Delocalization to self-trapping transition of a Bose fluid confined in a double well potential. An analysis via one- and two-body correlation properties

We revisit the coherent or delocalized to self-trapping transition in an interacting bosonic quantum fluid confined in a double well potential, in the context of full quantum calculations. We show that an $N$-particle Bose-Hubbard fluid reaches an stationary state through the two-body interactions. These stationary states are either delocalized or self-trapped in one of the wells, the former appearing as coherent oscillations in the mean-field approximation. By studying one- and two-body properties in the energy eigenstates and in a set of coherent states, we show that the delocalized to self-trapped transition occurs as a function of the energy of the fluid, provided the interparticle interaction is above a critical or threshold value. We argue that this is a type of symmetry-breaking continuous phase transition.Comment: 16 pages, 9 figure

Universal correlations along the BEC-BCS crossover

We show that the long-distance behavior of the two-body density correlation functions and the Cooper-pair probability density of a balanced mixture of a two-component Fermi gas at $T = 0$, is universal along the BEC-BCS crossover. Our result is demonstrated by numerically solving the mean-field BCS model for different finite short-range atomic interaction potentials. We find an analytic expression for the correlation length in terms of the chemical potential and the energy gap at zero momentum.Comment: 6 pages, 3 figure

On the order of BEC transition in weakly interacting gases predicted by mean-field theory

Predictions from Hartree-Fock (HF), Popov (P), Yukalov-Yukalova (YY) and $t$-matrix approximations regarding the thermodynamics from the normal to the BEC phase in weakly interacting Bose gases are considered. By analyzing the dependence of the chemical potential $\mu$ on temperature $T$ and particle density $\rho$ we show that none of them predicts a second-order phase transition as required by symmetry-breaking general considerations. In this work we find that the isothermal compressibility $\kappa_{T}$ predicted by these theories does not diverge at criticality as expected in a true second-order phase transition. Moreover the isotherms $\mu=\mu(\rho,T)$ typically exhibit a non-singled valued behavior in the vicinity of the BEC transition, a feature forbidden by general thermodynamic principles. This behavior can be avoided if a first order phase transition is appealed. The facts described above show that although these mean field approximations give correct results near zero temperature they are endowed with thermodynamic anomalies in the vicinity of the BEC transition. We address the implications of these results in the interpretation of current experiments with ultracold trapped alkali gases.Comment: 16 pages, 5 figure

Observation of Bose-Einstein condensation in an atomic trap in terms of macroscopic thermodynamic parameters

To overcome the difficulties in defining pressure for a gas confined in an inhomogeneous trap, we define single macroscopic parameters that behave like pressure and volume. We measure the phase diagram of a 87Rb Bose gas in a harmonic trap in terms of those macroscopic parameters obtained from the spatial distribution of atoms. Considering the relevant variables such as the trap potential V=(ωxωyωz)−1, number of atoms N, and temperature T, a parameter Π=Π(N,V,T) is introduced to characterize the overall macroscopic pressure of the system. We construct the phase diagram (Π vs T) identifying the main features related to the Bose-Einstein condensation (BEC) transition in a trapped gas. A thermodynamic description of the phase transition based on purely macroscopic parameters provides us with a description that does not need the local-density approximation. This procedure can be used to explore different aspects related to BEC such as the nature of the phase transition in a trapped gas.FAPESPCNPqCAPESUniversidad Nacional Autónoma de México (IN-116110

Suppression of decoherence via strong intra-environmental coupling

We examine the effects of intra-environmental coupling on decoherence by constructing a low temperature spin--spin-bath model of an atomic impurity in a Debye crystal. The impurity interacts with phonons of the crystal through anti-ferromagnetic spin-spin interactions. The reduced density matrix of the central spin representing the impurity is calculated by dynamically integrating the full Schroedinger equation for the spin--spin-bath model for different thermally weighted eigenstates of the spin-bath. Exact numerical results show that increasing the intra-environmental coupling results in suppression of decoherence. This effect could play an important role in the construction of solid state quantum devices such as quantum computers.Comment: 4 pages, 3 figures, Revtex fil

Generalized kinetic and evolution equations in the approach of the nonequilibrium statistical operator

The method of the nonequilibrium statistical operator developed by D. N. Zubarev is employed to analyse and derive generalized transport and kinetic equations. The degrees of freedom in solids can often be represented as a few interacting subsystems (electrons, spins, phonons, nuclear spins, etc.). Perturbation of one subsystem may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between particles or with a thermal bath. The generalized kinetic equations were derived for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. It was shown that the "collision term" had the same functional form as for the generalized kinetic equations for the system with small interactions among particles. The applicability of the general formalism to physically relevant situations is investigated. It is shown that some known generalized kinetic equations (e.g. kinetic equation for magnons, Peierls equation for phonons) naturally emerges within the NSO formalism. The relaxation of a small dynamic subsystem in contact with a thermal bath is considered on the basis of the derived equations. The Schrodinger-type equation for the average amplitude describing the energy shift and damping of a particle in a thermal bath and the coupled kinetic equation describing the dynamic and statistical aspects of the motion are derived and analysed. The equations derived can help in the understanding of the origin of irreversible behavior in quantum phenomena.Comment: 21 pages, Revte

Thermally Activated Resonant Magnetization Tunneling in Molecular Magnets: Mn_12Ac and others

The dynamical theory of thermally activated resonant magnetization tunneling in uniaxially anisotropic magnetic molecules such as Mn_12Ac (S=10) is developed.The observed slow dynamics of the system is described by master equations for the populations of spin levels.The latter are obtained by the adiabatic elimination of fast degrees of freedom from the density matrix equation with the help of the perturbation theory developed earlier for the tunneling level splitting [D. A. Garanin, J. Phys. A, 24, L61 (1991)]. There exists a temperature range (thermally activated tunneling) where the escape rate follows the Arrhenius law, but has a nonmonotonic dependence on the bias field due to tunneling at the top of the barrier. At lower temperatures this regime crosses over to the non-Arrhenius law (thermally assisted tunneling). The transition between the two regimes can be first or second order, depending on the transverse field, which can be tested in experiments. In both regimes the resonant maxima of the rate occur when spin levels in the two potential wells match at certain field values. In the thermally activated regime at low dissipation each resonance has a multitower self-similar structure with progressively narrowing peaks mounting on top of each other.Comment: 18 pages, 8 figure

Statistical Theory of Spin Relaxation and Diffusion in Solids

A comprehensive theoretical description is given for the spin relaxation and diffusion in solids. The formulation is made in a general statistical-mechanical way. The method of the nonequilibrium statistical operator (NSO) developed by D. N. Zubarev is employed to analyze a relaxation dynamics of a spin subsystem. Perturbation of this subsystem in solids may produce a nonequilibrium state which is then relaxed to an equilibrium state due to the interaction between the particles or with a thermal bath (lattice). The generalized kinetic equations were derived previously for a system weakly coupled to a thermal bath to elucidate the nature of transport and relaxation processes. In this paper, these results are used to describe the relaxation and diffusion of nuclear spins in solids. The aim is to formulate a successive and coherent microscopic description of the nuclear magnetic relaxation and diffusion in solids. The nuclear spin-lattice relaxation is considered and the Gorter relation is derived. As an example, a theory of spin diffusion of the nuclear magnetic moment in dilute alloys (like Cu-Mn) is developed. It is shown that due to the dipolar interaction between host nuclear spins and impurity spins, a nonuniform distribution in the host nuclear spin system will occur and consequently the macroscopic relaxation time will be strongly determined by the spin diffusion. The explicit expressions for the relaxation time in certain physically relevant cases are given.Comment: 41 pages, 119 Refs. Corrected typos, added reference