Universal dynamics of a soliton after an interaction quench

Abstract

We propose a new type of experimentally feasible quantum quench protocol in which a quantum system is prepared in a coherent, localized excited state of a Hamiltonian. During the evolution of this solitonic excitation, the microscopic interaction is suddenly changed. We study the dynamics of solitons after this interaction quench for a wide class of systems using a hydrodynamic approach. We find that the post-quench dynamics is universal at short times, i.e. it does not depend on the microscopic details of the physical system. Numerical support for these results is presented using generalized non-linear Schrödinger equation, relevant for the implementation of the proposed protocol with ultracold bosons, as well as for the integrable Calogero model in harmonic potential. Finally, it is shown that the effects of integrability breaking by a parabolic potential and by a power-law non-linearity do not change the universality of the short-time dynamics.PACS numbers: 03.75. Kk, 03.75.Lm, 05.45.Yv, 05.70.Ln, 02.30.Ik Recent years have witnessed a rising interest in nonequilibrium dynamics, which has been largely motivated by extraordinary progresses in the manipulation of manybody quantum systems [1][2][3][4][5][6][7][8][9][10][11][12]. This interplay between experimental and theoretical research is allowing the investigation of longstanding questions, such as under which conditions systems driven out of equilibrium can show universal behaviors and whether and how a system reaches equilibrium and possibly thermalizes [13][14][15][16][17][18][19][20][21][22][23], in particular in cold atom systems [24][25][26][27][28].A particularly interesting protocol used to identify paradigms of out-of-equilibrium dynamics is provided by the quantum quenches, in which, typically, a system described by a Hamiltonian H is prepared in its ground state and then, at a given moment of time, let evolved using a different Hamiltonian H [29]. Although a unitary evolution cannot relax the system to a true equilibrium, mounting evidences support a picture for which, in most cases, the expectation value of most local operators tending to a stationary value in the long time limit can be calculated through an effective density matrix describing the system [15][16][17][30][31][32][33][34][35][36]: that is, an arbitrary out-ofequilibrium many-body state in general evolves toward a state that effectively cannot be distinguished from a mixed state.In this work, inspired by these progresses and motivated by experimental considerations, we propose a new protocol based on a quench of the interaction on an inhomogeneous initial state localized in space: this protocol has the merit of showing universal dynamics already at short times after the quench, while to date most of the studies on universal effects in quantum quenches focus on long times. We focus in particular on one-dimensional (1d) systems, where localized solitonic states are present and stable in a variety of models, even though we expect that our results are valid in any dimension provided ...

Hydrodynamics of local excitations after an interaction quench in 1Dcold atomic gases

“…. As discussed in [35] a good agreement is found between the hydrodynamic results and the GP equation with a power-law r ( )  . We observe that such mean-field equations may fail in correctly describing interference between wavepackets, as shown for the Tonks-Girardeau limit g  ¥ in [73]: in general one expects anyway that the mean-field equations work better at short times with respect to long times.…”

“…One question at the forefront has been under which conditions (and in which sense) a system is able to reach an equilibrium, and whether this equilibrium can show universal characteristics such as thermalization [19][20][21][22][23][24][25][26][27][28][29]. Particularly useful in addressing such questions are setups based on cold atoms [30][31][32][33][34][35][36].…”

“…Variations to the usual quench protocol have been considered typically in two forms: the initial state was taken to be an excited state of the initial Hamiltonian [43], or the interaction was changed only locally [44][45][46][47][48]. In a recent work [35], we introduced a different protocol: we proposed to start with a local excitation and to let it evolve after a global interaction quench. In order to isolate the effect of the quench on the dynamics, the initial state is prepared as a solitonic excitation of the original Hamiltonian, that is, a state for which the one-particle density profile evolves without (almost) changing its shape.…”

“…We would like to stress that the proposed quench protocol could be implemented relatively easily in cold atoms experiments and that, by focusing on the short time universal dynamics, our predictions can be tested directly in the laboratory, which should be contrasted with typical large time results produced by other approaches and protocols. Universal properties of short time out-of-equilibrium dynamics has been considered in [35,[58][59][60].…”

Soliton splitting in quenched classical integrable systems

“…Recently, the problem of quenching the soliton profile in 1D BEC at finite density has been investigated in Refs. [58,59]. In Ref.…”