Thermal entanglement of two interacting qubits in a static magnetic field

We study systematically the entanglement of a two-qubit Heisenberg XY model in thermal equilibrium in the presence of an external arbitrarily-directed static magnetic field, thereby generalizing our prior work [G. Lagmago Kamta, A.F. Starace, Phys. Rev. Lett. 88, 107901 (2002)]. We show that a magnetic field having a component in the xy-plane containing the spin-spin interaction components produces different entanglement for ferromagnetic (FM) and antiferromagnetic (AFM) couplings. In particular, quantum phase transitions induced by the magnetic field-driven level crossings always occur for the AFM-coupled qubits, but only occur in FM-coupled qubits when the coupling is of Ising type or when the magnetic field has a component perpendicular to the xy-plane. When the magnetic field has a component in the xy-plane, the cut-off temperature above which the entanglement of both the FM- and AFM-coupled qubits vanishes can always be controlled using the magnetic field for any value of the XY coupling anisotropy parameter. Thus, by adjusting the magnetic field, an entangled state of two spins can be produced at any finite temperature. Finally, we find that a higher level of entanglement is achieved when the in-plane component of the magnetic field is parallel to the direction in which the XY exchange coupling is smaller.     

Quantum rotors with regular frustration and the quantum Lifshitz point

We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d _u = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation. Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998     

Beam splitter for spin waves in quantum spin network

We theoretically design and analytically study a controllable beam splitter for the spin wave propagating in a star-shaped (e.g., a Y-shaped beam) spin network. Such a solid state beam splitter can display quantum interference and quantum entanglement by the well-aimed controls of interaction on nodes. It will enable an elementary interferometric device for scalable quantum information processing based on the solid system.     

Spectral density method in quantum nonextensive thermostatistics and magnetic systems with long-range interactions

Motived by the necessity of explicit and reliable calculations, as a valid contribution to clarify the effectiveness and, possibly, the limits of the Tsallis thermostatistics, we formulate the Two-Time Green Functions Method in nonextensive quantum statistical mechanics within the optimal Lagrange multiplier framework, focusing on the basic ingredients of the related Spectral Density Method (SDM). Besides, to show how the SDM works, we have performed, to the lowest order of approximation, explicit calculations of the low-temperature properties for a quantum d-dimensional spin-1/2 Heisenberg ferromagnet with long-range interactions decaying as 1/r^p ( r is the distance between spins in the lattice).     

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     

On evaluation of transverse spin fluctuations in quantum magnets

A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations are locally enhanced at the low-U sites. Received 27 April 1998 and Received in final form 13 August 1998     

Vortices in quantum spin systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices. Received 2 October 1998     

Quantum phase transition of entanglement in Heisenberg spin model with quantized field

In this paper, we investigate the entanglement of a two-spin system with Heisenberg exchange interaction in a quantized field. The pairwise entanglement between bipartite subsystems is obtained. It is shown that the entanglement exhibits a quantum phase transition due to the variation of exchang coupling. Phase diagrams are obtained explicitly. The analogy of the quantum phase transition compared to the case under a classical field are addressed.     

Generalized quantum telecloning

We present a generalized telecloning (GTC) protocol where the quantum channel is non-optimally entangled and we study how the fidelity of the telecloned states depends on the entanglement of the channel. We show that one can increase the fidelity of the telecloned states, achieving the optimal value in some situations, by properly choosing the measurement basis at Alice's, albeit turning the protocol to a probabilistic one. We also show how one can convert the GTC protocol to the teleportation protocol via proper unitary operations.     

The dynamics of a central spin in quantum Heisenberg XY model

In the thermodynamic limit, we present an exact calculation of the time dynamics of a central spin coupling with its environment at finite temperatures. The interactions belong to the Heisenberg XY type. The case of an environment with finite number of spins is also discussed. To get the reduced density matrix, we use a novel operator technique which is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. The expectation value of the central spin and the von Neumann entropy are obtained.     

Exact ground states for two new spin-1 quantum chains, new features of matrix product states

We use the matrix product formalism to find exact ground states of two new spin-1 quantum chains with nearest neighbor interactions. One of the models, model I, describes a one-parameter family of quantum chains for which the ground state can be found exactly. In certain limit of the parameter, the Hamiltonian turns into the interesting case . The other model which we label as model II, corresponds to a family of solvable three-state vertex models on square lattices. The ground state of this model is highly degenerate and the matrix product states is a generating state of such degenerate states. The simple structure of the matrix product state allows us to determine the properties of degenerate states which are otherwise difficult to determine. For both models we find exact expressions for correlation functions.     

Far-infrared probe of size dispersion and population fluctuations in doped self-assembled quantum dots

We investigate the FIR magneto-optical transitions in doped self-assembled InAs quantum dots with an average filling ranging from 0.6 to 6 electrons per dot. Significant changes in the magnetic field dispersion, the line-width and the amplitude of the transitions are observed as the doping level is varied, in agreement with our theoretical calculations. We show that our technique is an effective tool to obtain informations regarding the dot size homogeneity and the electron filling uniformity.Received: 22 July 2003, Published online: 2 October 2003PACS: 73.21.La Quantum dots - 78.20.Ls Magnetooptical effects - 78.30.Fs III-V and II-VI semiconductors - 78.67.Hc Quantum dotsE. Deleporte: Present address: Laboratoire de Photonique Quantique et Moleculaire, École Normale Superieure de Cachan, 94235 Cachan Cedex, FranceJ.M. Gérard: Present address: CEA-Grenoble DRFMC/SP2M/PSC, Laboratoire de Physique des semiconducteurs, 38054 Grenoble, France     

Quantum teleportation via a two-qubit Heisenberg <Emphasis Type="Italic">XXZ</Emphasis> chain – effects of anisotropy and magnetic field

We study quantum teleportation via a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.     

Low temperature thermodynamics of inverse square spin models in one dimension

We present a field-theoretic renormalization group calculation in two loop order for classical O(N)-models with an inverse square interaction in the vicinity of their lower critical dimensionality one. The magnetic susceptibility at low temperatures is shown to diverge like with a=(N-2)/(N-1) and . From a comparison with the exactly solvable Haldane-Shastry model we find that the same temperature dependence applies also to ferromagnetic quantum spin chains. Received: 20 February 1998 / Revised: 27 April 1998 / Accepted: 30 April 1998     

Phase diagram of frustrated mixed-spin ladders in the strong-coupling limit

We study the ground-state properties of frustrated Heisenberg ferrimagnetic ladders with antiferromagnetic exchange interactions and two types of alternating sublattice spins. In the limit of strong rung couplings, we show that the mixed spin-1/2 and spin-1 ladders can be systematically mapped onto a spin-1/2 Heisenberg model with additional next-nearest-neighbor exchanges. The system is either in a ferrimagnetic state or in a critical spin-liquid state depending on the competition between the spin exchanges along the legs and the diagonal exchanges.     

Eliminating interactions between non-neighboring qubits in the preparation of cluster states in quantum molecules

We propose a scheme to eliminate the effect of non-nearest-neighbor qubits in preparing cluster state with double-dot molecules. As the interaction Hamiltonians between qubits are Ising-model and mutually commute, we can get positive and negative effective interactions between qubits to cancel the effect of non-nearest-neighbor qubits by properly changing the electron charge states of each quantum dot molecule. The total time for the present multi-step cluster state preparation scheme is only doubled for one-dimensional qubit chain and tripled for two-dimensional qubit array comparing with the time of previous protocol leaving out the non-nearest-neighbor interactions.     

Effects of phase decoherence on the entanglement of a two-qubit anisotropic Heisenberg XYZ chain with an in-plane magnetic field

We investigate the phase decoherence effects on the entanglement of a two-qubit anisotropic Heisenberg model with a nonuniform magnetic field in the x–z-plane. As a measure of the entanglement, the concurrence of the system is calculated. It is shown that when the magnetic field is along the z-axis, the nonuniform and uniform components of the field have no influence on the entanglement for the cases of and , respectively. But when the magnetic field is not along the z-axis, both the uniform and the nonuniform components of the field will introduce the decoherence effects. It is found that the effects of the Heisenberg chain's anisotropy in the Z-direction on the entanglement are dependent on the direction of the field. Moreover, the larger the initial concurrence is, the higher value it will exhibit during the time evolution of the system for a proper set of the parameters ν, Δ, θ, γ , B and b.     

The thermal Green functions in nonextensive quantum statistical mechanics

The thermal Green functions of the quantum-mechanical harmonic oscillator are constructed within the framework of nonextensive statistical mechanics with normalized q -expectation values. For the Tsallis index q greater than unity, these functions are found to be expressed analytically in terms of the Hurwitz zeta function. It is found that influence of the nonextensivity on the time-ordered thermal propagator is relevant only at the “on-shell” states. In particular, the finite-temperature contribution to the thermal propagator becomes enhanced for the strong nonextensivity. Received 30 September 1998     

Entanglement dynamics of a three-qubit system interacting with a quantum spin environment

We investigate the entanglement dynamics and decoherence of a three-qubit system under a quantum spin environment at a finite temperature in the thermodynamics limit. For the case under study, we find the evolution of pairwise entanglement depends not only on the initial states but also on the parameters related to the system and the spin environment. In addition, an undesirable entanglement sudden death occurs in the process of entanglement evolution, and this effect can be controlled by the coupling constant between two qubits, external magnetic field, and the interaction between the system and the environment.     

Spin singlet mott states and evidence for spin singlet quantum condensates of spin-one bosons in lattices

We have investigated spin singlet Mott states of spin-one bosons with antiferromagnetic interactions. These spin singlet states do not break rotational symmetry and exhibit remarkably different macroscopic properties compared with nematic Mott states of spin-one bosons. We demonstrate that the dynamics of spin singlet Mott states is fully characterized by even- or odd-class quantum dimer models. The difference between spin singlet Mott states for even and odd numbers of atoms per site can be attributed to a selection rule in the low energy sectors of on-site Hilbert spaces; alternatively, it can also be attributed to an effect of Berry’s phases on bosonic Mott states. We also discuss evidence for spin singlet quantum condensate of spin-one atoms. Our main finding is that in a projected spin singlet Hilbert space, the low energy physics of spin-one bosons is equivalent to that of a Bose-Hubbard model for spinless bosons interacting via Ising gauge fields. The other major finding is spin-charge separation in some one-dimensional Mott states. We propose charge-e spin singlet superfluid for an odd number of atoms per lattice site and charge-2e spin singlet superfluid for an even number of atoms per lattice site in one-dimensional lattices. All discussions in this article are limited to integer numbers of bosons per site.