Some non-classical properties of a class of new nonlinear coherent states

Some of the properties of a nonlinear coherent state associated with the centre of mass motion of trapped atoms are considered. Especially the autocorrelation function, motional quanta number distribution, the phase properties, the Husimi–Kano Q function and the Wigner–Moyal W function of this nonlinear coherent state are discussed. Jumps in the motional quanta distribution function are reported depending on the dependence on the Lamb–Dicke parameters.     

The phase evolution of a micromaser field without the rotating-wave approximation

Abstract

In a one-atom micromaser, the expression for the density matrix of the cavity field without the rotating-wave approximation (RWA) is derived using a perturbation method. The phase evolution of the cavity field is investigated without the RWA, and the results are compared with those within the RWA. It is shown that the virtual-photon processes make the symmetric phase distribution in the RWA asymmetric and cause additional quantum oscillation, which indicate the field's phase fluctuation and frequency shift. Virtual photons also cause an extra phase distribution to the field which is initially in a vacuum state. The unique characteristic of the phase properties in the course of forming a photon-number state is investigated. Other new phenomena such as the undamped oscillation of the phase variance against the injected atomic number are found.     

Non-classicality of photon-added-then-subtracted and photon-subtracted-then-added states

We formulate the density matrices of a quantum state obtained by first adding multi-photons to and then subtracting multi-photons from any arbitrary state as well as performing the same process in the reverse order. Considering the field to be initially in a thermal (or in an even coherent) state, we evaluate the photon number distribution, Wigner function and Mandel's Q parameter of the resulting field. We show graphically that the order in which multi-photons are added and subtracted has a noticeable effect on the temporal behavior of these statistical properties.     

The Relationship between Speed and Grain Size

On the assumption that the average size of latent-image speck required for developability, and the average number of absorbed quanta required to form a developable speck, are independent of grain size, it follows that speed should increase indefinitely with grain size.

Speed/grain-size relationships for experimental series of emulsions have been derived and compared with theoretical trends. These comparisons show that the number of quanta per grain required for developability steadily increases with size within the normal size range. In one series this led to an optimum and then a decrease of speed despite increasing grain size.

On exposure of emulsions to X-rays of such energy as to render one grain developable for each quantum absorbed, speed increases up to the largest grain size. In this case the number of electrons released by an X-ray quantum is such that large inefficiencies in formation of a developable latent-image speck can be tolerated. Excellent agreement between theoretical and experimental speed/grain-size relationships for direct X-rays provides justification for the assumptions made in calculating speed/grain-size relationships for light exposures.

On the basis of experimental evidence several explanations for the decrease of quantum sensitivity at large grain-sizes are rejected. The only feasible type of explanation is one in which the latent-image silver is dispersed over a number of sites at the grain surface. Such an effect may arise in part because the grain size becomes large compared with the average diffusion distance of an electron from its point of release.     

Quantum Cryptography with Photon Pairs

Abstract

Photons, randomly prepared in one of two non-orthogonal quantum states, are used for a cryptographic key distribution. If the receiver tests them one by one, he may either identify their state, or get an inconclusive (useless) result. If he tests them pairwise, he may also obtain information about their parity (whether or not they have the same state), without identifying each signal separately. While this procedure does not give a higher rate of information transmission, the parity-generated bits are more sensitive to attacks by an eavesdropper than bits obtained from single photons.     

Quantum state entanglement and readout of collective atomic-ensemble modes and optical wave packets by stimulated Raman scattering

Abstract

A proposal is made for the creation of macroscopic quantum states of collective atomic-ensemble variables by the use of stimulated Raman scattering (SRS), followed by conditional optical measurement. After the completion of the SRS process, one is able to reverse the process and to return all the atoms to their ground states in such a way that reads out an arbitrary quantum state of the collective atomic field and writes this state onto the outgoing optical field. This scheme can be used for the creation of entanglement between two distant atomic ensembles. The quantum analysis of the SRS process treats one-dimensional spatial-temporal propagation accurately. Remarkably, it is found that this multimode problem can be simplified to a two-mode problem involving spatial-temporal wave-packet modes of the optical and atomic collective fields. This improves the understanding of the entanglement created in this system.     

Homodyne tomography of classical and non-classical light

Abstract

States with explicit quantum character, such as squeezed vacuum and bright squeezed light, as well as coherent states and incoherent superpositions of coherent states were generated and analysed by tomographical methods. Wigner functions, photon-number distributions, density matrices and phase distributions were reconstructed with high accuracy. Features such as photon number oscillations, sub-Poissonian and super-Poissonian photon statistics, bifurcations of the phase distribution, and loss of coherence were observed, demonstrating the usefulness of quantum state reconstruction as an analysing tool in quantum optics experiments.     

Evolution of Coherent States in a Dispersionless Fibre with Saturable Nonlinearity and the Generation of Macroscopic Quantum-superposition States

Abstract

We study the evolution of a initially coherent state of an electromagnetic field propagating in a Kerr medium with saturable nonlinearity. By using the quantum phase distribution formalism, we analyse the dependence of the output signal phase configuration upon input field amplitude. We observe that the saturation of the nonlinear contribution of the refractive index of the propagation medium introduces interference effects that compromise the observation of macroscopically well distinguishable components of the output state. For input amplitudes much larger than a characteristic saturation amplitude the final state differs from the input state only by an overall phase shift. Possible relevance of the present results in the experimental search of Schrödinger cat-like states using semiconductor-doped glass optical fibres is discussed.     

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.     

Optomechanical effect on the Dicke quantum phase transition and quasi-particle damping in a Bose–Einstein condensate: a new tool to measure weak force

Abstract

We make a semi-classical steady state analysis of the influence of mirror motion on the quantum phase transition for an optomechanical Dicke model in the thermodynamic limit. An additional external mechanical pump is shown to modify the critical value of atom–photon coupling needed to observe the quantum phase transition. We further show how to choose the mechanical pump frequency and cavity–laser detuning to produce extremely cold condensates. The present system can be used as a quantum device to measure weak forces.     

Control of γ′ morphologyin nickel base superalloys through alloy design and densification processing under electric field

Abstract

The design and development of the future generation of nickel base superalloys for the demanding environments of rocket engines should be based on the metallurgical and structural characteristics of the γ′ phase. The distinctive features of this phase (e.g. strength, stability, size, shape, amount, distribution, uniformity, and order) can be controlled when a superalloy is appropriately designed and subsequently processed by an innovative solidification processing method. This concept has been successfully applied in the design and development of a superalloy. The resulting microstructure is almost perfect requiring no further treatment or processing.

MST/1954     

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.     

Ground state cooling,quantum state engineering and study of decoherence of ions in Paul traps

Abstract

We investigate single ions of ⁴⁰Ca⁺ in Paul traps for quantum information processing. Superpositions of the S_½ electronic ground state and the metastable D_5/2; state are used to implement a qubit. Laser light on the S_½ ? D_5/2 transition is used for the manipulation of the ion's quantum state. We apply sideband cooling to the ion and reach the ground state of vibration with up to 99.9% probability. Starting from this Fock state (n = 0), we demonstrate coherent quantum state manipulation. A large number of Rabi oscillations and a ms-coherence time is observed. Motional heating is measured to be as low as one vibrational quantum in 190ms. We also report on ground state cooling of two ions.     

Determining the state of a single cavity mode from photon statistics

Abstract

We present various schemes for measuring the quantum state of a single mode of the electromagnetic field. These involve measuring the photon statistics for the mode before and after an interaction with either one or two two-level atoms. The photon statistics conditioned on the final state of the atoms, for two choices of the initial set of atomic states, along with the initial photon statistics, may be used to calculate the complete quantum state in a simple manner. Alternatively, when one atom is used, two unconditioned sets of photon statistics, each after interaction with a single atom in different initial states, along with the initial photon statistics may be used to calculate the initial state in a simple manner. When the cavity is allowed to interact with just one atom, only pure cavity states which do not contain zeros in the photon distribution may be reconstructed. When two atoms are used we may reconstruct pure states which do not contain adjacent zeros in the photon distribution. Coherent states and number states are among those that may be measured with one-atom interaction, and squeezed states and ?Schrödinger cats‘ are among those that may be measured with a two-atom interaction.     

A quantitative study of the quantum interferometer in pure magnesium

The quantum interferometer oscillations observed in the transverse magnetoresistance of Mg at liquid helium temperatures forJ[11 0] andH[1 00] have been experimentally investigated in detail. A new method of analyzing these quantum interference oscillations has been developed which permits direct line shape comparison between the experimentally observed magnetoresistance oscillations and theoretical calculations based on the stacked-mirror model of quantum transport. By using the stacked-mirror model in conjunction with the line shape comparison technique, virtually all of the approximations made in the initial studies of the quantum interferometer have been eliminated. Distinct and striking line shape changes in the magnetoresistance oscillations, critically dependent on the angle between the direction of the applied magnetic field and the basal plane of the Mg crystal, have also been observed and analyzed. This phenomenon provides direct evidence for the existence of long-range quantum phase coherence of the electron states in the Mg crystal over dimensions of 0.3 mm, corresponding to a quantum state lifetime of 3.5×10^–10 sec. Experimental values for the three magnetic breakdown parameters that characterize the quantum interferometer in pure Mg areH ₁(k _H =0)=3000±75 G,H ₂(k _H =0)=10,000±1500 G, andH ₃(k _H =0)=1000±250 G. Experimental evidence is also presented which shows a magnetic field dependence of the quantum state lifetime for some of the crystals studied.Presented as a thesis to the Department of Physics, The University of Chicago, in partial fulfillment of the requirements for the Ph.D. degree.Supported by NSF Grant GS-39932.     

The orientational phase transition at a vortex in3He-B

The orientational phase transition in the vicinity of a single vortex in³He-B is studied. It is the phase transition from a uniformn-texture withn parallel to the magnetic field and the vortex line to ann-texture that is nonuniform near the vortex. The problem of the instability of the the uniformn-texture is equivalent to the quantum mechanical two-dimensional problem of a bound state in a field with an attractive potential 1/r ². The orientational phase transition at a vortex array is also considered. In the limit of large vortex density the orientational phase transition transforms to the phase transition studied by Gongadze et al. The theoretical results are compared with the observed phase transition at a vortex in³He-B.     

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.     

Phase properties of two-mode gaussian light fields with application to Raman scattering

Abstract

We investigate quantum phase properties of two-mode optical fields whose quasidistributions have Gaussian form. We show how to simplify the calculation of the joint phase distribution defined via radial integration of the quasidistribution related to s-ordering of the field operators. We find an analytical formula for the joint phase distribution when coherent components of both modes vanish. The general results are applied to analysis of quantum phase properties of the two-mode Stokes-anti-Stokes field generated by means of Raman scattering with a broad reservoir phonon system and strong coherent laser pumping.     

Materials science perspective of metal fatigue resistance

Abstract

An interdisciplinary view of metal fatigue in polycrystalline metals is presented. Fatigue resistance is defined in terms of the difficulty of crack growth in one of two possible directions, the first being related to the texture of a material, and the second to the orientation of the applied loading system. The fatigue initiation phase is considered to be negligible for polycrystalline metals, and fatigue limits are equated to one of two threshold conditions, one quantified in terms of microstructural fracture mechanics, and the other determined by continuum mechanics. The importance of the intensity and distribution of microstructural barriers to fatigue crack growth is underlined, especially in relation to mechanical conditions such as stress–strain state and to material conditions such as grain size and the shape and orientation of inclusions and their size relative to microstructural barriers.

MST/1883     

Back-action-induced Squeezed Light in a Detuned Quantum Non-demolition Scheme

Abstract

We describe the experimental observation and theoretical interpretation of a squeezing effect which occurs through the coupling of two light beams in a three-level atomic system. The origin of this effect can be attributed to the transfer of the intensity fluctuations of one beam to the phase fluctuations of the other one, followed by an optical feedback onto the intensity of the initial beam. The first step of the information transfer is similar to the one which occurs in a quantum non-demolition (QND) measurement of the intensity. The feedback effect is obtained through mixing of the phase and intensity quadratures, due to the detuning of the optical cavity which contains the nonlinear medium. Therefore the information obtained by the QND measurement is used to correct the intensity fluctuations of the signal beam by a build-in mechanism, which does not require any use of external electronics.