SciPost Phys. 12, 009 (2022) ·
published 7 January 2022
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Hybrid evolution protocols, composed of unitary dynamics and repeated, weak
or projective measurements, give rise to new, intriguing quantum phenomena,
including entanglement phase transitions and unconventional conformal
invariance. Defying the complications imposed by the non-linear and stochastic
nature of the measurement process, we introduce a scenario of
measurement-induced many body evolution, which possesses an exact analytical
solution: bosonic Gaussian measurements. The evolution features a competition
between the continuous observation of linear boson operators and a free
Hamiltonian, and it is characterized by a unique and exactly solvable
covariance matrix. Within this framework, we then consider an elementary model
for quantum criticality, the free boson conformal field theory, and investigate
in which way criticality is modified under measurements. Depending on the
measurement protocol, we distinguish three fundamental scenarios (a) enriched
quantum criticality, characterized by a logarithmic entanglement growth with a
floating prefactor, or the loss of criticality, indicated by an entanglement
growth with either (b) an area-law or (c) a volume-law. For each scenario, we
discuss the impact of imperfect measurements, which reduce the purity of the
wavefunction and are equivalent to Markovian decoherence, and present a set of
observables, e.g., real-space correlations, the relaxation time, and the
entanglement structure, to classify the measurement-induced dynamics for both
pure and mixed states. Finally, we present an experimental tomography scheme,
which grants access to the density operator of the system by using the
continuous measurement record only.
SciPost Phys. 10, 045 (2021) ·
published 22 February 2021
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We describe an efficient numerical method for simulating the dynamics and
steady states of collective spin systems in the presence of dephasing and
decay. The method is based on the Schwinger boson representation of spin
operators and uses an extension of the truncated Wigner approximation to map
the exact open system dynamics onto stochastic differential equations for the
corresponding phase space distribution. This approach is most effective in the
limit of very large spin quantum numbers, where exact numerical simulations and
other approximation methods are no longer applicable. We benchmark this
numerical technique for known superradiant decay and spin-squeezing processes
and illustrate its application for the simulation of non-equilibrium phase
transitions in dissipative spin lattice models.
Michael Schuler, Daniele De Bernardis, Andreas M. Läuchli, Peter Rabl
SciPost Phys. 9, 066 (2020) ·
published 9 November 2020
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The structure of solids and their phases is mainly determined by static
Coulomb forces while the coupling of charges to the dynamical, i.e., quantized
degrees of freedom of the electromagnetic field plays only a secondary role.
Recently, it has been speculated that this general rule can be overcome in the
context of cavity quantum electrodynamics (QED), where the coupling of dipoles
to a single field mode can be dramatically enhanced. Here we present a first
exact analysis of the ground states of a dipolar cavity QED system in the
non-perturbative coupling regime, where electrostatic and dynamical
interactions play an equally important role. Specifically, we show how strong
and long-range vacuum fluctuations modify the states of dipolar matter and
induce novel phases with unusual properties. Beyond a purely fundamental
interest, these general mechanisms can be important for potential applications,
ranging from cavity-assisted chemistry to quantum technologies based on
ultrastrongly coupled circuit QED systems.
Julian Huber, Peter Kirton, Stefan Rotter, Peter Rabl
SciPost Phys. 9, 052 (2020) ·
published 19 October 2020
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The effect of PT-symmetry breaking in coupled systems with balanced gain and
loss has recently attracted considerable attention and has been demonstrated in
various photonic, electrical and mechanical systems in the classical regime.
Here we generalize the definition of PT symmetry to finite-dimensional open
quantum systems, which are described by a Markovian master equation.
Specifically, we show that the invariance of this master equation under a
certain symmetry transformation implies the existence of stationary states with
preserved and broken parity symmetry. As the dimension of the Hilbert space
grows, the transition between these two limiting phases becomes increasingly
sharp and the classically expected PT-symmetry breaking transition is
recovered. This quantum-to-classical correspondence allows us to establish a
common theoretical framework to identify and accurately describe PT-symmetry
breaking effects in a large variety of physical systems, operated both in the
classical and quantum regimes.
