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]

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]

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

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]

Soluble model of interacting bosons trapped in harmonic potential: Quality of Bogoliubov approximation

M.A. Załuska-Kotur, M. Gajda and J. Mostowski

We study a system of trapped bosonic particles interacting by model harmonic forces. Our model allows for a detailed examination of the notion of an order parameter (a condensate wave function). By decomposing a single particle density matrix into coherent eigenmodes we study an effect of interaction on the condensate. We show that sufficiently strong interactions cause that the condensate disappears even if the whole system is in its lowest energy state. In the second part of our paper we discuss the validity of the Bogoliubov approximation by comparing its predictions with results inferred from the exactly soluble model. In particular we examine an energy spectrum, occupation, and fluctuations of the condensate. We conclude that Bogoliubov approach gives a quite accurate description of the system in the limit of weak interactions.

Acta Phys. Polon. A 100, 485 (2001)

On coherence of Bose fields

Mariusz Gajda, Magdalena Zaluska-Kotur, and Jan Mostowski

We study a system of interacting bosons at zero temperature in an atomic trap. Using wave function that models the ground state of interacting bosons we examine the concepts of the order parameter, off-diagonal order and coherence of the system. We suggest that the coherence length becomes much smaller than the size of the system if the number of trapped particles exceeds a certain limit. This behavior is related to the unavoidable existence of two different length scales -- one determined by the external potential and the second one depending on the two-body forces.

Opt. Express 8, 106 (2001)

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)

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

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)

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)

Band of localized electromagnetic waves in random arrays of dielectric cylinders

Marian Rusek, Arkadiusz Orłowski, and Jan Mostowski

Anderson localization of electromagnetic waves in random arrays of dielectric cylinders is studied. An effective theoretical approach based on analysis of probability distributions, not averages, is developed. The disordered dielectric medium is modeled by a system of randomly distributed two-dimensional electric dipoles. Spectra of certain random matrices are investigated and the appearance of the band of localized waves emerging in the limit of an infinite medium is discovered. It suggests deeper insight into the existing experimental results.

Phys. Rev. E 56, 4892 (1997)

Photon generation by time-dependent dielectric: A soluble model

Markus Cirone, Kazimierz Rzążewski and Jan Mostowski

A soluble model of electromagnetic field interacting with time-dependent dielectric medium is given. The main assumption is that the dielectric constant is switched rapidly from the initial to the final value. Generation of electromagnetic field and photon statistics are found.

Phys. Rev. A 55, 62 (1997)