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arXiv:1111.6520 · Physical Review A

Two-dimensional rocking ratchet for cold atoms

V. Lebedev, Ferruccio Renzoni

Published Aug 27, 2009• 22 citations
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Abstract

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, Y. Zolotaryuk, S. Flach, and O. Yevtushenko, 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 biharmonic forces in perpendicular directions, we demonstrate the possibility of generating a current in an arbitrary direction within the optical lattice plane.

DOI
10.1103/physreva.80.023422

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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, Y. Zolotaryuk, S. Flach, and O. Yevtushenko, 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 biharmonic forces in perpendicular directions, we demonstrate the possibility of generating a current in an arbitrary direction within the optical lattice plane.
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.
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.
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 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 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.