Showing papers on "Coherent states published in 1976"
TL;DR: In this paper, the concept of two-photon coherent states is introduced for applications in quantum optics, which is a simple generalization of the well-known minimum-uncertainty wave packets.
Abstract: The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.
1,661 citations
TL;DR: In this article, the problem of describing the Brownian motion of a quantum harmonic oscillator or free particle is treated in the formalism of quantum dynamical semigroups and certain inequalities involving the friction and diffusion coefficients and Planck's constant are derived.
176 citations
TL;DR: In this article, the coherent state for charged bosons is constructed, its properties are investigated and the corresponding classical model is discussed, and its properties and corresponding classical models are discussed.
Abstract: The coherent state for charged bosons is constructed, its properties are investigated and the corresponding classical model is discussed.
90 citations
TL;DR: In this article, a theory of large amplitude collective motion of a many-particle system is presented, which is relevant, for example, to nuclear fission. The theory is a combination of techniques used in many areas of physics and mathematics.
Abstract: A theory of large amplitude collective motion of a many-particle system is presented, which is relevant, for example, to nuclear fission. The theory is a combination of techniques used in many areas of physics and mathematics. The starting point is the application of the time-dependent Schrodinger equation to generate invariant subspaces of the Hamiltonian in the Hartree–Fock approximation. This is a generalization of the group-theoretical device of generating orbits of a group in the construction of reduced representations. It is shown how solutions of the time-dependent Schrodinger equation can be expressed as instantaneous stationary states of a constrained static Hamiltonian. Thus contact is made with the traditional cranking models and constrained Hartree–Fock theories of large amplitude collective motion. The collective motion is quantized using the Hill–Wheeler–Griffin method of generator coordinates in a basis of generalized coherent states. One is thereby able to exploit much of the theory of har...
86 citations
TL;DR: In this article, the statistical properties of superradiant pulses emitted by a system of many atoms were investigated and it was shown that the statistical behavior of the atoms is formally equivalent to that of a harmonic oscillator subject to linear amplitude amplification and driven by Gaussian white noise.
Abstract: We investigate the statistical properties of superradiant pulses emitted by a system of many atoms. By using a representation of the atomic density operator in terms of directed angular-momentum states (which are also known as atomic coherent states), we find that the statistical behavior of the atoms is formally equivalent to that of a harmonic oscillator subject to linear amplitude amplification and driven by Gaussian white noise. The emitted light pulses are then found to exhibit very large quantum fluctuations for atomic initial states corresponding to complete or nearly complete excitation. For all other atomic initial states the superradiant pulses show classical behavior.
70 citations
TL;DR: In this article, a generalized phase space method for spin operators is developed, which can be used to transform a Liouville equation into an ac-number equation, and is applied to the Heisenberg model of a magnet.
Abstract: A generalized phase space method for spin operators is developed. With the use of a spin coherent state representation, mapping rules from spin operators onto ac-number space are established; simple formulas to calculate the mappedc-number functions are also derived. A product theorem, which gives a way of mapping a product of operators, is obtained in an intuitive form. This can be advantageously used to transform a Liouville equation into ac-number equation. As an illustrative example, the method is applied to the Heisenberg model of a magnet.
49 citations
TL;DR: In this article, a self-contained treatment of the infrared problem in quantum electrodynamics is presented, which includes a derivation and proof of finiteness of modified reduction formulae for scattering in Coulomb potentials and unitary extensions of the relativistic Coulomb amplitudes in the forward direction.
26 citations
TL;DR: In this paper, the overlap integral for vibronic transitions with doubly and triply degenerate vibrations is calculated in closed form by means of the coherent state method and new recurrence relations are obtained for the overlap integrals.
Abstract: Overlap integrals for vibronic transitions with doubly and triply degenerate vibrations are calculated in closed form by means of the coherent state method. New recurrence relations are obtained for the overlap integrals. The possibility of regarding the overlap integral as a matrix element of some operator of a dynamical group representation leads to new sum rules for the Franck-Condon factors.
26 citations
TL;DR: In this article, explicit expressions for the Green functions of arbitrary relativistic quadratic quantum systems are obtained by the integrals-of-motion method and by the coherent states method.
Abstract: Explicit expressions for the Green functions of arbitrary relativistic quadratic quantum systems are obtained by the integrals-of-motion method and by the coherent states method. The normal forms of the relativistic quadratic hamiltonians are briefly discussed. The important special cases, such as the motion of Dirac and Klein-Gordon charged particles in the fields of a plane wave and in the uniform electric and magnetic fields are investigated in detail.
22 citations
TL;DR: In this article, the problem of obtaining perturbative solutions to the nonlinear differential equations which describe the motion of the x6 and quartically coupled oscillators is treated by the use of the well-known coherent state representation.
Abstract: The problem of obtaining perturbative solutions to the nonlinear differential equations which describe the motion of the x6 and quartically coupled oscillators is treated by the use of the well‐known coherent state representation. The results exhibit the basic qualitative features of nonlinearities and the characteristics of a coupled system in the weak coupling limit.
18 citations
TL;DR: In this paper, the general condition for a coherent state to remain coherent at all times is considered, and the condition for coherent states to be coherent at any given time is discussed.
TL;DR: In this paper, a Fokker-Planck equation describing the coherent spontaneous emission from a system of 3-level atoms is derived using the atomic coherent states representation, and the corresponding Langevin equations are discussed and their solutions for some special cases are presented.
TL;DR: In this article, the Korteweg-de Vries equation for interacting phonon systems has been derived from the coherent state representation of the phonon description of the one-dimensional anharmonic lattice, and it has been shown that the corresponding quantum state must be a state in which a large number of phonons are excited.
Abstract: has given physical explanation of their observation in terms of the strik ing properties of soliton solution associated with the Korteweg-de Vries equation, which has been derived on a continuum model of the one-dimensional anharmonic lattice. At the same time, he has emphasized that the conventional approach of the phonon description is not a suitable way to examine the recurrence phenomena observed by Fermi, Pasta and Ulam. Although vve appreciate the remarkable successes of the soliton concept £or various kinds of the nonlinear wave phenomena,'1 we can not completely discard the phonon picture in the description of physical properties of crystals. It would be worth while examining interrelationship between the soliton concept and the phonon description of the anharmonic lattice. Therefore, we have undertaken to derive the Korteweg-de Vries equation for the interacting phonon systems vvithin the scheme , of quantum mechanical approach. Since the soliton describes nonlinear propagation of a finite amplitude wave in the classical treatment, we e2):pect that the correspond mg quantum mechanical state must be a state in which a large number of phonons are excited. In the following sections, we illustrate that the coherent state representation of the system 41 enables us to derive, the Korteweg-de Vries equation for the in teracting phonons. In order to establish explicit correspondence between Zabusky's continuum approximation and the coherent state description of phonons, we derive
TL;DR: In this article, a first order perturbation solution of the general x2p+2 nonlinear oscillator in the coherent state representation was obtained. But this solution is not a first-order solution for the nonlinear nonlinear model.
TL;DR: The class of external fields for which the causal Green functions of the Klein-Gordon and Dirac equations can be calculated exactly by means of the methods of integrals of motion and coherent states is shown in this article.
Abstract: The class of external fields for which the causal Green functions of the Klein-Gordon and Dirac equations can be calculated exactly by means of the methods of integrals of motion and coherent states is shown. Several important examples are considered.
TL;DR: In this paper, the photon statistics of an arbitrary initial state by two photon absorption were investigated and a detailed discussion of the initial thermal and coherent states were given. But they were not shown to produce fields with the same photon statistics for arbitrary initial fields.
Abstract: Es wird gezeigt, das unter gewissen Voraussetzungen bei genugend groser Anfangsphotonenzahl das bei Zwei-Photonen-Absorption ubrigbleibende Feld nicht von den Anfangsbedingungen abhangt. Als Beispiele werden anfangs thermische und koharente Felder untersucht.
Change of the Photon Statistics of an Arbitrary Initial State by Two Photon Absorption
Assuming high enough initial photon numbers two photon absorption is shown to produce fields with the same photon statistics for arbitrary initial fields. Detailed discussions are given of the initial thermal and coherent states.
TL;DR: In this article, the authors generalize the path integral technique of quantum mechanics to provide direct expressions for energy eigenfunctions, and illustrate their technique with the harmonic oscillator.
Abstract: We generalize the path integral technique of quantum mechanics to provide direct expressions for energy eigenfunctions. We illustrate our technique with the harmonic oscillator.
TL;DR: In this article, a simple transformation, equivalent to the use of Glauber's coherent states (1963), is treated exactly, and the 'direct' part of the currently used Breit correction (1932) to the electron-electron interaction in relativistic Hartree-Fock theory is derived variationally.
Abstract: Canonical transformation techniques are used together with variational and perturbative methods to describe the effects of the coupling between electrons and the radiation field in the Coulomb gauge. A simple transformation, equivalent to the use of Glauber's coherent states (1963) is treated exactly, and the 'direct' part of the currently used Breit correction (1932) to the electron-electron interaction in relativistic Hartree-Fock theory is derived variationally. More general transformations leading to electron self-energy terms as well as electron-electron interaction corrections are discussed and compared to the procedure used by Mittleman (1972). The case where the unperturbed Hamiltonian is of Hartree-Fock type gives the generalized Breit interaction.
TL;DR: The expectation value of a quantum mechanical operator, taken in coherent states and suitably rescaled, is the solution of an initial value problem for the heat equation on phase space, in which ħ plays the role of time, and the classical observable is the distribution of temperature at ħ=0.
Abstract: The expectation value of a quantum mechanical operator, taken in coherent states and suitably rescaled, is the solution of an initial value problem for the heat equation on phase space, in which ħ plays the role of time, and the classical observable is the distribution of temperature at ħ=0.
TL;DR: In this article, the properties of a generalized coherent state (G.C.S) generated by the ideal stimulated two-photon laser are discussed and the photon distribution of Gaussian mixed state of G.c.S. is derived.
TL;DR: In this paper, the authors studied the coherent states and dynamics of a photon mode in the Dicke model Hamiltonian by using a method of diagonal coherent-state representation and showed that under a strong coupling condition, the ground state of the model Hamiltonians is characterized by simultaneous appearance of photon coherent state and that due to atomic polarization.
Abstract: Coherent states and dynamics of a photon mode in the Dicke model Hamiltonian are studied by using a method of diagonal coherent-state representation. It is shown that under a strong coupling condition the ground state of the model Hamiltonian is characterized by simultaneous appearance of a photon coherent state and that due to atomic polarization. The energy eigenvalue of such a combined coherent state is shown to be lower than that of the in which all atoms in a matter system are in their ground state while no photon is present. An exact solution for the time evolution of the coherent-state representation of the photon number operator is obtained in terms of the Jacobi elliptic functions. It is shown that periodic, pulse-like and stationary solutions exist under various initial conditions.
TL;DR: In this article, the quantization method developed by Hammer and Tucker, which is based upon a set of equations of motion and their conserved currents rather than a canonical formalism, is extended to interacting systems.
Abstract: The quantization method developed by Hammer and Tucker, which is based upon a set of equations of motion and their conserved currents rather than a canonical formalism, is extended to interacting systems. The operators of the theory are bilinear and are essentially self‐adjoint on a dense domain which is spanned by a suitably chosen subset of the coherent states. Both proper and improper gauge transformations of the second kind are discussed. For the proper case, the connection is given between these transformations and coherent states, which are discussed in detail. One interesting result is that a ’’smeared’’ Fock space can be constructed for a system where the particles have the same average quantum numbers. For the improper case, the gauge transformation of the second kind is related to the purely absolutely continuous measure. The formalism is applied to two examples. One is a Dirac field minimally coupled to a massive vector field, and the other is Klauder’s ultralocal models.
TL;DR: In this paper, a quasi-probability distribution function based on the coherent state for U(3) is presented, and its properties are investigated with the aid of this function it is shown that the co-operative spontaneous emission from a system of the three-level atoms can be described as a diffusion-like process on C 2 • in particular, the limit of validity of the semi- classical approach is examined.
Abstract: A quasi-probability distribution function based on the coherent state for U(3) is intro duced, and its properties are then investigated. With the aid of this function it is shown that the co-operative spontaneous emission from a system of the three-level atoms can be described as a diffusion-like process on C 2 • In particular, the limit of validity of the semi classical approach is examined. The case in which the semiclassical approach is not applicable can also be treated approximately by means of the Wiener-Hermite expansion method.
TL;DR: In this article, a survey of the connection between second order coherence effects is given, together with experimental examples, and the effect of the photon absorption statistics on the electron-density fluctuations in steady-state photoconductors is briefly discussed.
Abstract: This paper deals with various related subjects, viz. statistics of radiation fields, statistics of absorbed quanta in a time interval T , and photocurrent noise caused by photon absorption both for photoemissive cells and for photoconductors. Under the first heading we review the quantum-mechanical and pseudo-classical description of the field statistics, using Glauber's coherent state representation. Examples are given for thermal radiation, gaussian non-thermal radiation, and laser fields. The distributions for absorbed quanta in an interval T are discussed next; the connection between the stochastic point process of photon absorption and the statistics of photon counting is elucidated and moment rules connecting field intensity statistics and counting statistics are stated. Interval statistics are briefly discussed. From the moment rules, together with MacDonald's theorem, the spectrum of the photocurrent noise of photodiodes or photoemissive cells, consisting of a shot noise part and an excess photon noise part, is derived. A survey of the connection between the various second order coherence effects is given, together with experimental examples. Finally, the effect of the photon absorption statistics on the electron-density fluctuations in steady-state photoconductors is briefly discussed. The problem of stimulated emission and of reconciling Fermi electron output statistics is reconsidered and recommendations for further studies are made.
TL;DR: In this article, it was shown that adding retarted potentials to the Dicke Hamiltonian conserves the threshold condition of a phase transition in the A 2 -term.
TL;DR: In this paper, the localization of localized states as approximate eigenstates of translation-invariant Hamiltonians is discussed in a general way, and the translationally best localized state is shown to give the exact energy in the two-body problem.
Abstract: The method originally suggested by Peierls and Yoccoz for treating localized states as approximate eigenstates of translation-invariant Hamiltonians is discussed in a general way. For many-body systems interacting via two-body potentials, it is shown that the effective mass is correctly given by the method. The translationally best localized state is shown to give the exact energy in the two-body problem. Finally, it is shown that both the strong-coupling and weak-coupling regimes of the polaron can be discussed easily in terms of localized coherent states.
TL;DR: Using the Schwinger coupled boson representation of spin operators, a two Bose fluid like picture of a Heisenberg ferromagnet was derived in this paper, which does not involve many body interactions and the Liouville operator is a second order differential operator.
Abstract: Using the Schwinger coupled boson representation of spin operators, we have derived a two Bose fluid like picture of a Heisenberg ferromagnet. In the magnetised state belowTc one of these fluids can be regarded as composed of magnons, the latter being excitations of the second condensed Bose fluid. Employing the coherent states technique for Schwinger bosons we have formulated ac-number description of the Heisenberg model. In contrast to previous proposals our description does not involve many body interactions and the Liouville operator is a second order differential operator.
TL;DR: In this article, a method of describing an extended object in quantum field theory, referred to as a hadron, by a coherent state and treated as a variational approximation is presented.
Abstract: A convenient method of describing an extended object 111 quantum field theory, wh1ch '" regarded as a hadron, is presented. We describe the extended object by a coherent state and treat it on the basis of a variational approximation. The stability and orthogonality problems which are crucial in any attempt to render a physical significance to such a coherent state are investigated. From the stability condition, it lS shown that only the models which induce the spontaneous breakdown of symmetry have a stable coherent state. We also show that several topological conservation laws can be understood as a reflection of the orthogo nality properties of the Hilbert space. As simple examples, we discuss a self-coupled neutral scalar model, a charged scalar model, the Higgs model and the 0 (3) iso-triplet scalar model.