Local definiteness,primarity and quasiequivalence of quasifree Hadamard quantum states in curved spacetime

We prove that the GNS-representations of quasifree, Hadamard states on the Weyl-algebra of the quantized Klein-Gordon field propagating in an arbitrary globally hyperbolic spacetime are locally quasiequivalent. We also show that these representations satisfy local primarity and local definiteness if the spacetime is assumed to be ultrastatic. This implies that the local von Neumann algebras associated with these representations are typeIII ₁-factors for sufficiently small regions in ultrastatic spacetimes.Supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik     

Space-times with a stable adiabatic vacuum

The adiabatic particle definition of Parker [1] has found widespread acceptance (see, e.g., [2]) in the semiclassical approach to quantum gravity. We give sufficient conditions on a space-time so that, using the adiabatic particle definition, exactly zero particles are created; for these space-times the adiabatic vacuum is stable. The difficulties in formulating necessary conditions are discussed.This essay received an honorable mention from the Gravity Research Foundation for the year 1983-Ed.     

On the adiabatic limit of Hadamard states

We consider the adiabatic limit of Hadamard states for free quantum Klein–Gordon fields, when the background metric and the field mass are slowly varied from their initial to final values. If the Klein–Gordon field stays massive, we prove that the adiabatic limit of the initial vacuum state is the (final) vacuum state, by extending to the symplectic framework the adiabatic theorem of Avron–Seiler–Yaffe. In cases when only the field mass is varied, using an abstract version of the mode decomposition method we can also consider the case when the initial or final mass vanishes, and the initial state is either a thermal state or a more general Hadamard state.     

Preparation of entangled states by adiabatic passage

We propose a novel technique for the creation of entangled pairs of two-state systems based upon adiabatic passage induced by a suitably crafted time-dependent external field.     

Chaotic polaronic and bipolaronic states in the adiabatic Holstein model

A rigorous proof for the existence of bipolaronic states is given for the adiabatic Holstein model for any lattice at any dimension, periodic or not, and for an arbitrary band filling, provided that the electron-phonon coupling (in dimensionless units) is large enough. The existence of mixed polaronic-bipolaronic states is also proven, but for larger electron-phonon coupling. These states consist of arbitrary distributions of bipolarons (or of bipolarons and polarons) localized in real space which can be simply labeled by pseudospin configurations as for a lattice gas model. The theory not only applies to periodic crystals, but also to quasicrystals, amorphous structures, polymer network, etc.When these bipolaronic and mixed polaronic-bipolaronic states exist, it is proven that: (1) These bipolaronic (and mixed polaronic-bipolaronic) states exhibit a nonzero phonon gap with a nonvanishing lower bound and an electronic gap at the Fermi energy. (2) These structures are insulating. The perturbation generated by any local change in the bipolaronic or polaronic distribution or by any charged impurity or defect decays exponentially at long distance. (3) These bipolaronic (and mixed polaronic-bipolaronic) states persist for any uniform magnetic field. (4) For large enough electron-phonon coupling, the ground state of the extended adiabatic Holstein model is a bipolaronic state when there is no uniform magnetic field or when it is small enough. It becomes a mixed polaronic-bipolaronic state for large enough magnetic field (note that the mixed polaronic-bipolaronic states are magnetic).In one-dimensional models, the ground state is an incommensurate (or commensurate) charge density wave (CDW) as predicted by Peierls (this result is not rigorous, but has been confirmed numerically). It is proven that the ground state becomes a bipolaronic charge density wave (BCDW) at large enough electron-phonon coupling. The existence of a transition by breaking of analyticity (TBA), which was numerically observed as a function of the electron-phonon coupling, is then confirmed. In that case, the shape of the effective bipolaron can be numerically calculated. It is observed that its size diverges at the TBA. The physical properties of BCDWs are rather different from those predicted by standard charge density wave theory. Bipolaronic charge density waves can also exist in models which are not only low-dimensional, but purely two- or three-dimensional.The technique for proving these theorems is an application of the concept of anti-integrability initially developed for Hamiltonian dynamical systems. It consists in proving that the eigenstates of the (trivial) Hamiltonian (called antiintegrable) obtained by canceling all electronic and lattice kinetic terms survive as a uniformly continuous function of the electronic kinetic energy terms in the Hamiltonian up to a certain threshold.     

A physical characterization of the adiabatic vacuum in Robertson-Walker universe

As the red shift shows no sign of oscillatory behavior in an expanding universe we postulate that the energy _k of a scalar field does not oscillate in such a universe. In the massive case, expanding the differential equation for _k in mass powers, we find that the nonoscillatory solution coincides with the adiabatic solution up to them ⁶ order. We also demonstrate that this solution is unique for all the evolution of the universe with cosmological interest. Using the nonoscillatory solution as the one that defines the good vacuum state, we compute the particle and energy creation for a simple model of expanding universe. Both quantities turn out to be finite.     

Realistic teleportation of coherent states using squeezed vacuum states

This paper presents a realistic scheme for the teleportation of coherent states in which a two-mode squeezed vacuum state serves as the quantum channel and the position-sum and momentum-difference of two local modes serve as the measuring observables. The average fidelity of the teleportation of coherent states is derived for finite squeezing parameters and it turns out that fidelity greater than 1/2 cannot be achieved by using a classical channel alone and the probability distribution of the measurement result is a Gaussian distribution around the unknown parameter of the input coherent state with a width given by the squeezing parameter.     

Local transformations and KMS states

A unified approach to the DLR and KMS conditions is presented emphasizing local properties.     

Geometric phase for adiabatic evolutions of general quantum states

The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.     

Experimental preparation of topologically ordered states via adiabatic evolution

Topological orders are a class of exotic states of matter characterized by patterns of long-range entanglement. Certain topologically ordered systems are proposed as potential realization of fault-tolerant quantum computation. Topological orders can arise in two-dimensional spin-lattice models. In this paper, we engineer a time-dependent Hamiltonian to prepare a topologically ordered state through adiabatic evolution. The other sectors in the degenerate ground-state space of the model are obtained by applying nontrivial operations corresponding to closed string operators. Each sector is highly entangled, as shown from the completely reconstructed density matrices. This paves the way towards exploring the properties of topological orders and the application of topological orders in topological quantum memory.     

Nonlinear evolution of quantum states in the adiabatic regime

We investigate adiabatic evolution of quantum states as governed by the nonlinear Schr?dinger equation and provide examples of applications with a nonlinear tunneling model for Bose-Einstein condensates. Our analysis not only spells out conditions for adiabatic evolution of eigenstates but also characterizes the motion of noneigenstates which cannot be obtained from the former in the absence of the superposition principle. We find that Aharonov-Anandan phases play the role of classical canonical actions and are conserved in the adiabatic evolution of noneigenstates.     

Continuum three-body states using the hyperspherical adiabatic basis set

In this paper we investigate the feasibility of employing the hyperspherical adiabatic (HA) basis set to describe continuum three-nucleon states. In particular, the HA expansion is compared with the simpler expansion on hyperspherical harmonics (HH). A practical numerical application is presented using the MT-III potential.     

Nonclassicality of photon-added squeezed vacuum states

By applying the bosonic creation operator to squeezed vacuum states, this paper introduces a new kind of quantum states: photon-added squeezed vacuum states. It also presents an experimental approach to prepare these states, and investigates their quantum statistical properties by the numerical method. The results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, squeezing effects and negativities of the relevant Wigner functions.     

Charged two-dimensional magnetoexciton and two-mode squeezed vacuum states

A novel unitary transformation of the Hamiltonian that allows one to partially separate the center-of-mass motion for charged electron-hole systems in a magnetic field is presented. The two-mode squeezed oscillator states that appear at the intermediate stage of the transformation are used for constructing a trial wave function of a two-dimensional charged magnetoexciton.     

多粒子W态的绝热制备

通过利用时间依赖的外磁场,提出了绝热制备多粒子W态的新方法.同时给出了驱动n个自旋1/2粒子从未纠缠态到W态的相互作用哈密顿量以及绝热和非绝热演化条件,展示了能量和靶态布据随时间的演化图.     

Generation of cluster-type entangled squeezed vacuum states

We present a scheme to prepare cluster-type entangled squeezed vacuum states （CTESVS） by considering the two-photon interaction between a two-level atom and a high-quality cavity, driven by a strong classical field. After the realization of simple atomic measurements, the generation of CTESVS in four separate cavities is accomplished within the cavity decay time. In the case of large atom=cavity detuning, the scheme is immune to the effect of atomic spontaneous emission.     

Metastable states,the adiabatic theorem and parity violating geometric phases I

A system of metastable plus unstable states is discussed. The mass matrix governing the time development of the system is supposed to vary slowly with time. The adiabatic limit for this case is studied and it is shown that only the metastable states obtain the analogs of the dynamical and geometrical phase factors familiar from stable states. Abelian and non-Abelian geometric phase factors for metastable states are defined.