Julius Ruseckas

Non-Abelian gauge potentials for ultracold atoms with degenerate dark states.

We show that the adiabatic motion of ultracold, multilevel atoms in spatially varying laser fields can give rise to effective non-Abelian gauge fields if degenerate adiabatic eigenstates of the atom-laser interaction exist. A pair of such degenerate dark states emerges, e.g., if laser fields couple three internal states of an atom to a fourth common one under pairwise two-photon-resonance conditions. For this so-called tripod scheme we derive general conditions for truly non-Abelian gauge potentials and discuss special examples. In particular we show that using orthogonal laser beams with orbital angular momentum an effective magnetic field can be generated that has a monopole component.

Generalized Rashba-Dresselhaus spin-orbit coupling for cold atoms

We study the possibility for generating a new type of spin-orbit coupling for the center-of-mass motion of cold atoms, using laser beams that resonantly couple N atomic internal ground states to an extra state. After a general analysis of the scheme, we concentrate on the tetrapod setup (N = 4) where the atomic state can be described by a three-component spinor, evolving under the action of a Rashba-Dresselhaus-type spin-orbit coupling for a spin 1 particle. We illustrate a consequence of this coupling by studying the negative refraction of atoms at a potential step and show that the amplitude of the refracted beam is significantly increased in comparison to the known case of spin 1/2 Rashba-Dresselhaus coupling. Finally, we explore a possible implementation of this tetrapod setup, using stimulated Raman couplings between Zeeman sublevels of the ground state of alkali-metal atoms.

Nonlinear stochastic models of 1/f noise and power-law distributions

Starting from the developed generalized point process model of 1/f noise [B. Kaulakys et al., Phys. Rev. E 71 (2005) 051105] we derive the nonlinear stochastic differential equations for the signal exhibiting 1/fβ noise and 1/xλ distribution density of the signal intensity with different values of β and λ. The processes with 1/fβ are demonstrated by the numerical solution of the derived equations with the appropriate restriction of the diffusion of the signal in some finite interval. The proposed consideration may be used for modeling and analysis of stochastic processes in different systems with the power-law distributions, long-range memory or with the elements of self-organization.

1 / f noise from nonlinear stochastic differential equations

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/fbeta noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/fbeta noise, and provides further insights into the origin of 1/fbeta noise.

A long-range memory stochastic model of the return in financial markets

We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with an earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one-minute trading return in the NYSE.

Quasirelativistic behavior of cold atoms in light fields

We study the influence of three laser beams on the center-of-mass motion of cold atoms with internal energy levels in a tripod configuration. We show that, as for electrons in graphene, the atomic motion can be equivalent to the dynamics of ultrarelativistic two-component Dirac fermions. We propose and analyze an experimental setup for observing such a quasirelativistic motion of ultracold atoms. We demonstrate that the atoms can experience negative refraction and focusing by Veselago-type lenses. We also show how the chiral nature of the atomic motion manifests itself as an oscillation of the atomic internal state population, which depends strongly on the direction of the center-of-mass motion. For certain directions an atom remains in its initial state, whereas for other directions the populations undergo oscillations between a pair of internal states.

Light-induced effective magnetic fields for ultracold atoms in planar geometries

We propose a scheme to create an effective magnetic field for ultracold atoms in a planar geometry. The setup allows the experimental study of classical and quantum Hall effects in close analogy to solid-state systems including the possibility of finite currents. The present scheme is an extention of the proposal in Phys. Rev. Lett. 93, 033602 (2004), where the effective magnetic field is now induced for three-level Lambda-type atoms by two counterpropagating laser beams with shifted spatial profiles. Under conditions of electromagnetically induced transparency the atom-light interaction has a space-dependent dark state, and the adiabatic center-of-mass motion of atoms in this state experiences effective vector and scalar potentials. The associated magnetic field is oriented perpendicular to the propagation direction of the laser beams. The field strength achievable is one flux quantum over an area given by the transverse beam separation and the laser wavelength. For a sufficiently dilute gas the field is strong enough to reach the lowest Landau level regime.

Effective magnetic fields in degenerate atomic gases induced by light beams with orbital angular momenta

We investigate the influence of two resonant laser beams on the mechanical properties of degenerate atomic gases. The control and probe beams of light are considered to have orbital angular momenta (OAM) and act on the three-level atoms in the electromagnetically induced transparency configuration. The theory is based on the explicit analysis of the quantum dynamics of cold atoms coupled with two laser beams. Using the adiabatic approximation, we obtain an effective equation of motion for the atoms driven to the dark state. The equation contains a vector-potential-type interaction as well as an effective trapping potential. The effective magnetic field is shown to be oriented along the propagation direction of the control and probe beams containing OAM. Its spatial profile can be controlled by choosing proper laser beams. We demonstrate how to generate a constant effective magnetic field, as well as a field exhibiting a radial distance dependence. The resulting effective magnetic field can be concentrated within a region where the effective trapping potential holds the atoms. The estimated magnetic length can be considerably smaller than the size of the atomic cloud.

Stochastic nonlinear differential equation generating 1 / f noise

Starting from the simple point process model of 1/f noise, we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise, in any desirably wide range of frequency. A stochastic differential equation (the general Langevin equation with a multiplicative noise) that gives 1/f noise is derived. The solution of the equation exhibits the power-law distribution. The process with 1/f noise is demonstrated by the numerical solution of the derived equation with the appropriate restriction of the diffusion of the signal in some finite interval.

Herding model and 1/f noise

We provide evidence that for some values of the parameters a simple agent-based model, describing herding behavior, yields signals with 1/f power spectral density. We derive a non-linear stochastic differential equation for the ratio of number of agents and show, that it has the form proposed earlier for modeling of 1/fnoise with different exponents �. The non- linear terms in the transition probabilities, quantifying the herding behavior, are crucial to the appearance of 1/f noise. Thus, the herding dynamics can be seen as a microscopic explanation of the proposed non-linear stochastic differential equations generatingsignals with 1/fspectrum. Wealsoconsiderthepossiblefeedbackofmacroscopicstateonmicroscopictransitionprobabilities strengthening the non-linearity of equations and providing more opportunities in themodeling of processes exhibiting power-law statistics. Copyright c �EPLA, 2011