257 research outputs found
Finite-time quantum-to-classical transition for a Schroedinger-cat state
The transition from quantum to classical, in the case of a quantum harmonic
oscillator, is typically identified with the transition from a quantum
superposition of macroscopically distinguishable states, such as the
Schr\"odinger cat state, into the corresponding statistical mixture. This
transition is commonly characterized by the asymptotic loss of the interference
term in the Wigner representation of the cat state. In this paper we show that
the quantum to classical transition has different dynamical features depending
on the measure for nonclassicality used. Measures based on an operatorial
definition have well defined physical meaning and allow a deeper understanding
of the quantum to classical transition. Our analysis shows that, for most
nonclassicality measures, the Schr\"odinger cat dies after a finite time.
Moreover, our results challenge the prevailing idea that more macroscopic
states are more susceptible to decoherence in the sense that the transition
from quantum to classical occurs faster. Since nonclassicality is prerequisite
for entanglement generation our results also bridge the gap between
decoherence, which appears to be only asymptotic, and entanglement, which may
show a sudden death. In fact, whereas the loss of coherences still remains
asymptotic, we have shown that the transition from quantum to classical can
indeed occur at a finite time.Comment: 9+epsilon pages, 4 figures, published version. Originally submitted
as "Sudden death of the Schroedinger cat", a bit too cool for APS policy :-
Non-Markovian dynamics of a qubit
In this paper we investigate the non-Markovian dynamics of a qubit by
comparing two generalized master equations with memory. In the case of a
thermal bath, we derive the solution of the post-Markovian master equation
recently proposed in Ref. [A. Shabani and D.A. Lidar, Phys. Rev. A {\bf 71},
020101(R) (2005)] and we study the dynamics for an exponentially decaying
memory kernel. We compare the solution of the post-Markovian master equation
with the solution of the typical memory kernel master equation. Our results
lead to a new physical interpretation of the reservoir correlation function and
bring to light the limits of usability of master equations with memory for the
system under consideration.Comment: Replaced with published version (minor changes
A simple trapped-ion architecture for high-fidelity Toffoli gates
We discuss a simple architecture for a quantum Toffoli gate implemented using
three trapped ions. The gate, which in principle can be implemented with a
single laser-induced operation, is effective under rather general conditions
and is strikingly robust (within any experimentally realistic range of values)
against dephasing, heating and random fluctuations of the Hamiltonian
parameters. We provide a full characterization of the unitary and
noise-affected gate using three-qubit quantum process tomography
Phenomenological memory-kernel master equations and time-dependent Markovian processes
Do phenomenological master equations with memory kernel always describe a
non-Markovian quantum dynamics characterized by reverse flow of information? Is
the integration over the past states of the system an unmistakable signature of
non-Markovianity? We show by a counterexample that this is not always the case.
We consider two commonly used phenomenological integro-differential master
equations describing the dynamics of a spin 1/2 in a thermal bath. By using a
recently introduced measure to quantify non-Markovianity [H.-P. Breuer, E.-M.
Laine, and J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)] we demonstrate that
as far as the equations retain their physical sense, the key feature of
non-Markovian behavior does not appear in the considered memory kernel master
equations. Namely, there is no reverse flow of information from the environment
to the open system. Therefore, the assumption that the integration over a
memory kernel always leads to a non-Markovian dynamics turns out to be
vulnerable to phenomenological approximations. Instead, the considered
phenomenological equations are able to describe time-dependent and
uni-directional information flow from the system to the reservoir associated to
time-dependent Markovian processes.Comment: 5 pages, no figure
Limits in the characteristic function description of non-Lindblad-type open quantum systems
In this paper I investigate the usability of the characteristic functions for
the description of the dynamics of open quantum systems focussing on
non-Lindblad-type master equations. I consider, as an example, a non-Markovian
generalized master equation containing a memory kernel which may lead to
nonphysical time evolutions characterized by negative values of the density
matrix diagonal elements [S.M. Barnett and S. Stenholm, Phys. Rev. A {\bf 64},
033808 (2001)]. The main result of the paper is to demonstrate that there exist
situations in which the symmetrically ordered characteristic function is
perfectly well defined while the corresponding density matrix loses positivity.
Therefore nonphysical situations may not show up in the characteristic
function. As a consequence, the characteristic function cannot be considered an
{\it alternative complete} description of the non-Lindblad dynamics.Comment: Revised version. 4 pages, 1 figur
Driven harmonic oscillator as a quantum simulator for open systems
We show theoretically how a driven harmonic oscillator can be used as a
quantum simulator for non-Markovian damped harmonic oscillator. In the general
framework, the results demonstrate the possibility to use a closed system as a
simulator for open quantum systems. The quantum simulator is based on sets of
controlled drives of the closed harmonic oscillator with appropriately tailored
electric field pulses. The non-Markovian dynamics of the damped harmonic
oscillator is obtained by using the information about the spectral density of
the open system when averaging over the drives of the closed oscillator. We
consider single trapped ions as a specific physical implementation of the
simulator, and we show how the simulator approach reveals new physical insight
into the open system dynamics, e.g. the characteristic quantum mechanical
non-Markovian oscillatory behavior of the energy of the damped oscillator,
usually obtained by the non-Lindblad-type master equation, can have a simple
semiclassical interpretation.Comment: 10 pages, 4 figures. V2: Minor modifications and added 2 appendixes
for more details about calculation
Scaling of non-Markovian Monte Carlo wave-function methods
We demonstrate a scaling method for non-Markovian Monte Carlo wave-function
simulations used to study open quantum systems weakly coupled to their
environments. We derive a scaling equation, from which the result for the
expectation values of arbitrary operators of interest can be calculated, all
the quantities in the equation being easily obtainable from the scaled Monte
Carlo simulations. In the optimal case, the scaling method can be used, within
the weak coupling approximation, to reduce the size of the generated Monte
Carlo ensemble by several orders of magnitude. Thus, the developed method
allows faster simulations and makes it possible to solve the dynamics of the
certain class of non-Markovian systems whose simulation would be otherwise too
tedious because of the requirement for large computational resources.Comment: 10 pages, 3 figures. V2: Minor changes according to the referees'
suggestion
Open system dynamics with non-Markovian quantum jumps
We discuss in detail how non-Markovian open system dynamics can be described
in terms of quantum jumps [J. Piilo et al., Phys. Rev. Lett. 100, 180402
(2008)]. Our results demonstrate that it is possible to have a jump description
contained in the physical Hilbert space of the reduced system. The developed
non-Markovian quantum jump (NMQJ) approach is a generalization of the Markovian
Monte Carlo Wave Function (MCWF) method into the non-Markovian regime. The
method conserves both the probabilities in the density matrix and the norms of
the state vectors exactly, and sheds new light on non-Markovian dynamics. The
dynamics of the pure state ensemble illustrates how local-in-time master
equation can describe memory effects and how the current state of the system
carries information on its earlier state. Our approach solves the problem of
negative jump probabilities of the Markovian MCWF method in the non-Markovian
regime by defining the corresponding jump process with positive probability.
The results demonstrate that in the theoretical description of non-Markovian
open systems, there occurs quantum jumps which recreate seemingly lost
superpositions due to the memory.Comment: 19 pages, 10 figures. V2: Published version. Discussion section
shortened and some other minor changes according to the referee's suggestion
Dynamics of Entanglement and Bell-nonlocality for Two Stochastic Qubits with Dipole-Dipole Interaction
We have studied the analytical dynamics of Bell nonlocality as measured by
CHSH inequality and entanglement as measured by concurrence for two noisy
qubits that have dipole-dipole interaction. The nonlocal entanglement created
by the dipole-dipole interaction is found to be protected from sudden death for
certain initial states
Cavity losses for the dissipative Jaynes-Cummings Hamiltonian beyond Rotating Wave Approximation
A microscopic derivation of the master equation for the
Jaynes-Cummings model with cavity losses is given, taking into account the
terms in the dissipator which vary with frequencies of the order of the vacuum
Rabi frequency. Our approach allows to single out physical contexts wherein the
usual phenomenological dissipator turns out to be fully justified and
constitutes an extension of our previous analysis [Scala M. {\em et al.} 2007
Phys. Rev. A {\bf 75}, 013811], where a microscopic derivation was given in the
framework of the Rotating Wave Approximation.Comment: 12 pages, 1 figur
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