Showing papers on "Coherent states published in 1995"
TL;DR: This work discusses quantum cryptographic protocols based on the transmission of weak coherent states and presents a system, based on a symbiosis of two existing systems, for which the information available to the eavesdropper is significantly reduced and is therefore safer than the two previous ones.
Abstract: The safety of a quantum key distribution system relies on the fact that any eavesdropping attempt on the quantum channel creates errors in the transmission. For a given error rate, the amount of information that may have leaked to the eavesdropper depends on both the particular system and the eavesdropping strategy. In this work, we discuss quantum cryptographic protocols based on the transmission of weak coherent states and present a system, based on a symbiosis of two existing systems, for which the information available to the eavesdropper is significantly reduced. This system is therefore safer than the two previous ones. We also suggest a possible experimental implementation.
500 citations
TL;DR: In this article, the direction of emission of photoexcited electrons in semiconductors is controlled by adjusting the relative phase difference between a mid-infrared radiation and its second harmonic, which is achieved by using quantum interference of electrons produced with one-and two-photon bound-to-free intersubband transitions in AlGaAs/GaAs quantum well superlattices.
Abstract: The direction of emission of photoexcited electrons in semiconductors is controlled by adjusting the relative phase difference between a midinfrared radiation and its second harmonic. This is achieved by using quantum interference of electrons produced with one- and two-photon bound-to-free intersubband transitions in AlGaAs/GaAs quantum well superlattices.
272 citations
TL;DR: In this paper, the Fock space of definite flavor states is shown to be unitarily inequivalent to that of definite mass states, and the oscillation amplitude is found to be momentum dependent.
216 citations
TL;DR: In this article, it is shown that infinitely many vacua are accessible to memory printing in a way that in sequential information recording the storage of a new information does not destroy the previously stored ones, thus allowing a huge memory capacity.
Abstract: The quantum model of the brain proposed by Ricciardi and Umezawa is extended to dissipative dynamics in order to study the problem of memory capacity. It is shown that infinitely many vacua are accessible to memory printing in a way that in sequential information recording the storage of a new information does not destroy the previously stored ones, thus allowing a huge memory capacity. The mechanism of information printing is shown to induce breakdown of time-reversal symmetry. Thermal properties of the memory states, as well as their relation with squeezed coherent states, are finally discussed.
188 citations
TL;DR: A special degenerate form of the symmetry algebras of self-similar potentials is found to provide a natural $q$-analog of the Floquet theory.
Abstract: A variety of coherent states of the harmonic oscillator is considered. It is formed by a particular superposition of canonical coherent states. In the simplest case, these superpositions are eigenfunctions of the annihilation operator $A=P(d/dx+x)/\sqrt2$, where $P$ is the parity operator. Such $A$ arises naturally in the $q\to -1$ limit for a symmetry operator of a specific self-similar potential obeying the $q$-Weyl algebra, $AA^\dagger-q^2A^\dagger A=1$. Coherent states for this and other reflectionless potentials whose discrete spectra consist of $N$ geometric series are analyzed. In the harmonic oscillator limit the surviving part of these states takes the form of orthonormal superpositions of $N$ canonical coherent states $|\epsilon^k\alpha\rangle$, $k=0, 1, \dots, N-1$, where $\epsilon$ is a primitive $N$th root of unity, $\epsilon^N=1$. A class of $q$-coherent states related to the bilateral $q$-hypergeometric series and Ramanujan type integrals is described. It includes a curious set of coherent states of the free nonrelativistic particle which is interpreted as a $q$-algebraic system without discrete spectrum. A special degenerate form of the symmetry algebras of self-similar potentials is found to provide a natural $q$-analog of the Floquet theory. Some properties of the factorization method, which is used throughout the paper, are discussed from the differential Galois theory point of view.
128 citations
10 Jul 1995
TL;DR: In this paper, a spectral filter was used to remove part of the sidebands of the solitons and the maximum observed squeezing was 2.1 dB, and 5.5 dB excess noise was observed on the short wavelength side, 5.0 dB on the long wavelength side.
Abstract: justed to produce N > 1 solitons with a 1 nm bandwidth, readily-recognizable sidebands, and 12 pJ energies. Fundamental soliton energies were 6 pJ. Squeezing was observed when we used a spectral filter (a grating followed by a slit) to remove part of the sidebands. Typically, less than 5% of the soliton's energy was removed. Squeezing levels were determined by splitting the solitons equally onto two photodiodes with a 50/50 beamsplitter and using balanced direct detection with a delay line? A squeezing measurement is shown in Fig. 2. Directly subtracting the two photocurrents without a delay line gave the upper curve in Fig. 2(a). Inserting the delay line (and its loss) gave the lower curve. Subtracting the two curves gave the modulated noise spectrum in Fig. 2(b). The maxima of this noise spectrum corresponds to the SQL, and the minima corresponds to the squeezing, here about 2 dB. Two other shot-noise measurement methods (one using attenuated color center laser pulses as the SQL reference) gave nearly identical results, the maximum observed squeezing was 2.1 dB. Also, we measured the excess noise in the sidebands by moving the slit away from the soliton spectrum-center. 1.5 dB excess noise was observed on the shortwavelength side, 5.0 dB on the longwavelength side. No squeezing was seen for fundamental solitons. Our measurements suggest two possible mechanisms for the squeezing. The asymmetry of the noise in the sidebands suggests stimulated Raman scattering, which is known to move photons to the long wavelength side of solitons. The importance of sidebands suggests selfphase modulation and four-wave mixing are responsible. Probably the two effects interact. Summarizing, soliton photon-number squeezing exhibits several striking features. First, it is remarkably simple: all that is needed is propagation and filtering. This simplicity, and the small losses entailed by filtering, indicate highly energy-efficient squeezing. Second, solitons are increasingly being considered for high-bandwidth communications. Soliton photon-number squeezing might directly translate into enhanced detection efficiencies4 and reduced Gordon-Haus fluctuation noise.5
92 citations
TL;DR: The generic wave is shown to correspond to a two-band state in the quantum description of the system, while the limiting cases of solitons and phonons correspond to particle and hole excitations.
Abstract: We examine a collection of classical particles interacting with inverse-square two-body potentials in the thermodynamic limit of finite particle density. We find explicit large-amplitude density waves and soliton solutions for the motion of the system. Waves can be constructed as coherent states of either solitons or phonons (small-amplitude waves). Therefore, either solitons or phonons can be considered as the fundamental excitations. The generic wave is shown to correspond to a two-band state in the quantum description of the system, while the limiting cases of solitons and phonons correspond to particle and hole excitations.
92 citations
TL;DR: These discrete coherent-state superpositions provide experimental possibilities for generating an arbitrary quantum state of a single-mode electromagnetic field.
Abstract: A representation of a Fock state \ensuremath{\Vert}n〉 is given by a superposition of n+1 coherent states. These discrete coherent-state superpositions provide experimental possibilities for generating an arbitrary quantum state of a single-mode electromagnetic field.
85 citations
TL;DR: In this article, the classical and quantum probability distributions for both position and momentum are compared for several model systems admitting bound states including the harmonic oscillator, the infinite well, and the linear confining potential.
Abstract: The classical and quantum probability distributions for both position and momentum are compared for several model systems admitting bound states including the harmonic oscillator, the infinite well, and the linear confining potential (V(x)=F‖x‖). Examples corresponding to unbound systems, including the uniformly accelerating particle and the motion of a particle moving away from a point of unstable equilibrium, i.e., the ‘‘unstable oscillator’’ defined by V(x)=−kx2/2, are also considered. The quantum and classical distribution of kinetic and potential energy for the harmonic oscillator is briefly discussed.
80 citations
79 citations
TL;DR: In this article, the authors studied the dynamical algebra associated with a family of isospectral oscillator Hamiltonians through the analysis of its representation in the basis of energy eigenstates.
Abstract: The dynamical algebra associated with a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of the standard Heisenberg algebra, and it is dependent on a parameter omega >or=0. We call it the distorted Heisenberg algebra, where omega is the distortion parameter. The corresponding coherent states for an arbitrary omega are derived, and some particular examples are discussed in detail. A prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.
TL;DR: A simple and efficient method of determining the canonical structure of the generalized correlated states is presented, which shows relations in the multimode case that are the generalization of the Schroedinger-Robertson relation.
Abstract: The close relationship between the zero-point energy, the uncertainty relation, coherent states, squeezed states, and correlated states for one mode is investigated. This group theoretic perspective of the problem enables the parametrization and identification of their multimode generalization. A simple and efficient method of determining the canonical structure of the generalized correlated states is presented. Implication of canonical commutation relations for correlations are not exhausted by the Heisenberg uncertainty relation, not even by the Schroedinger-Robertson uncertainty inequality, but there are relations in the multimode case that are the generalization of the Schroedinger-Robertson relation.
TL;DR: In this paper, the theory of the harmonic oscillator with time-dependent frequency was reviewed by means of an approach based on an operator constant of the motion of the oscillator.
Abstract: The authors review the theory of the harmonic oscillator with time-dependent frequency by means of an approach based on an operator constant of the motion. With the help of this operator constant we define the ground state, the excited states and a coherent state of the oscillator and discuss the time dependence of these states through their Wigner functions. The authors derive the Wigner function of an arbitrary state at time t evolving in the time-dependent harmonic potential. Moreover, they calculate the correlation coefficient between position and momentum, which appears in the Schrodinger uncertainty relation. The authors illustrate their results for the example of a charged particle in the Paul trap.
TL;DR: In this article, the dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates, and a prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.
Abstract: The dynamical algebra associated to a family of isospectral oscillator Hamiltonians is studied through the analysis of its representation in the basis of energy eigenstates. It is shown that this representation becomes similar to that of the standard Heisenberg algebra, and it is dependent of a parameter $w\geq 0$. We name it {\it distorted Heisenberg algebra}, where $w$ is the distortion parameter. The corresponding coherent states for an arbitrary $w$ are derived, and some particular examples are discussed in full detail. A prescription to produce the squeezing, by adequately selecting the initial state of the system, is given.
TL;DR: In this article, it was shown that path integral formulas for SU(2) and SU(1,1) are WKB exact, if it is started from the trace of e−iTĤ, where H is given by a linear combination of generators.
Abstract: Using the generalized coherent states it is shown that the path integral formulas for SU(2) and SU(1,1) (in the discrete series) are WKB exact, if it is started from the trace of e−iTĤ, where H is given by a linear combination of generators. In this case, the WKB approximation is achieved by taking a large ‘‘spin’’ limit: J,K→∞, under which it is found that each coefficient vanishes except the leading term which indeed gives the exact result. It is further pointed out that the discretized form of path integral is indispensable, in other words, the continuum path integral expression sometimes leads to a wrong result. Therefore great care must be taken when some geometrical action would be adopted, even if it is so beautiful as the starting ingredient of path integral. Discussions on generalized coherent states are also presented both from geometrical and simple oscillator (Schwinger boson) points of view.
TL;DR: It is shown that Schr\"odinger cat states can have various nonclassical features such as the violation of the Cauchy-Schwarz inequality, sub-Poissonian photon-number statistics, and squeezing.
Abstract: We generalize the concept of Schr\"odinger cat states to macroscopic superpositions of two pairs coherent states We show that these states can have various nonclassical features such as the violation of the Cauchy-Schwarz inequality, sub-Poissonian photon-number statistics, and squeezing We propose schemes to generate these states
TL;DR: In the Heisenberg picture, the generalized invariant and exact quantum motions are found for a time-dependent forced harmonic oscillator and the eigenstate and the coherent state of the invariant are found and shown that the dispersions of these quantum states do not depend on the external force.
Abstract: The generalized invariant and the exact quantum motions are found in the Heisenberg picture for a harmonic oscillator with time-dependent mass and frequency in terms of classical solutions. It is shown that the Heisenberg pictures gives a relatively simpler picture that the Schr\"odinger picture and also manifestly exhibits the time independency of the invariant. We apply this method to the system with a linear sweep of frequency and Paul trap and study the squeezing properties.
TL;DR: By resorting to the Fock-Bargmann representation, this paper incorporated the quantum Weyl-Heisenberg algebra, q-WH, into the theory of entire analytic functions.
TL;DR: It is shown how the Wehrl entropy, a special case of the sampling entropy, is a useful discriminator between different kinds of superpositions and of statistical mixtures, and is determined essentially by the coherent-state content.
Abstract: We use the operational phase-space distributions and sampling entropies developed in the preceding paper [V. Bu\ifmmode \check{z}\else \v{z}\fi{}ek, C. H. Keitel, and P. L. Knight, Phys. Rev. A 51, 2575 (1995)] to discuss the nature of quantum interference between components of superpositions of states. We show how the Wehrl entropy, a special case of the sampling entropy, is a useful discriminator between different kinds of superpositions and of statistical mixtures, and is determined essentially by the coherent-state content. Apart from interference terms, this content is given by the quantum uncertainty of a single coherent state and the classical contribution to the number of coherent states necessary to tile the dominant phase-space ``patch'' representing the quantum state of interest. We illustrate these ideas using nonclassical superpositions of coherent states, where interference modifies the phase-space distributions, and show how these features are sensitive to dissipation.
01 Jan 1995
TL;DR: In this paper, a family of nonlinear Schroedinger Equations are used to represent the transformation of spin1/2 Particles in a curved spacetime with absolute time, and the results of these transformations are used for geometric quantization.
Abstract: Quantization, Field Theory, and Representation Theory: On Quantum Mechanics in a Curved Spacetime with Absolute Time (D. Canarutto et al.). Massless Spinning Particles on the Antide Sitter Spacetime (S. De Bievre, S. Mehdi). A Family of Nonlinear Schroedinger Equations: Linearizing Transformations and Resulting Structure (H.D. Doebner et al.). Modular Structures in Geometric Quantization (G.G. Emch). Diffeomorphism Groups and Anyon Fields (G.A. Goldin, D.H. Sharp). On a Full Quanization of the Torus (M.J. Gotay). Differential Forms on the Skyrmion Bundle (C. Gross). Explicitly Covariant Algebraic Representations for Transitional Currents of Spin1/2 Particles (M.I. Krivoruchenko). The Quantum Su(2,2)Harmonic Oscillator (W. Mulak). GeometricStochastic Quantization and Quantum Geometry (E. Prugovecki). Prequantization (D.J. Simms). Classical Yang-Mills and Dirac Fields in the Minkowski Space and in a Bag (J. Sniatycki). Symplectic Induction, Unitary Induction and BRST Theory (Summary) (G.M. Tuynman). Coherent States, Complex and Poisson Structures: Spin Coherent States for the Poincare Group (S.T. Ali, J.P. Gazeau). Coherent States and Global Differential Geometry (S. Berceanu). Natural Transformations of Lagrangians into pforms on the Tangent Bundle (J. Debecki). SL(2,IR)Coherent States and Itegrable Systems in Classical and Quantum Physics (J.P. Gazeau). Symplectic and Lagrangian Realization of Poisson Manifolds (M. Giordano et al.). From the Poincare-Cartan Form to a Gerstehhaber Algebra of Poisson Brackets in Field Theory (I.V. Kanatchikov). Geometric Coherent States, Membranes, and Star Products (M. Karasev). Integral Representation of Eigenfunctions and Coherent States for the Zeeman Effect (M. Karasev, E. Novikova). QDeformations and Quantum Groups, Noncommutative Geometry: Quantum Coherent States and the Method of Orbits (B. Jurco, P. tovicek). On the Deformation of Commutation Relations (W. Marcinek). The qdeformed Quantum Mechanics in the Coherent States Map Approach (V. Maximov, A. Odzijewicz). Quantization by Quadratic Polynomials in Creation and Annihilation Operators (W. Slowikowski). On Dirac Type Brackets (Yu.M. Vorobjev, R. Flores Espinoza). Quantum Trigonometry and Phasespace Propensity (K. Wodkiewicz, B.G. Englert). Noncommutative Space-Time Impled by Spin (S. Zadrzewski). Miscellaneous Problems of Quantum Dynamics: Spectrum of the Dirac Operator on the SU(2) Manifold as Energy Spectrum for the Polyaniline Macromolecule (H. Makaruk). On Geometric Methods in the Description of Quantum Fluids (R. Owczarek). Galactic Dynamics in the Siegel Halfplane (G. Rosensteel). Graded Contractions of so(4,2) (J. Tolar, P. Travnicek). The Berry Phase and the Geometry of Coset Spaces (E.A. Tolkachev, A.A. Tregubovich). Index.
TL;DR: In this paper, the path integral for one-dimensional sigma models, starting from a given Hamiltonian operator and states in a Hilbert space, is constructed and the correct Feynman rules are derived by explicit evaluation of the discretized propagators and vertices.
Abstract: We construct the path integral for one-dimensional non-linear sigma models, starting from a given Hamiltonian operator and states in a Hilbert space. By explicit evaluation of the discretized propagators and vertices we find the correct Feynman rules which differ from those often assumed. These rules, which we previously derived in bosonic systems \cite{paper1}, are now extended to fermionic systems. We then generalize the work of Alvarez-Gaum\'e and Witten \cite{alwi} by developing a framework to compute anomalies of an $n$-dimensional quantum field theory by evaluating perturbatively a corresponding quantum mechanical path integral. Finally, we apply this formalism to various chiral and trace anomalies, and solve a series of technical problems: $(i)$ the correct treatment of Majorana fermions in path integrals with coherent states (the methods of fermion doubling and fermion halving yield equivalent results when used in applications to anomalies), $(ii)$ a complete path integral treatment of the ghost sector of chiral Yang-Mills anomalies, $(iii)$ a complete path integral treatment of trace anomalies, $(iv)$ the supersymmetric extension of the Van Vleck determinant, and $(v)$ a derivation of the spin-$3\over 2$ Jacobian of Alvarez-Gaum\'{e} and Witten for Lorentz anomalies.
TL;DR: In this paper, it was shown that optical homodyne measurements of coherent states, and of superpositions of coherent state, can be described using the joint photon-number distribution for entangled coherent states.
Abstract: We show that optical homodyne measurements of coherent states, and of superpositions of coherent states, can be described using the joint photon-number distribution for entangled coherent states. The quadrature-phase distribution interference fringes for superpositions of macroscopically distinct coherent states (the so-called ``Schr\"odinger cat states'') are shown to arise from interference in the photon-number distribution for entangled coherent states. The entangled squeezed states are introduced here as squeezed superposition states which are optically mixed with an antisqueezed coherent local oscillator field (squeezing in the other quadrature) at a beam splitter, and we discuss the connection between entangled squeezed states and squeezed-state homodyne detection of squeezed light. Finally the relationship between interference in phase space and fringes in the joint photon-number distribution for the entangled squeezed state is explored.
TL;DR: In this paper, a new class of nonlinear evolution equations, satisfying the homogeneity condition, for pure and mixed quantum states is proposed and applied to investigate the relaxation processes in systems with equidistant spectra (spin and harmonic oscillator), both in discrete and continuous representations.
TL;DR: In this paper, the authors derived the c-number functions corresponding to the matrix elements and to the diagonal representative of the elements of the spin-J representation of the rotation group in a Bloch coherent state basis.
TL;DR: In this article, the density of states of a damped quantum-mechanical harmonic oscillator with Ohmic dissipation and a Drude-like cutoff was derived from the exact expression for the associated partition function using Tauberian theorems.
Abstract: We calculate the density of states of a damped quantum-mechanical harmonic oscillator which is described by a Caldeira-Leggett type model with Ohmic dissipation and a Drude-like cutoff. From the exact expression for the associated partition function, we derive the asymptotic behavior of the density of states using Tauberian theorems. An effective algorithm to evaluate the density of states is presented and examples are given. It is pointed out that the calculated density of states is an experimentally accessible quantity. (c) 1995 The American Physical Society
TL;DR: In this article, a modified Holstein-Primakoff realization of the SU(1,1) Lie algebra has been studied for photon states with simple phase-state representations.
Abstract: Statistical and phase properties and number-phase uncertainty relations are systematically investigated for photon states associated with the Holstein-Primakoff realization of the SU(1,1) Lie algebra. Perelomov's SU(1,1) coherent states and the eigenstates of the SU(1,1) lowering generator (the Barut-Girardello states) are discussed. A recently developed formalism, based on the antinormal ordering of exponential phase operators, is used for studying phase properties and number-phase uncertainty relations. This study shows essential differences between properties of the Barut-Girardello states and the SU(1,1) coherent states. The philophase states, defined as states with simple phase-state representations, relate the quantum description of the optical phase to the properties of the SU(1,1) Lie group. A modified Holstein-Primakoff realization is derived, and eigenstates of the corresponding lowering generator are discussed. These stares are shown to contract, in a proper limit, to the familiar Glauber coherent states.
TL;DR: In this paper, the Wigner and Q functions are calculated and some are plotted for C2,C3,C4,C5,C6,C7,C8,C9,C10,C11,C12,C13,C14,C15,C16,C17,C18,C19,C20,C21,C22,C23,C24,C25,C26,C27,C28,C29,C30,C31,C32,C33,C
Abstract: Crystallized Schrodinger cat states (male and female) are introduced on the base of extension of group construction for the even and odd coherent states of the electromagnetic field oscillator. The Wigner and Q functions are calculated and some are plotted forC2,C3,C4,C5,C3v Schrodinger cat states. Quadrature means and dispersions for these states are calculated and squeezing and correlation phenomena are studied. Photon distribution functions for these states are given explicitly and are plotted for several examples. A strong oscillatory behavior of the photon distribution function for some field amplitudes is found in the new type of states.
TL;DR: In this paper, a new family of stationary coherent states for the two-dimensional harmonic oscillator is presented, which are coherent in the sense that they minimize an uncertainty relation for observables related to the orientation and the eccentricity of an ellipse.
Abstract: A new family of stationary coherent states for the two-dimensional harmonic oscillator is presented. These states are coherent in the sense that they minimize an uncertainty relation for observables related to the orientation and the eccentricity of an ellipse. The wavefunction of these states is particularly simple and well localized on the corresponding classical elliptical trajectory. As the number of quanta increases, the localization on the classical invariant structure is more pronounced. These coherent states give a useful tool to compare classical and quantum mechanics and form a convenient basis to study weak perturbations.
TL;DR: In this paper, the properties of states generated by the application of the two-mode squeeze operator to the pair coherent states are studied and correlations between the modes and strong non-classical properties are to be expected.
Abstract: The properties of states generated by the application of the two-mode squeeze operator to the pair coherent states are studied. These states are the two-mode analogues of the single-mode squeezed states generated by the application of the single-mode squeeze operator to an ordinary coherent state. In the present case there are correlations between the modes and strong non-classical properties are to be expected. We study the statistical properties of the photon number distributions, squeezing, violations of the Cauchy-Schwartz inequality, quasiprobability distributions and the phase distributions.
TL;DR: The eigenvalue spectrum of the random matrix characterizing fluctuations from spatial uniformity is numerically investigated, and it is found that the spectrum is real, bounded, and has a gap between the largest eigen value (corresponding to the uniform solution) and the remaining N 2 1 eigenvalues (nonuniform solutions).
Abstract: We study coupled map lattices with a scaling form of connectivity and show that the dynamics of these systems exhibit a transition from spatial disorder to spatially uniform, temporal chaos as the scaling is varied. We numerically investigate the eigenvalue spectrum of the random matrix characterizing fluctuations from spatial uniformity, and find that the spectrum is real, bounded, and has a gap between the largest eigenvalue (corresponding to the uniform solution) and the remaining $N\ensuremath{-}1$ eigenvalues (nonuniform solutions). The width of this gap depends on the scaling exponent. We associate the transition to the coherent state with the appearance of this gap.