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arXiv:physics/0203056

Cold atoms in optical lattices :a Hamiltonian ratchet

T. S. Monteiro, Paul A. Dando, N. A. C. Hutchings, M. R. Isherwood

Published Mar 19, 2002• 0 citations
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Abstract

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 $D$ is asymmetric in momentum up to a finite time $t_r$. The quantum behaviour produces a corresponding asymmetry in the momentum distribution which is 'frozen-in' by Dynamical Localisation provided the break-time $t^* > t_r$. We conclude that the cold atom ratchets require $Db/ \hbar \sim 1$ where b is a small deviation from period-one pulses.

DOI
10.48550/arxiv.physics/0203056

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•Jan 1, 2005•0 citations
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.
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.
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.
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.
We use an atomic ratchet realized by applying short pulses of an optical standing-wave to a Bose–Einstein condensate to study the crossover between classical and quantum dynamics. The signature of the ratchet is the existence of a directed current of atoms, even though there is an absence of a net bias force. Provided that the pulse period is close to one of the resonances of the system, the ratchet behavior can be understood using a classical like theory which depends on a single variable containing many of the experimental parameters. Here we show that this theory is valid in both the true classical limit, when the pulse period is close to zero, as well as regimes when this period is close to other resonances where the usual scaled Planck's constant is nonzero. By smoothly changing the pulse period between these resonances we demonstrate how it is possible to tune the ratchet between quantum and classical types of behavior.
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.