545 research outputs found
One-dimensional many-body entangled open quantum systems with tensor network methods
We present a collection of methods to simulate entangled dynamics of open
quantum systems governed by the Lindblad equation with tensor network methods.
Tensor network methods using matrix product states have been proven very useful
to simulate many-body quantum systems and have driven many innovations in
research. Since the matrix product state design is tailored for closed
one-dimensional systems governed by the Schr\"odinger equation, the next step
for many-body quantum dynamics is the simulation of open quantum systems. We
review the three dominant approaches to the simulation of open quantum systems
via the Lindblad master equation: quantum trajectories, matrix product density
operators, and locally purified tensor networks. Selected examples guide
possible applications of the methods and serve moreover as a benchmark between
the techniques. These examples include the finite temperature states of the
transverse quantum Ising model, the dynamics of an exciton traveling under the
influence of spontaneous emission and dephasing, and a double-well potential
simulated with the Bose-Hubbard model including dephasing. We analyze which
approach is favorable leading to the conclusion that a complete set of all
three methods is most beneficial, push- ing the limits of different scenarios.
The convergence studies using analytical results for macroscopic variables and
exact diagonalization methods as comparison, show, for example, that matrix
product density operators are favorable for the exciton problem in our study.
All three methods access the same library, i.e., the software package Open
Source Matrix Product States, allowing us to have a meaningful comparison
between the approaches based on the selected examples. For example, tensor
operations are accessed from the same subroutines and with the same
optimization eliminating one possible bias in a comparison of such numerical
methods.Comment: 24 pages, 8 figures. Small extension of time evolution section and
moving quantum simulators to introduction in comparison to v
Vortex macroscopic superpositions in ultracold bosons in a double-well potential
We study macroscopic superpositions in the orbital rather than the spatial
degrees of freedom, in a three-dimensional double-well system. We show that the
ensuing dynamics of interacting excited ultracold bosons, which in general
requires at least eight single-particle modes and Fock
vectors, is described by a surprisingly small set of many-body states. An
initial state with half the atoms in each well, and purposely excited in one of
them, gives rise to the tunneling of axisymmetric and transverse vortex
structures. We show that transverse vortices tunnel orders of magnitude faster
than axisymmetric ones and are therefore more experimentally accessible. The
tunneling process generates macroscopic superpositions only distinguishable by
their orbital properties and within experimentally realistic times.Comment: 9 pages, 6 figure
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