Showing papers on "Coherent states published in 1975"
TL;DR: In this article, a fully quantum-mechanical treatment of resonant light scattering is presented, where the incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation.
Abstract: A fully quantum-mechanical treatment of resonant light scattering is presented. The incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation. Complete solutions are obtained for the correlated atom-field pure state vector, including multiphoton contributions of arbitrary order. The frequency spectrum of the scattered field is evaluated and is found to agree exactly with the result previously obtained by means of the quantum fluctuation-regression theorem. A derivation of the fluctuation-regression theorem and of the optical Bloch equations is given which is fully quantum mechanical and which relies upon no assumption of statistical factorization of atom and field states. The accuracy of the result found for the scattered - field spectrum is thus shown to be limited only by the assumption of the smallness of the saturated linewidth compared to the (optical) atomic resonance frequency. The one-photon approximation is analyzed in some detail. The method of adding an imaginary term to the upper-atomic-state energy is clarified, and it is shown how the vacuum and one-photon amplitudes thereby obtained may be used, within a simple and plausible iteration scheme, to construct the complete multiphoton spectrum. A variety of commonly used injection schemes and methods of representing atomic relaxation are discussed, and comparisons are made with results found by other authors. The entire analysis is performed with the aid of a canonical transformation which replaces the applied field by a $c$ number. It is thus proved quite rigorously and generally that the use of a $c$-number applied field is a fully quantum-mechanical procedure, provided only that radiation-reaction terms are retained.
260 citations
TL;DR: The connection between the integrals of the motion of a quantum system and its Green function was established in this paper, where it was shown that the Green function is the eigenfunction of the initial points of the system trajectory in the phase space of average coordinates and moments.
Abstract: The connection between the integrals of the motion of a quantum system and its Green function is established. The Green function is shown to be the eigenfunction of the integrals of the motion which describe initial points of the system trajectory in the phase space of average coordinates and moments. The explicit expressions for the Green functions of theN-dimensional system with the Hamiltonian which is the most general quadratic form of coordinates and momenta with time-dependent coefficients is obtained in coordinate, momentum, and coherent states representations. The Green functions of the nonstationary singular oscillator and of the stationary Schrodinger equation are also obtained.
131 citations
TL;DR: In this article, a general set of states on a lattice in the phase plane is considered, and the discrete set of von Neumann coherent states for a harmonic oscillator is a particular case of the above set.
Abstract: A general set of states on a lattice in the phase plane is considered. The discrete set of von Neumann coherent states for a harmonic oscillator is a particular case of the above set. The kq representation is used in an elementary proof of completeness and orthogonality of states on a discrete phase plane lattice.
124 citations
TL;DR: In this article, a homomorphism between the multimode field modes and the algebra describing multimode coherent states and projectors is established, which allows the projection of multimode fields onto the multilevel calculus.
Abstract: The properties of $r$-mode harmonic-oscillator coherent states are reviewed. In particular, the $\mathcal{D}$-algebra differential-operator realization of the creation and annihilation operators on the coherent states and their diagonal projectors is constructed. A homomorphism between the algebra describing $r$-field modes and the algebra describing $r$-level systems is exhibited explicitly. This homomorphism allows the projection of the multimode calculus onto the multilevel calculus. In particular, multimode coherent states and projectors can be used as generating functions for multilevel coherent states and projectors. In addition, the multilevel $\mathcal{D}$ algebra is constructed directly from the multimode $\mathcal{D}$ algebra under this homomorphism. For illustrative purposes, the $\mathcal{D}$ algebra for the diagonal coherent-state projectors for two-level atomic systems is presented explicitly in terms of a parametrization in the Bloch angles $\ensuremath{\theta}$ and $\ensuremath{\phi}$. Two classes of applications are treated: (a) the mapping of atomic-density-operator equations of motion into phase-space equations of motion for the quasiprobability weighting function $P$; (b) the construction of equations of motion for the diagonal elements $Q$ of the density operator in the coherent states. It is shown that the solution to either equation with the appropriate initial condition gives complete statistical information for the atomic system. It is shown explicitly that the functions $P$ and $Q$ are related by a convolution integral.
115 citations
TL;DR: In this paper, the surface-dependent correction terms for the case of a small blackbody bounded by two plane conducting surfaces are derived and a straightforward perturbation theory is used to obtain one-photon transition probabilities in terms of the surfacedependent response functions.
Abstract: In this paper the physical entities such as transition probabilities and the density of states are related to appropriate electromagnetic-field correlation functions and to appropriate response functions. Such response functions have already been computed in a previous paper and therefore these can be used to obtain surface-dependent corrections. It is shown how the density of states and hence Planck's law depends on the presence of surfaces. I explicitly calculate the correction terms for the case of a small blackbody bounded by two plane conducting surfaces. An appreciable correction occurs if the linear dimensions of the blackbody are of the order of a wavelength. Next electric-dipole-type transitions in atomic systems are considered and a straightforward perturbation theory is used to obtain one-photon transition probabilities in terms of the surface-dependent response functions. As an illustration of the surface-dependent terms, the transitions in presence of a conducting surface are considered. The transition probabilities show a marked increase or decrease depending on whether the dipole transition is parallel or perpendicular to the surface. Both stationary and nonstationary fields are considered. As a special case of nonstationary fields, the transitions in a coherent field are considered in detail. It is also shown how the coherent radiation field in presence of dielectrics can be realized. It is found that if the radiation field, in arbitrary geometries, is initially in vacuum state then at later times it would be found in a coherent state if perturbed by an external ($c$-number) electromagnetic field.
74 citations
TL;DR: In this paper, a new method of treating problems of spin systems is developed, in which spin operators are transformed into two kinds of boson operators according to Schwinger's method.
Abstract: A new method of treating problems of spin systems is developed, in which spin operators are transformed into two kinds of boson operators according to Schwinger's method Usual treatment of coherent state representation is generalized to spin systems with a fixed magnitude S Some basic properties and the relations to the atomic coherent state are investigated rather in details The method is applied to spin relaxation process and a corresponding Fokker-Planck type equation is obtained and solved to give a multiple relaxation process due to nonlinearities It is shown that our formulation has several advantages over other ones in some respects
69 citations
TL;DR: Stimulated two-photon emission is proposed as a possible mechanism for the generation of generalized coherent states as discussed by the authors, which have useful quantum properties not available in ordinary coherent states. But this mechanism is not suitable for generalization.
51 citations
TL;DR: In this article, two new derivations of the Wigner distribution function for a simple harmonic oscillator Hamiltonian were presented, one based on a modification of a theorem due to Messiah and the other based on coherent state representation of an oscillator.
40 citations
31 citations
TL;DR: The concept of coherent states for arbitrary Lie groups is suggested as a tool for explicitly obtaining an integral representation of the partition function, whenever the Hamiltonian has a dynamical group.
Abstract: The concept of coherent states for arbitrary Lie group is suggested as a tool for explicitly obtaining an integral representation of the partition function, whenever the Hamiltonian has a dynamical group. Two examples are thoroughly discussed: the case of the nilpotent group of Weyl related to a generic many-body problem with two-body interactions, and the case of\(\mathop \Pi \limits_{k^ \otimes }\)SU(1, 1)(κ) relevant for a superfluid system.
27 citations
TL;DR: In this paper, the coherent state constructed out of quantum oscillator states is employed to develop a method for solving the classical nonlinear oscillator problem and the perturbation solution of the Duffing oscillator is used to illustrate the method and to obtain the result of the classical procedure.
Abstract: The coherent state constructed out of quantum oscillator states is employed to develop a method for solving the classical nonlinear oscillator problem. The perturbation solution of the Duffing oscillator is used to illustrate the method and to obtain the result of the classical procedure.
TL;DR: In this paper, it has been proved that the coherent states are given by horospherical kernels and are the generalization of the plane waves for the case of symmetric spaces.
Abstract: Properties of system of the coherent states related to representations of the class I of principal series of the motion groups of symmetric spaces of rank 1 have been studied. It has been proved that such states are given by horospherical kernels and are the generalization of the plane waves for the case of symmetric spaces.
TL;DR: In this paper, phase properties of generalized coherent states obtained from usual Fock coherent states by adapting classical methods of statistical mechanics, in particular, the well-known procedure of thermodynamical limit, were studied.
TL;DR: In this article, the coherent superposition state of an atomic gas system excited by Doppler-free, two-photon absorption is analyzed and shown that this zero-momentum coherent state does not dephase by thermal motion of the atoms, but decays only by homogeneous relaxation mechanisms.
TL;DR: In this paper, a variational calculation of the small polaron wavefunctions in the representation in which the Hamiltonian no longer contains the electron coordinates is presented, where the spatial extent of the self-trapped electronic state must be taken into account in the construction of the tight-binding polaron Bloch functions.
Abstract: Linear superposition of coherent states is used in a variational calculation of the small polaron wavefunctions in the representation in which the Hamiltonian no longer contains the electron coordinates. It is shown that even in the case of very narrow bands the spatial extent of the self-trapped electronic state must be taken into account in the construction of the tight-binding polaron Bloch functions. Investigation of transport properties shows that the activation energy for the hopping motion diminishes relatively fast with increasing ratio of the rigid lattice band-width to the small-polaron binding energy. Explicit formulae for the variation of the activation energy have been derived for two cases: the interaction with optical phonons and the deformation-potential-type interaction with acoustic phonons.
TL;DR: In this paper, a formalism is presented to obtain approximate analytic expressions for the eigenstates and eigenvalues of a quantum double oscillator (QDO) and matrix elements of a large class of operators with respect to states of different double oscillators result as finite sums of explicit functions of the respective parameters.
Abstract: Abstract A formalism is presented to obtain approximate analytic expressions for the eigenstates and eigenvalues of a quantum double oscillator (QDO). The matrix elements of a large class of operators with respect to states of different double oscillators result as finite sums of explicit functions of the respective parameters. Matrix elements between states of a harmonic oscillator and a double oscillator are also determined. The analytic expressions were used to calculate Franck-Condon factors for electronic transitions including double oscillator anharmonicities.
TL;DR: In this article, it was shown how one may simply associate the problem of the isotropic oscillator to that of the hydrogenic atom in classical dynamics, particularly in its action-angle variable formulation, so that the solution of the one problem implies that of another.
Abstract: It is shown how one may simply associate the problem of the isotropic oscillator to that of the hydrogenic atom in classical dynamics, particularly in its action−angle variable formulation, so that the solution of the one problem implies that of the other. This relationship persists in the two−dimensional quantum mechanics and provides the key to the construction of a wave pocket solution for the isotropic oscillator in the region of large principal quantum number in three dimensions.
TL;DR: In this article, a study of the harmonic wave properties (intensity and coherence) in connection with the statistics of the fundamental: coherent, chaotic and non-ideal laser cases are considered for the fundamental.
Abstract: The author presents a study of the harmonic wave properties (intensity and coherence) in connection with the statistics of the fundamental: coherent (ideal laser), chaotic and non-ideal laser cases are considered for the fundamental. Two approximations of different order are considered and their validity range is studied. The author shows that a coherent wave generates a coherent harmonic only it its photon number is great, while a chaotic one always creates a harmonic with different statistics. He shows also that a fundamental with Lorentzian spectral width generates a harmonic with a coherence time four times smaller.
TL;DR: In this article, the Fokker-Planck equations for radiation propagating through a random medium using the q-c-number correspondence of the coherent state technique are obtained.
Abstract: Master and Fokker-Planck equations are obtained for radiation propagating through a random medium using the q-c-number correspondence of the coherent state technique. The corresponding equation for the antinormal characteristic function is solved by means of the method of characteristics. The master equation method and the recently developed method based on the Heisenberg equations and quantum characteristic function are shown to be equivalent. Some existence problems for the Glauber-Sudarshan weighting function are discussed. New light is thrown on approximations in the photocounting statistics used earlier.
TL;DR: In this paper, the theoretical explanation of radiation damping phenomena at the end-point of the decay spectrum is also clarified, in the context of the coherent states formulation of the asymptotic condition by using dimensional regularization techniques.
TL;DR: In this paper, the quantum dynamics for two coupled harmonic oscillators are presented and the assumed problem is shown to be isomorphic with a perturbed angular-momentum oscillator.
Abstract: The quantum dynamics for two coupled harmonic oscillators is presented. Using the coupled-boson representation, the assumed problem is shown to be isomorphic with a perturbed angular-momentum oscillator. The current operator is obtained and its associated expectation values with respect to the number states, coherent states (Glauber states), and atomic coherent states are given. The eigenvalue spectrum of the current operator is seen to be finite and discrete. An interesting correspondence between this analysis and past work on Josephson tunneling and quantum interference is discussed.
TL;DR: In this article, the minimum uncertainty relation which characterizes a coherent spin state is shown to be invariant under some special rotations and a model to interpret this result is given.
Abstract: The minimum uncertainty relation which characterizes a coherent spin state is shown to be invariant under some special rotations and a model to interpret this result is given. 'Intelligence' of coherent states is discussed in the light of this interpretation.
TL;DR: In this article, the quantum theory of a driven damped harmonic oscillator is presented and the time development of the density operator for the oscillator was obtained and its normally ordered generating functional was written.
Abstract: The quantum theory of a driven damped harmonic oscillator is presented. By using iteration methods the time development of the density operator for the oscillator is obtained and its normally ordered generating functional is written. The field of the oscillator appears to be the superposition of three fields. The first field, which shows the damping of the oscillator, is statistically similar to the one before the interaction; the second one is a coherent field that depends on the driving field; and the third describes a thermal field. In order to evaluate two-time averages by differentiation, a two-time generating functional of the oscillator is obtained. This functional allows two-time averages to be computed from one-time averages before the interaction.
TL;DR: In this article, the authors constructed wave packets which may be considered as an analog of the coherent states of the top and obtained new integral representations for the D-function; making use of those, various types of the asymptotic behavior of the D -function are obtained in the region of large quantum numbers.
Abstract: Wave packets which may be considered as an analog of the coherent states of the top are constructed. New integral representations are obtained for the D- function; making use of those, various types of the asymptotic behavior of the D- function are obtained in the region of large quantum numbers. (auth)
TL;DR: In this paper, a theory for the ground state of a degenerate Bose fluid in thermal equilibrium is formulated, where fluctuations in the condensate are treated in terms of the fluctuation operators C = a 0 -α, and thir conjugate, α 0 being the annihilation operator for the zero momentum state and the order parameter α the quasiaverage of α 0 .
Abstract: A theory is formulated for the ground state of a degenerate Bose fluid in thermal equilibrium The fluctuations in the condensate are treated in terms of the fluctuation operators C = a 0 -α, and thir conjugate, α 0 being the annihilation operator for the zero momentum state and the order parameter α the quasiaverage of α 0 The superfluid ground state is viewed as energy lowering by coherent excitations The coherent state is defined in terms of the normal modes in the superfluid phase The superfluid ground state is not the ground state of the type studied by Glassgold and Sauermann
TL;DR: The authors showed that coherent states as defined by Mikhailov, (see Teor. Mat. Fiz., no.15, p.367 of 1974) may be considered in certain special cases as intelligent states.
Abstract: Shows that coherent states as defined by Mikhailov, (see Teor. Mat. Fiz., no.15, p.367 of 1974) may be considered in certain special cases as intelligent states.
TL;DR: In this paper, an unambiguous construction of the cross sections via a proper $S$-matrix theory is presented. But the proof of finiteness of the reduction formulas to all orders of perturbation theory proceeds formally on the basis of dimensional extensions of eikonal expressions for the Green's functions calculated on the mass shell.
Abstract: Dimensional-regularization techniques are used for the reduction of coherent states in quantum electrodynamics. The primary emphasis is on an unambiguous construction of the cross sections via a proper $S$-matrix theory. The proof of finiteness of the reduction formulas to all orders of perturbation theory proceeds formally on the basis of dimensional extensions of eikonal expressions for the Green's functions calculated on the mass shell. The method is illustrated by concrete second-order calculations in the particular examples of pair production and electron scattering in a potential. In the last example, some problems arising because of the "symmetric" definition of the $S$ matrix are discussed on a pragmatic basis.
TL;DR: In this article, a canonical transformation is presented in which the effect of a coherent, classical, externally applied field (represented by a Glauber coherent state) is transferred from the boundary conditions to the hamiltonian, resulting in the addition of an external, classical field to the Hamiltonian.
TL;DR: In this paper, the authors proposed a new model for the multiplicity distribution in high-energy multiple production, where the final boson state in multiple production processes is described by a mixed state corresponding to the presence of a chaotic field around a coherent state.
Abstract: The multiplicity distribution is obtained on the assumption that the final boson state in the high-energy multiple production is described by a mixed state corresponding to the presence of a certain chaotic field Oike thermal fluctuation) around a coherent state. It is shown that the multiplicity distribution derived from the model fairly well reproduces recent experimental data and gives the KNO scaling in the high-energy limit. Many authors have presented rather mathematical models or formulas for the multiplicity distribution in multiple production processes on the basis of purely phenomenological analyses of recent experiments. At the next stage of the research work, it seems that we ought to find physical models favourable to the production mechanism. In this paper we propose, as one possible trial, a classical boson wave excitation model in which the final boson state in multiple production processes is described by a mixed state corresponding to the presence of a chaotic field around a coherent state. The model gives us a multiplicity distribution consistent with experiments, as will be seen later. Here we must briefly mention a preliminary work given by one of the pres ent authors (M.N.) ten years ago.1l His motivation was first to search for a