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arXiv:1511.08733 · Physical Review A

Dynamics of dissipative Bose-Einstein condensation

Stephan Caspar, F. Hebenstreit, D. Mesterházy, U.‐J. Wiese

Published Feb 2, 2016• 14 citations
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Abstract

We resolve the real-time dynamics of a purely dissipative $s=1/2$ quantum spin or, equivalently, hard-core boson model on a hypercubic $d$-dimensional lattice. The considered quantum dissipative process drives the system to a totally symmetric macroscopic superposition in each of the ${S}^{3}$ sectors. Different characteristic time scales are identified for the dynamics and we determine their finite-size scaling. We introduce the concept of cumulative entanglement distribution to quantify multiparticle entanglement and show that the considered protocol serves as an efficient method to prepare a macroscopically entangled Bose-Einstein condensate.

DOI
10.1103/physreva.93.021602

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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.
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We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of quantum spin models exactly in arbitrary dimensions, which is illustrated explicitly with two examples of driven-dissipative systems. We investigate their respective nonequilibrium steady states as well as the full real-time evolution on unprecedented system sizes. Characteristic time scales are derived analytically, which allows us to understand the nontrivial finite-size scaling of the dissipative gap. The corresponding scaling exponents are confirmed by solving numerically for the full real-time evolution of two-point correlation functions.