Quantum decoherence from adiabatic entanglement with external one or a few degrees of freedom

Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments [e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a coherent initial state, three illustrations are presented with their explicit solutions in this paper. Received 26 February 2000 and Received in final form 14 July 2000     

The effect and control on remaining the quantum correlation by the coupling symmetry between qubits and the bath

We study the dynamic evolution of quantum correlation of two interacting coupled qubits system in non-Markov environment, and quantify the quantum correlation using concurrence and quantum discord. We find that although both of them are physical quantities which measure the system characteristics of the quantum correlations, the quantum discord is more robust than concurrence, since it can keep a positive value even when the ESD happens. The quantum correlation of quantum system not only depends on the initial state but also strongly depends on the coupling ways between qubits and environment. For the given initial state, by keeping the coupling between qubits and environment in completely symmetric, we can completely avoid the effect the decoherence influenced on the quantum correlation and effectively prolong the survival time of quantum discord and concurrence. We also find that the stronger the interaction between qubits is, the more conducive the death of the quantum correlation is resisted.     

Stability investigation on quantum correlations of coupled qubits in non-Markovian process

Utilizing the concurrence and the quantum discord as the measure method, in this paper we compare and investigate the dynamic evolution features of quantum correlations of coupled qubits in non-Markovian process. We focus attention on decoherence effect influences the stability of quantum correlations. The investigation results show that because of the decoherence influence between the system and environment, the concurrence always evolves with time in oscillation form in the way of deaths and survivals, however, the quantum discord time evolution does not appear the deaths and survivals. The quantum discord survives obviously longer than concurrence, which indicates that quantum discord has a stronger ability to resist decoherence than entanglement. Through regulating and controlling the purity and entanglement of the initial quantum state, we can effectively suppress the decay of the quantum correlations, which is advantaged to complete the quantum information processing.     

Molecular spectra, quantum chaos, and scars

Low resolution features in the spectra of classically chaotic atomic and molecular systems are known to be related to recurrences induced by classical periodic motions. In this paper we study how such characteristics reveal in the LiNC/LiCN isomerizing molecular system, and describe how the transition from regularity to classical chaos that takes place in this system shows up at quantum level in the structure of the corresponding wavefunctions in the form of “scars”. To this end we use some projection techniques, based on the propagation of wave packets, which have been developed in our laboratory. In this way some regions at the border of the chaotic region can be detected, in which the systematics of “scar” formation can be studied at a very elementary level, without complications due to the high level density which are customarily used in this type of studies in order to achieve the semiclassical limit. Received: 16 March 1998 / Revised: 23 April 1998 / Accepted: 4 May 1998     

Higher-order <Emphasis Type="Bold">?</Emphasis> corrections in the semiclassical quantization of chaotic billiards

In the periodic orbit quantization of physical systems, usually only the leading-order ? contribution to the density of states is considered. Therefore, by construction, the eigenvalues following from semiclassical trace formulae generally agree with the exact quantum ones only to lowest order of ?. In different theoretical work the trace formulae have been extended to higher orders of ?. The problem remains, however, how to actually calculate eigenvalues from the extended trace formulae since, even with ? corrections included, the periodic orbit sums still do not converge in the physical domain. For lowest-order semiclassical trace formulae the convergence problem can be elegantly, and universally, circumvented by application of the technique of harmonic inversion. In this paper we show how, for general scaling chaotic systems, also higher-order ? corrections to the Gutzwiller formula can be included in the harmonic inversion scheme, and demonstrate that corrected semiclassical eigenvalues can be calculated despite the convergence problem. The method is applied to the open three-disk scattering system, as a prototype of a chaotic system. Received 10 September 2001 and Received in final form 3 January 2002     

Use of harmonic inversion techniques in the periodic orbit quantization of integrable systems

Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the periodic orbit sum and the uncertainty principle of the usual Fourier analysis, thus yielding results of high resolution and high precision. Based on the close analogy between periodic orbit trace formulae for regular and chaotic systems the technique is generalized in this paper for the semiclassical quantization of integrable systems. Thus, harmonic inversion is shown to be a universal tool which can be applied to a wide range of physical systems. The method is further generalized in two directions: firstly, the periodic orbit quantization will be extended to include higher order corrections to the periodic orbit sum. Secondly, the use of cross-correlated periodic orbit sums allows us to significantly reduce the required number of orbits for semiclassical quantization, i.e., to improve the efficiency of the semiclassical method. As a representative of regular systems, we choose the circle billiard, whose periodic orbits and quantum eigenvalues can easily be obtained. Received 24 February 2000 and Received in final form 22 May 2000     

Entanglement dynamics and decoherence of two-qutrit states under an XY quantum environment

The time evolution of entanglement and coherence of two-qutrit states under an XY quantum environment which can exhibit a quantum phase transition has been analyzed. From our results, we find that the quantum phase transition can enhance the entanglement decay and coherence loss when the system is weakly coupled to the environment. Furthermore, the effect of the anisotropy parameter and the size of the environment on entanglement dynamics and coherence has also been discussed.     

Classical impact parameter approximation: Application to atomic collisions with n independent electrons and to recoil analysis

We show that a classical Impact Parameter Method may be derived when taking fully into account the smallness of the ratio between the electron and nuclear masses. It allows to calculate, exactly as in the quantum version, projectile scattering and therefore recoil momenta required for the interpretation of recent measurements. We prove an additivity theorem which allows, in particular, to reduce the n-non-interacting electron problem to a set of n one-electron problems. Consequences for the interpretation of target recoil measurements are discussed. Received 25 June 1999     

Environment-induced nonclassical behaviour

We analyze the transient nonclassical behaviour of a single-mode field whose interaction with an environment is governed by the quantum optical master equation. Our analytic method makes use of the generalized characteristic function of the field state. First, we find a time at which all squeezing effects disappear by decoherence regardless of the initial state of the mode. In the case of an input even coherent state, an unusual modification of higher-order squeezing at low values of thermal mean occupancy transferred to the field is found and discussed. For the same initial state, we also perform a comprehensive analysis of the mixing process during the interaction with the reservoir. We prove that a maximum in the evolution of the 2-entropy of the attenuated mode exists on condition that its initial mean photon number exceeds the mean occupancy of the reservoir. This transient mixing enhancement can be considered as a quantum effect of the initial state on the mode damping. Received 22 April 1999 and Received in final form 2 November 1999     

Dissipative chaotic quantum maps: Expectation values, correlation functions and the invariant state

I investigate the propagator of the Wigner function for a dissipative chaotic quantum map. I show that a small amount of dissipation reduces the propagator of sufficiently smooth Wigner functions to its classical counterpart, the Frobenius-Perron operator, if . Several consequences arise: the Wigner transform of the invariant density matrix is a smeared out version of the classical strange attractor; time dependent expectation values and correlation functions of observables can be evaluated via hybrid quantum-classical formulae in which the quantum character enters only via the initial Wigner function. If a classical phase-space distribution is chosen for the latter or if the map is iterated sufficiently many times the formulae become entirely classical, and powerful classical trace formulae apply. Received 7 October 1999     

Non-partial-wave Coulomb-Born theory for the excitation of many-electron atomic ions II: Numerical description and application

A non-partial-wave Coulomb-Born theory is recently formulated to treat the excitation of many-electron atomic ions for impact by an arbitrary charged particle [Y.B. Duan et al., Phys. Rev. A 56, 2431 (1997)]. The multiple expansion of the transition matrix element is decomposed into the target form factor and the projectile form factor. These are the matrix elements of the tensor operators between quantum states so that any complicated wave function for the target ion can be employed. In this formal theory, an infinitesimally small positive quantity is introduced artificially to guarantee the convergence of integrals. As a supplementary part of the theory, we discuss how to choose the value of . It is found that the should be taken as functions of the momentum transfer and multipolarity . Illustrations are carried out by calculating the cross-sections for some typical transitions n _a l _a -n _b l _b of hydrogen-like ions for impact by electron, positron, and proton, respectively. The resulting cross-sections are in good agreement with ones produced by using a method available for ion targets with Slater-type orbitals [N.C. Deb, N.C. Sil, Phys. Rev. A 28, 2806 (1993)]. Comparisons demonstrate that the Coulomb-Born theory with non-partial wave analysis provides a powerful method to treat the excitation of many-electron atomic ions impact by an arbitrary charged particle. Received 6 April 1999     

A nonadiabatic semi-classical method for dynamics of atoms in optical lattices

We develop a semi-classical method to simulate the motion of atoms in a dissipative optical lattice. Our method treats the internal states of the atom quantum mechanically, including all nonadiabatic couplings, while position and momentum are treated as classical variables. We test our method in the one-dimensional case. Excellent agreement with fully quantum mechanical simulations is found. Our results are much more accurate than those of earlier semi-classical methods based on the adiabatic approximation.     

Quantum relativistic theory of an electron in terms of local observables

Dirac equation is reformulated in terms of real local observables, which are mean values of the wave function . The quadrivector current is shown to be a function of the potential vector and of other local observables. The equations describe the evolution of a four dimensional system T, X, Y, Z, and of two scalars, in the coordinate system ct, x, y, z. The current is proportional to the T vector. The Z vector is associated with the spin of the electron. Energy and gauge transformations correspond to rotations in the plane (X, Y). In the presence of a static field, the (real) solutions of the equations appear as eigenfunctions associated with energy eigenvalues. Received 7 September 1998     

Entangling atoms in photonic crystals

We propose a method for entangling a system of two-level atoms in photonic crystals. The atoms are assumed to move in void regions of a photonic crystal. The interaction between the atoms is mediated either via a defect mode or via a resonant dipole-dipole interaction. We show that these interactions can produce pure entangled atomic states. We analyze the problem with parameters typical for currently existing photonic crystals and Rydberg atoms and we show that the atoms can emerge from photonic crystals in entangled states. Depending on the linear dimensions of the crystal we estimate that a pair of atoms entangled in a photonic crystal can be separated by tens of centimeters. Receive 11 June 1999 and Received in final form 4 October 1999     

What does an observed quantum system reveal to its observer?

The evolution of a quantum system under observation becomes retarded or even impeded. We review this “quantum Zeno effect” in the light of the criticism that has been raised upon a previous attempt to demonstrate it, of later reexaminations of both the projection postulate and the significance of the observations, and of the results of a recent experiment on an individual cold atom. Here, the micro-state of the quantum system gets unveiled with the observation, and the effect of measurement is no longer mixed up with dephasing the object's wave function by the reactive effect of the detection. A procedure is outlined that promises to provide, by observation, an upper limit for the delay of even an exponential decay. Received 11 January 2001 and Received in final form 28 February 2001     

Multipartite entanglement dynamics and decoherence from a quantum-critical environment

We investigate the entanglement dynamics and decoherence of a multipartite system under an environment which can exhibit a quantum phase transition. Our result implies that the entanglement evolution depends not only on the size of the system and the quantum states of concern but also on the environment. In the sense of the linear entropy to measure decoherence induced by the environment, the decoherence-free subspaces have been identified for our model.     

Time-dependent formulation of the linear unitary transformation and the time evolution of general time-dependent quadratic Hamiltonian systems

A time-dependent closed-form formulation of the linear unitary transformation for harmonic-oscillator annihilation and creation operators is presented in the Schrödinger picture using the Lie algebraic approach. The time evolution of the quantum mechanical system described by a general time-dependent quadratic Hamiltonian is investigated by combining this formulation with the time evolution equation of the system. The analytic expressions of the evolution operator and propagator are found. The motion of a charged particle with variable mass in the time-dependent electric field is considered as an illustrative example of the formalism. The exact time evolution wave function starting from a Gaussian wave packet and the operator expectation values with respect to the complicated evolution wave function are obtained readily.     

Dependence on crystal parameters of the correlation time between signal and idler beams in parametric down conversion calculated in the Wigner representation

The theory of parametric down conversion within the framework of the Wigner representation has been treated recently in a series of papers using the standard model Hamiltonian. Here we take a more fundamental point of view studying the mechanism, inside the crystal, for the production of the signal and idler beams. We begin from the evolution equations for the quantum field operators, pass to the Wigner function and solve the resulting (Maxwell) equations with the use of the Green's function method. We derive the time dependence of the coincidence detection probability as a function of the parameters of the nonlinear crystal (in particular the length) the radius of the pumping beam, and the bandwidth of the filters in front of the detectors. Received 24 January 2000 and Received in final form 24 March 2000     

Quasiclassical Hamiltonians for large-spin systems

We extend and apply a previously developed method for a semiclassical treatment of a system with large spin S. A multisite Heisenberg Hamiltonian is transformed into an effective classical Hamilton function which can be treated by standard methods for classical systems. Quantum effects enter in form of multispin interactions in the Hamilton function. The latter is written in the form of an expansion in powers of J/(TS), where J is the coupling constant. Main ingredients of our method are spin coherent states and cumulants. Rules and diagrams are derived for computing cumulants of groups of operators entering the Hamiltonian. The theory is illustrated by calculating the quantum corrections to the free energy of a Heisenberg chain which were previously computed by a Wigner-Kirkwood expansion. Received 5 May 1999 and received in final form 24 September 1999