Dissipative Bose–Einstein condensation in contact with a thermal reservoir

Abstract

We investigate the real-time dynamics of open quantum spin-1/2 or hardcore boson systems on a spatial lattice, which are governed by a Markovian quantum master equation. We derive general conditions under which the hierarchy of correlation functions closes such that their time evolution can be computed semi-analytically. Expanding our previous work (2016 Phys. Rev. A 93 021602) we demonstrate the universality of a purely dissipative quantum Markov process that drives the system of spin-1/2 particles into a totally symmetric superposition state, corresponding to a Bose-Einstein condensate of hardcore bosons. In particular, we show that the finite-size scaling behavior of the dissipative gap is independent of the chosen boundary conditions and the underlying lattice structure. In addition, we consider the effect of a uniform magnetic field as well as a coupling to a thermal bath to investigate the susceptibility of the engineered dissipative process to unitary and nonunitary perturbations. We establish the nonequilibrium steady-state phase diagram as a function of temperature and dissipative coupling strength. For a small number of particles N, we identify a parameter region in which the engineered symmetrizing dissipative process performs robustly, while in the thermodynamic limit  ¥ N , the coupling to the thermal bath destroys any long-range order.

Integrability of one-dimensional Lindbladians from operator-space fragmentation

“…This allows one to obtain exact results on the dynamics of correlation functions [18][19][20][21][22][23] as well as entanglement-related quantities [24,25]. Furthermore, it has also been realized that in some models, not necessarily integrable, local correlation functions satisfy closed hierarchies of equations of motion, provided that the Lindbladian satisfies certain conditions [26][27][28][29][30][31][32] (although in these cases the full spectrum typically remains out of reach). Very recently, further progress has been made in this direction, with the discovery of Lindbladians that can be mapped onto known Yang-Baxter interacting integrable models [33][34][35][36][37][38][39][40][41][42].…”

Vortex formation and dynamics in two-dimensional driven-dissipative condensates

“…We emphasize, however, that the low-lying Fourier modes have a sizable amplitude at late times which again indicates that no global phase coherence is established. We note that this is in contract to dissipative Bose-Einstein condensation of hardcore bosons for which all low-lying Fourier modes decay at late times [24,25]. In fact, the asymptotic value G ∞ 0 strongly depends on the lattice size N as shown in Fig.…”

“…For instance, the hierarchy of time evolution equations of correlation functions closes for a purely dissipative process that drives a system of hardcore bosons into a Bose-Einstein condensate. In this specific case, it was shown that the dissipative gap that determines the long-time behavior of the quantum manybody system shows an intriguing finite-size scaling as a function of dimensionality which results in a increase of efficiency in higher dimensions [24,25]. It is, however, unclear whether this strong dependence of the time scales on dimensionality is a generic feature of tailored dissipative processes or rather a special property of the considered state preparation protocol.…”

Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation

“…A characteristic feature of these models is the fundamental boson or fermion operators in these models fulfil linear equations of motion and concomitantly so do the Green's functions of interest. Another step towards obtaining exact solutions of many particle Lindblad equations was the discovery that there exist classes of models in which some or all local correlation functions satisfy closed hierarchies of equations of motion [24,25,26,27,28,29,30]. This permits one to obtain some exact results on the dynamics although full solutions typically remain out of reach.…”