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)

Kinetic lattice gas model of collective diffusion in a one-dimensional system with long-range repulsive interactions

Magdalena A. Zauska-Kotur, Zbigniew W. Gortel

Collective diffusion is investigated within the kinetic lattice gas model for systems of particles in one dimension with repulsive long-range interactions which are known to result in a staircaselike phase diagram with an infinite sequence of incompressible crystalline phases separated one from another by unstable compressible liquidlike phases. Using a recently proposed [Gortel and Zauska-Kotur, Phys. Rev. B 70, 125431 (2004)] variational method, an analytic expression for the particle density dependence of the diffusion coefficient is derived in which commonly postulated static and kinetic factors are unambiguously identified. It is shown that while the static factor exhibits singular coverage dependence due to a sharp drop of compressibility when the system enters a crystalline phase, the kinetic factor may substantially modify this behavior. Depending on details of the activated state interactions controlling the migration kinetics the diffusion coefficient may also be singular or, at another extreme, it may be a continuously smooth function of density. In view of these observations recent results on efficient low temperature self-reorganization through devil's staircase phases in the dense Pb/Si(111)-× are discussed.

Phys. Rev. B vol. 74, 045405 - 1-16 (2006) [1/2]

Decoherence of entangled states in two-mode cavities

Janowicz M., Orłowski A.

Decoherence of the Schrödinger-cat states in two-mode cavities are discussed. The cat states are assumed to be produced by the measurement of the energy of a three-level atom which have passed through the cavity. The evolution of the field density matrix is obtained from the Lindblad form of the dissipater at zero temperature. It is shown that the decoherence time of the two-mode cat states critically depends on the degree of entanglement. Implications for decoherence of entanglement in the macroscopic scales are discussed.

J. Phys. B vol. 39, 1763-1771 (2006) [2/2]

Exponential beams of electromagnetic radiation

Iwo Bialynicki-Birula and Zofia Bialynicka-Birula

We show that in addition to well known Bessel, Hermite-Gauss, and Laguerre-Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of rho. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, but unlike Bessel beams they have a finite energy per unit beam length. The analysis of these beams is greatly simplified by an extensive use of the Riemann-Silberstein vector and the Whittaker representation of the solutions of the Maxwell equations in terms of just one complex function. The connection between the Bessel beams and the exponential beams is made explicit by constructing the exponential beams as wave packets of Bessel beams.

J. Phys. B vol. 39, 5545-5553 (2006) [1/2]

Anderson Localization of Electromagnetic Waves in Dielectric Media: Model Studies

Rusek M., Orłowski A.

Anderson localization of electromagnetic waves in random arrays of dielectric cylinders confined within a planar metallic waveguide is studied. The disordered dielectric medium is modeled by a system of randomly distributed 2D electric dipoles. An effective theoretical approach based on the method of images is developed. A clear distinction between isolated localized waves (which exist in finite media) and the band of localized waves (which appears only in the limit of the infinite medium) is presented. The Anderson transition emerging in the limit of an infinite medium is observed both in finite size scaling analysis of transmission and in the properties of the spectra of some random matrices. The sound physical interpretation of the obtained results suggests deeper insight into the existing experimental and theoretical work.

Acta Phys. Pol. A vol. 109 (1), 109-119 (2006) [KK, 2/2]

Formation of soliton trains in Bose-Einstein condensates by temporal Talbot effect

K. Gawryluk, M. Brewczyk, M. Gajda and J, Mostowski

We study the formation of matter-wave soliton trains in Bose–Einstein condensates confined in a box-like potential. We find that the generation of 'real' solitons understood as multipeak structures undergoing elastic collisions is possible if the condensate is released from the box into the harmonic trap only within well-defined time intervals. When the box-like potential is switched off outside the existing time windows, the number of peaks in a train changes resembling missing solitons observed in recent experiment (Strecker et al 2002 Nature 417 150). Our findings indicate that a new way of generating soliton trains in condensates through the temporal, matter-wave Talbot effect is possible.

J. Phys. B: At. Mol. Opt. Phys. 39 No 1

Dynamics of a relative superflow between a Bose-Einstein condensate and the thermal cloud

Łukasz Zawitkowski, Mariusz Gajda, and Kazimierz Rzewski

We use the classical fields approximation to study a translational flow of the condensate with respect to the thermal cloud in a weakly interacting Bose gas confined in a three-dimensional box. We study both subcritical and supercritical relative velocity cases and analyze in detail a state of stationary flow which is reached in the dynamics. This state corresponds to the thermal equilibrium, which is characterized by the relative velocity of the condensate and the thermal cloud. We observe two processes—re-thermalization and drag, both of which lead to a reduction of a relative velocity of the superflow. Yet only the drag process, which is observed above the critical velocity vcr , results in transferring a Bose-Einstein condensate to a slower moving mode. In this case the relative velocity of the flow suddenly drops to a value close to zero. Finally, we report the critical velocity to be for our parameters vcr=0.21c for the initial condition and vcreq=0.12c for re-thermalized superflow ( c being the Landau speed of sound), which is strikingly lower than Landau critical velocity, yet consistent with experiments.

Phys. Rev. A vol. 74, 043601 - 1-7 (2006) [1/3]

Dynamics of quasisolitons in degenerate fermionic gases

Emilia Witkowska and Mirosław Brewczyk

We investigate the dynamics of the system of multiple bright and dark quasisolitons generated in a one-component ultracold Fermi gas via the phase imprinting technique in terms of atomic orbitals approach. In particular, we analyze the collision between two bright quasisolitons and find that quasisolitons are subject to the superposition principle.

Phys. Rev. A 72, 023606 (2005)

Superluminal propagation of solitary kinklike waves in amplifying media

Maciej Janowicz and Jan Mostowski

It is shown that solitary-wave, kinklike structures can propagate superluminally in two- and four-level amplifying media with strongly damped oscillations of coherences. This is done by solving analytically the Maxwell-Bloch equations in the kinetic limit. It is also shown that the true wave fronts—unlike the pseudo wave fronts of the kinks—must propagate with velocity c, so that no violation of special relativity is possible. The conditions of experimental verification are discussed.

Phys. Rev. E vol. 73, 046613 - 1-9 (2006) [2/2]

Beams of electromagnetic radiation carrying angular momentum: The Riemann–Silberstein vector and the classical–quantum correspondence

Iwo Bialynicki-Birula, and Zofia Bialynicka-Birula

All beams of electromagnetic radiation are made of photons. Therefore, it is important to find a precise relationship between the classical properties of the beam and the quantum characteristics of the photons that make a particular beam. It is shown that this relationship is best expressed in terms of the Riemann–Silberstein vector – a complex combination of the electric and magnetic field vectors – that plays the role of the photon wave function. The Whittaker representation of this vector in terms of a single complex function satisfying the wave equation greatly simplifies the analysis. Bessel beams, exact Laguerre–Gauss beams, and other related beams of electromagnetic radiation can be described in a unified fashion. The appropriate photon quantum numbers for these beams are identified. Special emphasis is put on the angular momentum of a single photon and its connection with the angular momentum of the beam.

Opt. Commun. vol. 264, 342-351 (2006) [1/2]