This thesis reports the theoretical study of several cold atom ratchet systems. In particular the focus of the work is the determination of the ratchet current as a function of the ratchet parameters through analysis of the system symmetries and through numerical simulation. Ratchets are devices that exhibit directed motion in the absence of net forces. It is necessary to drive them away from thermal equilibrium so as to not violate the second law of thermodynamics. Currents are generated when the symmetries of the ratchet do not forbid it, a consequence of Curie's principle. An analysis of the symmetries will help determine for what parameters currents will be generated we perform such analyses in our investigations. The ratchets studied are modelled on the experimentally realised implementation of cold atoms in a driven optical lattice. Through the parameters of the driving and the optical lattice itself, we control the breaking of the symmetries and thus the generation of atomic currents. The precise relationship between current and ratchet parameters is explored by numerical simulation. In experiments the driving is achieved through a phase-modulation of the optical lattice beams. In numerical simulations we include the driving force directly in the equations of motion. We verify theoretically and numerically that the two approaches are equivalent. We have modelled the dynamics of atoms in light-fields through semiclassical and quantum treatments. The semiclassical treatment results in stochastic differential equations for the external degrees of freedom. These are simulated using the Monte-Carlo technique. For the fully quantum treatment we apply a stochastic trajectory method to simulate the master equation. We perform a comparison between different treatments for an over-damped ratchet.
This thesis reports the theoretical study of several cold atom ratchet systems. In particular the focus of the work is the determination of the ratchet current as a function of the ratchet parameters through analysis of the system symmetries and through numerical simulation. Ratchets are devices that exhibit directed motion in the absence of net forces. It is necessary to drive them away from thermal equilibrium so as to not violate the second law of thermodynamics. Currents are generated when the symmetries of the ratchet do not forbid it, a consequence of Curie's principle. An analysis of the symmetries will help determine for what parameters currents will be generated we perform such analyses in our investigations. The ratchets studied are modelled on the experimentally realised implementation of cold atoms in a driven optical lattice. Through the parameters of the driving and the optical lattice itself, we control the breaking of the symmetries and thus the generation of atomic currents. The precise relationship between current and ratchet parameters is explored by numerical simulation. In experiments the driving is achieved through a phase-modulation of the optical lattice beams. In numerical simulations we include the driving force directly in the equations of motion. We verify theoretically and numerically that the two approaches are equivalent. We have modelled the dynamics of atoms in light-fields through semiclassical and quantum treatments. The semiclassical treatment results in stochastic differential equations for the external degrees of freedom. These are simulated using the Monte-Carlo technique. For the fully quantum treatment we apply a stochastic trajectory method to simulate the master equation. We perform a comparison between different treatments for an over-damped ratchet.
This thesis describes the development and presents the results of a series of experiments on the ratchet effect with laser-cooled caesium atoms in a twodimensional dissipative optical lattice. The ratchet effect describes the directed motion of atoms that are undergoing an unbiased (time-average equal to zero) driving force, which can be realised experimentally using cold atoms in a driven optical lattice. The thesis describes the experimental set-up and methods used to cool and trap atoms in a two-dimensional optical lattice using well-known laser-cooling techniques, as well as the computer software used to control the experiment. It then goes on to present the results of ratchet experiments with cold atoms in the two-dimensional driven optical lattice. Using specific forms of the driving force – namely the biharmonic and splitbiharmonic driving – the atoms undergo directed transport even though the driving forces time-average to zero, corresponding to a manifestation of the ratchet effect. The ratchet transport of the atoms is characterised for various parameters of the driving force. The transport for quasiperiodic driving forces is considered by examining the velocity resonance as a function of relative frequency, and it is shown that the finite duration of the driving becomes a relevant parameter for determining the transport behaviour. An analysis of the structure of the velocity resonance is provided. The results of this work establish that quasiperiodic behaviour can only be guaranteed for long driving times and for those irrational numbers that have poor rational approximations. The final chapter presents the work performed at the National Physical Laboratory on the rubidium atomic fountain in order to measure the rubidium-87 ground-state hyperfine splitting frequency. This work led to a publication [57] and subsequent redefinition [7] of the official value based on those measurements.
This thesis describes three experiments with cold rubidium atoms. The first experiment implements a rocking ratchet with cold atoms in driven dissipative optical lattices, and explores a fundamental feature of ratchets: current reversals. It precisely investigates current reversals as observed by varying the driving frequency. It is found that this kind of current reversal in the frequency domain is determined by dissipation-induced symmetry breaking. The second experiment explores vibrational mechanics for a system of cold atoms in an optical lattice. A high frequency strong driving field was applied in order to renormalise the optical potential. It was observed that the amplitude of the potential is indeed renormalised and can be controlled by the high frequency driving field. This is detected by two methods: via the study of the diffusion properties and via the observation of the directed transport. The final experiment is the realisation and characterisation of a Bose-Einstein condensate of rubidium atoms.
Ratchets are devices that operate away from thermal equilibrium and can rectify zero-mean perturbations to achieve directed transport. We implement a ratchet system by using cold atoms in a driven optical lattice. This ratchet system can be precisely controlled experimentally, by adjusting either the driving parameters or the characteristics of the optical lattice. Directed transport in our ratchet is caused by rectification of either the driving force or fluctuations. We demonstrate under which conditions these types of rectification occur. Rectification of the driving force is a deterministic process, while rectification of fluctuations implies that the atoms act as Brownian motors. We show that resonant activation is the underlying mechanism of operation of these Brownian motors. The ratchet transport is controlled by symmetries of the system. The temporal symmetry of the system is normally broken by a time- asymmetric driving force. Here we show that for a system with symmetric driving and a symmetric potential, directed transport can also be caused by dissipation-induced breaking of time-reversal symmetry. This happens in the limit of small driving amplitude and large dissipation. We also study quasiperiodic driving of a cold atom ratchet and examine the relationship between symmetries and transport in this case. When mapping the route to quasiperiodicity we find a characteristic peak spectrum with transport occurring for certain ratios of frequencies. We characterize these peaks spectroscopically, and conclude that their shape is determined by the duration of driving. Finally, we investigate the coherency of transport with quasiperiodic driving and find large coherencies for certain driving parameters.
Brownian motors, or ratchets, are devices which "rectify" Brownian motion, i.e. they can generate a current of particles out of unbiased fluctuations. The ratchet effect is a very general phenomenon which applies to a wide range of physical systems, and indeed ratchets have been realized with a variety of solid state devices, with optical trap setups as well as with synthetic molecules and granular gases. The present article reviews recent experimental realizations of ac driven ratchets with cold atoms in driven optical lattices. This is quite an unusual system for a Brownian motor as there is no a real thermal bath, and both the periodic potential for the atoms and the fluctuations are determined by laser fields. Such a system allowed us to realize experimentally rocking and gating ratchets, and to precisely investigate the relationship between symmetry and transport in these ratchets, both for the case of periodic and quasiperiodic driving.
The central theme of this thesis is the directed transport of cold atoms in optical lattices. Several methods for producing such an outcome are proposed, experimentally realised and characterised, in both dissipative and non-dissipative regimes. Accordingly, this thesis may be thought to be composed of two parts. The first section reports results of directed transport in non-dissipative optical lattices, where we used the atom optics realisation of the delta-kicked rotor (DKR) as a model system. Initial experiments performed on this system showed evidence of dynamical localisation, the signature of quantum chaos, and we exploited the presence of the momentum boundary (a barrier to diffusion arising from the approximation of delta-kicks with finite width impulses) to produce asymmetric momentum diffusion. Breaking the DKR system symmetries produced directed diffusion due to chaotic dynamics alone. We observed directed transport in a spatially symmetric system whenever temporal symmetry was broken, and also when the spatial and temporal symmetry of the DKR were simultaneously broken. We also report the first experimental evidence for a 'double-DKR', where experiments performed using a kick sequence composed of closely spaced pairs of kicks instead of single kicks caused significant alterations in the observed behaviour of the kicked rotor system. The origin of this new behaviour was explained in the framework of kick-to-kick correlations and our results were found to be in excellent agreement with numerical simulations. The second part of this thesis describes the realisation of a Brownian ratchet in a 3D dissipative lattice, where fluctuations between different potential surfaces acted as the source of noise. These fluctuations were rectified by the application of a periodic, bi-harmonic driving force, which broke the temporal symmetry of the system. Both current reversal and stochastic resonance behaviour characteristic of a Brownian ratchet were observed.
Cold atoms in optical lattices are an ideal test bed to explore ratchet physics. This is largely due to the extreme tunability of optical lattice systems, which allows one to precisely control the shape of the potential and of any applied force, as well as to vary at will the level of dissipation. Since the very first demonstration of directed motion in a cold atom system by Mennerat-Robilliard et al. (1999), a number of experimental investigations with cold atoms in optical lattices have explored different aspects of the physics of ratchets. Here, the focus is first on the experiments in the classical regime which explored the relationship between symmetry and transport in a.c. driven ratchets. Experiments in the full quantum Hamiltonian regime are then described, and the unique features of such a regime highlighted. Ratchets in dissipative optical lattices Dissipative optical lattices Optical lattices are periodic potentials for atoms created by the interference of two or more laser fields.The detuning between the laser fields and the nearest atomic transition will emerge as a key parameter to describe the light–atom interaction. It is thus important to distinguish two very different situations: the case of fardetuned laser fields, and the case of near-resonant laser fields. For far-detuned laser fields, a purely conservative potential is produced. As will be discussed in the following sections, far-detuned optical lattices are ideal to model Hamiltonian systems. In the case of near-resonant laser fields, the interaction between the laser and the atoms may lead, under appropriate conditions, to dissipative dynamics. That is, for an appropriately arranged set of near-resonant optical lattices, a dissipative optical lattice, is produced, where the set of laser fields produce at once the periodic potential acting on the atoms and the cooling mechanism, which decreases their kinetic energy and lead to the trapping of the atoms at the bottom of potential wells. The principles behind the cooling mechanism, termed Sisyphus cooling for reasons which will become apparent in the following discussion, can be captured by considering the minimal configuration of a one-dimensional optical lattice and a J g = 1 / 2 → J e = 3 / 2 atomic transition. This is the simplest configuration in which Sisyphus cooling takes place.