Quantum Statistical Properties Research Articles

Biorthonormal eigenbasis of a Markovian master equation for the quantum Brownian motion

The solution to a quantum Markovian master equation of a harmonic oscillator weakly coupled to a thermal reservoir is investigated as a non-Hermitian eigenvalue problem in space coordinates. In terms of a pair of quantum action-angle variables, the equation becomes separable and a complete set of biorthogonal eigenfunctions can be constructed. Properties of quantum states, such as the change in the quantum coherence length, damping in the motion, and disappearance of the spatial interference pattern, can then be described as the decay of the nonequilibrium modes in the eigenbasis expansion. It is found that the process of gaining quantum coherence from the environment takes a longer time than the opposite process of losing quantum coherence to the environment. An estimate of the time scales of these processes is obtained.

Quantum Statistical Properties of Binomial Field Interacting with Two Entangled Atoms

Quantum statistical properties of the binomial field interacting with the two entangled atoms are investigated for the different initial conditions. It is found that the sub-Poissonian distribution and the antibunching effect can be presented for the certain ranges of the involved parameters.

Maximal sets of mutually unbiased quantum states in dimension 6

We study sets of pure states in a Hilbert space of dimension $d$ which are mutually unbiased (MU), that is, the moduli of their scalar products are equal to zero, one, or $1∕\sqrt{d}$. Each of these sets will be called a MU constellation, and if four MU bases were to exist for $d=6$, they would give rise to 35 different MU constellations. Using a numerical minimization procedure, we are able to identify only 18 of them in spite of extensive searches. The missing MU constellations provide the strongest numerical evidence so far that no seven MU bases exist in dimension 6.

From squeezed atom lasers to teleportation of massive articles

The development of the Raman atom laser promises to make available new techniques for accessing and manipulating the quantum statistical properties of Bose-Einstein condensates. In this work we show how, combined with the already existing methods for the manipulation of quantum states of light which are central to quantum optics, the Raman input-output coupling mechanisms potentially enable the production of quadrature squeezed and sub-Poissonian atomic beams, and entanglement between atomic and optical fields. We also propose a method of measuring the quantum statistics of the atomic beam by transferring them to an optical field. Finally, by combning these techniques, we propose a method of teleporting the atom laser beam from one trapped condensate to another.

Purely squeezed states for quantum deformed systems

The generalized purely squeezed states for primary shape-invariant potentials systems, quantum deformed by different models, are constructed by the ladder-operator method within an algebraic approach based on supersymmetric quantum mechanics. The characteristic properties of these states as well as their quantum statistical properties and squeezing effects for generalized quadrature observables are studied and analyzed in terms of the quantum deformation parameter q. An application is given for a quantum deformed Pöschl–Teller potential system, and numerical results are presented and discussed in detail.

Squeezing via coupling of Bose–Einstein condensates in a double-well potential with a cavity light field

Squeezing via the interaction between the cavity light field and the Bose–Einstein Condensate (BEC) in a double-well potential is considered within the context of the two-mode approximation. For the cavity light field initially in a coherent state, it is shown that by choosing appropriate parameters, quadrature squeezing of the cavity light field can be achieved and it exhibits periodic oscillation. We also study the case in which BEC is tuned to resonance by periodically modulating the trapping potential, and the quadrature squeezing of the cavity field exhibits periodic collapse and revival effect. Both analytic and numerical calculations are performed, and they are found to be in good agreement with each other. The result shows that the quantum statistical properties of the cavity light field can be manipulated by its coupling with the condensates in the double-well potential. On the other hand, dynamical properties of the condensates in the double-well potential will be reflected by the quadrature squeezing of the light field.

Effect of biased noise fluctuations on entanglement and statistical properties in a two-photon phase-sensitive laser

Analysis of the effects of the biased noise fluctuations on the quantum features and statistical properties of the cavity radiation of the two-photon phase-sensitive laser is presented. It turns out that the biased noise fluctuations that enter the cavity via the vibrations of the wall enhance the atomic coherence responsible for the entanglement of the cavity radiation due to the phase sensitivity of the involved cascade transitions. The two-mode squeezing of the superimposed radiation, entanglement of the cavity radiation, and mean number of the photon pairs are found to increase with the rate at which the atoms are injected into the cavity. The two-mode squeezing increases with the intensity of the biased noise fluctuations, but the mean number of the photon pairs decreases. Even then, it is possible to produce quite intense robust continuous variable entanglement in this scheme which is believed to be a motivation for further practical scrutiny. Moreover, the superimposed radiation exhibits super-Poissonian photon statistics with no finite joint probability for getting more photons in mode $b$ than mode $a$.

Optical Lattice Clocks with Non-Interacting Bosons and Fermions

We report on frequency comparison of two optical lattice clocks based on fermionic 87Sr trapped in 1D optical lattice and bosonic 88Sr in 3D one. We discuss that these two lattice clock configurations would optimize the lattice clocks' performance from the view point of the quantum statistical properties of interrogated atoms and optical lattice geometries. The frequency comparison of two optical clocks offers an important step to investigate the lattice clocks' uncertainty less than 10-15, where no working standard exists.

Dynamics of decoherence without dissipation in a squeezed thermal bath

We study a generic open quantum system where the coupling between the system and its environment is of an energy-preserving quantum nondemolition (QND) type. We obtain the general master equation for the evolution of such a system under the influence of a squeezed thermal bath of harmonic oscillators. From the master equation it can be seen explicitly that the process involves decoherence or dephasing without any dissipation of energy. We work out the decoherence-causing term in the high- and zero-temperature limits and check that they match with known results for the case of a thermal bath. The decay of the coherence is quantified as well by the dynamics of the linear entropy of the system under various environmental conditions. We make a comparison of the quantum statistical properties between QND and dissipative types of evolution using a two-level atomic system and a harmonic oscillator.

Intrinsic decoherence effects on quantum dynamics of the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation

In this paper, we study the influence of the intrinsic decoherence on quantum statistical properties of a generalized nonlinear interacting atom–field system, i.e., the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation. The model contains the nonlinearities of both the cavity–field and the atom–field coupling. Until now, very few exact solutions of nonlinear systems that include a form of decoherence have been presented. The main achievement of the present work is to find exact analytical solutions for the quantum dynamics of the nonlinear model under consideration in the presence of intrinsic decoherence. With the help of a supersymmetric transformation, we first put the model Hamiltonian into an appropriate form for treating the intrinsic decoherence. Then, by applying the superoperator technique, we find an exact solution of the Milburn equation for a nondegenerate two-photon f-deformed Jaynes–Cummings model. We use this solution to investigate the effects of the intrinsic decoherence on temporal evolution of various nonclassical properties of the system, i.e., atomic population inversion, atomic dipole squeezing, atom–field entanglement, sub-Poissonian photon statistics, cross correlation between the two modes and quadrature squeezing of the cavity field. Particularly, we compare the numerical results for three different cases of two-mode deformed, one-mode deformed, and nondeformed Jaynes–Cummings models. PACS Nos.: 42.50.Ct, 42.50.Dv, 03.65.Yz

New (p, q; μ, ν, f)-deformed states

We construct a new family of deformed states. These states are normalizable on the whole complex plane and continuous in their label z. Under fixed values of parameters, they allow the resolution of unity in the form of an ordinary integral with a positive weight function obtained through the analytic solution of the associated Stieltjes power-moment problem. In addition to the mathematical characteristics, the quantum statistical properties of these states are analytically and numerically discussed in detail in the context of conventional as well as deformed quantum optics. We find that, for non-deformed photons, the states exhibit quadrature squeezing and their photon number statistics is sub-Poissonian. On the other hand, for deformed photons, the states are super-Poissonian and no quadrature squeezing occurs.

Controlling statistical properties of stored light

A theoretical discussion is given of quantum statistical properties of outgoing light pulses after they have been stored in a medium of atoms in the tripod configuration. Such a system enables one to split or mix light signals at the storage stage. By changing the parameters of the driving fields used for light storage and release it is possible to control the photon distribution in the two output channels. The particular cases discussed here are a generalized Hong–Ou–Mandel interference, storing of squeezed states and a homodyne signal analysis.

Quantum statistical properties of some new classes of intelligent states associated with special quantum systems

Based on the nonlinear coherent states method, a general and simple algebraic formalism for the construction of ‘f-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 f(n). As some physical appearance of the proposed formalism, a few new classes of intelligent states associated with ‘center-of-mass motion of a trapped ion’, ‘harmonious states’ and ‘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.

RECENT PROGRESS IN THE DENSITY-MATRIX RENORMALIZATION GROUP

Over the last decade, the density-matrix renormalization group (DMRG) has emerged as the most powerful method for the simulation of strongly correlated one-dimensional (1D) quantum systems. Input from quantum information has allowed to trace the method's performance to the entanglement properties of quantum states, revealing why it works so well in 1D and not so well in 2D; it has allowed to devise algorithms for time-dependent quantum systems and, by clarifying the link between DMRG and Wilson's numerical renormalization group (NRG), for quantum impurity systems.

Scattering problem with nonlocal separable potential of rank-two: Application to statistical mechanics

In this paper, we present a formulation of statistical mechanics of a thermodynamic system consisting of free particles and independent correlated pairs interacting via nonlocal potential in terms of the scattering properties. Some quantum statistical properties such as energy, heat capacity, second virial coefficient, virial pressure and quantum correction of kinetic energy are described analytically. The difference between the resolvents of the interacting and free Hamiltonians, represented as R ^ ( z ) , that is associated with particle correlations is used for the evaluation of the properties. The statistical properties are related to correlated states, when making a pole expansion of the analytically continued momentum matrix element of R ^ ( z ) . The present work illustrates these relations for a three-dimensional nonlocal separable potential of rank-two.

Decomposing a pulsed optical parametric amplifier into independent squeezers

We discuss the concept of characteristic squeezing modes applied to a travelling-wave optical parametric amplifier pumped by an ultrashort pulse. The characteristic modes undergo decoupled single-mode squeezing transformations, and therefore they form a useful basis to describe the evolution of the entire multimode system. This provides an elegant and intuitive picture of quantum statistical properties of parametric fluorescence. We analyse the efficiency of detecting quadrature squeezing, and present results of numerical calculations for a realistic nonlinear medium.

A Spectral Order for Infinite Dimensional Quantum Spaces: A Preliminary Report

In 2002 Coecke and Martin created a Bayesian order for the finite dimensional spaces of classical states in physics and used this to define a similar order, the spectral order on the finite dimensional quantum states. These orders gave the spaces a structure similar to that of a domain. This allows for measuring information content of states and for determining which partial states are approximations of which pure states. In a previous paper the author extended the Bayesian order to infinite dimensional spaces of classical states. The order on infinite dimensional spaces retains many of the characteristics important to physics, but loses the domain theoretic structure. It becomes impossible to measure information content in the same way that it is done for the finite dimensional spaces, and the sense of approximation is lost. In this paper, we will use the Bayesian order to define a spectral order on the infinite dimensional spaces of quantum states.

Quantum statistical properties of the radiation field in spontaneous Raman and stimulated Raman processes

The initially prepared coherent state coupled to a third-order nonlinear medium is responsible for stimulated Raman and spontaneous Raman processes. By exploiting the analytical solutions of field operators for various modes, we investigate the quantum statistical properties for pure and two modes of the input coherent light responsible for stimulated Raman and spontaneous Raman processes. For spontaneous Raman processes the photons are unbunched for the pure and two-mode cases. By a suitable choice of phase, we obtain the bunching and antibunching of photons for stimulated Raman processes.

New Even and Odd Nonlinear Coherent States and Their Nonclassical Properties

Based on Roy and Roy's work (Roy, B. and Roy, P. (2000). Journal of Optics B: Quantum Semiclass. Opt. 2, 65), a new type of even and odd nonlinear coherent states (NCSs) are defined. They result from Schrodinger cat states for deformed field. Using the numerical method, we study nonclassical properties of the new even and odd NCSs. It is shown that quantum statistical properties of the new even and odd NCSs are quite different from those of the usual even and odd coherent states (CSs). It is found that the squeezing only consists in the new even NCS, and the amplitude-squared squeezing and antibunching effect appear for both new even and odd NCSs in some ranges of \beta\.

On entropy and information of quantum states

Shannon entropy and information are applied to study the properties of quantum states of a system in the probability representation of quantum mechanics. Examples of spin states and mixed Gaussian states of the two-mode system are considered. The relationship between the new entropy and the von Neumann entropy is reviewed. Two tomographic maps are considered within the framework of the star-product quantization. The explicit expression of tomographic entropy associated with photon-number tomogram of the two-mode state of photons is obtained in terms of Hermite polynomials of four variables.