Showing papers on "Coherent states published in 1992"
TL;DR: It is shown that there exist nonclassical intensity correlations at the output ports of the homodyne detectors which facilitate a test of local realism.
Abstract: The nonlinear Mach-Zehnder interferometer is presented as a device whereby a pair of coherent states can be transformed into an entangled superposition of coherent states for which the notion of entanglement is generalized to include nonorthogonal, but distinct, component states. Each mode is directed to a homodyne detector. We show that there exist nonclassical intensity correlations at the output ports of the homodyne detectors which facilitate a test of local realism. In contradistinction to previous optical schemes which test local realism, the initial state used here possesses a positive Glauber-Sudarshan representation and is therefore a semiclassical state. The nonlinearity itself is responsible for generating the nonclassical state.
426 citations
TL;DR: The nonclassical properties of quantum superpositions of coherent states of light are discussed and under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics are shown.
Abstract: In this paper we discuss the nonclassical properties of quantum superpositions of coherent states of light. Using general expressions for the Wigner functions of superposition states we analyze the consequences of quantum interference between coherent states. We describe in detail nonclassical properties of a superposition of two coherent states. In particular, we study the oscillatory behavior of the photon number distribution of the even and odd coherent states. We show under which conditions a superposition of two coherent states can exhibit second- and fourth-order squeezing or sub-Poissonian photon statistics. We examine the sensitivity of nonclassical effects such as oscillations in the photon number distribution or second-order squeezing to dissipation. We demonstrate that quantities such as the photon number distribution and interferences in phase space are highly sensitive to even a quite small dissipative coupling, because they depend on all moments of the field observables, and higher moments decay more rapidly than lower moments. Quantities such as quadrature squeezing, on the other hand, are more robust against dissipation because they involve only lower moments. Finally, we find a remarkable effect whereby fourth-order squeezing is generated by damping.
339 citations
TL;DR: Using a circular 37-SQUID (superconducting quantum interference device) sensor array, this article observed spontaneous transitions in neuromagnetic field patterns in the human brain which occur at a critical value of a systematically varied behavioral parameter.
218 citations
TL;DR: In this article, a two-level atom, with quantized centre-of-mass motion, is constrained to move in a one-dimensional harmonic potential, while interacting with a single-mode classical travelling light field.
Abstract: A single two-level atom, with quantized centre-of-mass motion, is constrained to move in a one-dimensional harmonic potential, while interacting with a single-mode classical travelling light field. When the atom's centre-of-mass motion is in a coherent state, we show that the atomic inversion exhibits collapses and revivals. Whereas in the Jaynes-Cummings model this behaviour occurs due to the discrete nature of the light field, in our case the behaviour is due to the discrete nature of the vibrational trap states. The Q-function for the external motion is also calculated and shown to break into two peaks in the collapse region. Finally the parameter ranges under which the collapses and revivals can be observed are discussed, as well as the possibility of an experiment.
195 citations
TL;DR: In this article, a potential model of a particle moving in a potential of a certain form has been found for which exact solutions are known for only a part of the spectrum (quasi-exactly solvable models).
160 citations
Book•
01 Nov 1992
TL;DR: In this paper, the authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics, and the group theoretical backgrounds for path integral applications, such as harmonic analysis, polar coordinate formulation, various techniques and path integration of SU(2) and SU(1,1) are discussed.
Abstract: The authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics and the group theoretical backgrounds for path integrals. Applications of harmonic analysis, polar coordinate formulation, various techniques and path integrals of SU(2) and SU(1,1) are discussed. Soluble examples presented include particle-flux system, a pulsed oscillator, magnetic monopole, the Coulomb problems in curved space and others. The second part deals with the SU(2) coherent states and their applications. Construction and generalization of the SU(2) coherent states, formulation of coherent path integrals for spin and unitary spin, and semiclassical quantization are presented. Applications are made to the study of quantum fluctuation, the nonlinear field model and phase holonomy. The final chapters present the theory of the SU(1,1) coherent states and their applications. The radial Coulomb problem, the Morse oscillator, and the large-N approximation are discussed. Applications to problems in quantum optics such as squeezed states, interaction with the squeezed vacuum states, and phase operator formalism are also included. This book is intended as an introduction to the subject as well as a work of reference.
143 citations
TL;DR: This study reveals how the simultaneous occurrence of two nonlinear processes affects the atomic dynamics.
Abstract: The collapse-and-revival phenomenon in the population inversion and the time evolution of the quasiprobability Q function of an atom undergoing a two-photon process are investigated when the cavity is supposed to be filled with a Kerr-like medium. An exact expression for the atomic population inversion has been given for a field initially in the coherent state. The closed form of this expression as well as that of the Q function are obtained under the high-field approximation. Also, the tendency toward inhibited decay of the excited state has been explicitly shown. This study reveals how the simultaneous occurrence of two nonlinear processes affects the atomic dynamics.
113 citations
TL;DR: A general treatment of the quantized harmonic oscillator with time-dependent mass and frequency is presented and exact coherent states for such systems are constructed.
Abstract: A general treatment of the quantized harmonic oscillator with time-dependent mass and frequency is presented. The treatment is also applied to the time-dependent oscillator under the action of a time-dependent perturbative potential. The treatment is based on the use of some time-dependent transformations and in the method of invariants of Lewis and Riesenfeld [J. Math. Phys. 10, 1458 (1969)]. Exact coherent states for such systems are also constructed.
100 citations
TL;DR: Based on the concept of generalized coherent states, a theory of mechanical systems is formulated in a way which naturally exhibits the mutual relation of classical and quantum aspects of physical phenomena as discussed by the authors.
Abstract: Based on the concept of generalized coherent states, a theory of mechanical systems is formulated in a way which naturally exhibits the mutual relation of classical and quantum aspects of physical phenomena.
85 citations
TL;DR: It is shown that under certain conditions the superposition states may exhibit nonclassical effects, such as two-mode squeezing, violation of the Cauchy-Schwartz inequality, and sub-Poissonian statistics.
Abstract: The superposition states from several two-mode coherent states are studied. It is shown that under certain conditions the superposition states may exhibit nonclassical effects, such as two-mode squeezing, violation of the Cauchy-Schwartz inequality, and sub-Poissonian statistics.
80 citations
TL;DR: In this paper, the properties of Weyl ordered products of quantum mechanical operators are investigated and the technique of integration within Weyl ordering products (IWWP) is introduced, and the overcompleteness relation of the coherent state is then recast into Weyl-ordered form.
Abstract: The properties of Weyl ordered products of operators are investigated and the technique of integration within Weyl ordered product (IWWP) is introduced. The overcompleteness relation of the coherent state is then recast into Weyl ordered form. In so doing, a new approach for Weyl ordering quantum mechanical operators is presented.
TL;DR: The Pegg-Barnett phase-operator formalism utilizes a finite basis set to represent operators of the harmonic oscillator, which enables the phase to be represented by a Hermitian operator, but rests on taking the dimensionality of the based set to infinity for observable quantities.
Abstract: The Pegg-Barnett phase-operator formalism utilizes a finite basis set to represent operators of the harmonic oscillator; this enables the phase to be represented by a Hermitian operator, but rests on taking the dimensionality of the basis set to infinity for observable quantities. Simultaneously, in their approach Pegg and Barnett consider quantum states of a harmonic oscillator which are normalized in the Fock space, i.e., the dimensionality of the basis set in which the states of the harmonic oscillator are defined is supposed to be infinite, while the phase operator is defined in the finite-dimensional basis set. In this paper we address the problem of a consistent definition of a coherent state within a finite state basis. We employ displacement operators to define such coherent states and numerically evaluate observables as a function of the size of the basis set. We investigate phase properties of these coherent states. We find that if the dimensionality of the state space is much larger than the mean occupation number of the coherent states, then the results obtained in the finite-dimensional basis are applicable in the case of a ordinary quantum-mechanical harmonic oscillator. These coherent states are minimum uncertainty states with respect to quadrature operators (i.e., the position and momentum operators) and do not exhibit quadrature squeezing. A weakly excited (compared with the dimensionality of the state space) coherent state in finite-dimensional basis is not strictly speaking a minimum uncertainty state with respect to the number and phase operators. We give definitions of amplitude and phase squeezing and show that weakly excited coherent states can be amplitude squeezed. In the high-intensity limit (again compared with the dimensionality of the state space) these states exhibit phase squeezing.
TL;DR: Using the time-dependent variational principle with a group theoretical coherent state defining the wave functions for electrons and nuclei, a system of coupled, first-order, nonlinear differential equations is obtained for a general molecular system.
Abstract: Using the time‐dependent variational principle with a group theoretical coherent state defining the wave functions for electrons and nuclei, a system of coupled, first‐order, nonlinear differential equations is obtained for a general molecular system. The equations form a classical Hamiltonian system within a generalized phase space that allows a systematic time‐dependent study of molecular processes. The approach is general and provides a computational framework for a variety of properties such as transition and excitation probabilities in atomic and molecular collisions, and molecular spectra such as vibrational spectra with anharmonicities. The basic approximation corresponding to the choice of a single determinantal wave function for the electrons and classical nuclei is analyzed. Illustrative applications to the p+H collision process and to vibrations of the H2O molecule exhibit good agreement with experiment and with other theoretical work.
TL;DR: In this paper, the quantum dynamics of a particle in a double-well potential under a monochromatic external driving force is computed by using a minimum-uncertainty Gaussian wave packet as an initial state.
Abstract: The quantum dynamics of a particle in a double-well potential under a monochromatic external driving force is computed by using a minimum-uncertainty Gaussian wave packet as an initial state. Irregular or regular time development of dynamical variables is obtained, depending on whether the initial wave packet is located in the classical chaotic sea or the regular region in phase space, respectively. Tunnelings between nonresonant islands and between resonant islands are obtained. Tunneling times between nonresonant islands decrease smoothly, in general, with the increase of the amplitude of the driving force, but tunneling times between resonant islands are more erratic.
TL;DR: In this article, the authors theoretically investigate the behavior of a two-level atom in a lossless cavity driven by an external field and find that the cavity field is excited to a coherent state whose amplitude is equal to that of the external field, but shifted 180 degrees in phase.
Abstract: In this paper we theoretically investigate the behavior of a two-level atom in a lossless cavity driven by an external field. Using classical electrodynamics to describe the external field while quantizing the cavity field, we find that the cavity field is excited to a coherent state whose amplitude is equal to that of the external field, but shifted 180\ifmmode^\circ\else\textdegree\fi{} in phase. This results in the disappearance of the atomic resonance fluorescence (i.e., the atom stops interacting with the fields). When we quantize the external field the effect persists. A fully quantized dressed-state approach provides some helpful insight and a nice analogy to another problem in which the resonance fluorescence vanishes.
TL;DR: In this paper, an SU(1, 1) Lie algebraic formulation is presented for investigating the linear dissipative processes in quantum optical systems, which is used for investigating a dissipative nonlinear oscillator, the quantum mechanical model of phase modulation, and the photon echo in the localized electron-phonon system.
Abstract: An SU(1,1) Lie algebraic formulation is presented for investigating the linear dissipative processes in quantum optical systems. The Liouville space formulation, thermo field dynamics, and the disentanglement theorem of SU(1,1) Lie algebra play essential roles in this formulation. In the Liouville space, the time‐evolution equation for the state vector of a system is solved algebraically by using the decomposition formulas of SU(1,1) Lie algebra and the thermal state condition of thermo field dynamics. The presented formulation is used for investigating a dissipative nonlinear oscillator, the quantum mechanical model of phase modulation, and the photon echo in the localized electron–phonon system. This algebraic formulation gives a systematic treatment for investigating the phenomena in quantum optical systems.
TL;DR: In this article, minimum uncertainty coherent states and annihilation operator coherent states for the Morse oscillator were derived and shown to be equivalent in the limit of small anharmonicity constant.
Abstract: Minimum uncertainty coherent states and annihilation operator coherent states for the Morse oscillator are derived and shown to be equivalent. They reduce, in the limit of small anharmonicity constant, or, equivalently, in the limit of large well depth, to the approximate coherent states derived previously from the use of generalized displacement operator.
TL;DR: In this paper, it was shown that the phenomenon of fractional revivals, which was observed in recent laser experiments on atomic wave packets, determines the long-time behavior of the Jaynes-Cummings model for a two-level atom interacting with a quantized cavity field.
Abstract: It is shown that the phenomenon of fractional revivals, which was observed in recent laser experiments on atomic wave packets, determines the long-time behavior of the Jaynes-Cummings model for a two-level atom interacting with a quantized cavity field. This provides an alternative mechanism for the generation of coherent superpositions of macroscopically distinguishable states of the field (so-called ``optical Schr\"odinger cats'') via resonant processes. The emergence of these states is associated with the appearance of atomic inversion revivals following each other 2, 3, 4, . . . times faster than the usual ones.
TL;DR: In this article, the algebra of q-fermion operators is re-examined and generalized q-oscillators defined for - infinity (q
Abstract: The algebra of q-fermion operators, developed earlier by two of the present authors is re-examined. It is shown that these operators represent particles that are distinct from usual spacetime fermions except in the limit q=1. It is shown that it is possible to introduce generalized q-oscillators defined for - infinity (q
TL;DR: In this paper, the authors investigated some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model.
Abstract: We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.
TL;DR: In this paper, the authors studied the time evolution of the atomic inversion of the two-level atom which is coupled to the q analogue of a single mode of the bosonic field, and found that q deformation of Heisenberg algebra may correspond to some effective nonlinear interaction of the cavity mode.
Abstract: In this paper we study the time evolution of the atomic inversion of the two-level atom which is coupled to the q analogue of a single mode of the bosonic field. The q field under consideration is supposed to be prepared initially in the q analogue of Glauber's coherent state. We find that q deformation of Heisenberg algebra may correspond to some effective nonlinear interaction of the cavity mode.
TL;DR: In this article, the classical limit of the q-analogue quantized radiation field was studied paralleling conventional quantum optics analyses, and the variance of the generic electric field was found to be ⩾ λ √ 2ϵ 0 V, where λ > 1 if q ≠ 1.
TL;DR: In this article, a Mach-Zehnder interferometer with a Kerr medium in one arm and a resonant two-level atom crossing one of the output ports was used to produce even and odd coherent states.
TL;DR: This theory treats a time-distributed measurement as a sequence of measurements in which at most one photon can be detected in an infinitesimal time, and shows that the average number of photons remaining in the measured field increases when a photon is detected and decreases when no photons are detected.
Abstract: This paper presents a general theory for a continuous quantum-nondemolition measurement of photon number. This theory treats a time-distributed measurement as a sequence of measurements in which at most one photon can be detected in an infinitesimal time, and shows that the average number of photons remaining in the measured field increases when a photon is detected and decreases when no photon is detected. The state of the measured system evolves nonunitarily and reduces continuously to a number state whose eigenvalue is uniquely determined by the average rate of photodetection and whose probability distribution coincides with the initial photon-number distribution
TL;DR: In this paper, a new approach based on the partial coherent theory of light is introduced to predict the radiative properties of a thin film, and the key element in the formulation is the complex degree of coherence, for which a general integral expression is obtained and further approximated algebraically for nearly monochromatic radiation.
Abstract: A new approach based on the partial coherent theory of light is introduced to predict the radiative properties of a thin film. General expressions obtained for the normal reflectance and transmittance of a thin film not only degenerate into the limiting results of the wave and the geometric optics in the coherent and incoherent cases, but also apply for all partial coherent states between the limits. The key element in the formulation is the complex degree of coherence, for which a general integral expression is obtained and further approximated algebraically for nearly monochromatic radiation. Limiting criteria and regime maps are established to demonstrate the range of applications for the various methods.
TL;DR: In this article, the authors investigated some of the basic features of the interaction of superpositions of coherent states of light with two-level atoms in the framework of the Jaynes-Cummings model.
Abstract: We investigate some of the basic features of the interaction of superpositions of coherent states of light with two-level atoms in the framework of the Jaynes-Cummings model. We compare the behaviour of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field. We investigate the collapses and revivals of the atomic inversion by studying the evolution of the Q function of the cavity field. We also establish the connection between the purity of the field and the collapses and revivals of the atomic inversion.
TL;DR: The results show that the k orthonormalized eigenstates can be represented as a linear superposition of k coherent states, and that all of them are minimum uncertainty states of the operators Z 1 and Z 2 for even and odd k.
Abstract: In this paper, we study first the connection of the k orthonormalized eigenstates of a k with coherent states, then, according to the higher-order squeezing defined by Zhang et al. [Phys. Lett. A 150, 27 (1990)], study the properties of the higher-order squeezing of k orthonormalized eigenstates. Our results show that the k orthonormalized eigenstates can be represented as a linear superposition of k coherent states, and that all of them are minimum uncertainty states of the operators Z 1 (N) and Z 2 (N) (N=mk, m=1,2,3,...) for even and odd k, and all of them have the Nth-order squeezing [N=(m+1/2)k, m=0,1,2,...] for even k
TL;DR: In this paper, the phase operator for a two-mode photon system is defined in terms of the relative number states, and its property is investigated in detail, and the average value and fluctuation of phase operator are calculated for coherent and squeezed states.
Abstract: The phase operator for a two-mode photon system is defined in terms of the relative-number states, and its property is investigated in detail. The phase operator thus defined has a unitary exponential form. It is shown that the average value and fluctuation of the phase operator, where one mode is in some physical state, such as a coherent or a squeezed state, and the other is in a vacuum state, are equivalent to those obtained by means of the Pegg–Barnett phase operator for a single-mode photon. The average value and fluctuation of the phase operator are calculated for coherent and squeezed states of a two-mode photon system.
TL;DR: A novel aspect of the formalism is the interpretation of physical states involving massless particles as Fock states and the occurrence of physical transitions in Fock space.
Abstract: We discuss the existence and properties of the asymptotic $S$ matrix in field theories with massless particles. We show for the classic case of the scattering of an electron in an external electromagnetic field that the $S$-matrix method yields the same results as the traditional cross-section method involving properly formed sums over physically degenerate initial as well as final states. In that case, we show that observables are independent of the particular choice of asymptotic Hamiltonian. We argue that the massless theory is unique and discuss its relation to the massless limit of the massive theory. Although the results do not depend on it, a novel aspect of our formalism is the interpretation of physical states involving massless particles as Fock states and the occurrence of physical transitions in Fock space.