Showing papers on "Coherent states published in 1990"

Coherent states: Theory and some Applications

Abstract: In this review, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented. The result is that, for a given dynamical group, the coherent states are isomorphic to a coset space of group geometrical space. Thus the topological and algebraic structure of the coherent states as well as the associated dynamical system can be extensively discussed. In addition, a quantum-mechanical phase-space representation is constructed via the coherent-state theory. Several useful methods for employing the coherent states to study the physical phenomena of quantum-dynamic systems, such as the path integral, variational principle, classical limit, and thermodynamic limit of quantum mechanics, are described.

Continuum fields in quantum optics.

Abstract: We formulate the quantum theory of optical wave propagation without recourse to cavity quantization. This approach avoids the introduction of a box-related mode spacing and enables us to use a continuum frequency space description. We introduce a complete orthonormal set of operators that can describe states of finite energy. The set is countable and the operators have all the usual properties of the single-mode frequency operators. With use of these operators a generalization of the single-mode normal-ordering theorem is proved. We discuss the inclusion of material dispersion and pulse propagation in an optical fiber. Finally, we consider the process of photodetection in free space, concluding with a discussion of homodyne detection with both local oscillator and signal fields pulsed.

Collapse and revival of the state vector in the Jaynes-Cummings model: An example of state preparation by a quantum apparatus.

Abstract: The evolution of the atomic state in the resonant Jaynes-Cummings model (a two-level atom interacting with a single mode of the quantized radiation field) with the field initially in a coherent state is considered. It is shown that the atom is to a good approximation in a pure state in the middle of what has been traditionally called the "collapse region. This pure state exhibits no Rabi oscillations and is reached independently of the initial state of the atom. For most initial states a total or partial "collapse of the wave function" takes place early during the interaction, at the conventional collapse time, following which the state vector is recreated, over a longer time scale. PACS numbers: 42.50.— p, 03.65.— w, 42.52.+x The Jaynes-Cummings model' (JCM) is perhaps the simplest nontrivial example of two interacting quantum systems: a two-level atom and a single mode of the radiation field. In addition to its being exactly solvable, the physical system that it represents has recently become experimentally realizable with Rydberg atoms in high-Q microwave cavities. Comparison of the predictions of the model with those of its semiclassical version have served to identify a number of uniquely quantum properties of the electromagnetic field; indeed, the model displays some very interesting dynamics, and the differences with the semiclassical theory are both profound and unexpected. The JCM would also appear to be an excellent model with which to explore some of the more puzzling aspects of quantum mechanics, such as the possibility (or impossibility) to describe an interacting quantum system by a state vector undergoing unitary evolution; i.e., the socalled "collapse of the wave function. " In the semiclassical version, the atom interacting with the classical electromagnetic field may at all times be described by a state vector evolving unitarily. What happens, however, when it is recognized that the field is itself a quantum system (which leads inevitably to "entanglement" )? This is the question addressed in this Letter. It does not seem to have been addressed before in full generality, although entanglement in the JCM dynamics plays an essential role in a recent measurement-theory-related proposal of Scully and Walther, and preparation of a pure state of the field in the JCM has been the subject of several theoretical investigations and may be close to being achieved experimentally. The resonant JCM interaction Hamiltonian may be written as Ht = hg(~a&(b (a+ a'(b)(a ~ ), ' is a coupling constant (d is the atomic dipole matrix element for the transition, m is the transition frequency, and Vis the mode volume), ~a) and ~b) are the upper and lower atomic levels, respectively, and a and a are the annihilation and creation operators of the field mode, which in the semiclassical theory are simply replaced by c numbers. The solution to the Schrodinger equation for the atom initially in state y(0)).,&,~ =a~a)+ p b) and field initially in state ttt(0))fi iu g„-OC„n) is ~y(t)) = g [[aC„cos(gOn+1 t) — ipC„s+i l(gnawn +1 t)]~ a& +[ — iaC„~sin(gran t)+pC„cos(gran

Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath.

Abstract: A method to determine the resolvent of a quantum system coupled to a harmonic-oscillator bath is derived by extending the continued-fraction theory of a Gaussian-Markovian bath that has been presented by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1989)]. The results are expressed in terms of continued fractions and apply to an oscillator bath with a general spectral density, corresponding to colored noise, at various temperatures. Exact values of the resolvent can be calculated for arbitrary strength of the system-bath interaction by making use of the convergence properties of the continued fractions. For the weak-interaction case these results agree with the quantum master equation. The physical meaning of the results is also discussed by a diagrammatic method. As an application, the result of the Gaussian-Markovian system is extended to the case of the low-temperature bath. Correlated (unfactorized) initial conditions are also discussed.

Quantum theory of soliton squeezing: a linearized approach

Abstract: A linearized quantum theory of soliton squeezing and detection is presented. The linearization reduces the quantum problem to a classical one. The classical formulation provides physical insight. It is shown that a quantized soliton exhibits uncertainties in photon number and phase, position (time), and momentum (frequency). Detectors for the measurement of all four operators are discussed. The squeezing of the soliton in the fiber is analyzed. An optimal homodyne detector for detection of the squeezing is presented that suppresses the noise associated with the continuum and the uncertainties in position and momentum.

Squeezing via one-dimensional distribution of coherent states.

Abstract: It is found that strong squeezing can be obtained by special superposition of coherent states along a straight line in the \ensuremath{\alpha} -plane. This mechanism opens new possibilities for squeezing, e.g., of the molecular vibrations during a Franck-Condon transition induced by a short coherent light pulse.

Control of Quantum-Mechanical Processes and Systems

Abstract: 1. The Problem of Control on the Quantum Level.- 1.1. Introduction.- 1.2. A Quantum Process as the Object of Control.- 1.3. Problems of Control in Different Descriptions.- 1.4. Obtaining a Prescribed Pure State or a State in its Vicinity.- 1.5. Control with the Aim of Obtaining a Specified Probability of a Given Pure State.- 1.6. Obtaining the Maximum (or Minimum) Probability of a Specified Value of a Physical Quantity.- 1.7. Obtaining a Desired Distribution of Probability Amplitudes for Values of Given Physical Quantities.- 1.8. Control of Quantum Averages and Moments of Physical Quantities.- 1.9. Control of the Distributions of Eigenvalues of Physical Quantities.- 1.10. Control of Operators of Physical Quantities.- 1.11. Measurement in Systems with Feedback.- 2. Controllability and Finite Control of Quantum Processes (Analytical Methods).- 2.1. Control of Pure States of Quantum Processes.- 2.2. Local Controllability in the Vicinity of a Pure State.- 2.3. Global Asymptotic Controllability of Pure States.- 2.4. Control of the Electron in a Rectangular Potential Well.- 2.5. Control of a Two-Spin System.- 2.6. Finite Control of a Particle Spin State.- 2.7. Control of Quantum Averages of Physical Quantities.- 2.8. Control of Coherent States of a One-Dimensional Quantum Oscillator by Means of an External Force.- 2.9. Control of a One-Dimensional Quantum Oscillator by Varying its Eigenfrequency.- 2.10. Obtaining a Specified Probability of a Given State of a Charged Particle by Means of an External Magnetic Field.- 2.11. Control of the State of a Free Particle by an External Force.- 2.12. Control of the Coefficients of Linear Differential Equations Impulse Control.- 2.13. Control of Magnetization.- 3. Controllability and Finite Control (Algebraic Methods).- 3.1. Algebraic Conditions for the Controllability of a Quantum Process.- 3.2. Control on the Motion Groups of Quantum Systems.- 3.3. The Structure of the Algebra of a Quantum System.- 3.4. The Accessible Set of Evolution Matrices.- 3.5. Designing Discrete Automata on Controlled Transitions of Quantum Systems.- 4. Optimal Control of Quantum-Mechanical Processes.- 4.1. General Formulation of the Control Problem for a Quantum Statistical Ensemble.- 4.2. Variational Control Problems.- 4.3. Necessary Conditions for an Extremum.- 4.4. Methods of Solving Boundary Value Optimization Problems.- 4.5. Methods of Direct Optimization on Unitary Groups.- 4.6. Maximization of the Probability of Observing a Given State of a Quantum System.- 5. Dynamical Systems with Stored Energy and Negative Susceptibility.- 5.1. The Effect of Negative Susceptibility of Dynamical Systems and its Applications.- 5.2. Synthesis of Bipolar Circuits with Negative Impedance and Negative Conductivity.- 5.3. Negative Susceptibility in Gyroscopically Related Systems.- 5.4. Transverse Susceptibility of a Rigid Dipole in an Inversely Directed Constant Field.- 5.5. Negative Susceptibility of a Parametrically Modulated Oscillator.- 5.6. Systems with Stored Energy.- 5.7. Static Susceptibility of Adiabatically Invariant Control Systems.- 5.8. Conditions for Negative Static Susceptibility in Quantum Systems.- 6. Negative Susceptibility in Parametrically Induced Magnetics.- 6.1. Induced Superdiamagnetism and its Application to Distributed Control.- 6.2. Superdiamagnetic States in Inversely Magnetized Ferromagnetic Media.- 6.3. Superdiamagnetism and Parametrically Stimulated Anomalous Gyrotropy.- 6.4. Low-Frequency Susceptibility of a Gyromagnetic Medium.- 6.5. Stability of Spin Waves in Longitudinal Pumping of Ferromagnetic Crystals.- 6.6. Applications.- Appendix 1. Mathematical Models of Quantum Processes.- Appendix 2. Controllability and Finite Control of Dynamical Systems.- A2.1. Controllability and Finite Control of Linear Finite-Dimensional Systems.- A2.2. Finite Control of Linear Distributed Systems.- A2.3. A New Differential Geometric Method of Solving the Problems of Finite Control of Non-Linear Finite-Dimensional Dynamical Systems.- Appendix 3. Continuous Media and Controlled Dynamical Systems (CDS's). The Maximum Principle for Substance Flow. The Laplacian of a CDS.- References.

SU(1,1) Squeezing of SU(1,1) Generalized Coherent States

Abstract: In this paper we have introduced a new class of the SU(1,1) coherent states which are the eigenstates of the generalized annihilation operator K_. We have also studied the SU(1,1) squeezing of the SU(1,1) generalized coherent states interacting with a nonlinear medium modelled as an anharmonic oscillator.

Chaos-revealing multiplicative representation of quantum eigenstates

Abstract: The quantisation of the two-dimensional toric and spherical phase spaces is considered in analytic coherent state representations. Every pure quantum state admits therein a finite multiplicative parametrisation by the zeros of its Husimi function. For eigenstates of quantised systems, this description explicitly reflects the nature of the underlying classical dynamics: in the semiclassical regime, the distribution of the zeros in the phase space becomes one-dimensional for integrable systems, and highly spread out (conceivably uniform) for chaotic systems. This multiplicative representation thereby acquires a special relevance for semiclassical analysis in chaotic systems.

Periodicity, phase, and entropy in models of two-photon resonance

Abstract: The excitation of Rydberg atom transitions by submillimeter-wavelength radiation in high-Q cavities forms the basis of the micromaser. The excitation dynamics of a micromaser is known to be dependent on the detailed photon statistics in the interaction cavity and can exhibit well-known collapses and revivals of the atomic inversion, dipole moment, and photon number. We study these effects in a two-photon model in which the time evolution is exactly periodic. We study the field entropy in two two-photon cases and link the fluctuations in the field phase to the changes in the field entropy. We also calculate the statistical Q function of the field and show how the periodicity of the two-photon dynamics is linked to a periodic splitting of the Q function in phase space. Finally this periodicity is linked to the nature of the atom-field dressed states involved in two-photon resonance.

Coherent state quantization of chern-simons theory

Abstract: Three-dimensional Chern-Simons gauge theories are quantized in a functional coherent state formalism. The connection with two-dimensional conformal field theory is found to emerge naturally. The normalized wave functionals are identified as generating functionals for the chiral blocks of two-dimensional current algebra.

Comment on the q-analogues of the harmonic oscillator

Abstract: The Heisenberg relation for the q-analogues of the quantum harmonic oscillator (introduced independently by Macfarlane and Biedenharn (1989) for the quantum group SU(2)q) is derived by a method analogous to that used by Schwinger (1968) for the SU(2) case. The author also speculates on the possible use of the quantum group as a generalisation of quantum mechanics.

A completeness relation for the q-analogue coherent states by q-integration

Abstract: q-integration is defined for the q-oscillator realization of quantum groups. This is used to prove a completeness relation for the q-analogue of the usual coherent states. These states are overcomplete.

Quantum mechanics in phase space: New approaches to the correspondence principle

Abstract: We present a time evolution equation that provides a novel basis for the treatment of quantum systems in phase space and for the investigation of the quantum‐classical correspondence. Through the use of a generalized Husimi transform, we obtain a phase space representation of the time‐dependent Schrodinger equation directly from the coordinate representation. Such an equation governs the time evolution of densities such as the Husimi density entirely in phase space, without recourse to a coordinate or momentum representation. As an application of the phase‐space Schrodinger equation, we compute the eigenfunctions of the harmonic oscillator in phase space, relate these to the Husimi transform of coordinate representation eigenstates, and investigate the coherent state, its time evolution, and classical limit (ℏ→0) for the probability density generated by this state. Finally, we discuss our results as they relate to the quantum‐classical correspondence, and quasiclassical trajectory simulations of quantum d...

Generation of discrete superpositions of coherent states in the anharmonic oscillator model

Abstract: The problem of generating discrete superpositions of coherent states in the process of light propagation through a nonlinear Kerr medium, which is modelled by the anharmonic oscillator, is discussed. It is shown that under an appropriate choice of the length (time) of the medium the superpositions with both even and odd numbers of coherent states can appear. Analytical formulae for such superpositions with a few components are given explicitly. General rules governing the process of generating discrete superpositions of coherent states are also given. The maximum number of well distinguished states that can be obtained for a given number of initial photons is estimated. The quasiprobability distribution Q( alpha , alpha *,t) representing the superposition states is illustrated graphically, showing regular structures when the component states are well separated.

Quantum beats of light hole and heavy hole excitons in quantum wells

Abstract: We report the first observation of quantum beats due to the interference of the polarization decay of heavy hole and light hole excitons in semiconductor quantum wells.

Quantum superpositions generated by quantum nondemolition measurements.

Abstract: We analyze a quantum nondemolition measurement scheme similar to that advocated by Song, Caves, and Yurke [Phys. Rev. A 41, 5261 (1990)] for generating superpositions of macroscopically distinct quantum states, but with the parametric amplifier and the back-action evader interchanged. We determine the asymptotic behavior of the output and obtain the conditions under which a superposition of two coherent states is approached. By presqueezing the signal port input, we find that gain requirements of the back-action evader are much less demanding.

Wave-packet evolution in the damped oscillator

Abstract: We demonstrate that, for a simple model of the damped oscillator, both the wave packet in the position representation and oscillator expectation values are insensitive to the rapid decay of off-diagonal coherences. This rapid decay is, however, seen in the von Neumann entropy for the oscillator and the wave packet in the number representation.

Wigner function for number and phase

Abstract: Various quasiprobability distributions have been developed in the past using the Hilbert space of the single-mode light field. The development of a quasiprobability distribution associated with a phase operator has previously been impossible because of the absence of a unique Hermitian phase operator defined on the Hilbert space. Recently, however, Pegg and Barnett [Europhys. Lett. 6, 483 (1988); Phys. Rev. A 39, 1665 (1989)] and Barnett and Pegg [J. Mod. Optics 36, 7 (1989)] introduced a new formalism that does allow the construction of a Hermitian phase operator and associated phase eigenstates. In this paper we develop a quasiprobability distribution associated with the number and phase operators of the single-mode light field in the new formalism. The new distribution, which we call the number-phase Wigner function, has properties analogous to the Wigner function. We also derive the number-phase Wigner representation of number states, phase states, general physical states, coherent states, and the squeezed vacuum. We find this new representation has features that are related to the number and phase properties of states. For example, the number-phase Wigner representation of a number state is nonzero only on a circle, while the representation of a phase state is only nonzero along a radial line.

Physical Number-phase Intelligent and Minimum-uncertainty States of Light

Abstract: The recently introduced Hermitian phase operator allows a phase-state representation of the single-mode light field. We find the requirement that a light field is in a physical state, that is, has finite energy moments, imposes strict and simple continuity conditions on the phase-amplitude distribution. We exploit these conditions to examine the physical intelligent and minimum-uncertainty states associated with the number-phase uncertainty relations, including those involving the Hermitian phase operator and its sine and cosine forms. The single number-state is found to be the only physical exact intelligent state and also the only physical exact minimum-uncertainty state for all the uncertainty relations considered. We construct states which are both physical states and approximately intelligent states. Under certain conditions coherent states, ideal squeezed states and the number-phase intelligent states associated with the Susskind-Glogower cosine and sine operators are found to be both physi...

Macroscopic quantum superpositions by means of single-atom dispersion.

Abstract: We show that macroscopic quantum superpositions of the electromagnetic field can be generated through amplification of microscopic quantum superpositions prepared in a single atom. Our scheme has the advantage that dissipation is negligible, and hence the superpositions are not rapidly destroyed.

Coherent states for the Morse oscillator.

Abstract: The explicit coordinate representation of coherent states for the Morse oscillator is derived and discussed, in the limit that the potential well is deep. Without this limit, such states can only be written as a finite sum that does evolve coherently but in a dilated time.

Nonclassical photon statistics of two-mode squeezed states.

Abstract: The concept of photon antibunching as a manifestation of nonclassical character in single-mode radiation is extended to two-mode radiation. A simple criterion for the existence of nonclassical effects in two-mode radiation is established. It implies that the intermode photon bunching, rather than antibunching, can play a key role in rendering two-mode radiation nonclassical. The two-mode squeezed vacuum states are used as simple examples to illustrate the essential point of the criterion. The criterion is then used to study the nonclassical properties of two types of two-mode squeezed states. A state generated by applying the squeeze operator to the two-mode vacuum first, followed by the displacement operator, is called a two-mode coherent squeezed state. If the order of the two operators is reversed, a two-mode squeezed coherent state is obtained. It is found that the latter has a much stronger tendency to become a nonclassical state than the former, assuming that the parameters involved are all the same. A measure of nonclassical depth of radiation is adopted. It is found that, according to this measure, the effect of squeezing in making two-mode coherent squeezed states nonclassical is not monotonic. Such phenomena do not occur in squeezed coherent states.

K-Photon Coherent States

Abstract: We have introduced an alternative definition of the generalized k-photon coherent states which exhibit kth-order squeezing for k  2.

On q-squeezed states

Abstract: The authors present the results of an analysis of the squeezing of components of the (conventional) electromagnetic field in quantum group analogues of the Heisenberg-Weyl (HW) coherent state and SU(1,1) squeezed state. They find that squeezing occurs for all finite-q values not equal to unity in the HW q-coherent state, in contrast to the usual case; and also in the SUq(1,1) case, although here less than in the usual (q=1) SU(1,1) squeezed state.

Cyclic quantum evolution and Aharonov-Anandan geometric phases in SU(2) spin-coherent states

Abstract: We show that cyclic quantum evolution can be realized and the Aharonov-Anandan (AA) geometric phase can be determined for any spin-j system driven by periodic fields Two methods are extended for the study of this problem: the generalized spin-coherent-state technique and the Floquet quasienergy approach Using the former approach, we have developed a generalized Bloch-sphere model and presented a SU(2) Lie-group formulation of the AA geometric phase in the spin-coherent state We show that the AA phase is equal to j times the solid angle enclosed by the trajectory traced out by the tip of a generalized Bloch vector General analytic formulas are obtained for the Bloch vector trajectory and the AA geometric phase in terms of external physical parameters In addition to these findings, we have also approached the same problem from an alternative but complementary point of view without recourse to the concept of coherent-state terminology Here we first determine the Floquet quasienergy eigenvalues and eigenvectors for the spin-j system driven by periodic fields This in turn allows the construction of the time-evolution propagator, the total wave function, and the AA geometric phase in a more general fashion