Geometric phases along quantum trajectories
- URL: http://arxiv.org/abs/2301.04222v4
- Date: Sun, 28 May 2023 11:14:47 GMT
- Title: Geometric phases along quantum trajectories
- Authors: Ludmila Viotti, Ana Laura Gramajo, Paula I. Villar, Fernando C.
Lombardo, Rosario Fazio
- Abstract summary: We study the distribution function of geometric phases in monitored quantum systems.
For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle.
For the same parameters, the density matrix does not show any interference.
- Score: 58.720142291102135
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: A monitored quantum system undergoing a cyclic evolution of the parameters
governing its Hamiltonian accumulates a geometric phase that depends on the
quantum trajectory followed by the system on its evolution. The phase value
will be determined both by the unitary dynamics and by the interaction of the
system with the environment. Consequently, the geometric phase will acquire a
stochastic character due to the occurrence of random quantum jumps. Here we
study the distribution function of geometric phases in monitored quantum
systems and discuss when/if different quantities, proposed to measure geometric
phases in open quantum systems, are representative of the distribution. We also
consider a monitored echo protocol and discuss in which cases the distribution
of the interference pattern extracted in the experiment is linked to the
geometric phase. Furthermore, we unveil, for the single trajectory exhibiting
no quantum jumps, a topological transition in the phase acquired after a cycle
and show how this critical behavior can be observed in an echo protocol. For
the same parameters, the density matrix does not show any singularity. We
illustrate all our main results by considering a paradigmatic case, a spin-1/2
immersed in time-varying a magnetic field in presence of an external
environment. The major outcomes of our analysis are however quite general and
do not depend, in their qualitative features, on the choice of the model
studied.
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