Showing papers on "Coherent states published in 1993"

Coherent states via decoherence.

Abstract: The rate at which pure initial states deteriorate into mixtures is computed for a harmonic oscillator interacting with an environment in thermal equilibrium. The decoherence process resulting from this interaction selects a set of states characterized by maximal stability (or minimal loss of predictive power) which can be quantified by the rate of increase in either linear or statistical entropy. In the weak coupling limit, coherent states are shown to produce the least entropy, thus becoming the natural counterparts of classical points in phase space.

Synthesis of arbitrary quantum states via adiabatic transfer of Zeeman coherence.

Abstract: A scheme for the preparation of general coherent superpositions of photon-number states is proposed. By strongly coupling an atom to a cavity field, atomic ground-state Zeeman coherence can be transferred by (coherent) adiabatic passage to the cavity mode and a general field state can be generated without atomic projection noise.

Quantum switches and nonlocal microwave fields.

Abstract: A scheme to realize an optical switch with quantum coherence between its ``open'' and ``closed'' states is presented. It involves a single atom in a superposition of circular Rydberg states crossing a high Q cavity. A combination of switches could be used to prepare a quantum superposition of coherent microwave field states located simultaneously in two cavities. Such nonclassical states and their decoherence due to cavity dissipation could be studied by performing atom correlation experiments.

Measurement of number-phase uncertainty relations of optical fields

Abstract: We have experimentally determined all of the quantities involved in the uncertainty relation for the phase and photon number of a mode of the electromagnetic field when the field mode is in a coherent state of small average photon number This is accomplished by determining the quantum state of the field using optical homodyne tomography, which uses measured distributions of electric-field quadrature amplitude to determine the Wigner function and hence the density matrix The measured state is then used to calculate the uncertainty product for the number and phase, as well as the expectation value of the commutator of the number and phase operators The experimental results agree with the quantum-mechanical predictions We also present measured phase- and photon-number distributions for these weak coherent states, as well as their measured complex wave functions

Coherence and incoherence in a globally coupled ensemble of pulse-emitting units

Abstract: A general theory of coherent behavior (``locking'') in a globally coupled ensemble of pulse-emitting units is presented. Each unit is modeled as a dynamic threshold device with arbitrary excitability function and noise. The interaction is described by a general linear-response kernel that includes a transmission delay. In the bulk limit, the dynamics is solved exactly. Two types of solutions are studied, viz., coherent states with synchronous activity of all units and incoherent stationary states, and their stability is analyzed in the low-noise limit.

Production of Schrödinger macroscopic quantum-superposition states in a Kerr medium

Abstract: We show how a special class of Schr\"odinger macroscopic quantum-superposition states can be produced by a coherent field propagating through a Kerr medium. We show that these states are eigenstates of the mth power of the photon-annihilation operator leading also to the possibility of producing these using multiphoton Jaynes-Cummings systems. We further show how superpositions of squeezed coherent states can be produced.

Non-classical Properties of Even and Odd Coherent States

Abstract: We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a 2. We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.

A quantum mechanical representation in phase space

Abstract: A quantum mechanical representation suitable for studying the time evolution of quantum densities in phase space is proposed and examined in detail. This representation on L2 (2) phase space is based on definitions of the operators P and Q in phase space that satisfy various correspondences for the Liouville equation in classical and quantum phase space, as well as quantum position and momentum L2 (1) spaces. The definitions presented here, P=p/2−iℏ∂/∂q and Q=q/2+iℏ∂/∂p, are related to definitions that have been recently proposed [J. Chem. Phys. 93, 8862 (1990)]. The resulting quantum phase space representation shares many of the mathematical properties of usual representations in coordinate and momentum spaces. Within this representation, time evolution equations for complex‐valued functions (wave functions) and their square magnitudes (distribution functions) are derived, and it is shown that the coordinate and momentum space time evolution equations can be recovered by a simple Fourier projection. ...

Squeezed states for general systems.

Abstract: We propose a ladder-operator method for obtaining the squeezed states of general symmetry systems. It is a generalization of the annihilation-operator technique for obtaining the coherent states of symmetry systems. We connect this method with the minimum-uncertainty method for obtaining the squeezed and coherent states of general potential systems, and comment on the distinctions between these two methods and the displacement-order method.

Coherent states on a circle and quantum interference.

Abstract: As a generalization of the optical Schrodinger cats, discrete sets of coherent states are considered on a circle in the a plane. It is shown that simple superpositions of Schrodinger cats exhibit amplitude squeezing, similarly to the case of a superposition of several coherent states along a straight line that shows quadrature squeezing. The interference fringes between the coherent states form the annuli of the Fock states in the Wigner-function picture. It is also shown that a continuous superposition of coherent states on a circle can serve as a basis for the representation of any state

Quantum statistics of a lossless beam splitter: SU(2) symmetry in phase space.

Abstract: A lossless beam splitter (a dielectric interface, a passive interferometer, or a linear coupler) changes the quantum state of two incident modes by an SU(2) transformation. Apart from phase shifting, the argument of the quadrature wave function of the system undergoes a rotation. Quasiprobabilities are changed by the inverse mode transformation. The use of balanced beam splitting allows the simultaneous measurement of conjugate quadrature components via homodyning the emerging beams with two strong coherent reference fields that differ in their phases by \ensuremath{\pi}/2. The measured probability distribution is given by a generalized Q function. It depends on the state of the field entering the second beam-splitter port. For a vacuum, the Q function will be obtained. The use of unbalanced beam splitting allows the measurement of a squeezed Q function without using squeezed states. Dissipation in Gaussian reservoirs corresponds exactly to a heuristic beam-splitter model. As a mathematical tool, the Fokker-Planck equation of damping in phase-sensitive reservoirs and the corresponding quantum master equation were solved. The dissipative decay of a Schr\"odinger-cat state was studied as an example. The sensitivity of quantum coherence with respect to damping can be interpreted geometrically.

The q -harmonic oscillator and the Al-Salam and Carlitz polynomials

Abstract: One more model of aq-harmonic oscillator based on theq-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form ofq-creation andq-annihilation operators,q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.

Two-photon absorption and nonclassical states of light.

Abstract: We investigate the dynamical evolution of nonclassical states of light undergoing a two-photon absorption process. We consider two distinct cases of initial states, a squeezed coherent state and an eigenstate of the two-photon annihilation operator (a superposition of macroscopically distinct coherent states). We analyze the fluctuations in the photon-number operator and in the quadrature components of the field. Whereas one-photon linear damping rapidly destroys quantum features such as squeezing, we demonstrate that substantial coherence is retained when such light interacts with a two-photon-absorbing reservoir. This surviving coherence is responsible for the preservation of squeezing in the steady state despite the effect of dissipation. We relate the origin of squeezing of initially unsqueezed light interacting with two-photon absorbers with the squeezing generated by simple superposition states of light.

Quantum theory of two-mode interactions in optically anisotropic media with cubic nonlinearities: Generation of quadrature- and polarization-squeezed light

Abstract: A quantum theory is derived for the propagation of two electromagnetic waves in an anisotropic medium with a cubic nonlinearity. In general, the dynamics are described by a Hamiltonian that corresponds to an anisotropic two-dimensional anharmonic oscillator. The degree of suppression of quantum fluctuations in the quadrature component of one wave decreases when another wave is present. When the nonlinear phase corrections associated with self-interaction of the waves are different, it is possible to create a polarization state of the optical field that is nonclassical, with quantum fluctuations in one of the Stokes parameters smaller than in the coherent state.

Statistics of difference events in homodyne detection.

Abstract: The statistics of the difference events in a balanced homodyne-detection scheme is studied without using the standard assumption of a strong, classical local oscillator. Starting from the quantum theory of photon counting, we derive the probability distribution for the difference events in the two detection channels. In the limit of the local oscillator being strong compared with the signal, the difference-number statistics tends to the statistics of the electric-field strength of the signal field. For weak signals, this limit may be obtained already far from a classical behavior of the local oscillator. While changing the local oscillator intensity, a transition of the observable concerning the signal field occurs from the photon-number difference towards the electric-field strength. Such a measurement scheme renders it possible to observe the quantum features of a coherent state or a single-photon state from the point of view of the field-strength statistics, a picture which is closely related to classical optics. The possibility to get some insight in the statistical properties of the phase difference of two microscopic fields is discussed.

Generalized Jaynes-Cummings models with a time-dependent atom-field coupling

Abstract: An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.

Photon statistics of superposition states in phase-sensitive reservoirs.

Abstract: Using the Wigner function formalism in phase space, we analyze the decay of quantum coherences in phase-sensitive reservoirs. We show that the decay rate of quantum coherences in phase-sensitive reservoirs can be significantly modified compared to the decay rate in ordinary (phase-insensitive) thermal reservoirs. Depending on the phases of the quantum system (field mode) and the squeezed reservoir, the decay rate of the quantum coherence can be either enhanced or significantly suppressed, which is in agreement with the results obtained recently by other methods [T. A. B. Kennedy and D. F. Walls, Phys. Rev. A 37, 152 (1988)]. We show that in an ideally squeezed reservoir with a high degree of squeezing, the decay rate of the quantum coherence (i.e., the decay rate of off-diagonal terms of the density matrix in the coherent-state basis) can be equal to the decay rate of the energy of the system (i.e., the decay rate of diagonal terms of the density matrix). Suppression of the decay rate of the quantum coherence leads to preservation of nonclassical effects such as the oscillations in the photon number distribution. Moreover, we find that some initial superposition states of light exhibiting super-Poissonian photon statistics can be transformed into intermediate sub-Poissonian states under the influence of phase-sensitive reservoirs.

Quantum tunneling in a Kerr medium with parametric pumping

Abstract: A quantum optical model with a classical phase space exhibiting nonlinear oscillations around two elliptic fixed points is investigated. The quantum system is found to display coherent tunneling between near coherent states of opposite phase centered at the classical fixed points.

Experimental determination of number-phase uncertainty relations.

Abstract: An experimental determination of the uncertainty product for the phase and photon number of a mode of the electromagnetic field is performed. The expectation value of the commutator that sets the lower bound for the uncertainty product is also determined experimentally. This is accomplished by using optical homodyne tomography to measure the density matrix of a small-photon-number coherent state. The experimental results agree with the quantum-mechanical predictions.

Macroscopic Superposition States of Light Via Two-photon Resonant Interaction of Atoms with Cavity Field

Abstract: We show that the resonant interaction between a two-level atom and a quantized field mode via two-photon transitions leads to extreme quantum entanglement between the atom and quantum field. Nevertheless during the time evolution there are moments at which the atom-field system becomes asymptotically disentangled. We investigate statistical properties of the pure-field states generated at such times. We show that at the quarter of the revival time the field is produced in the pure superposition state (Schrodinger cat state) composed of two coherent states with the same amplitude but which are out of phase by 90° (we obtain approximate analytical solution for this superposition state). We show that the interference between component states leads to non-classical oscillations in the photon number distribution. At the revival time the field is again in the pure state (we present an approximate analytical solution for the corresponding state vector). This pure state is not a superposition state. Neve...

Schrödinger-cat states of the electromagnetic field and multilevel atoms

Abstract: We demonstrate that the generalization of the two-level Jaynes-Cummings model to an N-level atom leads to the creation of up to N macroscopically distinct field states. These field states are Schmidt-orthogonalized superpositions of Fock states. They correspond to macroscopic states of the field, attainable with large mean photon numbers. Unlike the situation with a two-level atom and a coherent-state field, which evolves into a macroscopic coherent superposition state (a Schr\"odinger cat), we find that when the additional levels participate strongly in the excitation (e.g., all transitions are resonant with equal dipole moments) then the system does not evolve into a pure state.

Quantized geometry associated with uncertainty and correlation.

Abstract: The geometric structure of the law of quantum-state evolution is studied. The Fubini-Study metric induced on the quantum evolution submanifold of the projective Hilbert space is shown to be completely expressed by the uncertainties and correlations of various generators of evolutions. The Riemannian connection is expressed as a quantum-mechanical expectation value of a certain Hermitian operator. It is discussed that the metric carries some of quantum numbers contained in a given reference state, in general, and consequently the geometry is inherently quantized. These results are demonstrated by the simple examples of the squeezed coherent state, displaced number state, squeezed number state, and generalized coherent spin state

Effect of atomic coherence on the second- and higher-order squeezing in a two-photon three-level cascade atomic system.

Abstract: A three-level cascade atomic system is considered where atomic coherence can be achieved either by applying an intense pump field or initially preparing the atoms in a coherent superposition of the states. It is predicted that the system, under certain conditions, exhibits almost perfect squeezing outside the cavity. By using the steady-state Q solution it is also shown that certain higher-order squeezing can also be achieved inside the cavity, under a suitable choice of different parameters

Density-matrix theory of coherent phonon oscillations in germanium.

Abstract: The generation and detection processes of coherent phonon oscillations in germanium are described within an extended density-matrix model. In the relevant hierarchy of equations of motion for the generation of the phonon oscillation, the anisotropy of the hole distributions related to the anisotropy of the interband dipole matrix elements is identified as the driving force of the coherent vibration. The optical detection of coherent phonons in reflectivity is based on anisotropic band-gap modulations due to the coherent displacements, weighted with the deformation potential of the valence bands.

Quantum propagation in a Kerr medium: lossless, dispersionless fiber

Abstract: Intense light beams propagating in a lossless, dispersionless, single-mode optical fiber are subject to the Kerr effect, i.e., to the intensity-dependent refractive index of the fiber’s fused-silica core. Classically, Kerr-effect-induced self-phase modulation (SPM) can be used for spectral broadening of a picosecond pulse for grating-pair pulse compression down to femtosecond duration. Quantum mechanically, Kerr-effect-induced four-wave mixing (FWM) has been used to produce squeezed-state light. We present a quantum propagation theory for a lossless, dispersionless fiber with the Kerr nonlinearity. The theory includes classical SPM and quantum FWM within their regions of validity. It introduces a material time constant for the Kerr interaction, limiting the quantum phase shifts caused by the broadband zero-point fluctuations that accompany any input field, to develop a coarse-grained time multitemporal mode field analysis. Explicit expressions are obtained for the first and the second output-field moments when the fiber’s input field is in an arbitrary Gaussian state. These results are used to obtain homodyne-detection noise spectra, which are employed, in turn, to seek experimentally accessible manifestations of the Kerr time constant.