187 research outputs found
Floquet-Markov description of the parametrically driven, dissipative harmonic quantum oscillator
Using the parametrically driven harmonic oscillator as a working example, we
study two different Markovian approaches to the quantum dynamics of a
periodically driven system with dissipation. In the simpler approach, the
driving enters the master equation for the reduced density operator only in the
Hamiltonian term. An improved master equation is achieved by treating the
entire driven system within the Floquet formalism and coupling it to the
reservoir as a whole. The different ensuing evolution equations are compared in
various representations, particularly as Fokker-Planck equations for the Wigner
function. On all levels of approximation, these evolution equations retain the
periodicity of the driving, so that their solutions have Floquet form and
represent eigenfunctions of a non-unitary propagator over a single period of
the driving. We discuss asymptotic states in the long-time limit as well as the
conservative and the high-temperature limits. Numerical results obtained within
the different Markov approximations are compared with the exact path-integral
solution. The application of the improved Floquet-Markov scheme becomes
increasingly important when considering stronger driving and lower
temperatures.Comment: 29 pages, 7 figure
Magnetic operations: a little fuzzy physics?
We examine the behaviour of charged particles in homogeneous, constant and/or
oscillating magnetic fields in the non-relativistic approximation. A special
role of the geometric center of the particle trajectory is elucidated. In
quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an
element of non-commutative geometry which enters into the traditional control
problems. We show that its application extends beyond the usually considered
time independent magnetic fields of the quantum Hall effect. Some simple cases
of magnetic control by oscillating fields lead to the stability maps differing
from the traditional Strutt diagram.Comment: 28 pages, 8 figure
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
The Minimum-Uncertainty Squeezed States for for Atoms and Photons in a Cavity
We describe a six-parameter family of the minimum-uncertainty squeezed states
for the harmonic oscillator in nonrelativistic quantum mechanics. They are
derived by the action of corresponding maximal kinematical invariance group on
the standard ground state solution. We show that the product of the variances
attains the required minimum value 1/4 only at the instances that one variance
is a minimum and the other is a maximum, when the squeezing of one of the
variances occurs. The generalized coherent states are explicitly constructed
and their Wigner function is studied. The overlap coefficients between the
squeezed, or generalized harmonic, and the Fock states are explicitly evaluated
in terms of hypergeometric functions. The corresponding photons statistics are
discussed and some applications to quantum optics, cavity quantum
electrodynamics, and superfocusing in channeling scattering are mentioned.
Explicit solutions of the Heisenberg equations for radiation field operators
with squeezing are found.Comment: 27 pages, no figures, 174 references J. Phys. B: At. Mol. Opt. Phys.,
Special Issue celebrating the 20th anniversary of quantum state engineering
(R. Blatt, A. Lvovsky, and G. Milburn, Guest Editors), May 201
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