Destruction of a Bose-Einstein condensate by strong interactions

Mariusz Gajda, Magdalena A Zaluska-Kotur and Jan Mostowski

We study an exactly solvable system of trapped bosonic particles interacting by model harmonic forces. The model allows for a detailed examination of the order parameter (condensate wavefunction) as well as a concept of the off-diagonal and diagonal order. We analyse the effect of interactions on the condensate and show that sufficiently strong interactions (attractive or repulsive) lead to the destruction of the condensate. In the thermodynamic limit this destruction has a critical character. It is shown that the existence of the coherent state of bosons is related to the existence of two length scales determined by one- and two-particle reduced density matrices. The condensate can exist only if the two length scales are of the same order. Interactions, both repulsive and attractive, change their relative size which may lead to destruction of coherence in the system and depletion of the condensate. We suggest that this scenario is model independent.

J. Phys. B 33, 4003 (2000)

Symmetries and modes of wave fields in inhomogeneous media

J. Phys. A 33, 4779 (2000)

Maciej Janowicz

In this paper the 2D Helmholtz equation with space-dependent dielectric permittivity and/or magnetic permeability is considered. The structure of the determining equations for the symmetry generator is analysed. It allows one to find many nontrivial spatial profiles of dielectric functions for which one can still separate variables in both the Helmholtz equation and corresponding Hamilton-Jacobi equation. For the case of the Dirichlet problem of the half-plane in an inhomogeneous medium the diffractive modes of the field are characterized. Several specific examples are provided.

Novel quantum effects in light scattering from cold trapped atoms

A. Orlowski, M. Gajda, P. Krekora, R. J. Glauber and J. Mostowski

Both far off-resonance and resonant scattering of light from single atoms trapped by 3D harmonic potentials has thoroughly been studied. Novel effects are predicted for different physical regimes. We have shown that dynamics of the atomic center-of-mass strongly influences the scattering cross section. Possibility of using spectrum of the scattered light in far-off-resonance regime to nondestructively measure the temperature of ultracold atoms is advocated: off-resonance scattering can be used as an ‘optical thermometer’. The realistic Compton-like regime in resonant scattering has been investigated in detail. Another interesting quantum effect in resonant regime, which has not been discussed here due to the lack of space, is the time resolved scattering, showing up when the atom can remain in the excited state long enough to make many trips back and forth in the trap before emitting a photon. The possibility of the experimental observation of the predicted effects is now being scrutinized.

Quantum Communication, Computing, and Measurement 2

Spontaneous emission in the presence of a dielectric cylinder

Władysław Żakowicz and Maciej Janowicz

Spontaneous emission of photons by an atom placed near a dielectric cylindrical waveguide at an arbitrary position is analyzed using global free electromagnetic modes, satisfying necessary continuity conditions at the slab boundaries. These modes include the modes extended over the whole space (travelling) and the modes trapped to a waveguide (waveguided). To describe angular properties of the spontaneous emission, a parametrization of the travelling modes by the outgoing waves has been proposed. Angular characteristics of the travelling photon emission, distributions of the trapped photon emission, as well as the global decay rates have been calculated using the quantum approach and the standard perturbation theory. Difficulties due to the presence of sharp resonances (whispering gallery modes) among the travelling photons are pointed out.

Phys. Rev. A 62, 013820 (2000)

Interaction of a hydrogen atom with an intense pulse of vacuum ultraviolet radiation

J. Phys. B 33, 1271 (2000)

Mariusz Gajda, Jacek Krzywinski, Lukasz Plucinski and Bernard Piraux

The free electron laser (FEL) which is currently under construction at the DESY laboratory should deliver a photon beam in the vacuum ultraviolet (VUV) range. Coherent radiation of the FEL will soon allow for testing of the matter-electromagnetic field interaction under very exotic conditions. In this paper we study the ionization of a hydrogen atom by the intense (about 1016 W cm-2 ) beam of photons with energies of 17 eV. We compare exact numerical results with predictions of the perturbation theory showing the limits of its applicability and discussing requirements for the FEL pulse parameters which are necessary for observation of non-perturbative phenomena.

Non-Markovian decay of an atom coupled to a reservoir: modification by frequency modulation

Phys. Rev. A 61, 025802 (2000)

Maciej Janowicz

A two-level atom coupled to a reservoir with Lorentzian spectral response function is considered. It is shown that if the free oscillations of the atomic dipole are suitably modulated by an external field, then the dynamics of the spontaneous decay can be strongly modified. As a result, the probability of finding the atom in an excited state can be large even for very long times. This is because the frequency modulation may lead to both effective detuning of the atom from the resonance with reservoir modes and to effective cancellation of the coupling between the atom and the reservoir. Non-Markovian features of the reservoir are found to be essential for this effect to be observable. Conditions of experimental verifications are provided.

Fluctuations of the Weakly Interacting Bose-Einstein Condensate

Phys. Rev. Lett. 82, 4376 (1999)

Zbigniew Idziaszek, Mariusz Gajda, Patrick Navez, Martin Wilkens, and Kazimierz Rzążewski

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

Soluble model of many interacting quantum particles in a trap

Magdalena A. Załuska-Kotur, Mariusz Gajda, Arkadiusz Orłowski, and Jan Mostowski

Exact solutions to many-body interacting systems of both bosonic and fermionic particles confined to harmonic potential in an arbitrary number of dimensions are given. Energy levels and their degeneracies for trapped identical particles interacting via harmonic forces are calculated. This specific form of the interaction allows for analytical solutions. The mutual interaction, attractive or repulsive, modifies significantly the properties of the considered system. For a large number of particles the interaction essentially results in a frequency shift. Statistical properties (e.g., microcanonical and grand canonical partition functions) as well as some illustrative, physically relevant examples are discussed. Our results give an unusual opportunity for further studies of interacting systems in the framework of the exactly soluble model.

Phys. Rev. A 61, 033613 (2000)

Random Green matrices: From proximity resonances to Anderson localization

Marian Rusek, Jan Mostowski, and Arkadiusz Orłowski

Universal properties of the spectra of certain matrices describing multiple elastic scattering of scalar waves from a collection of randomly distributed point-like objects are discovered. The elements of these matrices are equal to the free-space Green’s function calculated for the differences between positions of any pair of scatterers. A striking physical interpretation within Breit-Wigner’s model of the single scatterer is elaborated. Proximity resonances and Anderson localization are considered as two illustrative examples.

Phys. Rev. A 61, 022704 (2000)

Optical generation of vortices in trapped Bose-Einstein condensates

Phys. Rev. A 60, R3381 (1999)

Ł. Dobrek, M. Gajda, M. Lewenstein, K. Sengstock, G. Birkl, and W. Ertmer

We demonstrate numerically the efficient generation of vortices in Bose-Einstein condensates (BECs) by using a “phase imprinting” method. The method consists of passing a far-off-resonant laser pulse through an absorption plate with an azimuthally dependent absorption coefficient, imaging the laser beam onto a BEC, and thus creating the corresponding nondissipative Stark-shift potential and condensate phase shift. In our calculations we take into account experimental imperfections. We also propose an interference method to detect vortices by coherently pushing part of the condensate using optically induced Bragg scattering.