16 research outputs found
Evolution of cat states in a dissipative parametric amplifier: decoherence and entanglement
The evolution of the Schr\"{o}dinger-cat states in a dissipative parametric
amplifier is examined. The main tool in the analysis is the normally ordered
characteristic function. Squeezing, photon-number distribution and reduced
factorial moments are discussed for the single- and compound-mode cases. Also
the single-mode Wigner function is demonstrated. In addition to the decoherence
resulting from the interaction with the environment (damped case) there are two
sources which can cause such decoherence in the system even if it is completely
isolated: these are the decay of the pump and the relative phases of the
initial cat states. Furthermore, for the damped case there are two regimes,
which are underdamped and overdamped. In the first (second) regime the signal
mode or the idler mode "collapses" to a statistical mixture (thermal field).Comment: 34 pages, 10 figure
Phase diffusion pattern in quantum nondemolition systems
We quantitatively analyze the dynamics of the quantum phase distribution
associated with the reduced density matrix of a system, as the system evolves
under the influence of its environment with an energy-preserving quantum
nondemolition (QND) type of coupling. We take the system to be either an
oscillator (harmonic or anharmonic) or a two-level atom (or equivalently, a
spin-1/2 system), and model the environment as a bath of harmonic oscillators,
initially in a general squeezed thermal state. The impact of the different
environmental parameters is explicitly brought out as the system starts out in
various initial states. The results are applicable to a variety of physical
systems now studied experimentally with QND measurements.Comment: 18 pages, REVTeX, 8 figure
Quantum statistical properties of some new classes of intelligent states associated with special quantum systems
Based on the {\it nonlinear coherent states} method, a general and simple
algebraic formalism for the construction of \textit{`-deformed intelligent
states'} has been introduced. The structure has the potentiality to apply to
systems with a known discrete spectrum as well as the generalized coherent
states with known nonlinearity function . As some physical appearance of
the proposed formalism, a few new classes of intelligent states associated with
\textit{`center of-mass motion of a trapped ion'}, \textit{`harmonious states'}
and \textit{`hydrogen-like spectrum'} have been realized. Finally, the
nonclassicality of the obtained states has been investigated. To achieve this
purpose the quantum statistical properties using the Mandel parameter and the
squeezing of the quadratures of the radiation field corresponding to the
introduced states have been established numerically.Comment: 13page
Sub-Poissonian statistics in order-to-chaos transition
We study the phenomena at the overlap of quantum chaos and nonclassical
statistics for the time-dependent model of nonlinear oscillator. It is shown in
the framework of Mandel Q-parameter and Wigner function that the statistics of
oscillatory excitation number is drastically changed in order-to chaos
transition. The essential improvement of sub-Poissonian statistics in
comparison with an analogous one for the standard model of driven anharmonic
oscillator is observed for the regular operational regime. It is shown that in
the chaotic regime the system exhibits the range of sub- and super-Poissonian
statistics which alternate one to other depending on time intervals. Unusual
dependence of the variance of oscillatory number on the external noise level
for the chaotic dynamics is observed.Comment: 9 pages, RevTeX, 14 figure
Chaos in a double driven dissipative nonlinear oscillator
We propose an anharmonic oscillator driven by two periodic forces of
different frequencies as a new time-dependent model for investigating quantum
dissipative chaos. Our analysis is done in the frame of statistical ensemble of
quantum trajectories in quantum state diffusion approach. Quantum dynamical
manifestation of chaotic behavior, including the emergence of chaos, properties
of strange attractors, and quantum entanglement are studied by numerical
simulation of ensemble averaged Wigner function and von Neumann entropy.Comment: 9 pages, 18 figure