809 research outputs found
Asymptotical photon distributions in the dissipative Dynamical Casimir Effect
Asymptotical formulas for the photon distribution function of a quantum
oscillator with time-dependent frequency and damping coefficients, interacting
with a thermal reservoir, are derived in the case of a large mean number of
quanta. Different regimes of excitation of an initial thermal state with an
arbitrary temperature are considered. New formulas are used to predict the
statistical properties of the electromagnetic field created in the experiments
on the Dynamical Casimir Effect which are now under preparation.Comment: 11 pages, accepted contribution to CEWQO 2009 proceedings (to appear
in Physica Scripta
Decoherence and thermalization dynamics of a quantum oscillator
We introduce the quantitative measures characterizing the rates of
decoherence and thermalization of quantum systems. We study the time evolution
of these measures in the case of a quantum harmonic oscillator whose relaxation
is described in the framework of the standard master equation, for various
initial states (coherent, `cat', squeezed and number). We establish the
conditions under which the true decoherence measure can be approximated by the
linear entropy . We show that at low temperatures and for
highly excited initial states the decoherence process consists of three
distinct stages with quite different time scales. In particular, the `cat'
states preserve 50% of the initial coherence for a long time interval which
increases logarithmically with increase of the initial energy.Comment: 24 pages, LaTex, 8 ps figures, accepted for publication in J. Opt.
Justification of the symmetric damping model of the dynamical Casimir effect in a cavity with a semiconductor mirror
A "microscopic" justification of the "symmetric damping" model of a quantum
oscillator with time-dependent frequency and time-dependent damping is given.
This model is used to predict results of experiments on simulating the
dynamical Casimir effect in a cavity with a photo-excited semiconductor mirror.
It is shown that the most general bilinear time-dependent coupling of a
selected oscillator (field mode) to a bath of harmonic oscillators results in
two equal friction coefficients for the both quadratures, provided all the
coupling coefficients are proportional to a single arbitrary function of time
whose duration is much shorter than the periods of all oscillators. The choice
of coupling in the rotating wave approximation form leads to the "mimimum
noise" model of the quantum damped oscillator, introduced earlier in a pure
phenomenological way.Comment: 9 pages, typos corrected, corresponds to the published version,
except for the reference styl
Vibrating Cavities - A numerical approach
We present a general formalism allowing for efficient numerical calculation
of the production of massless scalar particles from vacuum in a one-dimensional
dynamical cavity, i.e. the dynamical Casimir effect. By introducing a
particular parametrization for the time evolution of the field modes inside the
cavity we derive a coupled system of first-order linear differential equations.
The solutions to this system determine the number of created particles and can
be found by means of numerical methods for arbitrary motions of the walls of
the cavity. To demonstrate the method which accounts for the intermode coupling
we investigate the creation of massless scalar particles in a one-dimensional
vibrating cavity by means of three particular cavity motions. We compare the
numerical results with analytical predictions as well as a different numerical
approach.Comment: 28 pages, 19 figures, accepted for publication in J. Opt. B: Quantum
Semiclass. Op
Generation of microwave fields in cavities with laser-excited nonlinear media: competition between the second- and third-order optical nonlinearities
We discuss a scheme for the parametric amplification of the quantum fluctuations of the
electromagnetic vacuum in a three-dimensional microwave resonator, and report the preliminary
measurements to test its feasibility. In the present experimental scheme, the fundamental mode of
a microwave cavity is nonadiabatically perturbed by modulating the index of refraction of the
nonlinear optical crystal enclosed therein. Intense, multi-GHz laser pulses, such as those
delivered by a mode-locked laser source, impinge on the crystal to accomplish the n-index
modulation. We theoretically analyze the process of parametric generation, which is related to
the third-order nonlinear coefficient \u3c7(3) of the nonlinear crystal, and assess the suitable
experimental conditions for generating real photons from the vacuum. Second-order nonlinear
processes are first analyzed as a possible source of spurious photons in quantum vacuum
experiments when an ideal, mode-locked laser source is considered. The combination of a crystal
non-null \u3c7(2) coefficient and a real mode-locked laser system\u2014i.e. one featuring offset-fromcarrier
noise and unwanted secondary oscillations\u2014is also experimentally investigated, paving
the way for future experiments in three-dimensional cavities
Properties of Squeezed-State Excitations
The photon distribution function of a discrete series of excitations of
squeezed coherent states is given explicitly in terms of Hermite polynomials of
two variables. The Wigner and the coherent-state quasiprobabilities are also
presented in closed form through the Hermite polynomials and their limiting
cases. Expectation values of photon numbers and their dispersion are
calculated. Some three-dimensional plots of photon distributions for different
squeezing parameters demonstrating oscillatory behaviour are given.Comment: Latex,35 pages,submitted to Quant.Semiclassical Op
Quantum master equations from classical Lagrangians with two stochastic forces
We show how a large family of master equations, describing quantum Brownian
motion of a harmonic oscillator with translationally invariant damping, can be
derived within a phenomenological approach, based on the assumption that an
environment can be simulated by two classical stochastic forces. This family is
determined by three time-dependent correlation functions (besides the frequency
and damping coefficients), and it includes as special cases the known master
equations, whose dissipative part is bilinear with respect to the operators of
coordinate and momentum.Comment: 10 pages, no figure
Noether's Theorem and time-dependent quantum invariants
The time dependent-integrals of motion, linear in position and momentum
operators, of a quantum system are extracted from Noether's theorem
prescription by means of special time-dependent variations of coordinates. For
the stationary case of the generalized two-dimensional harmonic oscillator, the
time-independent integrals of motion are shown to correspond to special
Bragg-type symmetry properties. A detailed study for the non-stationary case of
this quantum system is presented. The linear integrals of motion are
constructed explicitly for the case of varying mass and coupling strength. They
are obtained also from Noether's theorem. The general treatment for a
multi-dimensional quadratic system is indicated, and it is shown that the
time-dependent variations that give rise to the linear invariants, as conserved
quantities, satisfy the corresponding classical homogeneous equations of motion
for the coordinates.Comment: Plain TeX, 23 pages, preprint of Instituto de Ciencias Nucleares,
UNAM Departamento de F\ii sica and Matem\'aticas Aplicadas, No. 01 (1994
Homodyne extimation of quantum states purity by exploiting covariant uncertainty relation
We experimentally verify uncertainty relations for mixed states in the
tomographic representation by measuring the radiation field tomograms, i.e.
homodyne distributions. Thermal states of single-mode radiation field are
discussed in details as paradigm of mixed quantum state. By considering the
connection between generalised uncertainty relations and optical tomograms is
seen that the purity of the states can be retrieved by statistical analysis of
the homodyne data. The purity parameter assumes a relevant role in quantum
information where the effective fidelities of protocols depend critically on
the purity of the information carrier states. In this contest the homodyne
detector becomes an easy to handle purity-meter for the state on-line with a
running quantum information protocol.Comment: accepted for publication into Physica Script
Quantum singular oscillator as a model of two-ion trap: an amplification of transition probabilities due to small time variations of the binding potential
Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we
apply the quantum singular time dependent oscillator model to describe the
relative one dimensional motion of two ions in a trap. We argue that the model
can be justified for low energy excited states with the quantum numbers , provided that the dimensionless constant characterizing the
strength of the repulsive potential is large enough, . Time
dependent Gaussian-like wave packets generalizing odd coherent states of the
harmonic oscillator, and excitation number eigenstates are constructed. We show
that the relative motion of the ions, in contradistinction to its center of
mass counterpart, is extremely sensitive to the time dependence of the binding
harmonic potential, since the large value of results in a significant
amplification of the transition probabilities between energy eigenstate even
for slow time variations of the frequency.Comment: 19 pages, LaTeX, 5 eps-figures, to appear on Phys. Rev. A, one
reference correcte
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