Showing papers on "Coherent states published in 1998"

Coherent states on the circle

Abstract: A careful study of the physical properties of a family of coherent states on the circle, introduced some years ago by de Bievre and Gonzalez (in 1992 Semiclassical behaviour of the Weyl correspondence on the circle Group Theoretical Methods in Physics vol I (Madrid: Ciemat)), is carried out. They were obtained from the Weyl-Heisenberg coherent states in by means of the Weil-Brezin-Zak transformation, they are labelled by the points of the cylinder , and they provide a realization of by entire functions (similar to the well known Fock-Bargmann construction). In particular, we compute the expectation values of the position and momentum operators on the circle and we discuss the Heisenberg uncertainty relation.

Bose-Einstein condensate in a double-well potential as an open quantum system

Abstract: We study the dynamics of a Bose-Einstein condensate in a double-well potential in the two-mode approximation. The dissipation of energy from the condensate is described by the coupling to a thermal reservoir of noncondensate modes. As a consequence of the coupling, the self-locked population imbalance in the macroscopic quantum self-trapping decays away. We show that a coherent state predicted by spontaneous symmetry breaking is not robust and decoheres rapidly into a statistical mixture due to the interactions between condensate and noncondensate atoms. However, via stochastic simulations we find that with a sufficiently fast measurement rate of the relative phase between the two wells the matter wave coherence is established even in the presence of the decoherence.

Quantum Algebras and q-Special Functions Related to Coherent States Maps of the Disc

Abstract: The quantum algebras generated by the coherent states maps of the disc are investigated. It is shown that the analytic realization of these algebras leads to a generalized analysis which includes standard analysis as well as q-analysis. The applications of the analysis to star-product quantizations and q-special functions theory are given. Among others the meromorphic continuation of the generalized basic hypergeometric series is found and a reproducing measure is constructed, when the series is treated as a reproducing kernel.

Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements

Abstract: We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.

Dynamical squeezing of photon-added coherent states

Abstract: We study the dynamical squeezing of the photon-added coherent state ~PACS! due to a time dependence of the frequency of the electromagnetic field oscillator in a cavity or a vibrational frequency of an ion inside an electromagnetic trap. Explicit expressions for the time dependence of various functions characterizing the quantum state, such as the photon distribution, the Wigner function, the mean values and variances of the quadrature components and of the photon number, show that the dynamically squeezed PACS possesses a larger squeezing coefficient than the usual squeezed states. The dynamical squeezing is accompanied by a change of the sub-Poissonian photon statistics to the super-Poissonian one. @S1050-2947~98!07410-1#

A general theory of phase-space quasiprobability distributions

Abstract: We present a general theory of quasiprobability distributions on phase spaces of quantum systems whose dynamical symmetry groups are (finite-dimensional) Lie groups. The family of distributions on a phase space is postulated to satisfy the Stratonovich - Weyl correspondence with a generalized traciality condition. The corresponding family of the Stratonovich - Weyl kernels is constructed explicitly. In the presented theory we use the concept of generalized coherent states, that brings physical insight into the mathematical formalism.

Mixed-order semiclassical dynamics in coherent state representation: The connection between phonon sidebands and guest-host dynamics

Abstract: The formalism of mixed-order semiclassical molecular dynamics in coherent state representation is developed and applied to calculations of quantum time correlation functions in extended systems. The method allows the consistent treatment of a selected number of degrees of freedom to second order in the stationary phase approximation, through the Herman and Kluk propagator, while the rest of the system is treated to zeroth order, using frozen Gaussians. The formulation is applied to calculate the absorption spectrum, of the B←X transition of Cl2 isolated in solid Ar a spectrum that shows zero-phonon lines and phonon sidebands with relative intensities that depend on the excited state vibrational level. The explicit simulation of quantum time correlation functions of the system consisting of 321 degrees of freedom, reproduces the spectrum and allows its interpretation in terms of the underlying molecular motions. Details of the dynamics of a chromophore coupled to lattice phonons are discussed.

Biophysical aspects of coherence and biological order.

Abstract: Biological Order * Thermodynamic Aspects of Order * Normal Modes * Quantum Mechanical Theory of Rate Equations * Energy Condensation * Coherence in Systems with Random Energy Supply * Spectral Transformation of Energy * Oscillating Electric Field Generated by Living Cells * Information Transfer Between Oscillation Systems * Interaction Between Vibration Systems * Heat Bath Coupling Effects * Coherent States in Cancer Cells.

The harmonic oscillator propagator

Abstract: The Feynman propagator for the harmonic oscillator is evaluated by a variety of path-integral-based means.

Exact coherent states of a one-dimensional quantum fluid in a time-dependent trapping potential

Abstract: We find exact coherent states for a one-dimensional quantum fluid interacting by an inverse-square pair potential, contained by a time-dependent harmonic trapping potential. These states are those that would evolve from the ground state of the time-independent problem. Correlations are determined, and a hydrodynamic description is shown to be exact. We treat the case of a nondissipative ``sloshing'' mode characteristic of superfluidity, free expansion where time-of-flight measurements do not give the momentum distribution, and a periodically varying trapping potential exhibiting alternating regions of stable and unstable behavior.

Coherent states and the classical limit on irreducible representations

Abstract: We give an explicit construction of the coherent states for an arbitrary irreducible representation. We also construct the symplectic structure on the manifold of coherent states, find canonical variables and discuss various classical limits of quantum-mechanical systems with relevant observables that obey commutation relations.

The Monge distance between quantum states

Abstract: We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q-functions). This quantity fulfils the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between corresponding points in the classical phase space. We compute analytically distances between certain states (coherent, squeezed, Fock and thermal) and discuss a scheme for numerical computation of Monge distance for two arbitrary quantum states.

Weyl functions and their use in the study of quantum interference

Abstract: Weyl functions are shown to be an important tool in quantum phase-space studies. Their properties are studied and relations with other quantities are derived. The use of Weyl functions for the understanding of quantum interference phenomena is discussed. The general theory is applied to superpositions of $m$ coherent states uniformly distributed on a circle (generalized Schr\"odinger cats). The properties of these states are explored and their interference behavior is discussed, using Weyl functions.

The su(1,1) Tavis-Cummings model

Abstract: A generic su(1,1) Tavis-Cummings model is solved both by the quantum inverse method and within a conventional quantum-mechanical approach. Examples of corresponding quantum dynamics including squeezing properties of the su(1,1) Perelomov coherent states for the multiatom case are given.

Chaotic inflation from a scalar field in nonclassical states

Abstract: We study chaotic inflation driven by a real, massive, homogeneous minimally coupled scalar field in a flat Robertson-Walker spacetime. The semiclassical limit for gravity is considered, whereas the scalar field is treated quantum mechanically by the technique of invariants in order to also investigate the dynamics of the system for non-classical states of the latter. An inflationary stage is found to be possible for a large set of initial quantum states, obviously including the coherent ones. States associated with a vanishing mean value of the field (such as the vacuum and the thermal) can also lead to inflation; however, for such states we cannot make a definitive prediction due to the importance of higher order corrections during inflation. The results for the above coupled system are described and their corrections evaluated perturbatively.

On Quantum Mechanical Aspects of Microtubules

Abstract: We discuss possible quantum mechanical aspects of MicroTubules (MT), based on recent developments in quantum physics. We focus on potential mechanisms for "energy-loss-free" transport along the microtubules, which could be considered as realizations of Frohlich's ideas on the role of solitons for superconductivity and/or biological matter. In particular, by representing the MT arrangements as cavities, we present a novel scenario on the formation of macroscopic (or mesoscopic) quantum-coherent states, as a result of the (quantum-electromagnetic) interactions of the MT dimers with the surrounding molecules of the ordered water in the interior of the MT cylinders. Such states decohere due to dissipation through the walls of the MT. Transfer of energy without dissipation, due to such coherent modes, could occur only if the decoherence time is larger than the average time scale required for energy transfer across the cells. We present some generic order of magnitude estimates or the decoherence time in a typical model for MT dynamics. Our conclusion is that the quantum coherent states play a role in energy transfer if the dissipation through the walls of the MT cavities is fairly suppressed, corresponding to damping time scales Tr≥10-4-10-5 sec, for moderately large MT networks. We suggest specific experiments to test the above-conjectured quantum nature of the microtubular arrangements inside the cell. These experiments are similar in nature to those in atomic physics, used in the detection of the Rabi-Vacuum coupling between coherent cavity modes and atoms. Our conjecture is that a similar Rabi-Vacuum-splitting phenomenon occurs in the absorption (or emission) spectra of the MT dimers, which would constitute a manifestation of the dimer coupling with the coherent modes in the ordered-water environment (dipole quanta), which emerge due to "super-radiance".

Quasiclassical path integral in coherent-state manifolds

Abstract: Quantization of classical dynamical systems with a Poisson structure on homogeneous Kahler manifolds is considered. The quantization follows the method invented by Berezin and represents the unitary transition operator as a quasiclassical path integral in the coherent-state basis. In case the coherent-state manifold appears as a (degenerate) rank-one co-adjoint orbit of the symmetry group, an explicit representation of the transition amplitude in terms of classical data can be derived for large values of the highest weight, which corresponds to the quasiclassical approximation. This representation is further shown to perfectly agree, in contrast to some earlier approaches, with the known exact results and may provide non-trivial asymptotics of physical relevance.

Quantum singular oscillator as a model of a two-ion trap: An amplification of transition probabilities due to small-time variations of the binding potential

Abstract: Following the paper by Combescure [Ann. Phys. (N.Y.) 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 $n\ensuremath{\ll}{n}_{\mathrm{max}}\ensuremath{\sim}100$, provided the dimensionless constant characterizing the strength of the repulsive potential is large enough ${g}_{*}\ensuremath{\sim}{10}^{5}$. 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 ${g}_{*}$ results in a significant amplification of the transition probabilities between energy eigenstate even for slow time variations of the frequency.

Meixner Oscillators

Abstract: Meixner oscillators have a ground state and an `energy' spectrum that is equally spaced; they are a two-parameter family of models that satisfy a Hamiltonian equation with a {\it difference} operator Meixner oscillators include as limits and particular cases the Charlier, Kravchuk and Hermite (common quantum-mechanical) harmonic oscillators By the Sommerfeld-Watson transformation they are also related with a relativistic model of the linear harmonic oscillator, built in terms of the Meixner-Pollaczek polynomials, and their continuous weight function We construct explicitly the corresponding coherent states with the dynamical symmetry group Sp(2,$\Re$) The reproducing kernel for the wavefunctions of these models is also found

Polarization quantum states of light in nonlinear distributed feedback systems; quantum nondemolition measurements of the Stokes parameters of light and atomic angular momentum

Abstract: A possibility of the formation of polarization- squeezed light in the case of interaction of two orthogonally polarized modes in a spatio-periodically nonlinear Kerr-like medium is considered. It is shown that the fluctuations of the Stokes parameters of light could be less than their fluctuations in a coherent state at the output of the medium. An analysis shows that the light polarization degree is not fixed in such a nonclassical state of light. We also introduce a new nonlinear parameter of light polarization associated with the fluctua- tion variances of three Stokes parameters. The value of the parameter is examined for different quantum states of light. A procedure for the quantum nondemolition (QND) measure- ment of the Stokes parameters of light is described for the first time. We show that the precision measurement of the Stokes parameter depending on phase could be used for the QND measurement of the phase difference of two orthogonally po- larized modes. The general description of the measurement procedure under study allows us to propose also a scheme for the QND measurement of angular momentum of atomic systems.

Semiclassical coherent-state path integrals for scattering

Abstract: We study the application of the semiclassical coherent-state path-integral technique to the problem of scattering. A numerical method based on initial-value trajectories and their stability information is proposed to solve the root search for the complex trajectories that determine the semiclassical propagator. Very good agreement between the numerically exact quantum and semiclassical results for the correlation function can be achieved for scattering from one-dimensional barrier as well as well-type potentials by using just one single complex trajectory at each time.

A scheme for the generation of multi-mode Schrödinger cat states

Abstract: A scheme is proposed for the generation of superpositions of multi-mode coherent states, i.e. multi-mode Schrodinger cat states. In the scheme a -type three-level atom is sent through many cavities filled with coherent fields. The whole system is entangled via the Raman atom-field interaction. Then the detection of the atom leaves the cavity system in a multi-mode cat state. Under certain conditions, such a cat state is identical to a Greenberger-Horne-Zeilinger state and thus can be used to test local realistic theories.