Quantum treatment of the time-dependent coupled oscillators under the action of a random force

In this communication we introduce the problem of time-dependent frequency converter under the action of external random force. We have assumed that the coupling parameter and the phase pump are explicitly time dependent. Using the equations of motion in the Heisenberg picture the dynamical operators are obtained, however, under a certain integrability condition. When the system is initially prepared in the even coherent states the squeezing phenomenon is discussed. The correlation function is also considered and it has been shown that the nonclassical properties are apparent and sensitive to any variation in the integrability parameter. Furthermore, the wave function in Schrödinger picture is calculated and used it to derive the wave function in the coherent states. The accurate definition of the creation and annihilation operators are also introduced and employed to diagonalize the Hamiltonian system.     

Hamiltonian quantum dynamics with separability constraints

Schroedinger equation on a Hilbert space H, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space PH. Separable states of a bipartite quantum system form a special submanifold of PH. We analyze the Hamiltonian dynamics that corresponds to the quantum system constrained on the manifold of separable states, using as an important example the system of two interacting qubits. The constraints introduce nonlinearities which render the dynamics nontrivial. We show that the qualitative properties of the constrained dynamics clearly manifest the symmetry of the qubits system. In particular, if the quantum Hamilton’s operator has not enough symmetry, the constrained dynamics is nonintegrable, and displays the typical features of a Hamiltonian dynamical system with mixed phase space. Possible physical realizations of the separability constraints are discussed.     

Distillation of continuous-variable entanglement with optical means

We present an event-ready procedure that is capable of distilling Gaussian two-mode entangled states from a supply of weakly entangled states that have become mixed in a decoherence process. This procedure relies on passive optical elements and photon detectors distinguishing the presence and the absence of photons, but does not make use of photon counters. We identify fixed points of the iteration map, and discuss in detail its convergence properties. Necessary and sufficient criteria for the convergence to two-mode Gaussian states are presented. On the basis of various examples we discuss the performance of the procedure as far as the increase of the degree of entanglement and two-mode squeezing is concerned. Finally, we consider imperfect operations and outline the robustness of the scheme under non-unit detection efficiencies of the detectors. This analysis implies that the proposed protocol can be implemented with currently available technology and detector efficiencies.     

Single atom entropy squeezing for two two-level atoms interacting with a binomial field

In this paper we consider a system of two two-level atoms interacting with a binomial field in an ideal cavity. We investigate the time evolution of the single atom entropy squeezing, atomic inversion and the linear entropy for the present system. Furthermore, the relationship between the entropy squeezing and the entanglement is investigated. It is shown that the amounts of the nonclassical effects exhibited in the entropy squeezing are dependent on the different initial conditions. The entropy squeezing can give information on the corresponding linear entropy.     

Coherent states of the inverted Caldirola-Kanai oscillator with time-dependent singularities

The coherent states for a system of time-dependent singular potentials coupled to inverted CK (Caldirola-Kanai) oscillator are investigated by employing invariant operator method and Lie algebraic approach. We considered Coulomb potential and inverse quadratic potential as singularities of the system. The spectrum of quantum states is discrete for λ < 0 while continuous for λ ? 0. The probability densities for both Fock state and coherent state are converged to the center as time goes by according to the dissipation of energy. We confirmed that the probability density in the coherent state oscillates back and forth like a classical wave packet.     

Strategies to measure a quantum state

We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy of the system. In contrast to previous approaches, we do not average over the possible unknown states but work out a “typical” probability distribution on the set of states, as implied by the experimental data. As a consequence, any measure of knowledge about the unknown state and thus any notion of “best strategy” (i.e., the choice of observables to be measured, and the number of times they are measured) depend on the unknown state. By learning from previously obtained data, the experimentalist re-adjusts the observable to be measured in the next step, eventually approaching an optimal strategy. We consider two measures of knowledge and exhibit all “best” strategies for the case of a two-dimensional Hilbert space. Finally, we discuss some features of the problem in higher dimensions and in the infinite dimensional case.     

ABCD rule involved in the product of general SU(1,1) squeezing operators and quantum states’ Fresnel transformation

Base on our preceding paper [H.Y. Fan, H.L. Lu, Opt. Commun. 258 (2006) 51] we find that there exists ABCD rule involved in the product of general SU(1,1) squeezing operators, which can be considered as the quantum optics countpart of the ABCD rule in classical optics. Both one- and two-mode cases are considered, especially, the ABCD theorem embodied in the Fresnel transformation of two-mode number state is exhibited.     

Effect of dissipation and reservoir temperature on squeezing exchange and emergence of entanglement between two coupled bosonic modes

We study the effect of a thermal reservoir on the squeezing transfer and entanglement between two identical harmonic oscillators, caused by a bilinear coupling of the RWA type. We analyze the evolution of the invariant squeezing coefficients of each mode for arbitrary initially factorized mixed states, as well as the separability coefficient based on Simon's criterion for Gaussian states. We show the importance of initial squeezing for the emergence of entanglement and the existence of critical temperatures above which no squeezing transfer or entanglement are possible.     

The laser-dressed potential binding energy of a hydrogenic impurity in a spherical quantum dot by the analytical transfer matrix method

The analytical transfer matrix method (ATMM) is efficient and accurate for understanding the nature of bound states. In this paper, it is applied to obtain the binding energy of a hydrogenic impurity placed at the center of the spherical quantum dots (QDs) in an intense laser field. Our results agree with the exact energies in Varshni [Superlattices Microstructures 30 (2001) 45]. Therefore, ATMM gives us an alternative approach to tackle the problem of impurities placed in nano-structures under intense laser fields.     

Teleportation fidelity as a probe of sub-Planck phase-space structure

We investigate the connection between sub-Planck structure in the Wigner function and the output fidelity of continuous-variable teleportation protocols. When the teleporting parties share a two-mode squeezed state as an entangled resource, high fidelity in the output state requires a squeezing large enough that the smallest sub-Planck structures in an input pure state are teleported faithfully. We formulate this relationship, which leads to an explicit relation between the fine-scale structure in the Wigner function and large-scale extent of the Wigner function, and we treat specific examples, including coherent, number, and random states and states produced by chaotic dynamics. We generalize the pure-state results to teleportation of mixed states.     

Remote preparation of a class of three-qubit states

We propose a remote state preparation (RSP) scheme of a three-particle Greenberger-Horne-Zeilinger (GHZ) class state by using three 2-qubit maximally entangled states as the quantum channel. The success probability of preparation and classical communication cost are calculated. Generally speaking, conditioned on Alice’s classical message, with probability 1/4 Bob can successfully prepare the original state by performing one appropriate unitary operation. However, for four kinds of special states, the success probability of preparation can be increased to 1/2 or even 1 after consuming some extra bits.     

Wave-function transformations by general SU(1, 1) single-mode squeezing and analogy to Fresnel transformations in wave optics

Following Dirac’s assertion: “… for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”, we find that the general SU(1, 1) single-mode squeezing operator F just corresponds to the generalized Fresnel transform (GFT) in wave optics. We derive the normal product form and canonical coherent state representation of F, whose matrix element in the coordinate representation is just the GFT. It is shown that F is a faithful representation of symplectic group which indicates that two successive GFTs is still a GFT. Applications of F in some other optical transforms, such as the Fresnel-wavelet transform, are presented.     

Scattering of spin-polarized electron in an Aharonov-Bohm potential

The scattering of spin-polarized electrons in an Aharonov-Bohm vector potential is considered. We solve the Pauli equation in 3 + 1 dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment of electron and magnetic field. Expressions for the scattering amplitude and the cross section are obtained for spin-polarized electron scattered off a flux tube of small radius. It is also shown that bound electron states cannot occur in this quantum system. The scattering problem for the model of a flux tube of zero radius in the Born approximation is briefly discussed.     

Variance squeezing and information entropy squeezing via Bloch coherent states in two-level nonlinear spin models

The nonclassical squeezing effect emerging from a nonlinear coupling model (generalized Jaynes–Cummings model) of a two-level atom interacting resonantly with a bimodal cavity field via two-photon transitions is investigated in the rotating wave approximation. Various Bloch coherent initial states (rotated states) for the atomic system are assumed, i.e., (i) ground state, (ii) excited state, and (iii) linear superposition of both states. Initially, the atomic system and the field are in a disentangled state, where the field modes are in Glauber coherent states via Poisson distribution. The model is numerically tested against simulations of time evolution of the based Heisenberg uncertainty relation variance and Shannon information entropy squeezing factors. The quantum state purity is computed for the three possible initial states and used as a criterion to get information about the entanglement of the components of the system. Analytical expression of the total density operator matrix elements at t > 0 shows, in fact, the present nonlinear model to be strongly entangled, where each of the definite initial Bloch coherent states is reduced to statistical mixtures. Thus, the present model does not preserve the modulus of the Bloch vector.     

Excited state quantum phase transitions in many-body systems

Phenomena analogous to ground state quantum phase transitions have recently been noted to occur among states throughout the excitation spectra of certain many-body models. These excited state phase transitions are manifested as simultaneous singularities in the eigenvalue spectrum (including the gap or level density), order parameters, and wave function properties. In this article, the characteristics of excited state quantum phase transitions are investigated. The finite-size scaling behavior is determined at the mean-field level. It is found that excited state quantum phase transitions are universal to two-level bosonic and fermionic models with pairing interactions.     

Quantum circuits for controlled teleportation of two-particle entanglement via a W state

A protocol for three-party controlled quantum teleportation is discussed. It is shown that an unknown two-particle entanglement can be teleported to any one of two receivers via the only one three-particle W state. We summarize all different unitary transformations performed by the receiver with a concise formula. The quantum circuits for the generalized measurement described by positive operator-valued measure (POVM), which is utilized to probabilistically distinguish the two non-orthogonal states, are explicitly constructed by means of quantum Toffoli gates. The efficient quantum circuits for implementing the teleportation are also provided.     

Unitary equivalence of different bipartite entangled states under unitary transformations

The unitary equivalence of different bipartite entangled states with continuous variables under unitary transformations are investigated. With the help of the technique of integration within an ordered product of operators, the corresponding unitary operators are also derived. These results may deepen people's understanding to the various bipartite entangled states, and enrich the representations and transformations theory in quantum mechanics.     

Nonclassical state via superposition of two coherent states (π/2 out of phase) and related entangled states

Nonclassical features of the superposition of two coherent states which are π/2 out of phase are discussed, such as sub-Poissonian photon statistics and quadrature squeezing, as well as negativity of the Wigner function. Special nonclassicality is found in the special state where the relative phase of superposition has relationship with the average photon number. The analysis of the amount of entanglement is also presented for the related two-mode entangled coherent states.     

Wavepacket dynamics, quantum reversibility, and random matrix theory

We introduce and analyze the physics of “driving reversal” experiments. These are prototype wavepacket dynamics scenarios probing quantum irreversibility. Unlike the mostly hypothetical “time reversal” concept, a “driving reversal” scenario can be realized in a laboratory experiment, and is relevant to the theory of quantum dissipation. We study both the energy spreading and the survival probability in such experiments. We also introduce and study the “compensation time” (time of maximum return) in such a scenario. Extensive effort is devoted to figuring out the capability of either linear response theory or random matrix theory (RMT) to describe specific features of the time evolution. We explain that RMT modeling leads to a strong non-perturbative response effect that differs from the semiclassical behavior.