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arXiv:cond-mat/0605695 · Physical Review A

Chaotic ratchet dynamics with cold atoms in a pair of pulsed optical lattices

Gabriel G. Carlo, Giuliano Benenti, Giulio Casati, Sandro Wimberger, O. Morsch, R. Mannella, E. Arimondo

Published Sep 22, 2006• 41 citations
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Abstract

We present a very simple model for realizing directed transport with cold atoms in a pair of periodically flashed optical lattices. The origin of this ratchet effect is explained and its robustness demonstrated under imperfections typical of cold atom experiments. We conclude that our model offers a clear-cut way to implement directed transport in an atom optical experiment.

DOI
10.1103/physreva.74.033617

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We present a very simple model for realizing directed transport with cold atoms in a pair of periodically flashed optical lattices. The origin of this ratchet effect is explained and its robustness demonstrated under imperfections typical of cold atom experiments. We conclude that our model offers a clear-cut way to implement directed transport in an atom optical experiment.
We investigate a new type of quantum ratchet which may be realized by cold atoms in a double-well optical lattice, pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate D is asymmetric in momentum up to a finite time t(r). The quantum behavior produces a corresponding asymmetry in the momentum distribution which is "frozen-in" by dynamical localization provided the break time t(*)>or=t(r). We conclude that the cold atom ratchets require Db/ variant Planck's over 2pi approximately 1, where b is a small deviation from period-one pulses.
We investigate a new type of quantum ratchet which may be realised by cold atoms in a double-well optical lattice which is pulsed with unequal periods. The classical dynamics is chaotic and we find the classical diffusion rate DDD is asymmetric in momentum up to a finite time trt_rtr​. The quantum behaviour produces a corresponding asymmetry in the momentum distribution which is 'frozen-in' by Dynamical Localisation provided the break-time t∗>trt^* > t_rt∗>tr​. We conclude that the cold atom ratchets require Db/ℏ∼1Db/ \hbar \sim 1Db/ℏ∼1 where b is a small deviation from period-one pulses.
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.
Using the method of quantum trajectories, we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for the implementation of the quantum ratchet effect with cold atoms in optical lattices.
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.