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Quantum Electronics and Laser Science Conference

Feedback control of atomic motion in optical lattices

Natalya V. Morrow, S.K. Dutta, Georg A. Raithel

Published Nov 13, 2002• 1 citation
Publisher

Abstract

Summary form only given. Atoms in an optical lattice, though very slow, perform a slight random motion that reflects the non-zero temperature of the trapped atoms. We are proposing a way of reducing such random motion using real-time feedback. The method is related to the stochastic cooling used to transversely cool particle beams. Another stochastic cooling method for laser-cooled atoms has been proposed in "Stochastic cooling of atoms using lasers," see Phys. Rev. A, vol. 58, p. 4757 (1998). Our scheme involves a measurement of the coherent redistribution of photons between different laser beams of the optical lattice.

DOI
10.1109/qels.2001.961933

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Summary form only given. Atoms in an optical lattice, though very slow, perform a slight random motion that reflects the non-zero temperature of the trapped atoms. We are proposing a way of reducing such random motion using real-time feedback. The method is related to the stochastic cooling used to transversely cool particle beams. Another stochastic cooling method for laser-cooled atoms has been proposed in "Stochastic cooling of atoms using lasers," see Phys. Rev. A, vol. 58, p. 4757 (1998). Our scheme involves a measurement of the coherent redistribution of photons between different laser beams of the optical lattice.
Optical lattices are periodic arrangements of laser cooled atoms trapped in potentials created by the interference of multiple laser beams. In this dissertation, we describe a series of experiments performed using optical lattices that exploit the coherence of atoms and we also look at new ways to cool the atoms. With a sudden shift of the optical lattice, atomic wavepackets can be created that evolve much like a classical particle. Using a photon redistribution technique, we have characterized the oscillation of wavepackets in the anharmonic potential wells. Atoms will quantum mechanically tunnel between lattice sites with a sufficiently shallow potential. Due to the structure of the optical lattices that are used, while the atom is tunneling, its internal angular momentum state must change. We use this change to detect and characterize the tunneling. The change in internal state leads to the formation of a new potential that acts on the atom, which is known as a gauge potential, which does not depend on the light intensity, but depends only on the geometry of the lattice. We have for the first time measured and characterized this gauge potential. Finally, by randomly modulating the lattice potential, we have demonstrated that tunneling can be suppressed. We have shown that an enhancement of the Sisyphus cooling process, which localizes atoms in the wells of an optical lattice, is possible using a bichromatic standing wave. A time of flight technique is used to verify the cooling improvement. We combine the techniques developed in these experiments and apply them to the cooling of the trapped atoms using a feedback mechanism, which is analogous to the well known technique of stochastic cooling in the field of beam physics. Lastly, we have laid the theoretical basis for using the ponderomotive force to create optical lattices for laser cooled Rydberg atoms. Rydberg atoms are attractive because of their many extreme properties, and the ability to trap Rydberg atoms into lattice sites will increase the range of experiments and measurements that can be made with them.
We consider the problem of controlling the motion of an atom trapped in an optical cavity using continuous feedback. In order to realize such a scheme experimentally, one must be able to perform state estimation of the atomic motion in real time. While in theory this estimate may be provided by a stochastic master equation describing the full dynamics of the observed system, integrating this equation in real time is impractical. Here we derive an approximate estimation equation for this purpose, and use it as a drive in a feedback algorithm designed to cool the motion of the atom. We examine the effectiveness of such a procedure using full simulations of the cavity QED system, including the quantized motion of the atom in one dimension.
In this thesis, detailed experimental studies and numerical simulations are presented of laser cooling mechanisms in dissipative optical lattices and results of the first realized three dimensional Brownian motor in optical lattices. A dissipative optical lattice is a periodic light shift potential, created in the interference patterns of laser beams. In this, atoms can be both cooled and trapped, and the most important relaxation mechanism is generally considered to be “Sisyphus cooling”. However, careful experimental and theoretical investigations indicate the presence of other cooling processes as well. This is studied by varying different parameters such as irradiance and frequency of the lattice light. The time evolution of atoms in optical lattices show strong evidence of a bimodal velocity distribution, where a population transfer between one mode containing “hot” atoms and one mode containing “cold” atoms is evident. The normal diffusion of atoms in optical lattices is characterized by isotrop random fluctuations and exhibit the nature of Brownian motion. We have realized a technique where this motion is rectified and controlled. This is done in a three dimensional double optical lattice. This Brownian motor has control properties for both its speed and its direction in three dimensions. Our three dimensional double optical lattice is created by using laser light, exploiting two transitions, in the D2 line of cesium. Two three dimensional optical lattices are spatially overlapped; each optical lattice traps atoms in one of two hyperfine ground states. The controllability comes about by inducing phase shifts in the lattice laser beams, which displace the lattices relative to each other. This type of highly controlled Brownian motor is of fundamental interest since Brownian motion is present in almost all systems and for the role they play in protein motors and the function of living cells, and for the potential applications in nanotechnology. Brownian motors of this kind also open the way to possible studies of quantum Brownian motors and quantum resonances that are predicted for atomic ratchets. Optical lattices, and especially double optical lattices, have also been suggested as a platform for quantum state manipulations due to the good isolation from environment and ambient effects. Most of the work in this thesis is a first step towards the implementation of quantum manipulation schemes in a double optical lattice.
We propose two schemes for cooling bosonic and fermionic atoms that are trapped in a deep optical lattice. The first scheme is a quantum algorithm based on particle number filtering and state dependent lattice shifts. The second protocol alternates filtering with a redistribution of particles by means of quantum tunnelling. We provide a complete theoretical analysis of both schemes and characterize the cooling efficiency in terms of the entropy. Our schemes do not require addressing of single lattice sites and use a novel method, which is based on coherent laser control, to perform very fast filtering.
We propose a method to laser-cool atoms based on stochastic cooling, first developed at CERN to cool antiprotons. Fluctuations in the momentum distribution will be detected in a pump-probe configuration with far-detuned lasers, and the appropriate correction kick will be accomplished with optical dipole potentials. Each stage of an iterative cooling process will involve measurement and feedback, with phase space remixing in between. We discuss possible applications of this method to magnetically trapped atoms and molecules.