Showing papers on "Coherent states published in 1988"
Book•
21 Jan 1988
TL;DR: The Landay Theory of Germi Liquids has been used in this paper to describe the second quantization and coherent states of the first quantization of a function at finite temperature.
Abstract: * Second Quantization and Coherent States * General Formalism at Finite Temperature * Perturbation Theory at Zero Temperature * Order Parameters and Broken Symmetry * Greens Functions * The Landay Theory of Germi Liquids * Further Development of Functional Integrals * Stochastic Methods
1,619 citations
TL;DR: In this paper, the wave function of an interacting family of one large parent and many Planck-sized "baby" universes is computed in a semiclassical approximation using an adaptation of Hartle-Hawking initial conditions.
503 citations
TL;DR: In this article, the authors examined the nonclassical properties of pair coherent states defined as the simultaneous eigenstates of the operator that annihilates photons in pairs and of the operation that gives the relative occupation number in the two modes.
Abstract: We examine the nonclassical properties of the pair coherent states defined as the simultaneous eigenstates of the operator that annihilates photons in pairs and of the operator that gives the relative occupation number in the two modes. We show that fields in such states have remarkable quantum features such as sub-Poissonian statistics correlations in the number fluctuations, squeezing, and violations of Cauchy–Schwarz inequalities. We show how such pair coherent states can be generated by the competition of different nonlinear processes in a two-photon medium. The quantam features occur not only in the transient domain but also survive in the steady state because of the balance between nonlinear processes.
250 citations
TL;DR: In this paper, it was shown that a single atom making two-photon transitions in an ideal cavity (Q = ∞) in the presence of an initial coherent state field will, as expected, continue to show the collapses and revivals of atomic inversion and the intensity-intensity correlation of the field.
Abstract: It is shown that a single atom making two-photon transitions in an ideal cavity (Q = ∞) in the presence of an initial coherent state field will, as expected, continue to show the collapses and revivals of atomic inversion and the intensity–intensity correlation of the field; however, these collapses and revivals are both compact and regular, in contrast to the one-photon case. This is because, although the several Rabi frequencies involved are incommensurate, for the two-photon case, unlike for the one-photon problem, they become commensurate in the limit of intense field. We derive analytic expressions for the atomic inversion and the intensity–intensity correlation in the case of direct, as well as homodyned, detection of the intracavity field. The effects of the Stark shift are discussed.
152 citations
132 citations
TL;DR: This work considers squeezed light described as an SU(1,1) coherent state interacting with a two-photon Jaynes-Cummings model of aTwo-level atom as a model for squeezing.
Abstract: We consider squeezed light described as an SU(1,1) coherent state interacting with a two-photon Jaynes-Cummings model of a two-level atom. We study the time variation of the mean photon number and also the variance of the field quadratures with particular regard to the squeezing.
104 citations
TL;DR: In this paper, an alternative proof of the fact that a function generating a basis of coherent states must have an infinitely long tail in either position space or momentum space is given. But the argument is a very natural one in which the Heisenberg Uncertainty Principle enters directly.
Abstract: We give an alternate proof of the fact that a function generating a basis of coherent states must have an infinitely long tail in either position space or momentum space. Our argument is a very natural one in which the Heisenberg Uncertainty Principle enters directly.
102 citations
TL;DR: In this paper, a new theory for large quantum fluctuations in a Fermion many-body system that cannot be described by fluctuations around the Hartree·Fock ground state but arises from resonance of different correlation structures was developed.
Abstract: We develop a new general theory for large quantum fluctuations in a Fermion many·body system that cannot be described by fluctuations around the Hartree·Fock ground state but arises from resonance of different correlation structures. We start with an exact coherent state representation of a Fermion system on a unitary group. We show that the Hamiltonian in the coherent state representation has a close connection with the Hartree·Fock energy functional. From this, we can derive a new approximation called the resonating Hartree·Fock approximation in which a state is approximated by a superposition of non· orthogonal Slater deterrp.inants with different correlation structures. We derive the variation equations to determine a resonating Hartree· Fock wavefunction. We show that the resonance between degenerate broken symmetry Slater determinants may partially recover the symmetry. We discuss how to choose trial Slater determinants in a resonating Hartree· Fock wavefunction. We suggest that resonance of Slater determinants representing localized defects, such as solitons, polarons and breathers, produced in the long range order of the HF ground state may be the most important content of large quantum fluctuations in condensed matter systems.
85 citations
TL;DR: In this article, it was shown that quantum gravity is non-renormalizable, even if it is based on some finite underlying theory, such as superstrings, and that the strength of these effective interactions cannot be predicted from the theory, but have to be fixed by measuring them.
61 citations
TL;DR: It is shown that classical linear canonical transformations are possible in the Wigner phase space and coherent and squeezed states are shown to be linear canonical transforms of the ground-state harmonic oscillator.
Abstract: It is shown that classical linear canonical transformations are possible in the Wigner phase space. Coherent and squeezed states are shown to be linear canonical transforms of the ground-state harmonic oscillator. It is therefore possible to evaluate the Wigner functions for coherent and squeezed states from that for the harmonic oscillator. Since the group of linear canonical transformations has a subgroup whose algebraic property is the same as that of the (2+1)-dimensional Lorentz group, it may be possible to test certain properties of the Lorentz group using optical devices. A possible experiment to measure the Wigner rotation angle is discussed.
61 citations
TL;DR: In this article, the statistical properties of various harmonic oscillator states that are linear superpositions of its energy eigenfunctions are described using only elementary quantum-mechanical concepts and the principles underlying the production of squeezed electromagnetic waves via parametric amplification or four-wave mixing, their measurement by homodyne detection, and the connection between squeezing and non-Poissonian counting statistics.
Abstract: Using only elementary quantum‐mechanical concepts, the statistical properties of various harmonic oscillator states that are linear superpositions of its energy eigenfunctions are described. These superpositions include coherent states and squeezed (or two‐photon coherent) states. The resulting Gaussian, minimum‐uncertainty wave packets are shown to oscillate back and forth for both coherent and squeezed states, but with an oscillating ‘‘width’’ for the squeezed states. Also examined are the principles underlying the production of squeezed electromagnetic waves via parametric amplification or four‐wave mixing, their measurement by homodyne detection, and the connection between squeezing and non‐Poissonian counting statistics.
TL;DR: In this article, the generalized Bogoliubov transformation for mixed systems of bosons and fermions is also obtained for the simple harmonic oscillator, and the invariant integration measure is calculated by studying transformation properties of supercoset variables.
Abstract: Coherent states for the harmonic oscillator representations of the noncompact supergroup Osp(1/2N,R) are introduced and the invariant integration measure is calculated by studying transformation properties of supercoset variables. The generalized Bogoliubov transformation for mixed systems of bosons and fermions is also obtained. An example for the simple harmonic oscillator is given.
TL;DR: In this article, the authors considered the possibility that changes of spatial topology occur as tunneling events in quantum gravity, and the creation of scalar and spinor particles during these tunneling transitions is studied.
TL;DR: In this article, the exact expressions for the atom-field probability amplitudes in the rotating-wave approximation are presented, and exact solutions are employed in the study of the quantum collapse and revivals of the atomic coherence.
Abstract: Interactions of two two-level atoms with a single-mode quantized radiation field are studied, and exact expressions for the atom-field probability amplitudes in the rotating-wave approximation are presented. These solutions are employed in the study of the quantum collapse and revivals of the atomic coherence.
TL;DR: The effects of the cavity damping on the phenomenon of collapse and revival in the population inversion of an atom in a two-photon process are investigated by using the dressed-atom approximation.
Abstract: The effects of the cavity damping on the phenomenon of collapse and revival in the population inversion of an atom in a two-photon process are investigated by using the dressed-atom approximation. Explicit results are given for a field initially in either a coherent or a two-photon coherent state. The cavity damping is expected to have more significant effects on two-photon transitions because the vacuum-field Rabi frequency for two-photon transitions is smaller than that for single-photon transitions.
TL;DR: In this paper, exact coherent states for a damped harmonic oscillator with time-dependent mass and frequency were constructed, and the new coherent states result exactly as partial cases of the coherent states of Yuen which are equivalent to the well-known squeezed states.
TL;DR: It is shown that a new phonon coherent state must be introduced to serve as the ground state of the phonon subsystem, so that the ground-state energy of the interacting system can be made a stable minimum and an appropriate condensationenergy of the superconducting ground state may be obtained.
Abstract: We have investigated the ground-state properties of a model system with a strong electron-phonon interaction. It is found that as long as the renormalized intersite electron correlation is attractive, a new type of Cooper pairing will occur whether the renormalized on-site electron correlation is repulsive or attractive. Furthermore, we have shown that a new phonon coherent state, named a two-phonon coherent state, must be introduced to serve as the ground state of the phonon subsystem, so that the ground-state energy of the interacting system can be made a stable minimum and an appropriate condensation energy of the superconducting ground state may be obtained. We have performed numerical calculations for the n = 1 case.
TL;DR: The present theoretical approach is used in the interpretation and the analysis of heterodyning experiments of a squeezed signal with a much stronger local oscillator in a coherent state.
Abstract: The quantum analysis of the influence of a beam splitter on photodetection statistics is discussed. The link between second-order correlation functions and various experimental quantities obtained in photon counting and spectrum analysis is clarified. The introduction of a ``vacuum field'' is interpreted as a mathematical transformation between two sets of creation-annihilation operators, which can be used as a mathematical device for simplifying the calculations. However, its physical interpretation as a real field is shown to be potentially confusing. The present theoretical approach is used in the interpretation and the analysis of heterodyning experiments of a squeezed signal with a much stronger local oscillator in a coherent state.
TL;DR: In this article, the authors quantized the world line supersymmetric action for a point particle of spin 1/2 using fermion coherent state methods and showed that the results of the Feynman path integral for this action is the Dirac propagator in a coherent state basis.
Abstract: Using fermion coherent state methods the authors quantise the world line supersymmetric action for a point particle of spin 1/2. They show that the results of the Feynman path integral for this action is the Dirac propagator in a coherent state basis. They also discuss ambiguities in the definition of the path-integral measure, give details of the superspace geometry of the spinning particle action and show how Majorana spacetime fermions are related to the real quantum mechanics of the spinning particle.
TL;DR: It is proved that a coherent state may be a valid vacuum in light-front field theory and how to solve for the ground state of the strong-coupling (${\ensuremath{\varphi}}^{4}$${)}_{2}$ problem on the light front is demonstrated.
Abstract: We demonstrate that a coherent state may be a valid vacuum in light-front field theory. Then by minimizing the sum of the expectation values of the light-front Hamiltonian and the momentum operators in a variational trial state, we evaluate the ground state (vacuum) of two-dimensional ${\ensuremath{\varphi}}^{4}$ field theory. The resulting expectation value in the coherent state is identical with the result of the effective-potential method in the equal-time formulation. Thus we demonstrate how to solve for the ground state of the strong-coupling (${\ensuremath{\varphi}}^{4}$${)}_{2}$ problem on the light front. We also discuss the calculation of excited states.
Book•
30 Jun 1988
TL;DR: In this article, the authors proposed a perturbation theory for a non-ideal Bose gas, which is based on a modified version of the classical stationary phase method.
Abstract: 1. Functional integrals In quantum theory.- 1. Gaussian functional integrals for systems of non-interacting particles.- Coherent states of harmonic oscillators. Partition functions.- Finite multiplicity approximations for partition functions. Functional- integral passage to the limit.- Functional methods of calculation.- Matrix elements of the statistical operator and the evolution operator.- The ideal Bose gas.- Green's functions.- 2. Methods of functional integration for interacting particles.- The stationary phase method. Extremals.- The harmonic Bose oscillator under the action of external forces.- The second variation and excitation spectrum.- Perturbation theory for a non-ideal Bose gas.- Fermi statistics.- Partial summation of diagrams.- Formulae for average values.- 2. Superfluid Bose systems.- 1. Perturbation theory for superfluid Bose systems.- Zero-temperature theory. Breakdown of symmetry.- Separation of the condensate.- Low-density Bose gas. Phonon character of the spectrum.- Higher diagrams of perturbation theory.- Superfluidity.- 2. The effective action functional for superfluid systems.- The method of integrating with respect to the rapid and slow variables.- The modified perturbation theory. Removal of infra-red divergences.- Two-dimensional and one-dimensional Bose systems. Superfluidity without a Bose condensate.- 3. Quantum vortices in superfluid systems.- The description of vortices by the method functional integration.- The electrodynamical analogue.- The role of the vortices in the phase transition.- 3. Superfluid Fermi systems.- 1. Perturbation theory for superfluid Fermi systems.- Superfluidity and long-range correlations in Fermi systems.- The diagram technique for superfluid Fermi systems.- The low-density Fermi gas.- One-particle excitations and the energy gap.- 2. Collective excitations in superfluid Fermi systems.- The method of integration with respect to rapid and slow fields forFermi systems.- Conversion to the effective action functional.- The Fermi gas.- Taking into account the Coulomb interaction.- The effective action functional for the 3He model.- Collective excitations.- The Fermi gas with attraction.- The Bose spectrum of the Fermi gas in the critical region.- The Bose spectrum of the Fermi gas at low temperatures.- The Bose spectrum with Coulomb interaction.- The 3He model.- The possibility of several superfluid phases in 3He.- The Bose spectrum of the 3He model in the critical region.- The low-temperature Bose spectrum of the B-phase of 3He.- The Bose spectrum of the A-phase.- 4. Interaction of radiation with matter. The linear theory.- 1. Coherent and thermal radiation.- Equations of the electromagnetic field in Hamiltonian form. Approximation of the given currents.- Single-mode radiation. The canonical distribution for the field of asignal with noise.- The Planck and Poisson distributions for the number of photons.- 2. The two-level system in an external field.- Dipole interaction.- The two-level system.- The resonance approximation.- The trilinear model of the interaction of light with matter.- The evolution of atoms in a given field.- Quasi-energy.- The adiabatic approximation.- 5. Superradiant phase transitions.- 1. The static field in the single-centre model of the interaction of matterwith single-mode radiation.- Three classical operators with constraints.- Quantum oscillators. Accounting for the constraint in the Canonical Gibbs ensemble.- Static ordering.- Non-resonance interaction. Accounting for the constraint in thegrand canonical ensemble.- The excitation spectrum.- 1. Functional integrals In quantum theory.- 1. Gaussian functional integrals for systems of non-interacting particles.- Coherent states of harmonic oscillators. Partition functions.- Finite multiplicity approximations for partition functions. Functional- integral passage to the limit.- Functional methods of calculation.- Matrix elements of the statistical operator and the evolution operator.- The ideal Bose gas.- Green's functions.- 2. Methods of functional integration for interacting particles.- The stationary phase method. Extremals.- The harmonic Bose oscillator under the action of external forces.- The second variation and excitation spectrum.- Perturbation theory for a non-ideal Bose gas.- Fermi statistics.- Partial summation of diagrams.- Formulae for average values.- 2. Superfluid Bose systems.- 1. Perturbation theory for superfluid Bose systems.- Zero-temperature theory. Breakdown of symmetry.- Separation of the condensate.- Low-density Bose gas. Phonon character of the spectrum.- Higher diagrams of perturbation theory.- Superfluidity.- 2. The effective action functional for superfluid systems.- The method of integrating with respect to the rapid and slow variables.- The modified perturbation theory. Removal of infra-red divergences.- Two-dimensional and one-dimensional Bose systems. Superfluidity without a Bose condensate.- 3. Quantum vortices in superfluid systems.- The description of vortices by the method functional integration.- The electrodynamical analogue.- The role of the vortices in the phase transition.- 3. Superfluid Fermi systems.- 1. Perturbation theory for superfluid Fermi systems.- Superfluidity and long-range correlations in Fermi systems.- The diagram technique for superfluid Fermi systems.- The low-density Fermi gas.- One-particle excitations and the energy gap.- 2. Collective excitations in superfluid Fermi systems.- The method of integration with respect to rapid and slow fields forFermi systems.- Conversion to the effective action functional.- The Fermi gas.- Taking into account the Coulomb interaction.- The effective action functional for the 3He model.- Collective excitations.- The Fermi gas with attraction.- The Bose spectrum of the Fermi gas in the critical region.- The Bose spectrum of the Fermi gas at low temperatures.- The Bose spectrum with Coulomb interaction.- The 3He model.- The possibility of several superfluid phases in 3He.- The Bose spectrum of the 3He model in the critical region.- The low-temperature Bose spectrum of the B-phase of 3He.- The Bose spectrum of the A-phase.- 4. Interaction of radiation with matter. The linear theory.- 1. Coherent and thermal radiation.- Equations of the electromagnetic field in Hamiltonian form. Approximation of the given currents.- Single-mode radiation. The canonical distribution for the field of asignal with noise.- The Planck and Poisson distributions for the number of photons.- 2. The two-level system in an external field.- Dipole interaction.- The two-level system.- The resonance approximation.- The trilinear model of the interaction of light with matter.- The evolution of atoms in a given field.- Quasi-energy.- The adiabatic approximation.- 5. Superradiant phase transitions.- 1. The static field in the single-centre model of the interaction of matterwith single-mode radiation.- Three classical operators with constraints.- Quantum oscillators. Accounting for the constraint in the Canonical Gibbs ensemble.- Static ordering.- Non-resonance interaction. Accounting for the constraint in thegrand canonical ensemble.- The excitation spectrum.- 2. The static field in the multi-centre model of the interaction of matter withsingle-mode radiation.- The grand canonical ensemble.- The average over the lattice variables. The effective action functional.- The equations for stationariness. Static solutions.- The superradiant phase transition and the statistics of the medium.- The excitation spectrum.- Non-resonance interaction of radiation with matter.- 3. Other models and a discussion of the results.- Spontaneous breakdown of symmetry.- The Dicke model with fluctuations of the parameters.- The influence of the interaction of the lattice with the field on the phase transition.- Superradiant ordering and seignetto-electricity.- 6. Superradiant coherent impulses.- 1. Non-linear interaction of light with matter.- Dicke superradiation.- The Maxwell-Bloch equations. Accounting for the damping.- The Lamb theory.- Solitons.- The threshold condition, randomization, and synergetics.- Irreversibility and the projection operator.- Integration over a closed time contour.- 2. The dynamics of the single-centre model of the interaction of lightwith matter.- The coherent dynamics of three Bose oscillators. Periodic solutionsand 2?-impulses.- The ?-impulses.- The two-mode single-centre model. The equations for the field andthe population-density levels.- The approximation of close frequencies. The dependence of the absorption coefficients on the initial conditions and parameters of the problem.- The influence of the detuning on the frequency of vibration of the field.- 3. The dynamics of the single-mode multi-centre model of the interaction oflight with matter.- The effective action for the field.- The approximation of weak non-linearity.- The approximation of strong non-linearity.- The vibrational and rotational states of the field oscillator.- Concluding Remarks.
AT&T1
TL;DR: In this article, a coherent state interacting with a suitable nonlinearity can be transformed into a quantum superposition of two coherent states 180° out of phase with each other, and the interference between the two macroscopic components of this Schrodinger's cat-like state can be detected with a homodyne detector.
Abstract: A coherent state interacting with a suitable nonlinearity can be transformed into a quantum superposition of two coherent states 180° out of phase with each other. The interference between the two macroscopic components of this Schrodinger's cat-like state can be detected with a homodyne detector.
TL;DR: In this paper, the authors considered two-mode Glauber coherent states and showed that they are ordinary coherent states with respect to new operatorsb1 andb2, which are themselves general linear (Bogolibov) transformations of the original operatorsa1,a2 and their hermitian conjugates.
Abstract: The states\(\hat \theta \)|A1A2〉 are considered, where the operators\(\hat \theta \) are associated with a unitary representation of the groupSp(4,ℝ), and the two-mode Glauber coherent states |A1A2> are joint eigenstates of the destruction operatorsa1 anda2 for the two independent oscillator modes. We show that they are ordinary coherent states with respect to new operatorsb1 andb2, which are themselves general linear (Bogolibov) transformations of the original operatorsa1,a2 and their hermitian conjugatesaδ1,aδ2. We further show how they may be regarded as the most general two-mode squeezed states. Most previous work on two-mode squeezed states appears to be based on more restrictive definitions than our own, and thereby reduces to special cases which are unified within our treatment.
TL;DR: An extensive study of the thermodynamics of a two-dimensional periodic array of ultrasmall Josephson junctions with and without a transverse magnetic field is presented and a quantum Monte Carlo algorithm is introduced to study a model that includes the Josephson energy.
Abstract: An extensive study of the thermodynamics of a two-dimensional periodic array of ultrasmall Josephson junctions with and without a transverse magnetic field is presented. A quantum Monte Carlo algorithm is introduced to study a model that includes the Josephson energy, ${E}_{J}$, as well as the charging energy, ${E}_{c}$, contributions. The superfluid density, internal energy, and specific heat for different lattice sizes and numbers of Monte Carlo simulation sweeps are studied as a function of the ratio \ensuremath{\alpha}=${E}_{c}$/${E}_{J}$, the temperature and the magnitude of the magnetic field. When \ensuremath{\alpha}\ensuremath{
e}0, it is found that as the temperature is lowered the model has two phase transitions. First, a second-order Berezinskii-Kosterlitz-Thouless (BKT) transition renormalized by the quantum fluctuations represented by a finite \ensuremath{\alpha}. Below this BKT transition the system has long-range phase coherence; thus it is a state with zero resistance. At lower temperatures, a first-order phase transition appears which is entirely due to the quantum fluctuations that nucleate vortex excitations. Below this ``quantum induced transition'' (QUIT) the model still has a finite but diminished superfluid density, thus indicating that the QUIT is between two different zero-resistance states, one dominated by thermal fluctuations and the other by quantum fluctuations. A QUIT is found to be more pronounced in the case where there is a magnetic field. The case studied here corresponds in the classical limit to the fully frustrated state. Finally, we discuss the physical properties of this new low-temperature phase as well as the necessary conditions to test this prediction experimentally.
TL;DR: In this article, it was shown that Lorentz boosts are area-preserving canonical transformations in the phase space of the light-cone variables, and the harmonic oscillator is discussed in detail as an illustrative example for the covariant realization of the uncertainty principle.
Abstract: It is shown that, in the phase-space representation of quantum mechanics, the uncertainty relation can be stated in terms of the integral invariant of Poincare. The uncertainty relation for spreading free wave packets is discussed as an illustrative example. This phase-space approach can be extended to the relativistic regime. It is shown that Lorentz boosts are area-preserving canonical transformations in the phase space of the light-cone variables. The harmonic oscillator is discussed in detail as an illustrative example for the covariant realization of the uncertainty principle.
TL;DR: In this article, it was shown that the large γ of heavy-electron materials is predominantly a single-ion effect: γ α 1 T K, and that the most interesting physical effects occur in the low-temperature coherent state of a chemically ordered lattice of these ions.
TL;DR: In this article, a simple one-dimensional model for many-electron and phonon interacting systems was proposed, and it was shown that in order to arrive at a stable minimum of the total energy, the ordinary polaronic state must be replaced by the squeezed coherent state in which the phonon subsystem is in the two-phonon coherent state.
TL;DR: The pseudospin tensor as discussed by the authors is a higher-order generalization of the pseudoprecession tensor, which can be used to study fluctuations and squeezing in the semi-classical Dicke model and the ideal parametric amplifier.
Abstract: The semi-classical Dicke model and the ideal parametric amplifier are described by Hamiltonians linear in the SU(2) and SU(1, 1) group generators, respectively. We use the usual pseudospin vector as well as its SU(1, 1) analog to give a unified description of the dynamics of the coherent states in these models. The pseudospin vector obeys a precession (or pseudoprecession) equation; hence simple geometrical arguments can be used to relate its evolution to that of the coherent-state parameters. To study fluctuations and squeezing we introduce the pseudospin tensor, which is a higher-order generalization of the pseudospin vector. The pseudospin tensor obeys a generalized precession equation that can be factored into scalar, vector, and quadrupole parts and solved exactly by application of the Cayley–Hamilton theorem. Squeezing is related directly to the behavior of the. pseudospin tensor and can therefore be calculated without invoking the group-theoretical disentangling formulas. Our approach is thus elementary in character. It also provides an attractive and closely parallel geometrical account of coherent-state evolution and squeezing in the two models.