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.
Jan Gelhausen, Michael Buchhold, Achim Rosch, Philipp Strack
SciPost Phys. 1, 004 (2016) ·
published 23 October 2016
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The fields of quantum simulation with cold atoms [1] and quantum optics [2]
are currently being merged. In a set of recent pathbreaking experiments with
atoms in optical cavities [3,4] lattice quantum many-body systems with both, a
short-range interaction and a strong interaction potential of infinite range
-mediated by a quantized optical light field- were realized. A theoretical
modelling of these systems faces considerable complexity at the interface of:
(i) spontaneous symmetry-breaking and emergent phases of interacting many-body
systems with a large number of atoms $N\rightarrow\infty$, (ii) quantum optics
and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics
of driven, open quantum systems. Here we propose what is possibly the simplest,
quantum-optical magnet with competing short- and long-range interactions, in
which all three elements can be analyzed comprehensively: a Rydberg-dressed
spin lattice [5] coherently coupled to a single photon mode. Solving a set of
coupled even-odd sublattice Master equations for atomic spin and photon
mean-field amplitudes, we find three key results. (R1): Superradiance and a
coherent photon field can coexist with spontaneously broken magnetic
translation symmetry. The latter is induced by the short-range nearest-neighbor
interaction from weakly admixed Rydberg levels. (R2): This broken even-odd
sublattice symmetry leaves its imprint in the light via a novel peak in the
cavity spectrum beyond the conventional polariton modes. (R3): The combined
effect of atomic spontaneous emission, drive, and interactions can lead to
phases with anomalous photon number oscillations. Extensions of our work
include nano-photonic crystals coupled to interacting atoms and multi-mode
photon dynamics in Rydberg systems.
