4,467 research outputs found
Multi-mode entanglement of N harmonic oscillators coupled to a non-Markovian reservoir
Multi-mode entanglement is investigated in the system composed of coupled
identical harmonic oscillators interacting with a common environment. We treat
the problem very general by working with the Hamiltonian without the
rotating-wave approximation and by considering the environment as a
non-Markovian reservoir to the oscillators. We invoke an -mode unitary
transformation of the position and momentum operators and find that in the
transformed basis the system is represented by a set of independent harmonic
oscillators with only one of them coupled to the environment. Working in the
Wigner representation of the density operator, we find that the covariance
matrix has a block diagonal form that it can be expressed in terms of multiples
of and matrices. This simple property allows to treat
the problem to some extend analytically. We illustrate the advantage of working
in the transformed basis on a simple example of three harmonic oscillators and
find that the entanglement can persists for long times due to presence of
constants of motion for the covariance matrix elements. We find that, in
contrast to what one could expect, a strong damping of the oscillators leads to
a better stationary entanglement than in the case of a weak damping.Comment: 21 pages, 4 figure
Non-Markovian entanglement dynamics of quantum continuous variable systems in thermal environments
We study two continuous variable systems (or two harmonic oscillators) and
investigate their entanglement evolution under the influence of non-Markovian
thermal environments. The continuous variable systems could be two modes of
electromagnetic fields or two nanomechanical oscillators in the quantum domain.
We use quantum open system method to derive the non-Markovian master equations
of the reduced density matrix for two different but related models of the
continuous variable systems. The two models both consist of two interacting
harmonic oscillators. In model A, each of the two oscillators is coupled to its
own independent thermal reservoir, while in model B the two oscillators are
coupled to a common reservoir. To quantify the degrees of entanglement for the
bipartite continuous variable systems in Gaussian states, logarithmic
negativity is used. We find that the dynamics of the quantum entanglement is
sensitive to the initial states, the oscillator-oscillator interaction, the
oscillator-environment interaction and the coupling to a common bath or to
different, independent baths.Comment: 10 two-column pages, 8 figures, to appear in Phys. Rev.
Synchronization, quantum correlations and entanglement in oscillator networks
Synchronization is one of the paradigmatic phenomena in the study of complex
systems. It has been explored theoretically and experimentally mostly to
understand natural phenomena, but also in view of technological applications.
Although several mechanisms and conditions for synchronous behavior in
spatially extended systems and networks have been identified, the emergence of
this phenomenon has been largely unexplored in quantum systems until very
recently. Here we discuss synchronization in quantum networks of different
harmonic oscillators relaxing towards a stationary state, being essential the
form of dissipation. By local tuning of one of the oscillators, we establish
the conditions for synchronous dynamics, in the whole network or in a motif.
Beyond the classical regime we show that synchronization between (even
unlinked) nodes witnesses the presence of quantum correlations and
entanglement. Furthermore, synchronization and entanglement can be induced
between two different oscillators if properly linked to a random network.Comment: 10 pages, 5 figures, submitted to Scientific Report
Entanglement dynamics in presence of diversity under decohering environments
We study the evolution of entanglement of a pair of coupled, non-resonant
harmonic oscillators in contact with an environment. For both the cases of a
common bath and of two separate baths for each of the oscillators, a full
master equation is provided without rotating wave approximation. This allows us
to characterize the entanglement dynamics as a function of the diversity
between the oscillators frequencies and their mutual coupling. Also the
correlation between the occupation numbers is considered to explore the degree
of quantumness of the system. The singular effect of the resonance condition
(identical oscillators) and its relationship with the possibility of preserving
asymptotic entanglement are discussed. The importance of the bath's memory
properties is investigated by comparing Markovian and non-Markovian evolutions
Quantum correlations and synchronization measures
The phenomenon of spontaneous synchronization is universal and only recently
advances have been made in the quantum domain. Being synchronization a kind of
temporal correlation among systems, it is interesting to understand its
connection with other measures of quantum correlations. We review here what is
known in the field, putting emphasis on measures and indicators of
synchronization which have been proposed in the literature, and comparing their
validity for different dynamical systems, highlighting when they give similar
insights and when they seem to fail.Comment: book chapter, 18 pages, 7 figures, Fanchini F., Soares Pinto D.,
Adesso G. (eds) Lectures on General Quantum Correlations and their
Applications. Quantum Science and Technology. Springer (2017
"Hot Entanglement"? -- A Nonequilibrium Quantum Field Theory Scrutiny
The possibility of maintaining entanglement in a quantum system at finite,
even high, temperatures -- the so-called `hot entanglement' -- has obvious
practical interest, but also requires closer theoretical scrutiny. Since
quantum entanglement in a system evolves in time and is continuously subjected
to environmental degradation, a nonequilibrium description by way of open
quantum systems is called for. To identify the key issues and the contributing
factors that may permit `hot entanglement' to exist, or the lack thereof, we
carry out a model study of two spatially-separated, coupled oscillators in a
shared bath depicted by a finite-temperature scalar field. From the Langevin
equations we derived for the normal modes and the entanglement measure
constructed from the covariance matrix we examine the interplay between direct
coupling, field-induced interaction and finite separation on the structure of
late-time entanglement. We show that the coupling between oscillators plays a
crucial role in sustaining entanglement at intermediate temperatures and over
finite separations. In contrast, the field-induced interaction between the
oscillators which is a non-Markovian effect, becomes very ineffective at high
temperature. We determine the critical temperature above which entanglement
disappears to be bounded in the leading order by the inverse frequency of the
center-of-mass mode of the reduced oscillator system, a result not unexpected,
which rules out hot entanglement in such settings.Comment: 13 pages, 2 figure
Quantum Entanglement at High Temperatures? II. Bosonic Systems in Nonequilibrium Steady State
This is the second of a series of three papers examining how viable it is for
entanglement to be sustained at high temperatures for quantum systems in
thermal equilibrium (Case A), in nonequilibrium (Case B) and in nonequilibrium
steady state conditions (Case C). The system we analyze here consists of two
coupled quantum harmonic oscillators each interacting with its own bath
described by a scalar field, set at temperatures . For
\textit{constant bilinear inter-oscillator coupling} studied here (Case C1)
owing to the Gaussian nature, the problem can be solved exactly at arbitrary
temperatures even for strong coupling. We find that the valid entanglement
criterion in general is not a function of the bath temperature difference, in
contrast to thermal transport in the same NESS setting [1]. Thus lowering the
temperature of one of the thermal baths does not necessarily help to safeguard
the entanglement between the oscillators. Indeed, quantum entanglement will
disappear if any one of the thermal baths has a temperature higher than the
critical temperature . With the Langevin equations derived we give a full
display of how entanglement dynamics in this system depends on ,
, the inter-oscillator coupling and the system-bath coupling strengths. For
weak oscillator-bath coupling the critical temperature is about the order
of the inverse oscillator frequency, but for strong oscillator-bath coupling it
will depend on the bath cutoff frequency. We conclude that in most realistic
circumstances, for bosonic systems in NESS with constant bilinear coupling,
`hot entanglement' is largely a fiction. In Paper III we will examine the case
(C2) of \textit{time-dependent driven coupling } which contains the parametric
pumping type described in [2] wherein entanglement was first shown to sustain
at high temperatures.Comment: 47 pages, 9 figure
Quantum Brownian motion of multipartite systems and their entanglement dynamics
We solve the model of N quantum Brownian oscillators linearly coupled to an
environment of quantum oscillators at finite temperature, with no extra
assumptions about the structure of the system-environment coupling. Using a
compact phase-space formalism, we give a rather quick and direct derivation of
the master equation and its solutions for general spectral functions and
arbitrary temperatures. Since our framework is intrinsically nonperturbative,
we are able to analyze the entanglement dynamics of two oscillators coupled to
a common scalar field in previously unexplored regimes, such as off resonance
and strong coupling.Comment: 10 pages, 6 figure
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