We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures merit. While latter is maximized by a Gaussian cloner, former not: for symmetric 1-to-2 cloner 0.6826, compared to $2/3$ in setting. This can be realized an optical parametric amplifier certain non-Gaussian bimodal states. Finally, we show that $1\mathrm{\text{-to-}}\ensuremath{\infty}$ $1/2$. It achieved scheme cannot surpassed even supplemental bound entangled

We study the Bose-Einstein condensate (BEC) with a fixed number of particles. On basis conventional statistical mechanics we introduce the, so called, Maxwell's demon ensemble, where only particle transfer (without energy exchange) is allowed. show that this new ensemble can be used for microcanonical description system. apply our formalism to case BEC in harmonic trap and give analytic expressions ground state fluctuations. compare these exact numerical results obtained relatively small condensates.

We present two novel matter-wave Sagnac interferometers based on ring- shaped time-averaged adiabatic potentials (TAAP). For both the atoms are put into a superposition of different spin states and manipulated independently using elliptically polarized rf-fields. In first interferometer accelerated by spin-state-dependent forces then travel around ring in guide. second one fully trapped during entire interferometric sequence moved "buckets". Corrections to ideal phase investigated for cases....

We present the experimental observation of a magnetically tuned resonance phenomenon in spin mixing dynamics ultracold atomic gases. In particular, we study magnetic field dependence conversion F=2 (87)Rb spinor condensates crossover from interaction dominated to quadratic Zeeman dynamics. discuss observations framework as well matter wave four mixing. Furthermore, show that validity range single mode approximation for is significantly extended at high field.

We present measurements and a theoretical model for the interplay of spin-dependent interactions external magnetic fields in atomic spinor condensates. highlight general features such as quadratic Zeeman dephasing its influence on coherent spin mixing processes by focusing specific superposition state $F=1$ $^{87}\mathrm{Rb}$ Bose-Einstein condensate. In particular, we observe transition from oscillations to thermal equilibration.

Abstract Via the hierarchy of correlations, we study doublon-holon pair creation in 
the Mott state Fermi-Hubbard model (in higher dimensions)
induced by a time-dependent electric field.
Special emphasis is placed on analogy to electron-positron from vacuum quantum electrodynamics (QED).
We find that accuracy and applicability
of this depends spin structure background.
For Ising type anti-ferromagnetic order, derive an effective Dirac equation....

We study the quench from Mott-insulator to superfluid phase in Bose-Hubbard model and investigate spatial-temporal growth of coherence, that is, locking between initially uncorrelated sites. To this end, we establish a hierarchy correlations via controlled expansion into inverse powers coordination number $1/Z$. It turns out off-diagonal long-range order spreads with constant propagation speed, forming local condensate patches, whereas correlator follows diffusionlike rate.

We study the Bose-Hubbard and Fermi-Hubbard models in (formal) limit of large coordination numbers $Z\ensuremath{\gg}1$. Via an expansion into powers $1/Z$, we establish a hierarchy correlations which facilitates approximate analytical derivation time evolution reduced density matrices for one two sites, etc. With this method, quantum dynamics (starting ground state) after quench, i.e., suddenly switching tunneling rate $J$ from zero to finite value, is still Mott regime. find that approach...

The dynamics of the collective excitations a lattice Bose gas at zero temperature is systematically investigated using time-dependent Gutzwiller mean-field approach. excitation modes are determined within framework linear-response theory as solutions generalized Bogoliubov--de Gennes equations valid in superfluid and Mott-insulator phases arbitrary values parameters. expression for sound velocity derived this approach coincides with hydrodynamic relation. We calculate transition amplitudes...

We investigate the class of quantum cloning machines that equally duplicate all real states in a Hilbert space arbitrary dimension. By using no-signaling condition, namely, cannot make superluminal communication possible, we derive an upper bound on fidelity this machines. Then, for each dimension d, construct optimal symmetric cloner whose saturates bound. Similar calculations can also be performed order to recover universal d dimensions.

We consider the role of weak interatomic interactions on fluctuations number condensed atoms within canonical and microcanonical ensembles. Unlike corresponding case ideal gas this is not a clean, well-defined problem mathematical physics. Two related reasons are following: there no unique way defining condensate fraction interacting system exact energy levels known.

We study the Mott phase of Bose-Hubbard model on a tilted lattice. On (Gutzwiller) mean-field level, tilt has no effect -- but quantum fluctuations entail particle-hole pair creation via tunneling. For small potential gradients (long-wavelength limit), we derive quantitative analogy to Sauter-Schwinger effect, i.e., electron-positron out vacuum by an electric field. large tilts, obtain resonant tunneling related Bloch oscillations.

We study a quantum quench in the Bose-Hubbard model where tunneling rate J is suddenly switched from zero to finite value Mott regime. In order solve many-body dynamics far equilibrium, we consider reduced density matrices for number of lattice sites and split them up into on-site operators, i.e., mean field, plus two-point three-point correlations etc. Neglecting higher correlations, are able numerically simulate time-evolution (e.g., their effective light-cone structure) comparably large sites.

It is shown that any quantum operation perfectly clones the entanglement of all maximally-entangled qubit pairs cannot preserve separability. This ``entanglement no-cloning'' principle naturally suggests some approximate cloning nevertheless allowed by mechanics. We investigate a separability-preserving optimal machine duplicates states two qubits, resulting in 0.285 bits per clone, while local only yields 0.060 clone.

We have studied the phase diagram of a quasi-two-dimensional interacting Bose gas at zero temperature in presence random potential created by laser speckles. The superfluid fraction and particles with momentum are obtained within mean-field Gross-Pitaevskii theory diffusion Monte Carlo simulations. find transition from to insulating state when strength disorder grows. Estimations critical parameters compared predictions percolation Thomas-Fermi approximation. Analytical expressions for...

In many condensed-matter systems, it is very useful to introduce a quasi-particle approach, which based on some sort of linearization around suitable background state. order be systematic and controlled approximation, this should justified by an expansion into the powers small control parameter. Here, we present method for general lattice Hamiltonians with large coordination numbers Z 1, 1/Z. demonstrate generality our method, apply various spin as well Bose Fermi–Hubbard model.

We show that the spatial entanglement of two twin images obtained by parametric down conversion is complete, i.e., concerns both amplitude and phase. By considering a homodyne detection scheme, which allows comparison field quadrature components pixel pixel, Einstein-Podolsky-Rosen correlations are shown to exist between symmetrical pixels images. The best possible correlation adjusting phase profile local oscillator in amplification area. results for hold even absence any input image, pure...

We have found a quantum cloning machine that optimally duplicates the entanglement of pair $d$-dimensional systems prepared in an arbitrary isotropic state. It maximizes formation contained two copies any maximally entangled input state, while preserving separability unentangled states. Moreover, it cannot increase For large $d$, each clone tends to one-half which corresponds classical behavior. Finally, we investigate local cloner, yields clones with one-fourth large-$d$ limit.

We propose different spectroscopic methods to explore the nature of thermal excitations a trapped Bose condensed gas: 1) four photon process probe uniform region in trap center: 2) stimulated Raman order analyze influence momentum transfer resulting scattered atom distribution. apply these address specifically energy spectrum and scattering amplitude transition between two hyperfine levels gas atoms. In particular, we exemplify potential offered by proposed techniques contrasting expected,...

The expansion of the partition function for large coordination number $Z$ is a long-standing method and has formerly been used to describe Ising model at finite temperatures. We extend this approach study interacting Bose gas An analytical expression free energy derived which valid weakly strongly bosons. transition line separates superfluid phase from Mott insulating or normal shown fillings $\ensuremath{\langle}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}\ensuremath{\rangle}=1$...

We derive exact thermodynamic identities relating the average number of condensed atoms and root-mean-square fluctuations determined in different statistical ensembles for weakly interacting Bose gas confined a box. This is achieved by introducing concept auxiliary partition functions model Hamiltonians that do conserve total particles. Exploiting such identities, we provide first, completely analytical prediction microcanonical particle gas. Such fluctuations, as function volume V box are...

Based on the dielectric formalism in generalized random phase approximation, we generalize description of a Bose-Einstein condensed gas to allow for relative velocity between superfluid and normal fluid. In this model, determine critical dynamically as transition point stable unstable dynamics. Unlike zero temperature case, at finite dilute is lower than sound velocity. The requirement Galilean invariance essential obtain an invariant result necessitates use gapless conserving approximation.

We study the ground state of a uniform Bose gas at zero temperature in Hartree–Fock–Bogoliubov (HFB) approximation. find solution HFB equations which obeys Hugenholtz–Pines theorem. This imposes macroscopic squeezing to condensed and as consequence displays large particle number fluctuations. Particle conservation is restored by building appropriate U(1) invariant via superposition squeezed states. The distribution this new calculated well its fluctuations present normal behavior.

We investigate the entanglement dynamics between two distant qubits by analyzing correlations in quantum Ising model. Starting from spin system a paramagnetic regime enforced external magnetic field $B$, we then switch on ferromagnetic spin-spin coupling $J$. Using large coordination number expansion, consider limiting switching regimes: (1) adiabatic, which monitors evolution of ground state through transition to an ordered state; and (2) instantaneous (quench) instead propagation...