Showing papers on "Coherent states published in 1970"
TL;DR: In this paper, time-dependent invariants for a nonstationary harmonic oscillator and for a charged particle in a varying axially symmetric classical electromagnetic field are found, and the Green's functions are obtained in closed form.
Abstract: New time-dependent invariants for the $N$-dimensional nonstationary harmonic oscillator and for a charged particle in a varying axially symmetric classical electromagnetic field are found. For these quantum systems, coherent states are introduced, and the Green's functions are obtained in closed form. For a special type of electromagnetic field which is constant in the remote past and future, the transition amplitudes between both arbitrary coherent states and energy eigenstates are calculated and expressed in terms of classical polynomials. The adiabatic approximation and adiabatic invariants are discussed. In the special case of a particle with time-dependent mass, the solution of the Schr\"odinger equation is found. The symmetry of nonstationary Hamiltonians is discussed, and the noncompact group $U(N, 1)$ is shown to be the group of dynamical symmetry for the time-dependent $N$-dimensional oscillator.
204 citations
TL;DR: In this paper, a quasiclassical approach to coherent spontaneous emission from a system of two-level atoms interacting with a quantized radiation field is presented. But the quantum effects that are lost in the selfconsistent field approximation are not considered.
Abstract: Coherent spontaneous emission from a system of $N$ two-level atoms interacting with a quantized radiation field is treated for the case in which Dicke's "cooperation number" $r$ is macroscopically large. It is shown how to modify the quasiclassical approach to this problem to incorporate quantum effects that are lost in the self-consistent-field approximation. The statistics of the emitted radiation are found to vary markedly with the initial state of the system of atoms. The photon statistics tend to that typical of blackbody radiation when the initial state of the atomic system is that which would result from incoherent pumping ($m\ensuremath{\sim}r$). When, on the other hand, the atoms are initially in a superradiant state ($m\ensuremath{\ll}r$), the emitted radiation may be represented approximately by a coherent state.
151 citations
TL;DR: In this article, the authors derived a Fokker-planck equation to describe the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system.
Abstract: Spontaneous emission from a system of $N$ identical two-level atoms is considered using a master equation recently derived by the author. The master equation describing the time evolution of the phase-space distribution function associated with the reduced density operator of the atomic system is obtained. This master equation, which is of the type of a Fokker-Planck equation, is used to derive the equation of motion for the mean values of various atomic operators characterizing the physical properties of the system. This leads to a hierarchy of equations, which is decoupled by making a suitable approximation. The intensity of the spontaneously emitted radiation is then calculated. Next, the spontaneous emission from geometrically small systems is considered. For this case, the master equation is solved exactly, and an exact expression for the radiation rate is obtained. The exact solution of the master equation is also used to calculate the normally ordered correlation functions for the electric field. Section V deals with the spontaneous emission from a system of harmonic oscillators, the size of the system being small compared to a wavelength. The master equation for this problem is also solved exactly, and it is shown that this system also leads to superradiant emission in some cases, e.g., if all the oscillstors are excited initially to some coherent state $|{z}_{0}〉$.
149 citations
TL;DR: In this article, a complete set of coherent-state wave packets for an electron in a uniform magnetic field has been constructed, which are the eigen states of two ladder operators that annihilate the zero-angular-momentum ground state.
Abstract: A complete set of coherent-state wave packets has been constructed for an electron in a uniform magnetic field. These states are nonspreading packets of minimum uncertainty that follow the classical motion. Use was made of the ladder operators that generate all the eigen-states of the Hamiltonian from any one energy eigenstate. The coherent states are the eigenstates of the two ladder operators that annihilate the zero-angular-momentum ground state. We have calculated the partition function, exploiting advantages of the coherent-state basis. The Landau diamagnetism and the de Haas-van Alphen oscillations are contained in the coherent-state framework.
128 citations
TL;DR: In this article, new invariants, coherent states and transition amplitudes are constructed for non-stationary forced oscillators, and the Franck-Condon factor is calculated.
103 citations
TL;DR: In this article, a criterion for the existence of a selfadjoint and semibounded momentum operator in a non-Fock representation of the free photon field given by a coherent state was derived.
Abstract: A criterion is derived for the existence of a selfadjoint and semibounded momentum operator in a non-Fock representation of the free photon field given by a coherent state. The representation of the translation group is constructed and it is shown that the rotation group, hence the homogeneous Lorentz group, cannot be unitarily implemented in the so-called infrared sectors.
78 citations
TL;DR: In this paper, a number of properties of harmonic oscillator wave functions in three dimensions are derived using a generating function technique, such as the matrix element between two-particle central potentials.
63 citations
TL;DR: In this article, the quantum statistics of continuous space time dependent electromagnetic fields are analyzed by means of functionals and a masterequation is derived for the density operator which is a functional of the field operators.
Abstract: The quantum statistics of continuous space time dependent electromagnetic fields is analyzed by means of functionals. The case of a field propagating in a thermal reservoir serves as a simple example to illustrate the succeeding steps: a masterequation is derived for the density operator which is a functional of the field operators. By means of the coherent state representation for continuous fields the masterequation is transformed into a functional differential equation in the function space, spanned by the coherent state amplitudes. This equation is of the Fokker-Planck type and determines a Gaussian process for a continuum of variables or a field. It is solved by determining the characteristics in function space of the associated equation of motion for the characteristic functional and subsequent functional integration. The solution is used to calculate some correlation functions and the spectral function of the field.
16 citations
TL;DR: In this paper, it was shown that the local dispersion in number in the condensed part of an ideal Einstein-Bose gas is small and appropriate to a Poisson distribution, contrary to the usual result obtained using the grand canonical ensemble.
Abstract: It is argued that the grand canonical ensemble is not appropriate for describing local properties of a closed system when the system has off-diagonal long-range order over distances of the order of the dimensions of the system (e.g., when there is a condensation into a single-particle state). It is shown that the local dispersion in number in the condensed part of an ideal Einstein-Bose gas is “small” (appropriate to a Poisson distribution), contrary to the usual result obtained using the grand canonical ensemble. This leads to an approximation in which the condensed part of the system is represented locally by a coherent state. It is further argued that these considerations serve as a rationale for breaking gauge symmetry whereas the usual arguments (based on analogy with ferromagnetism) are not appropriate.
15 citations
TL;DR: In this paper, the authors examined the nonlinear dynamics of the turn-on of a Q-switched laser (or maser) oscillator and obtained an accurate analytical solution for the distribution, which describes the probability that the field intensity has a certain value at a certain time after the initiation of the Q-switch.
Abstract: We examine the nonlinear dynamics of the turn-on of a Q -switched laser (or maser) oscillator. The description of the laser is fully quantal, including fluctuations. We use the coherent state representation for the field, and treat the atoms adiabatically. We obtain for the first time an accurate analytical solution for the distribution, which describes the probability, in an ensemble of identically prepared lasers, that the field intensity has a certain value at a certain time after the initiation of the Q -switch. The most easily observable fluctuation effect is a timing jitter in the turn-on, amounting to about two and one-half times the time constant, which describes the early exponential rise of the field intensity. An example is presented, using parameters approximating those of a 1-mW helium-neon laser.
12 citations
TL;DR: In this paper, the behavior of a quantum-mechanical harmonic oscillator under a random perturbation of the form $f(t){q}^{2}$ is discussed.
Abstract: The behavior of a quantum-mechanical harmonic oscillator under a random perturbation of the form $f(t){q}^{2}$ is discussed. Equations are obtained governing the time evolution of the Wigner function and the weight function for the $P$ representation. The latter function satisfies a fourth-order differential equation, in contrast to the simpler second-order equation obeyed by the Wigner function.
TL;DR: In this article, it was shown that a coherent state cannot remain coherent when interacting with a two level atomic model commonly used in laser theory, and it was also shown that coherent states cannot be maintained when using a two-level atomic model.
TL;DR: In this article, the authors make a systematic study of the properties of generalized phase operators and show that the coefficients of transformation from the number eigenstates to these are orthogonal polynomials in the eigenvalue parameter.
Abstract: Following the demonstration by Lerner that the phase (cosine and sine) operators for a harmonic oscillator can be much more general than the specific set considered earlier in the literature, we make a systematic study of the properties of such generalized phase operators We determine their eigenstates and show that the coefficients of transformation from the number eigenstates to these are, quite generally, orthogonal polynomials in the eigenvalue parameter Using these generalizedC andS operators the number-phase minimum uncertainty state is given Finally we point out that though the commutator [C, S] cannot be made to vanish, nevertheless one can constructC andS in such a way that their commutator has a vanishing expectation value with respect to all coherent states having a given mean occupation number exceeding unity
TL;DR: The meaning of the term coherence is reviewed here and it is shown how these apparently different uses of the word coherence can be understood in terms of a single concept involving interference, minimum uncertainty, and cohering of the wave packet that describes the system.
Abstract: The concept of coherence has been applied in the quantum theory of radiation and matter as well as in classical optics. We review here the meaning of the term in each case and show how these apparently different uses of the word coherence can be understood in terms of a single concept involving interference (nonzero cross terms), minimum uncertainty, and cohering (uniform variance) of the wave packet that describes the system. Self-induced transparency, superradiance, and superconductivity are discussed as dramatic examples of coherence.
TL;DR: In this article, the authors propose a generalization of Dirae's method for the problem of the quan tum harmonic-osci cation of a charged part in the presence of a magnetic field.
Abstract: In recent years, some interes t has been raised by the problem of the quan tum harmonic-osci l la tor wi th a coupling cons tant K(t), which is a funct ion of t ime (1.2). The impor tance of this p roblem has been stressed by the analysis of the mot ion of a charged part ic le in the presence of a magnet ic field H~(t), which has a fixed direct ion bu t changes i ts in tens i ty wi th t ime (1). The reason of this note is tha t , among these recent studies, the most na tura l approach is surprisingly absent. We will describe i t here, and we will analyse some easily solvable potent ials . W e say t h a t i t is a ve ry na tura l approach, because i t consists in a ve ry na ive general ization of Dirae 's method. I n order to in t roduce it, we remark tha t the Dirae creat ion opera tor (in the t imeindependen t case) could be considered as the opera tor t ha t gives a solution once applied to another solution (for ins tance the vacuum). So we in t roduce an opera tor A ( x , ~ /~x , t) with the p rope r ty tha t , once appl ied to a solut ion of the SehrSdinger equat ion , i t gives another solution. The expl ici t form of this opera tor A is obta ined by means of a simple differential equat ion wi th one and only one solution. W e then find an explici t solution of the t ime-dependen t SchrSdinger equat ion , as a simple general izat ion of the vacuum wave function. App ly ing i tc ra t ive ly the A opera to r we obta in an explici t form for a set of solutions. Noth ing can be said, however , abou t the general case.
TL;DR: In this article, the Peierls equation for the time rate of change of the mean number of polaritons in a dielectric crystal was derived using coherent states as a basis.
Journal Article•
TL;DR: In this paper, the problem of mapping the annihilation and creation operators associated with a pseudo-oscillator onto the c-number functions is studied from a unified point of view.
Abstract: The problem of mapping the operator functions of
$$\hat b$$
and
$$\hat b^\dag $$
, which are the annihilation and creation operators associated with a pseudo-oscillator, onto thec-number functions is studied from a unified point of view. The approach is similar to the one recently developed by Agarwal and Wolf for the case of the ordinary oscillator. The results are illustrated by means of a number of examples. The phase-space distributions corresponding to Weyl’s, normal and antinormal orderings are studied in detail and the explicit representations for them in terms of coherentstate matrix elements are given. The connection with the so-called semiclassical description is also established.
01 Jan 1970
TL;DR: In this article, the probability distribution for phase measurements on the radiation field which consists of one single mode for the number states and the coherent states was calculated and the new phase operator constructed by Varga and Aks was used.
TL;DR: In this article, an interacting Bose gas at T = 0, with a pair Hamiltonian where there exists a generalized condensation in state is investigated up to an upper limit k 0 in momentum space.
Abstract: An interacting Bose gas atT=0, with a pair Hamiltonian where there exists a generalized condensation in state is investigated up to an upper limitk0 in momentum space Corresponding to the idea that an ideal Bose gas can be represented by a coherent state, each operator is replaced by a coherent field operator It is then found that for a particular choice of the potential, the transformations and procedures of Bogoliubov type lead to a stable energy spectrum with a gap at finite volume, but to a photon spectrum at infinite volume Though a major portion of the interaction in momentum space is negative, a minimum point in the energy-density diagram is indicated
01 Jan 1970
TL;DR: In this paper, a coherent state representation for the spin system was defined by transforming the Heisenberg model Hamiltonian to Bose operators and a hard core repulsive interaction was used to include the effects of the spin commutators exactly.
Abstract: Abstract By transforming the Heisenberg model Hamiltonian to Bose operators it becomes possible to define a coherent state representation for the spin system. This representation proves to be a useful basis for evaluating the partition function in a manner similar to that used previously for a superfluid. A hard core repulsive interaction is used to include the effects of the spin commutators exactly. The scattering of two spin waves is solved to all orders of perturbation theory in this formalism and used to rederive the low temperature series expansions due to Dyson. The results using the hard core interaction are compared with those using Dyson's dynamical interaction alone. The method is extended to give some results for the case of an anisotropic exchange interaction.