Reconstruction of the polarization states of a biphoton field

A method for reconstructing an arbitrary quantum state of an optical system in Hilbert space with dimension d = 4 is discussed. Such states can be realized using a collinear frequency-nondegenerate regime of generating spontaneous parametric down-conversion. The method has been tested for a number of polarization states of a biphoton field. The high accuracy of the reconstruction of the states (above 99%) indicates that the procedures proposed for reconstructing the quantum state of the system are adequate.     

Stability of Equilibria with a Condensate

A quantum system composed of a spatially infinitely extended free Bose gas with a condensate, interacting with a quantum dot, which can trap finitely many Bosons, has multiple equilibria at fixed temperature. We extend the notion of return to equilibrium to systems possessing a multitude of equilibrium states and show that the above system returns to equilibrium in a weak coupling sense: any local perturbation of an equilibrium state converges in the long time limit to an asymptotic state. The latter is, modulo an error term, an equilibrium state which depends, in an explicit way, on the initial local perturbation. The error term vanishes in the small coupling limit.We deduce this stability result from properties of structure and regularity of eigenvectors of the Liouville operator, the generator of the dynamics. Among our technical results is a virial theorem for Liouville type operators which has new applications to systems with and without a condensate.Supported by a CRM-ISM postdoctoral fellowship and by McGill University     

一种新的单光源多波长双向量子密钥分发系统

针对"即插即用"双向量子密钥分发系统传输效率低的实际问题, 详细分析了系统低效的原因和当前的解决方案, 提出了一种单光源多波长双向量子密钥分发方案. 该方案采用波分复用器件作为滤波器来产生量子密钥分发所需的多波长信号. 与其他多波长方案相比, 该方案的优点是在实现高速多波长量子密钥分发时, 不再受外界控制源调制速率和精度等性能的影响, 不再带来多激光器引入的边信道攻击的缺陷, 且整体系统易于集成. 该方案为"即插即用"量子密钥分发系统的高效研究提供了一个新的参考方案.     

Full counting statistics of a general quantum mechanical variable

We present a quantum mechanical framework for defining the statistics of measurements of , A(t) being a quantum mechanical variable. This is a generalization of the so-called full counting statistics proposed earlier for DC electric currents. We develop an influence functional formalism that allows us to study the quantum system along with the measuring device while fully accounting for the back action of the detector on the system to be measured. We define the full counting statistics of an arbitrary variable by means of an evolution operator that relates the initial and final density matrices of the measuring device. In this way we are able to resolve inconsistencies that occur in earlier definitions. We suggest two schemes to observe the so defined statistics experimentally.Received: 30 June 2003, Published online: 15 October 2003PACS: 73.50.Td Noise processes and phenomena - 73.23.-b Electronic transport in mesoscopic systems - 74.40.+k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.)     

Quantum coherence dynamics of a three-level atom in a two-mode field

The correlated dynamics of a three-level atom resonantly coupled to an electromagnetic cavity field is calculated (Λ, V, and L models). A diagrammatic representation of quantum dynamics is proposed for these models. As an example, Λ-atom dynamics is examined to demonstrate how the use of conventional von Neumann’s reduction leads to internal decoherence (disentanglement-induced decoherence) and to the absence of atomic coherence under multiphoton excitation. The predicted absence of atomic coherence is inconsistent with characteristics of an experimentally observed atom-photon entangled state. It is shown that the correlated reduction of a composite quantum system proposed in [18] qualitatively predicts the occurrence and evolution of atomic coherence under multiphoton excitation if a seed coherence is introduced into any subsystem (the atom or a cavity mode).     

Quantum tomography as a new approach to simulating quantum processes

A new method is proposed for ab initio calculations of nonstationary quantum processes on the basis of a probability representation of quantum mechanics with the help of a positive definite function (quantum tomogram). The essence of the method is that an ensemble of trajectories associated with the characteristics of the evolution equation for the quantum tomogram is considered in the space where the quantum tomogram is defined. The method is applied for detailed analysis of transient tunneling of a wave packet. The results are in good agreement with the exact numerical solution to the Schrödinger equation for this system. The probability density distributions are obtained in the coordinate and momentum spaces at consecutive instances. For transient tunneling of a wave packet, the probability of penetration behind the barrier and the time of tunneling are calculated as functions of the initial energy.     

Remote State Preparation of a Two-Atom Entangled State in Cavity QED

A physical scheme for remotely preparing a diatomic entangled state based on the cavity QED technique is presented in this paper. The quantum channel is composed of a two-atom entangled state and a three-atom entangled W state. The non-resonant interaction between two atoms and cavity is utilized at sender’s side to distribute the information among the quantum channel, and the original state can be transmitted to either one of the two receivers. It shows that an extra cavity and an atom are needed at the final receiver’s side as an auxiliary system if the non-maximally entangled states are worked as the quantum channel. The total success probabilities for the two receivers are not equal to each other except that the states of the quantum channel are maximally entangled.     

Breakdown of a topological phase: quantum phase transition in a loop gas model with tension

We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model--the toric code--which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of "magnetic" vortices, leading to confinement of the elementary "charge" excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and relate our results to error rates for topological quantum computations.     

Formation of a gapless quantum spin liquid upon orbital ordering in a chain

The exchange mechanism of the ordering of electrons on e _g orbitals has been estimated by the quantum Monte Carlo method with the nclusion of the hopping integrals through an anion in a one-dimensional system. A magnetic state in the form of a gapless quantum spin liquid has been found. The plateau existence region in the field-dependence of the magnetization, as well as the wave vector of the modulation of the magnetic structure with Q = π/2 in the (magnetic field-exchange alternating) plane, is determined.     

A Quantum System of Pseudospins and a Structural Transformation in a Strained Crystal

It is shown that an unstable crystal structure in a stress field can be treated as a quantum system of pseudospins. A stimulating strain field gives rise to quantum tunneling of atoms. The latter effect is a physical cause for a coherent behavior of the crystal in a stress-concentrator zone wherein the material undergoes the nonequilibrium structural transformation a highly-excited state under load.     

Ground-state properties of a one-dimensional system of dipoles

A one-dimensional (1D) Bose system with dipole-dipole repulsion is studied at zero temperature by means of a quantum Monte Carlo method. It is shown that, in the limit of small linear density, the bosonic system of dipole moments acquires many properties of a system of noninteracting fermions. At larger linear densities, a variational Monte Carlo calculation suggests a crossover from a liquidlike to a solidlike state. The system is superfluid on the liquidlike side of the crossover and is normal deep on the solidlike side. Energy and structural functions are presented for a wide range of densities. Possible realizations of the model are 1D Bose atomic systems, with permanent dipoles or dipoles induced by static field or resonance radiation; or indirect excitons in coupled quantum wires; etc. We propose parameters of a possible experiment and discuss manifestations of the zero-temperature quantum crossover.     

Wegner Bounds for a Two-Particle Tight Binding Model

We consider a quantum two-particle system on a lattice with interaction and in presence of an IID external potential. We establish Wegner-type estimates for such a model. The main tool used is Stollmann’s lemma.     

Localization in a quantum spin Hall system

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.     

Quantum Contextuality for a Three-Level System Sans Realist Model

Recently, an interesting form of non-classical effect which can be considered as a form of contextuality within quantum mechanics, has been demonstrated for a four-level system by discriminating the different routes that are taken for measuring a single observable. In this paper, we provide a simpler version of that proof for a single qutrit, which is also within the formalism of quantum mechanics and without recourse to any realist hidden variable model. The degeneracy of the eigenvalues and the Lüder projection rule play important role in our proof.     

Effective Dynamics of a Tracer Particle Interacting with an Ideal Bose Gas

We study a system consisting of a heavy quantum particle, called the tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All particles have non-relativistic kinematics. The tracer particle is driven by an external potential and couples to the gas particles through a pair potential. We compare the quantum dynamics of this system to an effective dynamics given by a Newtonian equation of motion for the tracer particle coupled to a classical wave equation for the Bose gas. We quantify the closeness of these two dynamics as the mean-field limit is approached (gas density ${\to \infty}$ ). Our estimates allow us to interchange the thermodynamic with the mean-field limit.     

Eigenfunctions in a Two-Particle Anderson Tight Binding Model

We establish the phenomenon of Anderson localisation for a quantum two-particle system on a lattice with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.     

Quantum Entanglement and Correlation Lengths of a S-wave Superconductors in the Presence of a Weak Constant External Potential

By considering a s-wave Bardeen-Cooper-Schrieffer superconductor, as a many body system, subject to a weak constant external potential, U, using perturbed linearized Gorkov equations at zero temperature and calculating perturbed Green’s functions up to the first approximation, we obtain the two-particle space-spin density matrix of the system. Then, we investigate the effect of the potential on bipartite entanglement (via concurrence) of electron spins of a Cooper pair and also quantum discord in terms of the potential and the relative distance of electrons of a Cooper pair, r. At some fixed values of r, concurrence is zero and does not change until U increases and receives to a special value. Specially, quantum entanglement length and quantum correlation length (in which quantum discord becomes zero) with respect to the potential are derived. We result that by increasing the potential, these lengths are increased. At higher values of U, quantum correlation length is not very sensitive to changes in U. Finally, the relation between these lengths is given.     

1/<Emphasis Type="Italic">Q</Emphasis> expansion for the energy spectrum of quantum dots

A new method is proposed for calculating the energy spectrum and the wave functions of N-electron quantum dots with an arbitrary confining potential. The method consists in expansion with respect to a dimensionless quantum parameter 1/Q, which is expressed in terms of the ratio of the characteristic Coulomb energy of electron-electron interaction to the characteristic energy of one-particle transition in a confining potential. Two-electron quantum dots with a parabolic confining potential in an external magnetic field are considered. Strongly correlated states of the system and the spin rearrangement in a strong magnetic field are analyzed. Analytic expressions are obtained for the energy and the wave functions of the system. It is shown that restriction of the analysis only to the first three terms in the quantum-parameter expansion gives an accuracy of one percent when calculating the energy even for values of Q on the order of unity, i.e., for the presently implementable GaAs quantum dots. The expressions for energy obtained are in a good agreement with the experimental data for quantum dots in a perpendicular magnetic field.     

Entangled spin states of a Bose condensate in an electromagnetic field

We consider the formation of entangled quantum states for an atomic Bose condensate interacting with an external electromagnetic field in a single-particle state under conditions of change in various regimes for exchange interaction processes. These states of the Bose system have high phase coherence and are accompanied by the generation of squeezed states of a new type in terms of the parameters defined by a combination of transition operators for the condensate atoms and external-field photons with an appropriate polynomial deformation of the algebra SU(2). We show that localized quantum structures corresponding to stable elementary excitations of the atoms and the field in the condensate can be formed in principle. We also analyze the purely quantum effects of collapse and revival for the level populations of the Bose condensate and the change in atomic statistics as well as determine the conditions for the formation of superstructure of these unsteady states for the Bose system.     

Thermal quantum correlations of a spin-1/2 Ising-Heisenberg diamond chain with Dzyaloshinskii-Moriya interaction

We investigate the properties of thermal quantum correlations in an infinite spin-1/2 Ising-Heisenberg diamond chain with Dzyaloshinskii-Moriya(DM) interaction. The thermal quantum discord(TQD) and the thermal entanglement(TE)are discussed as two kinds of important methods to measure the quantum correlation, respectively. It is found that DM interaction plays an important role in the thermal quantum correlations of the system. It can enhance the thermal quantum correlations by increasing DM interaction. Furthermore, the thermal quantum correlations can be promoted by tuning the external magnetic field and the Heisenberg coupling parameter in the antiferromagnetic system. It is shown that the behaviors of TQD differ from those of TE. TQD is more robust against decoherence than TE. For the measurement of TQD, the "regrowth" phenomenon occurs in the ferromagnetic system. We also find that the anisotropy favors the thermal quantum correlations of the system with weak DM interaction.