arXiv subjects

S. S. Mizrahi

Publications and source records attributed to S. S. Mizrahi.

29 records · Page 2Linked to original sources

arXiv2004

The Wigner function associated to the Rogers-Szego polynomials

We show here that besides the well known Hermite polynomials, the q-deformed harmonic oscillator algebra admits another function space associated to a particular family of q-polynomials, namely the Rogers-Szego polynomials. Their main properties are presented, the associated Wigner function is calculated and its properties are discussed. It is shown that the angle probability density obtained from the Wigner function is a well-behaved function defined in the interval [-Pi,Pi), while the action probability only assumes integer values greater or equal than zero. It is emphasized the fact that the width of the angle probability density is governed by the free parameter q characterizing the polynomial.

quant-ph↗

arXiv2003

A consistent quantum model for continuous photodetection processes

We are modifying some aspects of the continuous photodetection theory, proposed by Srinivas and Davies [Optica Acta 28, 981 (1981)], which describes the non-unitary evolution of a quantum field state subjected to a continuous photocount measurement. In order to remedy inconsistencies that appear in their approach, we redefine the `annihilation' and `creation' operators that enter in the photocount superoperators. We show that this new approach not only still satisfies all the requirements for a consistent photocount theory according to Srinivas and Davies precepts, but also avoids some weird result appearing when previous definitions are used.

quant-ph↗

arXiv2002

Creating quanta with "annihilation" operator

An asymmetric nature of the boson `destruction' operator $\hat{a}$ and its `creation' partner $\hat{a}^{\dagger}$ is made apparent by applying them to a quantum state $|ψ>$ different from the Fock state $|n>$. We show that it is possible to {\em increase} (by many times or by any quantity) the mean number of quanta in the new `photon-subtracted' state $\hat{a}|ψ>$. Moreover, for certain `hyper-Poissonian' states $|ψ>$ the mean number of quanta in the (normalized) state $\hat{a}|ψ>$ can be much greater than in the `photon-added' state $\hat{a}^{\dagger}|ψ> $. The explanation of this `paradox' is given and some examples elucidating the meaning of Mandel's $q$-parameter and the exponential phase operators are considered.

quant-ph↗

arXiv2002

Controlling quantum entanglement through photocounts

We present a protocol to generate and control quantum entanglement between the states of two subsystems (the system ${\cal S}$) by making measurements on a third subsystem (the monitor ${\cal M}$), interacting with ${\cal S}$. For the sake of comparison we consider first an ideal, or instantaneous projective measurement, as postulated by von Neumann. Then we compare it with the more realistic or generalized measurement procedure based on photocounting on ${\cal M}$. Further we consider that the interaction term (between ${\cal S}$ and ${\cal M}$) contains a quantum nondemolition variable of ${\cal S}$ and discuss the possibility and limitations for reconstructing the initial state of ${\cal S}$ from information acquired by photocounting on ${\cal M}$.

quant-ph↗

arXiv2000

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 $1-{Tr}\hatρ^2$. 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.

quant-ph↗

arXiv2000

Quantum to Classical Transition from the Cosmic Background Radiation

We have revisited the Ghirardi-Rimini-Weber-Pearle (GRWP) approach for continuous dynamical evolution of the state vector for a macroscopic object. Our main concern is to recover the decoupling of the state vector dynamics for the center-of-mass (CM) and internal motion, as in the GRWP model, but within the framework of the standard cosmology. In this connection we have taken the opposite direction of the GRWP argument, that the cosmic background radiation (CBR) has originated from a fundamental stochastic hitting process. We assume the CBR as a clue of the Big Bang, playing a main role in the decoupling of the state vector dynamics of the CM and internal motion. In our model, instead of describing a continuous spontaneous localization (CSL) of a system of massive particles as proposed by Ghirardi, Pearle and Rimini, the Itô stochastic equation accounts for the intervention of the CBR on the system of particles. Essentially, this approach leads to a pre-master equation for both the CBR and particles degrees of freedom. The violation of the principle of energy conservation characteristic of the CSL model is avoided as well as the additional assumption on the size of the GRWP's localization width necessary to reach the decoupling between the collective and internal motions. Moreover, realistic estimation for the decoherence time, exhibiting an interesting dependence on the CBR temperature, is obtained. From the formula for the decoherence time it is possible to analyze the transition from micro to macro dynamics in both the early hot Universe and the nowadays cold one. The entropy of the system under decoherence is analyzed and the emergent `pointer basis' is discussed. In spite of not having imposed a privileged basis, in our model the position still emerges as the preferred observable as in the CSL model.

quant-ph↗

arXiv2000

Continuous pumping and control of mesoscopic superposition state in a lossy QED cavity

Here we consider the continuous pumping of a dissipative QED cavity and derive the time-dependent density operator of the cavity field prepared initially as a superposition of mesoscopic coherent states. The control of the coherence of this superposition is analyzed considering the injection of a beam of two-level Rydberg atoms through the cavity. Our treatment is compared to other approaches.

quant-ph↗

arXiv1999

Information Transfer in the Course of a Quantum Interaction

We discuss the problem of the information transfer (exchange of states configuration) between two interacting quantum systems along their evolution in time. We consider the specific case of two modes of the electromagnetic field with rotating wave coupling interaction (up-conversion in a nonlinear crystal). We verify that for certain initial states of the fields the swapping of state configuration occurs with conservation of the mean energy of each mode (without energy transfer), characterising thus pure information flow.

quant-ph↗

arXiv1998

Stationary States in Saturated Two-Photon Processes and Generation of Phase-Averaged Mixtures of Even and Odd Quantum States

We consider a relaxation of a single mode of the quantized field in a presence of one- and two-photon absorption and emission processes. Exact stationary solutions of the master equation for the diagonal elements of the density matrix in the Fock basis are found in the case of completely saturated two-photon emission. If two-photon processes dominate over single-photon ones, the stationary state is a mixture of phase averaged even and odd coherent states.

quant-ph↗

arXiv1998

Finite-Length Soliton Solutions of the Local Homogeneous Nonlinear Schroedinger Equation

We found a new kind of soliton solutions for the 5-parameter family of the potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the Schrödinger equation. In contradistinction to the "usual'' solitons like {\cosh[b(x-kt)]}^{-a}\exp[i(kx-ft)], the new {\em Finite-Length Solitons} (FLS) are nonanalytical functions with continuous first derivatives, which are different from zero only inside some finite regions of space. The simplest one-dimensional example is the function which is equal to {\cos[g(x-kt)]}^{1+d}\exp[i(kx-ft)] (with d>0) for |x-kt|<π/(2g), being identically equal to zero for |x-kt|>π/(2g). The FLS exist even in the case of a weak nonlinearity, whereas the ``usual'' solitons exist provided the nonlinearity parameters surpass some critical values.

quant-ph↗

arXiv1997

Collisional Semiclassical Aproximations in Phase-Space Representation

The Gaussian Wave-Packet phase-space representation is used to show that the expansion in powers of $\hbar$ of the quantum Liouville propagator leads, in the zeroth order term, to results close to those obtained in the statistical quasiclassical method of Lee and Scully in the Weyl-Wigner picture. It is also verified that propagating the Wigner distribution along the classical trajectories the amount of error is less than that coming from propagating the Gaussian distribution along classical trajectories.

physics.atom-ph↗