Spinor condensate of 87Rb as a dipolar gas

Tomasz Świsłocki, Mirosław Brewczyk, Mariusz Gajda, Kazimierz Rzążewski

We consider a spinor condensate of 87Rb atoms in F=1 hyperfine state confined in an optical dipole trap. Putting initially all atoms in m_F=0 component we find that the system evolves towards a state of thermal equilibrium with kinetic energy equally distributed among all magnetic components. We show that this process is dominated by the dipolar interaction of magnetic spins rather than spin mixing contact potential. Our results show that because of a dynamical separation of magnetic components the spin mixing dynamics in 87Rb condensate is governed by dipolar interaction which plays no role in a single component rubidium system in a magnetic trap.

arxiv.org 0901.1763

Elementary excitations of a two-component Fermi system using the atomic-orbital approach

Tomasz Świsłocki, Tomasz Karpiuk, and Miroslaw Brewczyk

We investigate the ground state properties of normal and superfluid phases of a mixture of Fermi atoms at zero temperature in a quasi-one-dimensional harmonic trap. Assuming pairing occurs in the Hartree-Fock single-particle states (obtained using atomic orbitals approach) we calculate the spectrum of elementary excitations of the system. We find that for strong enough attraction between different kinds of fermions the state consisting of Cooper pairs becomes energetically favorable. For even stronger attraction a discontinuity located at the Fermi surface appears in the spectrum of elementary excitations. At the same time the chemical potential changes its sign and the system goes from the gas of Cooper pairs to the condensed phase of molecular dimers realizing the BCS to Bose-Einstein condensate crossover in one-dimensional space.

Phys. Rev. A 77, 033603 (2008)

Segregation in a noninteracting binary mixture

Filip Krzyżewski and Magdalena A. Załuska-Kotur

Process of stripe formation is analyzed numerically in a binary mixture. The system consists of particles of two sizes, without any direct mutual interactions. Overlapping of large particles, surrounded by a dense system of small particles, induces indirect entropy driven interactions between large particles. Under an influence of an external driving force the system orders and stripes are formed. Mean width of stripes grows logarithmically with time, in contrast to a typical power law temporal increase observed for driven interacting lattice gas systems. We describe the mechanism responsible for this behavior and attribute the logarithmic growth to a random walk of large particles in a random potential created by the site blocking due to the small ones.

Phys. Rev. E 77, 031502 (2008)

Resonant Einstein–de Haas Effect in a Rubidium Condensate

Krzysztof Gawryluk, Miroslaw Brewczyk, Kai Bongs, and Mariusz Gajda

We theoretically consider a spin polarized, optically trapped condensate of 87Rb atoms in F=1. We observe a transfer of atoms to other Zeeman states due to the dipolar interaction which couples the spin and the orbital degrees of freedom. Therefore the transferred atoms acquire an orbital angular momentum. This is a realization of the Einstein–de Haas effect in systems of cold gases. We find resonances which make this phenomenon observable even in very weak dipolar systems, when the Zeeman energy difference on transfer is fully converted to rotational kinetic energy.

Phys. Rev. Lett. 99, 130401 (2007)

Coherent representation approach to damping of two-level systems

Janowicz Maciej; Karakula Sylwia; Mostowski Jan

A characteristic function for spin systems is applied to investigate the dissipation and decoherence of one and two two-level atoms. Particular attention is devoted to the Schrödinger cat-like states of two two-level systems. It has been demonstrated that the decoherence time and the phase damping rate depend linearly on the number of degrees of freedom for the maximally entangled initial state. Use of various characteristic functions to describe the decoherence processes is advocated. Two realizations of the SU(2) group are discussed in this context. The first one is based on the homomorphism of SU(2) and the group of rotations, the second one takes as its basis the Schwinger coupled-boson representation of angular-momentum operators as well as the definition of the characteristic function provided by Scully and Wódkiewicz.

J. Phys. B vol. 39, 5199-5213 (2006) [2/3]

Comparison of Gain--Loss Asymmetry Behavior for Stocks and Indexes

Magdalena A. Zaluska-Kotur, Krzysztof Karpio, Arkadiusz Orlowski

Investment horizon approach has been used to analyze indexes of Polish stock market. Optimal time horizon for each return value is evaluated by fitting appropriate function form of the distribution. Strong asymmetry of gain--loss curves is observed for WIG index, whereas gain and loss curves look similar for WIG20 and for most stocks of individual companies. The gain--loss asymmetry for these data, measured by a coefficient, that we postulated before [submitted to {ITALIC Physica A}], has opposite sign to this for WIG index.

Acta Phys. Polonica B Vol. 37, No. 11

Cellular automaton approach to electromagnetic wave propagation in dispersive media

M.W. Janowicz, J.M.A. Ashbourn, Arkadiusz Orłowski, Jan Mostowski

Extensions of Białynicki-Birula's cellular automaton are proposed for studies of the one-dimensional propagation of electromagnetic fields in Drude metals, as well as in both transparent, dispersive and lossy dielectrics. These extensions are obtained by representing the dielectrics with appropriate matter fields, such as polarization together with associated velocity fields. To obtain the different schemes for the integration of the resulting systems of linear partial differential equations, split-operator ideas are employed. Possible further extensions to two-dimensional propagation and for the study of left-handed materials are discussed. The stability properties of the cellular automaton treated as a difference scheme are analysed.

P. Roy. Soc. A - Math. Phy. vol. 462, 2927-2948 (2006) [3/4]

Hydrogen atom in phase space : the Wigner representation

Ludmiła Praxmeyer, Jan Mostowski and Krzysztof Wódkiewicz

We have found an effective method of calculating the Wigner function, being a quantum analogue of joint probability distribution of position and momentum, for bound states of nonrelativistic hydrogen atom. The formal similarity between the eigenfunctions of nonrelativistic hydrogen atom in the momentum representation and Klein-Gordon propagators has allowed the calculation of the Wigner function for an arbitrary bound state of the hydrogen atom. These Wigner functions for some low lying states are depicted and discussed.

J. Phys. A vol. 39, 14143-14151 (2006) [1/3]

Classification of zero-energy resonances by dissociation of Feshbach molecules

Thomas M. Hanna, Krzysztof Góral, Emilia Witkowska, and Thorsten Köhler

We study the dissociation of Feshbach molecules by a magnetic field sweep across a zero-energy resonance. In the limit of an instantaneous magnetic field change, the distribution of atomic kinetic energy can have a peak indicating dominance of the molecular closed-channel spin configuration over the entrance channel. The extent of this dominance influences physical properties such as stability with respect to collisions, and so the readily measurable presence or absence of the corresponding peak provides a practical method of classifying zero-energy resonances. Currently achievable ramp speeds, e.g., those demonstrated by Dürr [Phys. Rev. A 70, 031601 (2005)], are fast enough to provide magnetic field changes that may be interpreted as instantaneous. We study the transition from sudden magnetic field changes to asymptotically wide, linear ramps. In the latter limit, the predicted form of the atomic kinetic energy distribution is independent of the specific implementation of the two-body physics, provided that the near-resonant scattering properties are properly accounted for.

Phys. Rev. A vol. 74, 023618 - 1-10 (2006) [1/4]

Statics and dynamics of Bose-Einstein condensates in double square well potentials

E. Infeld, P. Ziń, J. Gocałek, and M. Trippenbach

We treat the behavior of Bose-Einstein condensates in double square well potentials of both equal and different depths. For even depth, symmetry preserving solutions to the relevant nonlinear Schrödinger equation are known, just as in the linear limit. When the nonlinearity is strong enough, symmetry breaking solutions also exist, side by side with the symmetric one. Interestingly, solutions almost entirely localized in one of the wells are known as an extreme case. Here we outline a method for obtaining all these solutions for repulsive interactions. The bifurcation point at which, for critical nonlinearity, the asymmetric solutions branch off from the symmetry preserving ones is found analytically. We also find this bifurcation point and treat the solutions generally via a Josephson junction model. When the confining potential is in the form of two wells of different depth, interesting phenomena appear. This is true of both the occurrence of the bifurcation point for the static solutions and also of the dynamics of phase and amplitude varying solutions. Again a generalization of the Josephson model proves useful. The stability of solutions is treated briefly.

Phys. Rev. E 74, 026610 (2006)