78 research outputs found
Quantum theory of light scattering in a one-dimensional channel: Interaction effect on photon statistics and entanglement entropy
We provide a complete and exact quantum description of coherent light
scattering in a one-dimensional multi-mode transmission line coupled to a
two-level emitter. Using recently developed scattering approach we discuss
transmission properties, power spectrum, the full counting statistics and the
entanglement entropy of transmitted and reflected states of light. Our approach
takes into account spatial parameters of an incident coherent pulse as well as
waiting and counting times of a detector. We describe time evolution of the
power spectrum as well as observe deviations from the Poissonian statistics for
reflected and transmitted fields. In particular, the statistics of reflected
photons can change from sub-Poissonian to super-Poissonian for increasing
values of the detuning, while the statistics of transmitted photons is strictly
super-Poissonian in all parametric regimes. We study the entanglement entropy
of some spatial part of the scattered pulse and observe that it obeys the area
laws and that it is bounded by the maximal entropy of the effective four-level
system.Comment: 22 pages, 6 figures; discussion extended, references adde
Universal Dynamics Near Quantum Critical Points
We give an overview of the scaling of density of quasi-particles and excess
energy (heat) for nearly adiabatic dynamics near quantum critical points
(QCPs). In particular we discuss both sudden quenches of small amplitude and
slow sweeps across the QCP. We show close connection between universal scaling
of these quantities with the scaling behavior of the fidelity susceptibility
and its generalizations. In particular we argue that the Kibble-Zurek scaling
can be easily understood using this concept. We discuss how these scalings can
be derived within the adiabatic perturbation theory and how using this approach
slow and fast quenches can be treated within the same framework. We also
describe modifications of these scalings for finite temperature quenches and
emphasize the important role of statistics of low-energy excitations. In the
end we mention some connections between adiabatic dynamics near critical points
with dynamics associated with space-time singularities in the metrics, which
naturally emerges in such areas as cosmology and string theory.Comment: 19 pages, Contribution to the book "Developments in Quantum Phase
Transitions", edited by Lincoln Carr; revised version, acknowledgement adde
Integrable Floquet dynamics
We discuss several classes of integrable Floquet systems, i.e. systems which
do not exhibit chaotic behavior even under a time dependent perturbation. The
first class is associated with finite-dimensional Lie groups and
infinite-dimensional generalization thereof. The second class is related to the
row transfer matrices of the 2D statistical mechanics models. The third class
of models, called here "boost models", is constructed as a periodic interchange
of two Hamiltonians - one is the integrable lattice model Hamiltonian, while
the second is the boost operator. The latter for known cases coincides with the
entanglement Hamiltonian and is closely related to the corner transfer matrix
of the corresponding 2D statistical models. We present several explicit
examples. As an interesting application of the boost models we discuss a
possibility of generating periodically oscillating states with the period
different from that of the driving field. In particular, one can realize an
oscillating state by performing a static quench to a boost operator. We term
this state a "Quantum Boost Clock". All analyzed setups can be readily realized
experimentally, for example in cod atoms.Comment: 18 pages, 2 figures; revised version. Submission to SciPos
Many-body localization in the Fock space of natural orbitals
We study the eigenstates of a paradigmatic model of many-body localization in
the Fock basis constructed out of the natural orbitals. By numerically studying
the participation ratio, we identify a sharp crossover between different phases
at a disorder strength close to the disorder strength at which subdiffusive
behaviour sets in, significantly below the many-body localization transition.
We repeat the analysis in the conventionally used computational basis, and show
that many-body localized eigenstates are much stronger localized in the Fock
basis constructed out of the natural orbitals than in the computational basis.Comment: Submission to SciPos
Non-ergodicity in the Anisotropic Dicke model
We study the ergodic -- non-ergodic transition in a generalized Dicke model
with independent co- and counter rotating light-matter coupling terms. By
studying level statistics, the average ratio of consecutive level spacings, and
the quantum butterfly effect (out-of-time correlation) as a dynamical probe, we
show that the ergodic -- non-ergodic transition in the Dicke model is a
consequence of the proximity to the integrable limit of the model when one of
the couplings is set to zero. This can be interpreted as a hint for the
existence of a quantum analogue of the classical Kolmogorov-Arnold-Moser
theorem. Besides, we show that there is no intrinsic relation between the
ergodic -- non-ergodic transition and the precursors of the normal --
superradiant quantum phase transition.Comment: 5 pages, 4 figure
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