Creating quantum entanglement between multi-atom Dicke states and two cavity modes

We present a scheme to create quantum entanglement between multi-atom Dicke states and two cavity modes by passing N three-level atoms in Λ configuration through a resonant two-mode cavity one by one. We further show that such a scheme can be used to generate arbitrary two-mode N-photon entangled states, arbitrary superposition of Dicke states, and a maximal entangled state of Dicke states. These states may find applications in the demonstration of quantum non-locality, high-precision spectroscopy and quantum information processing.     

Non-conditioned generation of Schrödinger cat states in a cavity

We investigate the dynamics of a two-level atom in a cavity filled with a nonlinear medium. We show that the atom-field detuning δ and the nonlinear parameter χ⁽³⁾ may be combined to yield a periodic dynamics, allowing the generation of almost exact superpositions of coherent states (Schrödinger cats). By analysing the atomic inversion and the field purity, we verify that any initial atom-field state is recovered at each revival time, and that a coherent field interacting with an excited atom evolves to a superposition of coherent states at each collapse time. We show that a mixed field state (statistical mixture of two coherent states) evolves towards an almost pure field state as well (Schrödinger cat). We discuss the validity of these results by using the field fidelity and the Wigner function.     

Four-photon Coherent States

Abstract

We present a detailed discussion of a type of four-photon coherent state defined as right eigenstates of the operator â ⁴ where â is the usual annihilation operator. There are actually four sets of states that need to be considered, namely those containing as the lowest number states ¦0>, ¦1>, ¦2>, or ¦3>. These correspond to the possible unique superpositions of the ordinary coherent states ¦±α> and ¦±iα>. We discuss the nonclassical properties of these states such as photon antibunching and squeezing. The usual second order squeezing does not exist for these states but higher order squeezing and square field amplitude squeezing do exist. Also discussed are the quasiprobability distributions, namely the P-function, the Q-function and the Wigner function. Finally, a method of generating these states based on the competition between a four-photon parametric process and incoherent losses from four-photon absorption is presented.     

Fock states generation in a kicked cavity with a nonlinear medium

Abstract

We discuss a model of a cavity filled with a passive nonlinear ?Kerr‘ medium and periodically kicked by a series of ultra-short laser pulses. The nonlinear medium is described by the (2q ? 1)th nonlinearity X ^(2q?1). We find analytical formulas describing the field states inside the cavity. We show that such a system can produce, depending on the order of the nonlinearity, superpositions of several Fock states with the small photon numbers (0,1; 0,1,2; etc). In particular, the one-photon state can be approached during the evolution of the system with X ⁽³⁾ nonlinearity provided the cavity losses are negligible. The purity of states generated in this process, however, can be seriously degraded by the cavity damping. We perform numerical calculations to validate our analytical results.     

Reconstruction of quantum states of spin systems via the Jaynes principle of maximum entropy

Abstract

We apply the Jaynes principle of maximum entropy for the partial reconstruction of correlated spin states. We determine the minimum set of observables which is necessary for the complete reconstruction of the most correlated states of systems composed of spins 1/2 (e.g. the Bell and the Greenberger-Horne-Zeilinger states). We investigate to what extent an incomplete measurement can reveal non-classical features of correlated spin states.     

Evidence of Electron–Phonon Interaction in Al-Substituted Mg1?xAlxB2

Phonon density of states in Al substituted Mg_1–x Al _x B₂ has been studied by means of inelastic neutron scattering experiments with pulsed neutron time-of-flight technique. Phonon dynamics have a significant role for realizing superconductivity in the recent discovered superconductor MgB₂. We present a systematic investigation on generalized phonon density of states (PDOS) up to E = 120 meV on Al content of x = 0.1, 0.25, and 0.5. We have clearly observed a large effect on the PDOS by Al substitution; a large energy shift occurs around at 70 meV and 89 meV. We have also observed a visible increase of PDOS at a particular energy range below T _c. Those phonon states are related with E _2g mode to be expected to have a strong coupling with the electron states at the –A region.     

Low-temperature properties of anisotropic superconductors with kondo impurities

We present a self-consistent theory of superconductors in the presence of Kondo impurities, using large-N slave-boson methods to treat the impurity dynamics. The technique is tested on the s-wave case and shown to give good results compared to other methods forT _K >T _c . We calculate low temperature thermodynamic and transport properties for various superconducting states, including isotropic s-wave and representative anisotropic model states with line and point nodes on the Fermi surface.     

The Validity of Ortho and Para States of Hydrogen at Megabar Pressures

It is well established that the single molecule ortho-para states of hydrogen remain valid in the low pressure solid. In this paper we show that on theoretical grounds the concept of ortho-para states for the molecules in a solid should remain valid to megabar pressures and probably until the Wigner-Huntington dissociative transition to the atomic solid is reached. We calculate the density dependence of the mixing of para states into ortho states and give a general discussion of the density dependence of conversion rates.     

Production of Macroscopic Schrödinger Cat States from Weak Quantized Cavity Fields Interacting with Atoms Driven by Classical Fields

Abstract

We show that macroscopic superposition (Schrödinger cat) states of a quantized single-mode cavity field can be produced via the interaction of this field with a two-level atom which is driven by a classical field even for small initial intensities of the quantized cavity mode. We show that with a properly chosen driving field an almost pure superposition state with arbitrary amplitudes and phases of component states can be produced.     

Parity measurements in quantum optical metrology

We investigate the utility of parity detection to achieve Heisenberg-limited phase estimation for optical interferometry. We consider the parity detection with several input states that have been shown to exhibit sub-shot-noise interferometry with their respective detection schemes. We show that with parity detection, all these states achieve the sub-shot-noise limited phase uncertainty. Thus making the parity detection a unified detection strategy for quantum optical metrology. We also consider quantum states that are a combination of a NOON state and a dual-Fock state, which gives a great deal of freedom in the preparation of the input state, and is found to surpass the shot-noise limit.     

Non-classical Properties of Even and Odd Coherent States

Abstract

We present a detailed discussion of even and odd coherent states defined as eigenstates of the single mode two-photon annihilation operator a ². We study the non-classical properties such as squeezing, higher-order squeezing, and photon antibunching. Also discussed are the various quantum quasiprobability distributions, namely the P function, which is shown to be highly singular, the Q function, and the Wigner, which can take on negative values for these states. Finally, we present a discussion of a possible mechanism for the generation of such states based on the competition between parametric amplification and the incoherent losses from two-photon resonant absorption.     

Andreev Reflection in Unitary and Non-Unitary Triplet States

The quasiparticle reflection and transmission properties at normal conductor-superconductor interfaces are examined for unitary and non-unitary spin triplet pairing states recently discussed in connection with Sr ₂ RuO ₄ . We find resonance peaks in the Andreev reflection amplitude, which are related to surface bound states in the superconductor. They lead to conductance peak features below the quasiparticle gap in the superconductor. The symmetry of the pairing state determines the specific dependence of the peak on the angle of incidence. Based on this observation we propose a possible experiment which allows to distinguish between different superconducting states.     

Phase properties of coherent phase and generalized geometric states

Abstract

We examine some properties of a class of partial phase states of a single field mode. The quasiprobability distribution function and the phase properties of both the generalized geometric and even geometric states are investigated. The relation between the coherent phase states and the SU(1, 1) coherent states is sought.     

Electronic States Around Vortex Cores in the t-J Model

The electronic states around vortex cores in high-T _c superconductors are studied using the two-dimensional t-J model. It is found that the region around the core where the zero-energy peak (ZEP) can be seen in the local density of states (LDOS) becomes smaller as the system approaches the optimum-doped from the overdoped region. We also show that the LDOS without the ZEP can be found in the vortex cores near the optimum doping region, where the vortex cores becomes sufficiently small.     

Crossover from Cooper Pairing to Bose Condensation in van Hove Superconductors with Localized States

We showed that in a two-dimensional superconductor with logarithmic density of states (van Hove superconductor) the crossover between weak and strong coupling is possible. The influence of localized states induced by impurities on this transition has been studied at T=0.     

Experimental evidence for phase-locked states in stacked long Josephson junctions

We fabricated and tested samples consisting of two long stacked Josephson junctions with direct access to the intermediate electrode, whose thickness is smaller than London penetration depth λ ^L . The electrodes are patterned so that the junctions can be independently biased in the overlap configuration. We report the observation of fluxon-antifluxon phase-locked states in zero external magnetic field and the measurements concerning the range of stability of such states as a function of the bias currents. There is strong evidence for the existence of fluxon-antifluxon pairs even when one of the two junctions is biased on the McCumber curve. We also report the observation of several mutually phase-locked states induced by large rf signals (but not phase-locked to the rf field), that can be interpreted as fluxon-antifluxon oscillating in the stack.     

Multi-cluster dynamics in coupled phase oscillator networks

In this paper, we examine robust clustering behaviour with multiple nontrivial clusters for identically and globally coupled phase oscillators. These systems are such that the dynamics is completely determined by the number of oscillators N and a single scalar function g(?) (the coupling function). Previous work has shown that (a) any clustering can stably appear via choice of a suitable coupling function and (b) open sets of coupling functions can generate heteroclinic network attractors between cluster states of saddle type, though there seem to be no examples where saddles with more than two nontrivial clusters are involved. In this work, we clarify the relationship between the coupling function and the dynamics. We focus on cases where the clusters are inequivalent in the sense of not being related by a temporal symmetry, and demonstrate that there are coupling functions that give robust heteroclinic networks between periodic states involving three or more nontrivial clusters. We consider an example for N = 6 oscillators where the clustering is into three inequivalent clusters. We also discuss some aspects of the bifurcation structure for periodic multi-cluster states and show that the transverse stability of inequivalent clusters can, to a large extent, be varied independently of the tangential stability.     

Energy scale of the pairing model with energy-dependent density of state

The critical temperature of a pairing model for HT _c S has been calculated using an energy-dependent density of states. We showed that the problem which is connected with the van Hove scenario is very sensitive to the energy scale and to the behavior of the density of states at low and high energy.     

A bivariate optimal replacement policy for a multistate repairable system

In this paper, a deteriorating simple repairable system with k+1 states, including k failure states and one working state, is studied. It is assumed that the system after repair is not “as good as new” and the deterioration of the system is stochastic. We consider a bivariate replacement policy, denoted by (T,N), in which the system is replaced when its working age has reached T or the number of failures it has experienced has reached N, whichever occurs first. The objective is to determine the optimal replacement policy (T,N)^* such that the long-run expected profit per unit time is maximized. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. We prove that the optimal policy (T,N)^* is better than the optimal policy N^* for a multistate simple repairable system. We also show that a general monotone process model for a multistate simple repairable system is equivalent to a geometric process model for a two-state simple repairable system in the sense that they have the same structure for the long-run expected profit (or cost) per unit time and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results.