A simple demonstration of the Pancharatnam phase as a geometric phase

Abstract

To demonstrate the Pancharatnam phase as a geometric (Berry's) phase, each polarization state must be obtained by projecting the previous state on it. We describe a simple interferometric arrangement for such a demonstration which only uses a single rotation linear analyser to introduce a continuously variable phase difference between the two beams.     

Berry phase and interference effects in three-level atoms

A theoretical analysis of Berry's phases, which is based on the Cartan subalgebra, is given for three-level atomic systems. The analysis is developed under the adiabatic approximation and is related to topological fibre bundle theories. The topological Berry's phases derived in the present study, are related to phase shifts and can be applied, also, for partial cycles. Some possible applications of the present theory are discussed, for three-level and two-level atomic systems, interacting with nearly resonant monochromatic fields, under the semiclassical and rotating-wave approximations.     

On the Multiphoton Multimode Interaction Between a Two Level Atom and a Quantum Electromagnetic Radiation Field

Abstract

The multiphoton multimode generalization of Jaynes-Cummings Hamiltonian is both derived and linearized in the paper: it is derived from a first-principle Hamiltonian by adiabatic elimination and then shown to be exactly linearized to a form of a Jaynes-Cummings Hamiltonian, which enables an easy solution.     

Second law implications of a magnetocaloric effect adiabatic phase transition of type I superconductor particles

Abstract

The nature of the thermodynamic behaviour of type I superconductor particles having a cross-section less than the Ginzburg-Landau temperature dependent coherence length ξ(T) is discussed for a magnetic field-induced adiabatic phase transition from the superconductive state to the normal state. The magnetocaloric effect adiabatic phase transition of a particle-dimensioned specimen is characterized by a decrease in entropy, suggesting a quantum limit to traditional formulations of the second law, evidenced by attainment of a final process temperature below that resulting from the isentropic magnetocaloric effect adiabatic phase transition of a bulk dimensioned specimen.     

Vacuum induced berry phase: Theory and experimental proposal

Abstract

We investigate quantum effects in geometric phases arising when a two-level system is interacting with a quantized electromagnetic field. When the system is adiabatically driven along a closed loop in the parameter space, signatures of the field quantization are observable in the geometric phase. We propose a feasible experiment to measure these effects in cavity QED and also analyse the semi-classical limit, recovering the usual Berry phase results.     

Realistic eight-port homodyne detection and covariant phase space observables

We consider the quantum optical eight-port homodyne detection scheme in the case that each of the associated photon detectors is assigned with a different quantum efficiency. We give a mathematically rigorous and strictly quantum mechanical proof of the fact that the measured observable (positive operator measure) in the high-amplitude limit is a smearing of the covariant phase space observable related to the ideal measurement, that is, the measurement performed with fully efficient detectors. The result is proved for an arbitary parameter field. Furthermore, we investigate some properties of the measured observable. In particular, we show that detector inefficiencies do not affect the observable's ability to distinguish between different states.     

The effect of quantum dispersion on laboratory feedback optimal control

Abstract

The effect of quantum dispersion (i.e. a multitude of quantum states corresponding to each value of an observable) on laboratory feedback optimal control is studied. It is shown by numerical and analytical means that including the variance of the observable in the objective functional as well as the presence of modest noise in the controls can steer the system into a low-variance quantum state or, if possible, into an eigenstate of the observable.     

Atomic motion in a standing-wave squeezed light field

Abstract

We investigate atomic motion in the standing-wave field of a cavity driven by coherent light plus broad-band-squeezed vacuum. We assume the bad-cavity limit and adiabatically eliminate the cavity mode, deriving a master equation for the atomic variables alone. From this master equation we study the (one-dimensional) atomic motion both in the semiclassical approximation and using quantum Monte Carlo wavefunction simulations. The light force and momentum diffusion are shown to be strongly dependent on the relative phase between the coherent and squeezed fields and, using a dressedstate analysis, we identify observable effects unique to the reduced quantum noise that characterizes squeezed-vacuum light.     

Quantum phase measurements and non-classical polarization states of light

Abstract

In our paper we consider the non-classical behaviour of both the Hermitian (observable) Stokes parameters of light and the phase difference of two modes that describe the quantum polarization states of optical field. To characterize the degree of polarization of light we introduce a new quantity taking into account the quantum properties of different quantum states of two orthogonally polarized modes. The problem of determination of the phase difference in two modes of optical field for the quantum polarization states of light is discussed. To describe in general such a quantum field we introduce two pairs of the phase operators: the phase angles for the Stokes parameters of light in a three-dimensional picture of the Poincaré sphere. We also consider a special type of the eight-port polarization interferometer (polarimeter) for simultaneous homodyne detection of both the Stokes parameters of light and the polarization phase operators and their fluctuations as well. Using an anisotropic (spatioperiodic) Kerr-like nonlinear medium associated with the polarization interferometer we could generate and also observe the polarization-squeezed phase states of light. The fluctuations in the phase difference between two orthogonally polarized modes for these non-classical states are less than the fluctuations for light in coherent state.     

The Adiabatic Phase and Pancharatnam's Phase for Polarized Light

Abstract

In 1955 Pancharatnam showed that a cyclic change in the state of polarization of light is accompanied by a phase shift determined by the geometry of the cycle as represented on the Poincaré sphere. The phase owes its existence to the non-transitivity of Pancharatnam's connection between different states of polarization. Using the algebra of spinors and 2 × 2 Hermitian matrices, the precise relation is established between Pancharatnam's phase and the recently discovered phase change for slowly cycled quantum systems. The polarization phase is an optical analogue of the Aharonov-Bohm effect. For slow changes of polarization, the connection leading to the phase is derived from Maxwell's equations for a twisted dielectric. Pancharatnam's phase is contrasted with the phase change of circularly polarized light whose direction is cycled (e.g. when guided in a coiled optical fibre).     

Quantum theory of two-mode nonlinear directional couplers

Abstract

The quantum two-mode nonlinear directional coupler exhibits intriguing variations on the self-trapping effect seen in the corresponding classical model. We study and compare the quantum counterparts of this phenomenon for number and coherent state inputs, and discuss their relation to the nature of the eigenvalues and eigenvectors of the Hamiltonian.     

Phase distribution and superstructures on the phase correlation of copropagating electromagnetic fields

Abstract

The phase distribution and phase correlation of two initially coherent electromagnetic field modes copropagating through a lossless nonlinear medium are investigated. We show that the number of distinguishable components in the phase distribution depends on the set of nonlinear parameters through a simple relation and that it is connected with the number of entangled field states as well as the number of components that a single field state acquires after propagating through the medium. The phase correlation between the two field modes is shown to exhibit a rich pattern of collapses and revivals, similar to those observed in the quantum inversion of several generalizations of the Jaynes-Cummings model and is related to beats of the various eigenstates of the total Hamiltonian.     

Quantum Amplifier Performance of Strongly Driven Atomic Systems

Abstract

In this paper we consider the gain obtained in strongly driven and damped atomic systems within the framework of quantum amplifier theory. The atomic system suffices to break the time-reversal symmetry and no rigged reservoirs or continuous spectra are needed. We consider both the driven two-level system and Λ-type systems. We derive master equations for the boson mode using adiabatic elimination techniques and use these equations to determine the amplifier performance of the systems. We find that in both cases the quantum limit on the noise can be approached without introducing any quantum features of the strong driving field. The basic interaction event between the amplified bosons and the atomic system suffices to saturate the noise limit. Ideal amplifier performance is, however, found only in the limit when the driving field is far off resonance, and then the ensuing gain becomes very small. The result is understandable because in this limit little population is accumulated on the upper level which drives the noise through spontaneous emission. We believe our method and main conclusions to be quite universal, and they provide insight into the operation of quantum amplifiers.     

Bell's inequality tests: from photons to B-mesons

We analyse the recent claim that a violation of a Bell's inequality has been observed in the B-meson system [A. Go, J. Mod. Opt. 51 991 (2004)]. The results of this experiment are a convincing proof of quantum entanglement in B-meson pairs similar to that shown by polarization entangled photon pairs. However, we conclude that the tested inequality is not a genuine Bell's inequality and thus cannot discriminate between quantum mechanics and local realistic approaches.     

Operator separation of variables for adiabatic problems in quantum and wave mechanics

Linear problems in mathematical physics where the adiabatic approximation is used in a wide sense are studied. From the idea that all these problems can be treated as problems with an operator-valued symbol, a general regular scheme of adiabatic approximation based on operator methods is proposed. This scheme is a generalization of the Born–Oppenheimer and Maslov methods, the Peierls substitution, etc. The approach proposed in this paper allows one to obtain “effective” reduced equations for a wide class of states inside terms (i.e., inside modes, subbands of dimensional quantization, etc.) with possible degeneration taken into account. Next, by application of asymptotic methods, in particular the semiclassical approximation method, to the reduced equation, the states corresponding to a distinguished term (effective Hamiltonian) can be classified. It is shown that the adiabatic effective Hamiltonian and the semiclassical Hamiltonian can be different, which results in the appearance of “nonstandard characteristics” while passing to classical mechanics. This approach is used to construct solutions of several problems in wave and quantum mechanics, particularly problems in molecular physics, solid-state physics, nanophysics and hydrodynamics.     

A note on the measurement of phase space observables with an eight-port homodyne detector

It is well known that the Husimi Q-function of the signal field can actually be measured by the eight-port homodyne detection technique, provided that the reference beam (used for homodyne detection) is a very strong coherent field so that it can be treated classically [see e.g. Leonhardt, U.; Paul, H. Phys. Rev. A 1993, 47, R2460–R2463]. Using recent rigorous results on the quantum theory of homodyne detection observables [Kiukas, J.; Lahti, P. J. Mod. Opt., in press (see arXiv:0706.4436v1 [quant-ph])], we show that any phase space observable, and not only the Q-function, can be obtained as a high amplitude limit of the signal observable actually measured by an eight-port homodyne detector. The proof of this fact does not involve any classicality assumption.     

Variations on adiabatic passage in optical control of molecular processes

Abstract

A number of variations on adiabatic passage for the realization of efficient and selective population transfer in both the gas and liquid phases are presented. The advantageous use of decaying quantum states and/or the influence of continuous measurements during the population transfer are stressed and an intriguing adiabatic passage scheme, which is sensitive to the relative phases of the control laser fields, is introduced.     

The problem of substance in chemistry — an approach by means of large deviation statistics

Different substances can phenomenologically be defined by use of Gibbs' phase rule. In quantum mechanics, on the other hand, the notion of a substance is not clearly understood: The thermal density operator D_β corresponding to some Hamiltonian and some chosen inverse temperature β is uniquely defined, which implies that different isomers exhibit the same thermal density operator. Coexistence of isomers, substances or phases at some temperature, on the other hand, would need different thermal density operators, one for each isomer, substance or phase. Here we try to understand this problem for the classical van der Waals gas using large deviation statistics. We show that the gaseous and liquid phase of the van der Waals gas emerge with increasing numbers of particles. Intermediate states — neither gaseous nor liquid — exist but die out with increasing number of particles. Extension of our method to quantum mechanics is not straightforward, but looks promising.