arXiv subjects

Jakub Zakrzewski

Publications and source records attributed to Jakub Zakrzewski.

At least 163 records · Page 9Linked to original sources

arXiv2006

The Mott insulator phase of the one dimensional Bose-Hubbard model: a high order perturbative study

The one dimensional Bose-Hubbard model at a unit filling factor is studied by means of a very high order symbolic perturbative expansion. Analytical expressions are derived for the ground state quantities such as energy per site, variance of on-site occupation, and different correlation functions. These findings are compared to numerics and good agreement is found in the Mott insulator phase. Our results provide analytical approximations to important observables in the Mott phase, and are also of direct relevance to future experiments with ultra cold atomic gases placed in optical lattices. We also discuss the symmetry of the Bose-Hubbard model associated with the sign change of the tunneling coupling.

cond-mat.other↗

arXiv2006

Time resolved quantum dynamics of double ionization in strong laser fields

Quantum calculations of a 1+1-dimensional model for double ionization in strong laser fields are used to trace the time evolution from the ground state through ionization and rescattering to the two electron escape. The subspace of symmetric escape, a prime characteristic of nonsequential double ionization, remains accessible by a judicious choice of 1-d coordinates for the electrons. The time resolved ionization fluxes show the onset of single and double ionization, the sequence of events during the pulse, and the influences of pulse duration, and reveal the relative importance of sequential and non-sequential double ionization, even when ionization takes place during the same field cycle.

physics.atom-ph↗

arXiv2006

Strongly correlated Fermi-Bose mixtures in disordered optical lattices

We investigate theoretically the low-temperature physics of a two-component ultracold mixture of bosons and fermions in disordered optical lattices. We focus on the strongly correlated regime. We show that, under specific conditions, composite fermions, made of one fermion plus one bosonic hole, form. The composite picture is used to derive an effective Hamiltonian whose parameters can be controlled via the boson-boson and the boson-fermion interactions, the tunneling terms and the inhomogeneities. We finally investigate the quantum phase diagram of the composite fermions and we show that it corresponds to the formation of Fermi glasses, spin glasses, and quantum percolation regimes.

cond-mat.other↗

arXiv2005

Mean field dynamics of superfluid-insulator phase transition in a gas of ultra cold atoms

A large scale dynamical simulation of the superfluid to Mott insulator transition in the gas of ultra cold atoms placed in an optical lattice is performed using the time dependent Gutzwiller mean field approach. This approximate treatment allows us to take into account most of the details of the recent experiment [Nature 415, 39 (2002)] where by changing the depth of the lattice potential an adiabatic transition from a superfluid to a Mott insulator state has been reported. Our simulations reveal a significant excitation of the system with a transition to insulator in restricted regions of the trap.

cond-mat.other↗

arXiv2004

Atomic Fermi-Bose mixtures in inhomogeneous and random lattices: From Fermi glass to quantum spin glass and quantum percolation

We investigate atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices in the limit of strong atom-atom interactions. We derive the effective Hamiltonian describing the dynamics of the system and discuss its low temperature physics. We demonstrate possibility of controlling the interactions at local level in inhomogeneous but regular lattices. Such a control leads to the achievement of Fermi glass, quantum Fermi spin glass, and quantum percolation regimes involving bare and/or composite fermions in random lattices.

cond-mat.other↗

arXiv2004

Non-sequential double ionization of molecules

Double ionization of diatomic molecules by short linearly polarized laser pulses is analyzed. We consider the final stage of the ionization process, that is the decay of a highly excited two electron molecule, which is formed after re-scattering. The saddles of the effective adiabatic potential energy close to which simultaneous escape of electrons takes place are identified. Numerical simulations of the ionization of molecules show that the process can be dominated by either sequential or non-sequential events. In order to increase the ratio of non-sequential to sequential ionizations very short laser pulses should be applied.

physics.atom-ph↗

arXiv2003

A realistic example of chaotic tunneling: The hydrogen atom in parallel static electric and magnetic fields

Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel uniform static electric and magnetic fields, where tunneling is followed by ionization along the fields direction. Depending on the magnetic quantum number, one may observe either a standard Porter-Thomas distribution of tunneling rates or, for strong scarring by a periodic orbit parallel to the external fields, strong deviations from it. For the latter case, a simple model based on random matrix theory gives the correct distribution.

nlin.CD↗

arXiv2002

Non-dispersive wave packets in periodically driven quantum systems

With the exception of the harmonic oscillator, quantum wave-packets usually spread as time evolves. We show here that, using the nonlinear resonance between an internal frequency of a system and an external periodic driving, it is possible to overcome this spreading and build non-dispersive (or non-spreading) wave-packets which are well localized and follow a classical periodic orbit without spreading. From the quantum mechanical point of view, the non-dispersive wave-packets are time periodic eigenstates of the Floquet Hamiltonian, localized in the nonlinear resonance island. We discuss the general mechanism which produces the non-dispersive wave-packets, with emphasis on simple realization in the electronic motion of a Rydberg electron driven by a microwave field. We show the robustness of such wavepackets for a model one-dimensional as well as for realistic three dimensional atoms. We consider their essential properties such as the stability versus ionization, the characteristic energy spectrum and long lifetimes. The requirements for experiments aimed at observing such non-dispersive wave-packets are also considered. We also discuss other related phenomena in atomic and molecular physics as well as possible further extensions of the theory.

quant-ph↗

arXiv2002

Stirring Bose-Einstein condensate

By shining a tightly focused laser light on the condensate and moving the center of the beam along the spiral line one may stir the condensate and create vortices. It is shown that one can induce rotation of the condensate in the direction opposite to the direction of the stirring.

cond-mat↗

arXiv2002

Manipulating the shape of electronic non-dispersive wave-packets in the hydrogen atom: numerical tests in realistic experimental conditions

We show that combination of a linearly polarized resonant microwave field and a parallel static electric field may be used to create a non-dispersive electronic wavepacket in Rydberg atoms. The static electric field allows for manipulation of the shape of the elliptical trajectory the wavepacket is propagating on. Exact quantum numerical calculations for realistic experimental parameters show that the wavepacket evolving on a linear orbit can be very easily prepared in a laboratory either by a direct optical excitation or by preparing an atom in an extremal Stark state and then slowly switching on the microwave field. The latter scheme seems to be very resistant to experimental imperfections. Once the wavepacket on the linear orbit is excited, the static field may be used to manipulate the shape of the orbit.

quant-ph↗

arXiv2002

Collective excitation of trapped degenerate Fermi gases

We show that the slow driving of a focused laser beam through the cloud of trapped cold fermions allows for a creation of the collective excitation in the system. The method, proposed originally by us for bosons, seems to be quite feasible experimentally -- it requires only an appropriate change in time of the potential in atomic traps, as realized in laboratories already.

cond-mat.stat-mech↗

arXiv2001

Kepler Map for H atom driven by microwaves with arbitrary polarization

Dynamics of hydrogen atom driven by microwave field of arbitrary polarization is approximated by the discrete mapping. The map describes the change of dynamical variables from an aphelion or a perihelion to the next one. The results are compared with numerical simulation and previous approximations.

nlin.CD↗

arXiv2001

Simple method for excitation of a Bose-Einstein condensate

An appropriate, time-dependent modification of the trapping potential may be sufficient to create effectively collective excitations in a cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions and should allow the creation of both dark solitons and vortices.

quant-ph↗

arXiv2001

Breakdown of correspondence in chaotic systems: Ehrenfest versus localization times

Breakdown of quantum-classical correspondence is studied on an experimentally realizable example of one-dimensional periodically driven system. Two relevant time scales are identified in this system: the short Ehrenfest time t_h and the typically much longer localization time scale T_L. It is shown that surprisingly weak modification of the Hamiltonian may eliminate the more dramatic symptoms of localization without effecting the more subtle but ubiquitous and rapid loss of correspondence at t_h.

nlin.CD↗

arXiv2001

A method for collective excitation of Bose-Einstein condensate

It is shown that by an appropriate modification of the trapping potential one may create collective excitation in cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions. It seems to be feasible experimentally --- it requires only a proper change in time of the potential in atomic traps, as realized in laboratories already.

quant-ph↗

arXiv2001

Driven Rydberg atoms reveal quartic level repulsion

The dynamics of Rydberg states of a hydrogen atom subject simultaneously to uniform static electric field and two microwave fields with commensurate frequencies is considered in the range of small fields amplitudes. In the certain range of the parameters of the system the classical secular motion of the electronic ellipse reveals chaotic behavior. Quantum mechanically, when the fine structure of the atom is taken into account, the energy level statistics obey predictions appropriate for the symplectic Gaussian random matrix ensemble.

quant-ph↗

arXiv2000

Breaking time reversal symmetry in chaotic driven Rydberg atoms

We consider the dynamics of Rydberg states of the hydrogen atom driven by a microwave field of elliptical polarization, with a possible additional static electric field. We concentrate on the effect of a resonant weak field - whose frequency is close to the Kepler frequency of the electron around the nucleus - which essentially produces no ionization of the atom, but completely mixes the various states inside an hydrogenic manifold of fixed principal quantum number. For sufficiently small fields, a perturbative approach (both in classical and quantum mechanics) is relevant. For some configurations of the fields, the classical secular motion (i.e. evolution in time of the elliptical electronic trajectory) is shown to be predominantly chaotic. Changing the orientation of the static field with respect to the polarization of the microwave field allows us to investigate the effect of generalized time-reversal symmetry breaking on the statistical properties of energy levels.

nlin.CD↗

arXiv1999

Chaotic Rydberg atoms with broken time-reversal symmetry

The dynamics of Rydberg states of atomic hydrogen perturbed simultaneously by a static electric field and a resonant microwave field of elliptical polarization is analysed in the quantum perturbative limit of small amplitudes. For some configurations, the secular motion (i.e. evolution in time of the elliptical electronic trajectory) may be classically predominantly chaotic. By changing the orientation of the static field with respect to the polarization of the microwave field, one can modify the global symmetries of the system and break any generalized time-reversal invariance. This has a dramatic effect on the statistical properties of the energy levels.

chao-dyn↗