Showing papers on "Coherent states published in 1987"
TL;DR: In this article, a semi-classical approach of the heavy-ion collision theory in the intermediate energy domain (10−100 MeV incident kinetic energy per nucleon) based on the Vlasov equation and its extension, when the residual interaction is accounted for through a collision kernel, is presented.
190 citations
166 citations
TL;DR: The theory of balanced homodyne and heterodyne detection was developed for inputs in which the signal field is in an arbitrary quantum state and the localoscillator field was in a highly excited coherent state as mentioned in this paper.
Abstract: The theory of balanced homodyne and heterodyne detection is developed for inputs in which the signal field is in an arbitrary quantum state and the local-oscillator field is in a highly excited coherent state. Exact expressions are derived for the photocount moment-generating functions in the special case of a coherent signal. For more general signals, the first two moments of the photocount probability distribution are determined. The moments are evaluated for the examples of a coherent signal with a chaotic noise component, and for squeezed light derived from a degenerate and from a non-degenerate parametric amplifier. The corresponding moments for direct detection are obtained so that comparisons can be made. The Kelley-Kleiner photocount distribution formula is adapted to balanced detection schemes. Light beams are characterized throughout by their energy fluxes, and the theory accordingly describes steady-state experiments.
137 citations
TL;DR: In this paper, the two-photon absorption process was studied by considering the interaction of a quantized single-mode field with an effective two-level atom through intermediate states, and the equations of motion of the coupled atom-field probability amplitudes for the effective twolevel atom were obtained after adiabatically eliminating the intermediate states.
Abstract: The two-photon absorption process is studied by considering the interaction of a quantized single-mode field with an effective two-level atom through intermediate states. The equations of motion of the coupled atom–field probability amplitudes for the effective two-level atom are obtained after adiabatically eliminating the intermediate states. These equations are then solved in the rotating-wave approximation. The time constants associated with the Rabi oscillation, collapse, and revival of the atomic inversion are derived, and the photon statistics are discussed with special reference to photon antibunching.
120 citations
Book•
10 Dec 1987
TL;DR: In this paper, the vector coherent state method is applied to the construction of a group theoretically sound orthonormal Wigner supermultiplet basis, which can be used for vector coherent states.
Abstract: 1. Introduction.- 2. The vector coherent state method.- 3. Detailed examples.- 4. Other applications.- 5. The calculation of SU(3) Wigner coefficients.- 6. An indirect application of vector coherent state theory: Construction of a group theoretically sound orthonormal Wigner supermultiplet basis.
114 citations
TL;DR: In this article, the state of the optical field at the output of a beam splitter is expressed directly in terms of the state at the input via the diagonal coherent state representation.
101 citations
TL;DR: In this paper, it was shown that for a wide class of nonlinear Hamiltonians, an essentially classical initial state will evolve into the coherent superposition of distinguishable quantum states.
Abstract: Here it is shown that, for a wide class of nonlinear Hamiltonians, an essentially classical initial state will evolve into the coherent superposition of distinguishable quantum states. The detection of the interference fringes can be performed by beating the light leaving the nonlinear optical medium with light from a local oscillator. A model for the loss in the detection apparatus is introduced. The squeezed-vacuum technique is introduced finally as a means of enhancing the interference fringes displaying the distinguishable quantum state.
93 citations
90 citations
77 citations
TL;DR: In this paper, the authors calculate Berry's phase and the Hannay angle for some physically interesting coherent states with the parameters characterising the coherent states taken to be slowly varying, and they find that the harmonic oscillator coherent states provide an example for which, although the Hanay angle is zero, Berry phase is non-zero.
Abstract: The authors calculate Berry's phase and the Hannay angle for some physically interesting coherent states with the parameters characterising the coherent states taken to be slowly varying. Interestingly, they find that the harmonic oscillator coherent states provide an example for which, although the Hannay angle is zero, Berry's phase is non-zero.
74 citations
TL;DR: In this article, the authors derived the spectrum of spatial modes of the Fabry-Perot cavity and quantized the electromagnetic field in terms of a continuous set of mode creation and destruction operators.
Abstract: The quantum limits on measurements of small changes in the length of a Fabry-Perot cavity are calculated. The cavity is modelled by a pair of dissimilar mirrors oriented perpendicular to a one-dimensional axis of infinite extent. The continuous spectrum of spatial modes of the system is derived, and the electromagnetic field is quantized in terms of a continuous set of mode creation and destruction operators. Coherent state and squeezed vacuum-state excitations of the field are characterized by energy flow, or intensity, variables. The determination of small changes in the cavity length by observations of fringe intensity is considered for schemes in which the cavity is simultaneously excited by coherent and squeezed vacuum-state inputs. The contributions to the limiting resolution from photocount and radiation-pressure length uncertainties are evaluated. These properties of the Fabry-Perot cavity are compared with the corresponding results for the Michelson interferometer.
TL;DR: In this article, a quantum-statistical description of noise in interferometers is given in terms of the Wigner distribution function, where the input field can be in a variety of states such as a Fock state, a coherent state or a squeezed coherent state.
Abstract: A quantum-statistical description of noise in interferometers is given in terms of the Wigner distribution function. The interferometer may contain an amplifier in one of its arms. The input field can be in a variety of states such as a Fock state, a coherent state or a squeezed coherent state. The Wigner function of the output field at the detector is shown to have a general Gaussian form with non-zero complex field amplitude and with other parameters related to the characteristics of the input field, amplifier and beam splitters, etc. An explicit form of the photon-number distribution is given. Higher-order correlations of the output field can be obtained from the Gaussian property of the Wigner function.
TL;DR: In this article, a polygonal expansion of the discontinuous paths that enter the path integral is proposed to obtain the second-order coherent states for spin systems, and the results are in agreement with only one of the previous approaches, the one developed on Glauber's coherent states by means of a direct WKB approximation.
Abstract: The semiclassical time‐dependent propagator is studied in terms of the SU(2) coherent states for spin systems. The first‐ and second‐order terms are obtained by means of a detailed calculation. While the first‐order term was established in the earlier days of coherent states the second‐order one is a subject of contradiction. The present approach is developed through a polygonal expansion of the discontinuous paths that enter the path integral. The results here presented are in agreement with only one of the previous approaches, i.e., the one developed on Glauber’s coherent states by means of a direct WKB approximation. It is shown that the present approach gives the exact result in a simple case where it is also possible to observe differences with previous works.
TL;DR: In this paper, it was shown that the super-Pioncare algebra is violated by the standard light-cone gauge superstring hamiltonians, since the supercharge anticommulator generates local, 4-string contact interactions at O(λ2), where λ is the coupling of the 3-vertex.
TL;DR: In this article, the authors examine the possibility of generating squeezed states out of coherent states by external changes of the oscillator frequency and explore the two limiting cases of an adiabatic and a sudden change.
Abstract: The Hilbert space of a harmonic oscillator with frequency ω can be spanned by the overcomplete set of coherent states of a second oscillator with frequency ω'. These states are squeezed states of the first oscillator. We examine the possibility of generating squeezed states out of coherent states by external changes of the oscillator frequency and explore the two limiting cases of an adiabatic and a sudden change. Only the latter results in squeezing, while in the former symmetrical uncertainities in coordinate and momentum turn out to be adiabatic invariants.
TL;DR: Using the Caldirola-Kanai Hamiltonian for the damped harmonic oscillator, exact coherent states were constructed in this paper, which satisfy the properties which coherent states should generally have.
Abstract: Using the Caldirola-Kanai Hamiltonian for the damped harmonic oscillator, exact coherent states are constructed. These new coherent states satisfy the properties which coherent states should generally have.
TL;DR: In this paper, the authors introduced states of correlated pairs of atoms with the property that the collective atomic dipole operators exhibit squeezing, and constructed these multi-atom squeezed states by analogy with the multimode squeezed states and thermofield states of the radiation field.
Abstract: We introduce states of correlated pairs of atoms with the property that the collective atomic dipole operators exhibit squeezing. These multiatom squeezed states are constructed by analogy with the multimode squeezed states and thermofield states of the radiation field. Atoms prepared in a multiatom squeezed state can radiate strongly squeezed light. The production of multiatom squeezing might be possible by using coherent excitation and population trapping techniques.
TL;DR: In this paper, the authors defined a unified class of states that includes the Holstein-Primakoff realizations of SU(2) and SU(1, 1) as well as the standard harmonic oscillator coherent states (Weyl-Heisenberg group) and squeezed states in a general framework that allows also non-Hermitian realizations.
Abstract: The multiphoton squeezed states defined in this paper are generalizations of the conventional coherent (Glauber) and squeezed (Yuen) states previously discussed by many authors. We define multiphoton generalizations of the latter by a unified class of states that includes the Holstein–Primakoff realizations of SU(2) and SU(1, 1) as well as the standard harmonic oscillator coherent states (Weyl–Heisenberg group) and squeezed states in a general framework that allows also non-Hermitian realizations. We determine the squeezing properties of these states in a unified formalism and study numerically their dependence on the parameter classifying the states.
TL;DR: In this paper, the dynamical properties of a two-level atom interacting with a single non-decaying mode of an electromagnetic field in a binomial state are studied, and the statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated.
Abstract: The dynamical properties of a two-level atom interacting with a single non-decaying mode of an electromagnetic field in a binomial state are studied. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated. The binomial state reduces to a pure number state and a pure coherent state in different limits. Hence it enables us to study how the sinusoidal Rabi oscillations in a pure number state develop to give rise to the phenomenon of collapse and revival which has been studied extensively in the coherent-state field. In addition, the binomial state exhibits squeezing for certain values of parameters, but it is not a minimum-uncertainty-product state.
01 Sep 1987
TL;DR: Using the Caldirola-Kanai Hamiltonian for the damped harmonic oscillator, exact coherent states are constructed that satisfy the properties which coherent states should generally have.
Abstract: Using the Caldirola-Kanai Hamiltonian for the damped harmonic oscillator, exact coherent states are constructed. These new coherent states satisfy the properties which coherent states should generally have.
TL;DR: In this article, the authors show that ordinary coherent light interacting with a non-absorbing nonlinear medium modelled as an anharmonic oscillator gives rise to enhanced and reduced phase fluctuations as well as squeezing.
TL;DR: In this paper, the coherent states of a harmonic oscillator are introduced following Schrodinger's definition and the equivalence with other definitions is established, and the basic properties of these states are discussed in some detail.
Abstract: The coherent states of a harmonic oscillator are introduced following Schrodinger’s definition and the equivalence with other definitions is established. The basic properties of these states are discussed in some detail.
TL;DR: In this paper, the authors show how the usual P and Q representations of operators in terms of pure states can be extended to finite temperatures with the corresponding mixed states, and various relations between them are demonstrated.
Abstract: The pure Glauber (harmonic oscillator) coherent states provide a very useful basis for many purposes. They are complete in the sense that an arbitrary state in the Hilbert space may be expanded in terms of them. Furthermore, the well known P representation provides a diagonal expansion of an arbitrary operator in the Hilbert space in terms of the projection operators onto the coherent states. The authors study the extensions of these results to the analogous mixed states which describe comparable harmonic oscillator systems in thermodynamic equilibrium at non-zero temperatures. Their results are given for the general density operator which describes the mixed squeezed coherent states of the displaced and squeezed harmonic oscillator. They show how these squeezed coherent mixed states similarly provide a very convenient complete description of a Hilbert space. In particular they show how the usual P and Q representations of operators in terms of pure states may be extended to finite temperatures with the corresponding mixed states, and various relations between them are demonstrated. The question of the existence of the generalised P representation for an arbitrary operator is further examined and some pertinent theorems are proven. They also show how their results relate to the Glauber-Lachs formalism in quantum optics for mixtures of coherent and incoherent radiation. Particular attention is focused both on the interplay between the quantum mechanical and thermodynamical uncertainties and on the entropy associated with such mixed states.
TL;DR: In this article, the newly established single-complex-variable state vector set for the two-dimensional harmonic oscillator in Fock space is generalized to describe an electron moving in a uniform magnetic field.
TL;DR: This work defines k'-photon uncertainties in k-photon states, and shows that all such calculations can be correlated using a fractional photon index r\ensuremath{\equiv}k'/k.
Abstract: We define k'-photon uncertainties \ensuremath{\Delta}${X}_{(k\mathcal{'})}$,\ensuremath{\Delta}${P}_{(k\mathcal{'})}$ in k-photon states, and show that all such calculations can be correlated using a fractional photon index r\ensuremath{\equiv}k'/k. We exemplify by choosing as k-photon states the coherent states of the k-photon generalized harmonic oscillator, and also the group-theoretic coherent states corresponding to Holstein-Primakoff realizations of SU(2) and SU(1,1). We compute the squeezing obtained in these cases, and show that they have a common limit.
01 Jan 1987
TL;DR: In this paper, a review of the experimental investigation done in Florence on dynamical instabilities and deterministic chaos in Quantum Optics is presented, where a set of experiments are reported on the characterization of nonlinear transients and of their statistical features.
Abstract: This chapter presents a review of the experimental investigation done in Florence on dynamical instabilities and deterministic chaos in Quantum Optics. In a dissipative system such as a laser we distinguish between a transient regime, strongly dependent on the initial conditions, and an asymptotic one, where the motion is confined on an attractor independent of the initial conditions. First, laser transients carry relevant information on the birth or death of a coherent state. Thus, a set of experiments is reported on the characterization of nonlinear transients and of their statistical features. Second, the onset of deterministic chaos is studied by referring to the invariant properties of lowdimensional attractors, in order to isolate the characteristics of chaos from the random fluctuations due to the coupling with a thermal reservoir. For this purpose, attention is focused on single-mode homogeneous-line lasers, whose dynamics is ruled by a low number of coupled variables. In the examined cases, experiments and theoretical model are in close agreement. In particular, when many attractors co-exist for the same parameter values (generalized multistability) the presence of random noise induces long lived transients with 1/f like low frequency spectra.
TL;DR: In this article, the authors formulate a general-relativistic concept of quantum geometry capable of describing the behaviour of quantum Lorentz frames in free fall in arbitrary external gravitational fields.
Abstract: We formulate a general-relativistic concept of quantum geometry capable of describing the behaviour of quantum Lorentz frames in free fall in arbitrary external gravitational fields. The mathematical framework suited to this task turns out to be that of Hilbert bundles over a space-time manifold of mean stochastic locations of quantum test particles, with fibres soldered to the base manifold at each given mean space-time location. Furthermore, these fibre bundles incorporate connections compatible with the Hermitian structure. Quantum propagation results from the parallel transport governed by these connections and applied to generalized coherent states, whereas the Hermitian structure supplies the transition probabilities required for the construction of quantum frame and particle propagators. All resulting fibre bundles are shown to possess nonzero curvature forms, which in the generic case incorporate the symplectic 2-form of the cotangent bundle of the base manifold, the pseudo-Riemannian curvature of that manifold and additional components resulting from Maxwell and Yang-Mills connections. In addition, their structure groups incorporate stochastic phase space representations of the Poincare group in a manner that supplies manifest Poincare gauge invariance of the resulting quantum space-time framework.
TL;DR: In this paper, the effect of the curvature invariant operator on the initial singularity of the Gowdy T3*R cosmology was investigated. But the results were limited to the singularity in the Gaussian model.
Abstract: Quantum effects on the initial singularity of the Gowdy T3*R cosmology are studied This is done by calculating the expectation values of the curvature invariant operator Rmu nu alpha beta Rmu nu alpha beta in suitable quantum states It is found that eigenstates of 'particle' number do not introduce inhomogeneities into the model whereas linear combinations of these states such as the coherent states do It is also found that the classical singularity persists
TL;DR: In this article, it was shown that the spin system corresponds to periodic and anti-periodic solutions with extremal energy levels in the 2S + 1 lowest bands (S is the spin).
Abstract: The technique developed in an earlier paper by the authors is used in conjunction with a representation of generalized coherent states to find new effective periodic potential fields that rigorously describe stationary states of (pseudo) spin systems of the type of a two-axis paramagnet in a magnetic field. The potentials depend strongly on several parameters, their profiles are rich in distinctive features of the type of double wells, two-hump barriers, fourfold minima and maxima, and in the bands interesting structural transformation take place (finite-gap property, band pairing, etc.). It is shown that the spin system corresponds to periodic and antiperiodic solutions with extremal energy levels in the 2S + 1 lowest bands (S is the spin). On the basis of the established spin-coordinate correspondence, new classes of exact solutions of the Schroedinger equation are found for energy bands with simple explicit expressions for the energy levels and wave functions for S = 0, 1/2, 1, 5/2, 3, 7/2, 4, 9/2, 5. The potentials are expressed in terms of elliptic functions and contain as special cases the finite-gap Lame-Ince potential and the Eckart and Morse potentials. Effective potentials are also constructed for Hamiltonians of the group SU(1,1).
TL;DR: In this article, a new single-complex-variable state vector set for the two-dimensional harmonic oscillator in Fock space, its orthonormal and completeness properties are examined using IWOP (integration within ordered product of operators).