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.
Oct 8, 1999
Sep 30, 1999
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.
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.
Sep 14, 1999
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)
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)
Aug 24, 1999
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)
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)
Jul 7, 1999
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.
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.
Optical generation of vortices in trapped Bose-Einstein condensates
Phys. Rev. A 64, 043601 (2001)
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.
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.
Jun 1, 1999
Motion of vortex lines in quantum mechanics
Iwo Bialynicki-Birula, Zofia Bialynicka-Birula and Cezary Śliwa
Exact analytic solutions of the time-dependent Schrödinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are identified. Vortex creation and annihilation and vortex interactions are illustrated in the special cases of the free motion, the motion in the harmonic potential, and in the constant magnetic field. Similar analysis of the vortex motions is carried out also for a relativistic wave equation.
Phys. Rev. A 61, 032110 (2000)
Exact analytic solutions of the time-dependent Schrödinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are identified. Vortex creation and annihilation and vortex interactions are illustrated in the special cases of the free motion, the motion in the harmonic potential, and in the constant magnetic field. Similar analysis of the vortex motions is carried out also for a relativistic wave equation.
Phys. Rev. A 61, 032110 (2000)
Apr 5, 1999
Bands of localized electromagnetic waves in random collections of dielectric particles
Turkish Journal of Physics 23, 879 (1999)
Marian RUSEK, Arkadiusz ORŁOWSKI
Anderson localization of electromagnetic waves in random arrays of dielectric cylinders is studied. An effective theoretical approach based on the finite size scaling analysis of transmission is developed. The disordered dielectric medium is modeled by a system of randomly distributed 2D electric dipoles. The appearance of the band of localized waves emerging in the limit of an infinite medium is discovered. It suggests deeper insight into existing experimental and theoretical results.
Marian RUSEK, Arkadiusz ORŁOWSKI
Anderson localization of electromagnetic waves in random arrays of dielectric cylinders is studied. An effective theoretical approach based on the finite size scaling analysis of transmission is developed. The disordered dielectric medium is modeled by a system of randomly distributed 2D electric dipoles. The appearance of the band of localized waves emerging in the limit of an infinite medium is discovered. It suggests deeper insight into existing experimental and theoretical results.
Electromagnetic waves in disordered dielectric media: coupled-dipole model
Turkish Journal of Physics 23, 887 (1999)
Arkadiusz ORŁOWSKI and Marian RUSEK
An effective approach to multiple scattering of electromagnetic waves by disordered dielectric media is developed. A self-consistent energy-conserving coupled-dipole model is used. Applications to the Anderson localization of electromagnetic waves are presented. A complete set of Maxwell's equations is used to describe the propagation of waves and the vector character of the electromagnetic field is fully taken into account.
Arkadiusz ORŁOWSKI and Marian RUSEK
An effective approach to multiple scattering of electromagnetic waves by disordered dielectric media is developed. A self-consistent energy-conserving coupled-dipole model is used. Applications to the Anderson localization of electromagnetic waves are presented. A complete set of Maxwell's equations is used to describe the propagation of waves and the vector character of the electromagnetic field is fully taken into account.
Collective diffusion on hexagonal lattices - repulsive interactions
Surf. Sc. 441, 320 (1999)
ZAŁUSKA-KOTUR M. A. ; KRUKOWSKI S. ; TURSKI Ł. A.
Diffusion of interacting particle on a hexagonal lattice is studied by use of Monte Carlo simulations for a range of densities and temperatures including ordered and disordered phases. The decay of the initially prepared density perturbation is analyzed. Fast, local ordering happens at the beginning of system relaxation and clearly separates as a function of time the much slower global diffusion process. Locally equilibrated density perturbation decays according to the macroscopic diffusion equation, which allows a collective diffusion coefficient to be calculated. The density dependence of the collective diffusion coefficient is shown for several temperatures above and below the critical temperature.
ZAŁUSKA-KOTUR M. A. ; KRUKOWSKI S. ; TURSKI Ł. A.
Diffusion of interacting particle on a hexagonal lattice is studied by use of Monte Carlo simulations for a range of densities and temperatures including ordered and disordered phases. The decay of the initially prepared density perturbation is analyzed. Fast, local ordering happens at the beginning of system relaxation and clearly separates as a function of time the much slower global diffusion process. Locally equilibrated density perturbation decays according to the macroscopic diffusion equation, which allows a collective diffusion coefficient to be calculated. The density dependence of the collective diffusion coefficient is shown for several temperatures above and below the critical temperature.
Mar 5, 1999
New effects in light scattering from cold atoms trapped by harmonic potentials
A. Orlowski, M. Gajda, P. Krekora, R. J. Glauber, and J. Mostowski
First, we study the scattering of light by a single ultracold, trapped atom initially in the ground state of the trapping harmonic potential. We find interesting features of the scattering in the regime where the atomic recoil energy is much larger than the separation between oscillatory trap levels. Although we present the quan-tum mechanical expression for the scattering cross section, special attention is paid to the semiclassical analysis of the process. We show that the major characteristics of the scattering might be deduced from two conservation laws: conservation of energy and momentum in absorption and emission of photon process separately. These conservation laws impose a strong correlation between scattered-light characteristics and the position of the trapped atom at the moment of photon emission. A detailed analysis of the far-off resonance scattering of light from a single atom trapped in an isotropic harmonic potential is also given. In this case, we are able to assume a more realistic, i.e., thermal, initial state of the atomic center of mass. An exact closed-form expression for the differential scattering cross section is derived from a general S-matrix theory of scattering. The possibility of measuring the density–density correlation functions in light-scattering experiments is discussed.
Opt. Spectrosc. 87, 645 (1999)
First, we study the scattering of light by a single ultracold, trapped atom initially in the ground state of the trapping harmonic potential. We find interesting features of the scattering in the regime where the atomic recoil energy is much larger than the separation between oscillatory trap levels. Although we present the quan-tum mechanical expression for the scattering cross section, special attention is paid to the semiclassical analysis of the process. We show that the major characteristics of the scattering might be deduced from two conservation laws: conservation of energy and momentum in absorption and emission of photon process separately. These conservation laws impose a strong correlation between scattered-light characteristics and the position of the trapped atom at the moment of photon emission. A detailed analysis of the far-off resonance scattering of light from a single atom trapped in an isotropic harmonic potential is also given. In this case, we are able to assume a more realistic, i.e., thermal, initial state of the atomic center of mass. An exact closed-form expression for the differential scattering cross section is derived from a general S-matrix theory of scattering. The possibility of measuring the density–density correlation functions in light-scattering experiments is discussed.
Opt. Spectrosc. 87, 645 (1999)
Interference without interference: Directional properties of spontaneous emission
A. Orlowski and W. Zakowicz
A fully quantum-mechanical description of the spontaneous emission from an excited two-level atom placed in front of the two slit interferometer is given. Global modes of the electromagnetic field in a two slit system are derived within the Kirchhoff-Huygens diffraction approximation, serving as a base for the field quantization. The standard Fermi’s golden rule, supplemented by a factor coming from the nontrivial mode structure caused by the presence of the two slit interferometer, is used to show that interference results from the position dependent coupling between the atom and different field modes of the system.
Opt. Spectrosc. 87, 500 (1999)
A fully quantum-mechanical description of the spontaneous emission from an excited two-level atom placed in front of the two slit interferometer is given. Global modes of the electromagnetic field in a two slit system are derived within the Kirchhoff-Huygens diffraction approximation, serving as a base for the field quantization. The standard Fermi’s golden rule, supplemented by a factor coming from the nontrivial mode structure caused by the presence of the two slit interferometer, is used to show that interference results from the position dependent coupling between the atom and different field modes of the system.
Opt. Spectrosc. 87, 500 (1999)
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