Spectroscopy of Collective Excitations in Interacting Low-Dimensional Many-Body Systems Using Quench Dynamics

Abstract

We study the problem of rapid change of the interaction parameter (quench) in a many-body lowdimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.

Normal and anomalous solitons in the theory of dynamical Cooper pairing

“…(13). At t → ±∞ the system tends to an eigenstate of the BCS Hamiltonian (3) with order parameter ∆ a .…”

“…Examples include non-stationary Kondo and other impurity models [1][2][3][4][5][6][7][8][9], quenched Luttinger liquids [10][11][12][13], electron spin dynamics induced by hyperfine interactions [14][15][16][17][18][19][20][21][22] etc. On the theory side, there is a considerable effort to develop new approaches to nonequilibrium many-body physics.…”

Quench of a symmetry-broken ground state

“…The system, initially, prepared in an equilibrium state, undergoes to an abrupt change of the Hamiltonian parameters. As a consequence, the system, in general, will be no more at the equilibrium and hence it will start to evolve under the action of the new Hamiltonian [13][14][15][16][17][18]. For several models and initial conditions, under the effect of a quench, all the local physical quantities equilibrate exponentially in time and, at the end, the time evolution would produce a steady state that looks locally thermal [19].…”

Quench echo and work statistics in integrable quantum field theories

“…On the other hand, it can be considered as the first step for the application to a quench in the sine-Gordon model, which can be obtained by analytical continuation of the interaction coupling parameter of the shG model from real to imaginary values. A quantum quench in the sine-Gordon model can actually be experimentally implemented, for example in systems of split 1d Bose-Einstein quasi-condensates that interact through a longitudinal potential barrier that behaves like a Josephson junction [113,114].…”