We study the long-range force arising from the absorption of non-saturating laser beams in a two-dimensional cloud of cold atoms. The force created by the lasers is attractive and similar to the usual Newtonian gravity along the beam. The cloud is composed of bosonic strontium 88 cooled and trapped on the intercombination line. Transferring the atoms in a two-dimensional optical dipole trap in a magical wavelength configuration, a canonical non-equilibrium phase transition is expected. Below a critical temperature, selfgravitating particles in two dimensions can collapse, nearly by the same mechanism stars are forming. We observed experimentally transient compressions, a halfway satisfactory result originating from the power limitation of our dipole trap. The second part of the thesis focuses on the theoretical realization a minimal Brownian motor within a system of trapped particles in 2D, similarly to our experimental situation. The phenomenon characterizing the Brownian motor is the appearance of a macroscopic current of particles. We have shown that this direct transport of particles is independent of the details of the trapping potential and obtained if and only if two symmetries are jointly broken: By the presence of two heat baths along orthogonal directions together and an anisotropic trap misaligned from the temperature axes.
We study the long-range force arising from the absorption of non-saturating laser beams in a two-dimensional cloud of cold atoms. The force created by the lasers is attractive and similar to the usual Newtonian gravity along the beam. The cloud is composed of bosonic strontium 88 cooled and trapped on the intercombination line. Transferring the atoms in a two-dimensional optical dipole trap in a magical wavelength configuration, a canonical non-equilibrium phase transition is expected. Below a critical temperature, selfgravitating particles in two dimensions can collapse, nearly by the same mechanism stars are forming. We observed experimentally transient compressions, a halfway satisfactory result originating from the power limitation of our dipole trap. The second part of the thesis focuses on the theoretical realization a minimal Brownian motor within a system of trapped particles in 2D, similarly to our experimental situation. The phenomenon characterizing the Brownian motor is the appearance of a macroscopic current of particles. We have shown that this direct transport of particles is independent of the details of the trapping potential and obtained if and only if two symmetries are jointly broken: By the presence of two heat baths along orthogonal directions together and an anisotropic trap misaligned from the temperature axes.
In two dimensions, a system of self-gravitating particles collapses and forms a singularity in finite time below a critical temperature Tc. We investigate experimentally a quasi-two-dimensional cloud of cold neutral atoms in interaction with two pairs of perpendicular counterpropagating quasiresonant laser beams, in order to look for a signature of this ideal phase transition: indeed, the radiation pressure forces exerted by the laser beams can be viewed as an anisotropic, and nonpotential, generalization of two-dimensional self-gravity. We first show that our experiment operates in a parameter range which should be suitable to observe the collapse transition. However, the experiment unveils only a moderate compression instead of a phase transition between the two phases. A three-dimensional numerical simulation shows that both the finite small thickness of the cloud, which induces a competition between the effective gravity force and the repulsive force due to multiple scattering, and the atomic losses due to heating in the third dimension contribute to smearing the transition.
This thesis includes both experimental and theoretical investigations of fluctuation-induced transport phenomena, presented in a series of nine papers, by studies of the dynamics of cold atoms in dissipative optical lattices. With standard laser cooling techniques about 108 cesium atoms are accumulated, cooled to a few μK, and transferred into a dissipative optical lattice. An optical lattice is a periodic light-shift potential, and in dissipative optical lattice the light field is sufficiently close to resonance for incoherent light scattering to be of importance. This provides the system with a diffusive force, but also with a friction through laser cooling mechanisms. In the dissipative optical lattices the friction and the diffusive force will eventually reach a steady state. At steady state, the thermal energy is low enough, compared to the potential depth, for the atoms to be localized close to the potential minima, but high enough for the atoms to occasionally make inter-well flights. This leads to a Brownian motion of the atoms in the optical lattices. In the normal case these random walks average to zero, leading to a symmetric, isotropic diffusion of the atoms. If the optical lattices are tilted, the symmetry is broken and the diffusion will be biased. This leads to a fluctuation-induced drift of the atoms. In this thesis an investigation of such drifts, for an optical lattice tilted by the gravitational force, is presented. We show that even though the tilt over a potential period is small compared to the potential depth, it clearly affect the dynamics of the atoms, and despite the complex details of the system it can, to a good approximation, be described by the Langevin equation formalism for a particle in a periodic potential. The linear drifts give evidence of stop-and-go dynamics where the atoms escape the potential wells and travel over one or more wells before being recaptured. Brownian motors open the possibility of creating fluctuation-induced drifts in the absence of bias forces, if two requirements are fulfilled: the symmetry has to be broken and the system has to be brought out of thermal equilibrium. By utilizing two distinguishable optical lattices, with a relative spatial phase and unequal transfer rates between them, these requirements can be fulfilled. In this thesis, such a Brownian motor is realized, and drifts in arbitrary directions in 3D are demonstrated. We also demonstrate a real-time steering of the transport as well as drifts along pre-designed paths. Moreover, we present measurements and discussions of performance characteristics of the motor, and we show that the required asymmetry can be obtained in multiple ways.
In this thesis, both experimental studies and numerical simulations of ultracold atoms in optical potentials are presented in a collection of nine scientific papers. In particular, noise-induced transport in dissipative optical lattices and superfluid properties of Bose-Einstein condensates have been studied. Noise is usually regarded as a complication to most systems and as something that needs to be minimized. However, in a series of experiments at Umeå University, noise has been shown to play a key role for laser-cooled cesium atoms trapped in dissipative optical lattices. By using a combination of two dissipative optical lattices, where the relative spatial phase between them can be controlled, a so-called Brownian motor can be realized, where energy can be extracted from the inherent noise. In the experiment, this energy is used to control the transport of the laser-cooled atoms in real time and along pre-designed paths. This thesis also presents a way to characterize this system in terms of energy conversion efficiency and coherence of the transport, which may allow for a more straightforward comparison with other systems that rely on noise rectification. In the studies, it is also shown that the noise triggers a downward drift due to gravity, even though the optical potential should support the atoms. Further investigation of this might help to understand the underlying principles of laser cooling, as well as showing that the system might be suitable as a flexible test bed for statistical physics. In close relation to the experimental system, two numerical simulations are also presented, one in which different ways to induce asymmetries between two periodic potentials are investigated, and one in which a proposal for detecting quantum walks is explored. In the second part of the thesis, a work from the Joint Quantum Institute is presented, where a long-lived persistent current in a toroidal Bose-Einstein condensate, held in an all-optical trap, is created. The critical velocity of the superflow is measured in the presence of a tunable barrier. The system can be seen as a first realization of an elementary closed-loop atom circuit. Finally a theoretical study of the crossover between one- and two-dimensional systems is presented, in particular the transition between a two-dimensional superfluid to a one-dimensional Mott insulator is investigated.
We propose to use a cloud of laser-cooled atoms in a quasi-two-dimensional trap to investigate a nonequilibrium collapse phase transition in the presence of a gravitational-like interaction. Using theoretical arguments and numerical simulations, we show that, like in two-dimensional gravity, a transition to a collapsed state occurs below a critical temperature. In addition and as a signature of the nonequilibrium nature of the system, persistent particle currents, dramatically increasing close to the phase transition, are observed.
In this thesis, detailed experimental studies and numerical simulations are presented of laser cooling mechanisms in dissipative optical lattices and results of the first realized three dimensional Brownian motor in optical lattices. A dissipative optical lattice is a periodic light shift potential, created in the interference patterns of laser beams. In this, atoms can be both cooled and trapped, and the most important relaxation mechanism is generally considered to be “Sisyphus cooling”. However, careful experimental and theoretical investigations indicate the presence of other cooling processes as well. This is studied by varying different parameters such as irradiance and frequency of the lattice light. The time evolution of atoms in optical lattices show strong evidence of a bimodal velocity distribution, where a population transfer between one mode containing “hot” atoms and one mode containing “cold” atoms is evident. The normal diffusion of atoms in optical lattices is characterized by isotrop random fluctuations and exhibit the nature of Brownian motion. We have realized a technique where this motion is rectified and controlled. This is done in a three dimensional double optical lattice. This Brownian motor has control properties for both its speed and its direction in three dimensions. Our three dimensional double optical lattice is created by using laser light, exploiting two transitions, in the D2 line of cesium. Two three dimensional optical lattices are spatially overlapped; each optical lattice traps atoms in one of two hyperfine ground states. The controllability comes about by inducing phase shifts in the lattice laser beams, which displace the lattices relative to each other. This type of highly controlled Brownian motor is of fundamental interest since Brownian motion is present in almost all systems and for the role they play in protein motors and the function of living cells, and for the potential applications in nanotechnology. Brownian motors of this kind also open the way to possible studies of quantum Brownian motors and quantum resonances that are predicted for atomic ratchets. Optical lattices, and especially double optical lattices, have also been suggested as a platform for quantum state manipulations due to the good isolation from environment and ambient effects. Most of the work in this thesis is a first step towards the implementation of quantum manipulation schemes in a double optical lattice.
At temperatures near the absolut zero, a gas, here atomic sodium vapour, with high enough density cannot be described as tiny balls moving around as in classical physics. Since the temperature is low, the atoms are so slow that the matterwave of each atom starts to extend over the size of the atom and even over the interatomic distance. Therefore, they start to interfere like waves. Quantum mechanics start to dominate the physics in this regime. Further, depending on the sort of atoms (bosons or fermions) the atoms prefer to be in the same state or avoid to be in the same state. In the case of bosons as in the thesis, if the temperature is lowered to sub micro Kelvin temperature, a new state of matter appears after a phase transition - a macroscopic, standing wave, the Bose-Einstein condensate. This leads to a new phenomena: superfluidity - frictionless flow, second sound, vorticity and coherent scattering effects to name a few. The atoms are trapped in a elongated trap as in most of the experiments in ultra cold gasses. Usually experiments are done in a regime where the atoms seldomly collide with each other while travelling from one end to the other end of the cloud. In this experiment, however, the atoms collide many times with each other when they oscillate in the trap. This means that the cloud is hydrodynamic and leads to a very different behaviour. Two different sound waves (first and second sound), heat conduction, and collisional dominated transport can be observed in this case. The fact that the gas is weakly interacting allows comparison with current theory. At very low temperatures as in the experiments described in the thesis, the Bose character strongly alters the collisions of the atoms. The outcome of the collision does not only depend on the colliding atoms, but also on the atoms near by in phase space. The experiments outlined in this thesis cover some aspects of physics involved. Vortices have been created and observed in the Bose-Einstein condensate that rested in a weak trap. Both sound modes first and second sound have been observed with slight local heating. In the regime considered, first sound, that has not been observed in a dilute Bose-Einstein condensate before, is mainly a modulation in local temperature and not density. In another experiment a particular effect is observed when the cloud is only axially hydrodynamic. When the trap is suddenly axially relaxed, the cloud creats a strip pattern that is in the radial direction and moving outward. The analysis of this experiment suggests that this is only the case when the cloud is indeed only axially hydrodynamic. The last chapter describs a spin drag experiment. In this experiment two spin species of atoms are prepared and on one of them a force is applied. Through collisions, the other species is dragged along. This effect is Bose enhanced at temperatures approaching the transition temperature to a Bose-Einstein condensate which is observed and matches recent theory.