted in an anomalous way and that the gas behaves as a low-temperature classical gas. The harmonic confinement accelerates the depopulation of the gas and introduces a novel decay regime, which we thoroughly characterise.

DOI
10.21468/scipostphys.12.1.044

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We study the dynamics of a one-dimensional Bose gas in presence of strong two-body losses. In this dissipative quantum Zeno regime, the gas fermionises and its dynamics can be described with a simple set of rate equations. Employing the local density approximation and a Boltzmann-like dynamical equation, the description is extended to take into account an external potential. We show that in the absence of confinement the population is depleted in an anomalous way and that the gas behaves as a low-temperature classical gas. The harmonic confinement accelerates the depopulation of the gas and introduces a novel decay regime, which we thoroughly characterise.
We report the demonstration of cooling by three-body losses in a Bose gas. We use a harmonically confined one-dimensional (1D) Bose gas in the quasicondensate regime and, as the atom number decreases under the effect of three-body losses, the temperature T drops up to a factor of 4. The ratio k_{B}T/(mc^{2}) stays close to 0.64, where m is the atomic mass and c the speed of sound in the trap center. The dimensionless 1D interaction parameter γ, evaluated at the trap center, spans more than 2 orders of magnitudes over the different sets of data. We present a theoretical analysis for a homogeneous 1D gas in the quasicondensate regime, which predicts that the ratio k_{B}T/(mc^{2}) converges towards 0.6 under the effect of three-body losses. More sophisticated theoretical predictions that take into account the longitudinal harmonic confinement and transverse effects are in agreement within 30% with experimental data.
We consider strong two-body losses in bosonic gases trapped in one-dimensional optical lattices. We exploit the separation of timescales typical of a system in the many-body quantum Zeno regime to establish a connection with the theory of the time-dependent generalized Gibbs ensemble. Our main result is a simple set of rate equations that capture the simultaneous action of coherent evolution and two-body losses. This treatment gives an accurate description of the dynamics of a gas prepared in a Mott insulating state and shows that its long-time behavior deviates significantly from mean-field analyses. The possibility of observing our predictions in an experiment with 174Yb^{174}\mathrm{Yb}174Yb in a metastable state is also discussed.
We show that two-body losses induce a collective excitation in a harmonically trapped one-dimensional Bose gas, even in the absence of a quench in the trap or any other external perturbation. Focusing on the dissipatively fermionized regime, we perform an exact mode expansion of the rapidity distribution function and characterize the emergence of the collective motion. We find clear coherent oscillations in the widths of the gas both in position and rapidity space as well as in the phase-space quadrupole mode of the gas. We compare this motion to that of the well-known breathing mode in the absence of losses and find that they differ in the motion of the density profile. We also discuss the role of losses in the collective motion of the gas following various other protocols, such as the removal of losses after a finite hold time, and when the harmonic trap is also quenched.
We analyze the ground-state and low-temperature properties of a one-dimensional Bose gas in a harmonic trapping potential using the numerical density-matrix renormalization group. Calculations cover the whole range from the Bogoliubov limit of weak interactions to the Tonks-Girardeau limit. Local quantities such as density and local three-body correlations are calculated and shown to agree very well with analytic predictions within a local-density approximation. The transition between temperature-dominated to quantum-dominated correlation is determined. It is shown that despite the presence of the harmonic trapping potential, first-order correlations display, over a large range, the algebraic decay of a harmonic fluid with a Luttinger parameter determined by the density at the trap center.
A Bose gas in a double well is investigated in the presence of single-particle, two-body, and three-body asymmetric loss. The loss induces an interesting decay behavior of the total population as well as a possibility to control the dynamics of the system. In the noninteracting limit with asymmetric single-body dissipation, the dynamics of the populations can be obtained analytically. The general many-body problem requires, however, an adequate approximation. We use a mean-field approximation and the Bogoliubov back reaction beyond mean-field truncation, which we extend up to three-body loss. Both methods are compared with exact many-body Monte Carlo simulations.
Following the idea of the density-functional approach, we develop a generalized Bogoliubov theory of an interacting Bose gas confined in a one-dimensional harmonic trap by using a local chemical potential, calculated with the Lieb-Liniger exact solution, as the exchange energy. At zero temperature, we use the theory to describe collective modes of a finite-particle system in all interaction regimes from the ideal gas limit to the mean-field Thomas-Fermi regime and to the strongly interacting Tonks-Girardeau regime. At finite temperature, we investigate the temperature dependence of collective modes in the weak-coupling regime by means of a Hartree-Fock-Bogoliubov theory with Popov approximation. By emphasizing the effects of finite particle number and nonzero temperature on collective-mode frequencies, we compare our results with a recent experimental measurement [E. Haller et al., Science 325, 1224 (2009)] and some previous theoretical predictions. We show that the experimental data are still not fully explained within current theoretical framework.