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arXiv:1112.0851

Driven Ratchets for Cold Atoms

Ferruccio Renzoni

Published Dec 5, 2011• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1112.0851

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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.
Brownian motors are devices which "rectify" Brownian motion, i.e. they can generate a current of particles out of unbiased fluctuations. Brownian motors are important for the understanding of molecular motors, and are also promising for the realization of new nanolelectronic devices. Among the different systems that can be used to study Brownian motors, cold atoms in optical lattices are quite an unusual one: there is no thermal bath and both the potential and the fluctuations are determined by laser fields. In this Lecture notes recent experimental implementations of Brownian motors using cold atoms in optical lattices are reviewed.
Brownian motors are devices which "rectify" Brownian motion, i.e. they can generate a current of particles out of unbiased fluctuations. Brownian motors are important for the understanding of molecular motors, and are also promising for the realization of new nanolelectronic devices. Among the different systems that can be used to study Brownian motors, cold atoms in optical lattices are quite an unusual one: there is no thermal bath and both the potential and the fluctuations are determined by laser fields. In this Lecture notes recent experimental implementations of Brownian motors using cold atoms in optical lattices are reviewed.
Brownian motors are devices which ‘rectify’ Brownian motion, i.e. they can generate a current of particles out of unbiased fluctuations. Brownian motors are important for the understanding of molecular motors, and are also promising for the realization of new nano-electronic devices. Among the different systems that can be used to study Brownian motors, cold atoms in optical lattices are quite an unusual one: there is no thermal bath and both the potential and the fluctuations are determined by laser fields. In this article recent experimental implementations of Brownian motors using cold atoms in optical lattices are reviewed.
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.
Cold atoms in optical lattices have emerged as an ideal system to investigate the ratchet effect, as demonstrated by several recent experiments. In this work we analyze theoretically two aspects of ac-driven transport in cold-atom ratchets. We first address the issue of whether, and to what extent, an ac-driven ratchet for cold atoms can operate as a motor. We thus study theoretically a dissipative motor for cold atoms, as obtained by adding a load to a 1D nonadiabatically driven rocking ratchet. We demonstrate that a current can be generated also in the presence of a load, e.g., the ratchet device can operate as a motor. Correspondingly, we determine the stall force for the motor, which characterizes the range of loads over which the device can operate as a motor, and the differential mobility, which characterizes the response to a change in the magnitude of the load. Second, we compare our results for the transport in an ac-driven ratchet device with the transport in a dc-driven system. We observe a peculiar phenomenon: the double-harmonic ac force stabilizes the dynamics, allowing the generation of uniform directed motion over a range of momentum much larger than what is possible with a dc bias. We explain such a stabilization of the dynamics by observing that a nonadiabatic ac drive broadens the effective cooling momentum range and forces the atom trajectories to cover such a region. Thus the system can dissipate energy and maintain a steady-state energy balance. Our results show that in the case of a finite-range velocity-dependent friction, a ratchet device may offer the possibility of controlling the particle motion over a broader range of momentum with respect to a purely biased system, although this is at the cost of a reduced coherency.
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.