Dissipative Optical Lattice Research Articles

Defect-induced discrete breather in dissipative optical lattices with weak nonlinearity

It is widely believed that the discrete breather (DB) can only be created when the nonlinearity is strong in nonlinear systems. However, we here establish that this belief is incorrect. In this work, we systemically investigate the generation of DBs induced by coupling of the defects and nonlinearity for Bose-Einstein condensates in dissipative optical lattices. The results show that, only in a clean lattice is strong nonlinearity a necessary condition for generating of DB; whereas, if the lattice has a defect, the DBs can also be discovered even in weak nonlinearity, and its generation turns out to be controllable. In addition, we further reveal a critical interval of the defect in weak nonlinearity, within which DBs can be found, while outside DBs do not exist. Furthermore, we also explore the impact of multiple defects on the generation of DBs, and analyze the underlying physical mechanisms of these interesting phenomena. The results not only have the potential to be used for more precise engineering in the DB experiments, but also suggest that the DB may be ubiquitous since the defects and dissipation are unavoidable in real physics.

Brillouin propagation modes of cold atoms undergoing Sisyphus cooling.

An exact expression for the average velocity of cold atoms in a driven, dissipative optical lattice in terms of the amplitudes of atomic density waves is derived from semiclassical equationsfor the phase space densities of the Zeeman ground-state sublevels. The calculations are for a J_{g}=1/2→J_{e}=3/2 transition, as it is customary in theoretical studies of Sisyphus cooling. While the driver, an additional beam of small amplitude, sets the atoms into directed motion, the new expression permits the quantification of the contribution to the atomic motion of a specific atomic wave, revealing unexpected counterpropagating contributions from many modes. Additionally, the method is shown to provide the generic threshold for the transition into the regime of infinite density, regardless of the details, or even the presence, of driving.

Observation of stochastic resonance in directed propagation of cold atoms

Randomly diffusing atoms confined in a dissipative optical lattice are illuminated by a weak probe of light. The probe transmission spectrum reveals directed atomic propagation that occurs perpendicular to the direction of probe beam propagation. Resonant enhancement of this directed propagation is observed as we vary the random photon scattering rate. We experimentally characterize this stochastic resonance as a function of probe intensity and lattice well depth. A simple model reveals how the probe-excited atomic density waves and optical pumping rates conspire to create directed atomic propagation within a randomly diffusing sample.

Opto-thermophoretic superlattice for atoms

We propose and study a dissipative optical superlattice for manipulation of resonant particles (atoms, ions and similar ones) located in a transparent buffer gas. Its working principle is based on the simultaneous effect of a longitudinal rectified gradient force and a transverse thermophoretic force in the field of collinear superposition of bichromatic cosine-Gaussian laser beams. As a result, there occurs a strong periodic stratification of the gas manifested in the accumulation and sharp localization of the resonant particles at the nodes of the superlattice and their cooling. Moreover, in the case of linearly polarized light beams, there appear circulating currents of the resonant particles (the so-called Brownian vortices) in the gas. Unlike the traditional dissipative optical lattices, in the superlattice under consideration, transverse particle confinement is implemented only due to the light-induced thermophoretic force, associated with the finiteness of the effective radius of the light beams.

Directed ratchet transport of cold atoms and fluxons driven by biharmonic fields: A unified view.

This paper discusses two retrodictions of the theory of ratchet universality which explain previous experimental results concerning directed ratchet transport of cold atoms in dissipative optical lattices in one case and of fluxons in uniform annular Josephson junctions in the other, both driven by biharmonic fields. It has to be emphasized that these retrodictions are in sharp contrast with the current standard explanation of such experimental results, and they offer optimal control of the ratchetlike motion of such entities. New experimental proposals with cold atoms and fluxons are discussed, providing additional tests for novel predictions from ratchet universality.

Infinite density for cold atoms in shallow optical lattices

Infinite densities are non-normalizable quasi-probability distributions that can describe the long-time properties of systems when ergodicity is broken and the equilibrium Boltzmann-Gibbs distribution fails. Their experimental observation has remained elusive so far. We here perform semiclassical Monte Carlo simulations of cold atoms in dissipative optical lattices with realistic parameters. We show that the momentum infinite density, as well as its scale invariance, should be observable in shallow potentials. We further evaluate the momentum autocorrelation function both in the stationary and nonstationary, aging regime.

Beyond Boltzmann–Gibbs statistical mechanics in optical lattices

Cold atoms in dissipative optical lattices exhibit an unusual transport behaviour that cannot be described within Boltzmann–Gibbs statistical mechanics. New theoretical tools and concepts need thus be developed to account for their observable macroscopic properties. Here we review recent progress achieved in the study of these processes. We emphasize the generality of the findings for a broad class of physical, chemical and biological systems, and discuss open questions and perspectives for future work. Cold atoms trapped in dissipative optical lattices can behave in ways that cannot be described within the framework of Boltzmann–Gibbs statistical mechanics. Recent theoretical and experimental developments may lead to a better understanding of these processes.

Gain-controlled dissipative soliton routing in optical lattices

We demonstrate an effective mechanism for gain-controlled soliton routing in dissipative optical lattices. An effective particle model reveals the essential features of soliton dynamics in such structures. The results presented are directly applicable to general inhomogeneous systems where interplay between gain and loss mechanisms occurs. Focusing on the complexity of soliton dynamics rather than on the complexity of their profiles we have analyzed scenarios that are promising for all-optical control concepts and applications.

State engineering for a Bose-Einstein condensate in an optical lattice by means of a periodic sublattice of dissipative sites

We introduce the notion of dissipative periodic lattice as an optical lattice with periodically distributed dissipative sites and argue that it allows to engineer unconventional Bose-Einstein superfluids with the complex-valued order parameter. We consider two examples, the one-dimensional dissipative optical lattice, where each third site is dissipative, and the dissipative honeycomb optical lattice, where each dissipative lattice site neighbors three non-dissipated sites. The tight-binding approximation is employed, which allows one to obtain analytical results. In the one-dimensional case the condensate is driven to a coherent Bloch-like state with non-zero quasimomentum, which breaks the translational periodicity of the dissipative lattice. In the two-dimensional case the condensate is driven to a zero quasimomentum Bloch-like state, which is a coherent superposition of four-site discrete vortices of alternating vorticity with the vortex centers located at the dissipative sites.

Experimental measurement of efficiency and transport coherence of a cold-atom Brownian motor in optical lattices

The rectification of noise into directed movement or useful energy is utilized by many different systems. The peculiar nature of the energy source and conceptual differences between such Brownian motor systems makes a characterization of the performance far from straightforward. In this work, where the Brownian motor consists of atoms interacting with dissipative optical lattices, we adopt existing theory and present experimental measurements for both the efficiency and the transport coherence. We achieve up to 0.3% for the efficiency and 0.01 for the Péclet number.

Fluctuation-induced drift in a gravitationally tilted optical lattice

Experimental and theoretical studies are made of Brownian particles trapped in a periodic potential, which is very slightly tilted due to gravity. In the presence of fluctuations, these will trigger a measurable average drift along the direction of the tilt. The magnitude of the drift varies with the ratio between the bias force and the trapping potential. This can be closely compared to a theoretical model system, based on a Fokker-Planck-equation formalism. We show that the level of control and measurement precision we have in our system, which is based on cold atoms trapped in a three-dimensional dissipative optical lattice, makes the experimental setup suitable as a testbed for fundamental statistical physics. We simulate the system with a very simplified and general classical model, as well as with an elaborate semiclassical Monte Carlo simulation. In both cases, we achieve good qualitative agreement with experimental data.

Nonlinear patterns in Bose-Einstein condensates in dissipative optical lattices

It is shown that the one-dimensional nonlinear Schr\"odinger equation with a dissipative periodic potential, nonlinear losses, and a linear pump allow for the existence of stable nonlinear Bloch states which are attractors. The model describes a Bose-Einstein condensate with inelastic two- and three-body interactions loaded in an optical lattice with losses due to inelastic interactions of the atoms with photons.

Two-dimensional rocking ratchet for cold atoms

We investigate experimentally a two-dimensional rocking ratchet for cold atoms, realized by using a driven three-beam dissipative optical lattice. AC forces are applied in perpendicular directions by phase-modulating two of the lattice beams. As predicted by the general theory [S. Denisov et al., Phys. Rev. Lett. 100, 224102 (2008)], we observe a rectification phenomenon unique to high-dimensional rocking ratchets, as determined by two single-harmonic drivings applied in orthogonal directions. Also, by applying two bi-harmonic forces in perpendicular directions, we demonstrate the possibility of generating a current in an arbitrary direction within the optical lattice plane.

Self-organization in dissipative optical lattices

We show that the transition from Gaussian to the q-Gaussian distributions occurring in atomic transport in dissipative optical lattices can be interpreted as self-organization by recourse to a modified version of Klimontovich’s S-theorem. As a result, we find that self-organization is possible in the transition regime, only where the second moment ⟨p2⟩ is finite. Therefore, the nonadditivity parameter q is confined within the range 1<q<53, although the whole spectrum of q values, i.e., 1<q<3, is considered theoretically possible. The range of q values obtained from the modified S-theorem is also confirmed by the experiments carried out by Douglas et al. [Phys. Rev. Lett. 96, 110601 (2006)].

Ratchet effect in an optical lattice with biharmonic driving: A numerical analysis

We analyze numerically a rocking ratchet for cold atoms. The ratchet setup consists of a spatially symmetric dissipative optical lattice, and a biharmonic driving force. This setup corresponds to recent experimental realizations. We investigate the dependence of the features of the current generation on the scattering rate, which plays the role of the noise strength. Such a dependence is then used to investigate the origin of current reversals and of the rectification of fluctuations in a cold atom ratchet with broken Hamiltonian time symmetry.

Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice

Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.

Compensation of the influence of loss for a spatial soliton in a dissipative modulated Bessel optical lattice

Propagation of a spatial soliton in a dissipative modulated Bessel optical lattice is investigated, both analytically and numerically. The dynamic evolution equations for beam width, amplitude, and curvature wavefront are obtained by a variational approach. It is shown that by properly increasing the modulation depth of refractive index of the optical lattice, the loss effect can be compensated exactly to fulfill a stable spatial soliton propagation.

A nonadiabatic semi-classical method for dynamics of atoms in optical lattices

We develop a semi-classical method to simulate the motion of atoms in a dissipative optical lattice. Our method treats the internal states of the atom quantum mechanically, including all nonadiabatic couplings, while position and momentum are treated as classical variables. We test our method in the one-dimensional case. Excellent agreement with fully quantum mechanical simulations is found. Our results are much more accurate than those of earlier semi-classical methods based on the adiabatic approximation.

Tunable Tsallis Distributions in Dissipative Optical Lattices

We demonstrated experimentally that the momentum distribution of cold atoms in dissipative optical lattices is a Tsallis distribution. The parameters of the distribution can be continuously varied by changing the parameters of the optical potential. In particular, by changing the depth of the optical lattice, it is possible to change the momentum distribution from Gaussian, at deep potentials, to a power-law tail distribution at shallow optical potentials.

Cold collisions in dissipative optical lattices

In the past, light-assisted cold collisions between laser cooled atoms have been widely studied in magneto-optical atom traps (MOTs). We describe here theoretical studies of dynamical interactions, specifically cold collisions, between atoms trapped in near-resonant, dissipative optical lattices. The developed quantum-mechanical model is based on Monte Carlo wave-function simulations and combines atomic cooling and collision dynamics in a single framework. It turns out, that the radiative heating mechanism affects the dynamics of atomic cloud in a red-detuned lattice in a way that is not directly expected from the MOT studies. The optical lattice and position dependent light-matter coupling introduces selectivity of collision partners. Atoms, which are most mobile and energetic, are strongly favored to participate in collisions, and are more often ejected from the lattice, than the slow ones in the laser parameter region selected for study. For blue-detuned lattices, we study how optical shielding emerges as a natural part of the lattice and look for ways to optimize the effect. The simulations are computationally very demanding and would obviously benefit from the simplification schemes. We present some steps to this direction by showing how it is possible to calculate collision rates in near-resonant lattices in a fairly simple way.