Field In Coherent State Research Articles

Collapse and revival in Aharonov-Bohm electron interference experiment

It is shown that in the presence of even and odd coherent state field the collapse and revival (CR) phenomenon can occur in Aharonov-Bohm electron interference, which is closely related to the quantum fluctuation of the field. CR phenomenon reflects the effects of quantum noise of the field on the dynamic behaviour of electron interference. For coherent state field and number state field there is no CR to occur, which means that CR is due to both wave and particle aspects of the field.

Macroscopic field superpositions from collective interactions

We study the generation of both coherent superpositions and mixtures of field states through the interaction of an initially coherent field state with a collection of two-level atoms. The proposed scheme to build up a given superposition is based on effective dispersive interactions which arise from both the large detuning limit and the strong-field limit. The coherent superposition is obtained by interacting with a classical field after the cluster leaves the cavity followed by a measurement of the atomic population.

Dynamic behaviour of electron interference in the two-mode SU(1,1) coherent state field

Aharonov-Bohm-type electron interference in the presence of the two-mode SU(1,1) coherent state(CS) field is investigated. The visibility of the time-averaged interference pattern is discussed for this state, and a comparison with classical cases is made. It is shown that the time evolution of the intensity of electron interference exhibits collapse and revival (CR) phenomenon for this state. The fluctuation in electron interference, and its relation to CR phenomenon are also discussed.

Competing interactions and quantum nonspreading wave packets.

We study the evolution of a single mode of the quantized electromagnetic field interacting with both a collection of resonant two-level atoms and a Kerr medium. Each of these interactions separately leads to a spreading of the initial field coherent states. Acting simultaneously, these two mechanisms of dispersion can cancel each other for special initial atomic states, allowing the propagation of field wave packets without spreading in the quantum phase space.

Phase Properties of Multiphoton Jaynes-Cummings Model

The multiphoton Jaynes-Cummings model is analyzed for phase properties of a coherent field state. The phase variances tend to the values for a field with a randomly distributed phase of one-photon Jaynes-Cummings model and the off-resonant two-photon Jaynes-Cummings model. Revival of oscillations in the far off-resonant two-photon Jaynes-Cummings model occur much later. On the other hand, the variance of the on-resonant two-photon Jaynes-Cummings model variances oscillate periodically.

Quantum States and Number-Phase Uncertainty Relations Measured by Optical Homodyne Tomography

Experiments have been performed to determine the Wigner distribution and the density matrix (and for pure states the wave function) of a light mode, by using tomographic inversion of a set of measured probability distributions for quadrature amplitudes. From these measurements the quantum distributions of optical phase and photon number have been obtained. The measurements of quadrature-amplitude distributions for a temporal mode of the electromagnetic field are carried out using balanced homodyne detection. We refer to this new method as optical homodyne tomography. Given the measured density matrix, one can experimentally infer any of the various quantum distributions of optical phase, in particular the Pegg—Barnett (or, equivalently, Shapiro—Shepard) phase distribution, the marginal Wigner distribution, and the Vogel-Schleich operational phase distribntion. We have used this approach to make measurements of the number-plase uncertainty relation for coherent-state fields. The coherent states do not attain the minimum value for the number-phase uncertainty product, as set by the expectation value of the commutator of the number and phase operators; this is true theoretically and experimentally.

STATISTICAL PROPERTIES OF SU(1,1) COHERENT STATES OF LIGHT AND ITS INFLUENCE ON DYNAMICAL BEHAVIORS OF THE ATOM

In this paper, we study the properties of two kinds of SU(1,1) coherent states of light with Bargman index k=1/4 and k=3/4 and show that they posses different quantum statistical properties. The atomic dynamical behavior in a two-photon Jaynes-Cummings model with initial SU(1,1)coherent state field are discussed. We show that the time evolution of atomic inversion displays peculiar periodic oscillation and pulse which are very different from coherent states of light.

Quantum switches and nonlocal microwave fields.

A scheme to realize an optical switch with quantum coherence between its ``open'' and ``closed'' states is presented. It involves a single atom in a superposition of circular Rydberg states crossing a high Q cavity. A combination of switches could be used to prepare a quantum superposition of coherent microwave field states located simultaneously in two cavities. Such nonclassical states and their decoherence due to cavity dissipation could be studied by performing atom correlation experiments.

Schrödinger-cat states of the electromagnetic field and multilevel atoms.

We demonstrate that the generalization of the two-level Jaynes-Cummings model to an N-level atom leads to the creation of up to N macroscopically distinct field states. These field states are Schmidt-orthogonalized superpositions of Fock states. They correspond to macroscopic states of the field, attainable with large mean photon numbers. Unlike the situation with a two-level atom and a coherent-state field, which evolves into a macroscopic coherent superposition state (a Schr\"odinger cat), we find that when the additional levels participate strongly in the excitation (e.g., all transitions are resonant with equal dipole moments) then the system does not evolve into a pure state.

Periodic Squeezing in the Tavis-Cummings Model

Abstract By utilizing our previous operator solution [17], we have investigated the squeezing in the radiation field of the Tavis-Cummings model (collective N ≫ 1 two-level atoms interacting with a resonant single cavity quantized mode). With field and atoms initially in coherent field state strong or weak and atomic coherent state (of few excited atoms), periodic time-dependent squeezing in the field and the macroscopic polarization is expressed in terms of Jacobian elliptic functions of the first kind. The statistical investigations are carried out for the quasiprobability distribution functions (Wigner function and Q function). The distribution function of the field quadrature has a variance less (greater) than that for a coherent state if this quadrature is squeezed (unsqueezed).

Jaynes-Cummings model with quasiclassical fields: The effect of dissipation.

An approximate solution is given for the Jaynes-Cummings model with cavity losses, i.e., the problem of a two-level atom interacting with a single mode of the quantized radiation field, in the rotating-wave approximation, when the field is damped by a reservoir at zero temperature. The approximate solution is derived for initial coherent field states with moderately large numbers of photons. It is simpler in form than earlier results derived by other authors and, over the appropriate parameter range, substantially more accurate than some of them, as shown by direct numerical integration of the master equation. In particular, it is found that an earlier treatment of this problem based on a secular approximation is seriously flawed, in that the conditions for its validity are much more restrictive than was previously believed. Among the results derived it is shown that, just as for the lossless case, when the atom is initially prepared in one of the semiclassical eigenstates the evolution is very simple, with the field and the atomic dipole drifting together in phase. For moderate losses this leads, as in the lossless case, to a ``state preparation''; i.e., to a good approximation, the state of the atom at a specific time can be made independent of its initial state. The effect of losses on the recently discovered ``Schr\odinger cat'' state of the field is also analyzed. It is found that, although the dissipation destroys the coherence of the macroscopic superposition very rapidly, preparation and observation of the ``cat'' should be possible with the cavity quality factors reported in recent micromaser experiments.

The amplitude-squared, sum and difference squeezing in the interaction of two quantized field modes with a two-level atom

The sum, difference and amplitude-squared squeezing are investigated for a generalized Jaynes-Cummings model with two field modes. Different initial states for the two-level atom are considered, and the dependence on the relative phases between the atomic and field coherent states is investigated.

Non-classical effects in Jaynes-Cummings model: effect of the phases

The effect of the change of phases in the field coherent state and in the atomic coherent state on the raduction of the fluctuations in atomic variables, and on the normal and amplitude-squared squeezing in the Jaynes-Cummings model is investigated. It is found that these phenomena are sensitive to the changes of phase in the atomic and field coherent states. The occurence of the amplitude-squared squeezing during the period of collapse is shown to be the result of interference between the slowly oscillating functions in the expressions for the parameters of these phenomena.

Effect of detuning and coherence phase on normal squeezing

The effects of detuning as well as the relative phases between the atomic coherence and the field coherent state on the squeezing phenomenon for the one-photon and two-photon Jaynes-Cummings model are investigated. Amounts of normal squeezing can be improved by appropriate choices of detuning and phases. The relation between the collapses and revivals phenomenon and squeezing is made transparent.

Many-atom Jaynes-Cummings model without rotating-wave approximation

The contribution of the counter-rotating terms in the many-atom Jaynes-Cummings model is examined. Numerical results for the time evolution and time averages of the atomic population inversion for various numbers of atoms and different initial fields (Fock and coherent-state fields) are presented. The results demonstrate the significance of the counter-rotating terms.

The broadening of the phase distribution due to linear amplification

It is explicitly shown that the phase probability distribution of an initially coherent field state is broadened due to strong linear amplification by a factor √2 if the initial photon number is not to small. Generally, the broadening of the phase distribution by a high-gain and minimum-noise amplifier is mediated by certain coefficients which where derived in an earlier paper and are here invetigated in more detail. In addition we derive these coefficients by a new approach exactly and show their importance for the inevitable noise of the amplification process.

FEATURES OF EVOLUTION FOR STATISTICAL DISTRIBU-TION OF PHOTON IN TWO-PHOTON JAYNES-CUMMINGS MODEL

The general expression of the statistical distribution function of photons in two-photon Jaynes-Cummings model (JCM) is derived. The expression can be applied to the cases of any initial light field and any initial atomic state. Under exact two-photon resonance, the features of evolution for the statistical distribution of photons in JCM with the initial coherent state field and the initial squeeze state field are studied in detail. These two cases show striking difference.

Magnetism of U(Ru 1−xRh x) 2Si 2 in the coherent Kondo state

We demonstrate here that the peak temperature of the susceptibility is an important parameter to characterize the antiferromagnetic transition temperature and a metamagnetic transition field in coherent Kondo state of mixed compounds U(Ru 1− x Rh x 2 Si 2 for x ≲ 0.06.

Characteristics of Rabi oscillations in the two-mode squeezed state of the field.

The phenomenon of collapses and revivals of Rabi oscillations is studied for a two-level atom undergoing either one- or two-photon transitions in the two-mode squeezed state field inside a lossless cavity. The qualitative behavior of this phenomenon is found to be different as compared with corresponding coherent-state fields. Analytic expressions for excitation probabilities are obtained. Also, the statistical aspect of the field in terms of intensity-intensity correlations is discussed.

Atoms in fock state fields: I. Exact analytical results

A theoretical analysis of the fundamental problem of two-level atomic systems radiatively decaying and coupled to Fock state radiation fields is presented. First, for a broad-band Fock state field and for a single two-level atom the Einstein radiation rate equation is derived within a scheme of matter-field statistical decorrelation. This holds too for N > 1 “independent” two-level atoms. Second, for a single-mode Fock state field exact analytical solution for the atomic inversion, in the single-atom case, is derived within the rotating wave approximation. For N > 1 cooperative two-level atoms exact results are also derived in the steady state regime. In a thermodynamic limit where N→ ∞, the scaled atomic inversion is expressed as Poisson-Charlier polynomials. Connection with earlier results for coherent and incoherent (chaotic) state fields is made. Of mathematical interest: a formal expression for the cofactor elements in terms of the original elements of a triangular matrix is derived in appendix B.