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Physical Review Letters

Tunneling Resonances and Coherence in an Optical Lattice

Boon-Keng Kevin Teo, Jeffrey R. Guest, Georg A. Raithel

Published Apr 10, 2002• 8 citations
Publisher

Abstract

The center-of-mass quantization of atoms trapped in a gray optical lattice is observed to manifest itself in the steady-state properties of the atoms. Modulations in the lifetime and macroscopic magnetization as a function of an applied B field are attributed to quantum mechanical tunneling resonances and are shown to exist only under conditions which afford spatial coherence of the trapped atoms over several lattice wells and coherence times that exceed the tunneling period.

DOI
10.1103/physrevlett.88.173001

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The center-of-mass quantization of atoms trapped in a gray optical lattice is observed to manifest itself in the steady-state properties of the atoms. Modulations in the lifetime and macroscopic magnetization as a function of an applied B field are attributed to quantum mechanical tunneling resonances and are shown to exist only under conditions which afford spatial coherence of the trapped atoms over several lattice wells and coherence times that exceed the tunneling period.
The magnetization and lifetimes of atoms in gray optical lattices exhibit modulations as functions of an applied B field that are attributed to tunneling resonances between neighboring lattice wells. Expanding on previous observations, we show how these modulations depend on well depth, and we derive spin temperatures for the system. A band-structure-based model and quantum Monte Carlo wave-function simulations are used to explain these results. We predict subrecoil structures in the velocity distributions; these structures undergo systematic variations when the applied magnetic field is varied. Dramatically different behaviors for bosonic and fermionic spin systems are found and explained.
Summary form only given. The AC-Stark shift of a set of interfering laser beams together with the Zeeman interaction with external magnetic fields provide flexible mechanisms for coherently controlling atomic wave packets. When detuned far from atomic resonance, these optical lattices can trap cold atoms with minimal dissipation and thus provide an ideal environment for observing quantum coherent phenomena. We consider a one dimensional lattice of double wells produced by counterpropagating linearly polarized laser beams and a static magnetic field transverse to the laser wave vectors.
This dissertation reports on the experimental study of coherent wavepacket dynamics of cesium atoms in the double-well potentials of a one-dimensional, far-off-resonance optical lattice. An optical lattice is the periodic potential produced by the light shift interaction of an atom with the light field of interfering laser beams. With the proper choice of laser parameters and external magnetic fields, an array of double-well potentials is created. Using the techniques of laser cooling, atoms are trapped in the lattice and are prepared in a pure state through a combination of enhanced laser cooling in a near-resonance lattice and state selection in an accelerated far-off-resonance lattice. The atoms are prepared on one side of the double-well potential, and the atomic wavepackets will then oscillate between the left and right localized states of the double-well potential. Entanglement between the internal and external degrees of freedom makes it possible to follow the center-of-mass motion of the atoms by measuring the ground state magnetic populations via Stern-Gerlach analysis. The coherent dynamics of these wavepackets was studied under various combinations of lattice parameters such as lattice depth, applied transverse and longitudinal magnetic fields. There is excellent agreement between the experimentally measured oscillation frequencies and those predicted from a numerical analysis of the bandstructure of the lattice. For certain lattice parameters the total energy of the atom is below the potential barrier and the coherent motion corresponds to tunneling through a classically forbidden barrier. At specific times during the oscillation the atomic wavepacket corresponds to a coherent superposition of the mesoscopically distinct left and right localized states.
Summary form only given. It has been predicted that topological potentials play a significant role in gray optical lattices. However, so far there has been no direct experimental demonstration of their existence. Unlike light-shift potentials, which, in the case of low saturation, scale as the laser intensity, topological (or gauge) potentials are intensity independent and solely depend on the topology of the lattice, which is determined by the detuning, beam geometry and magnetic fields. In our experiment, /sup 87/Rb atoms are collected in a standard magneto-optic trap and loaded into a 1D optical lattice. The lattice is formed by counterpropagating, orthogonally polarized laser beams. The minima of the trapping potential form at the antinodes of the standing waves and, as a result of optical pumping, the wells are alternately occupied. When an atom tunnels from one type of well to another, it must then flip its magnetic spin state. The gauge potential is associated with the energy needed for this change. In this gray lattice, the potential wells are shallow due to the weak interaction with the light field. Shallow potentials are necessary for tunneling. We use two schemes to observe tunneling. In the first, we use an auxiliary weak laser pulse to selectively depopulate one of the two types of wells. We observe tunneling by measuring the population in each type of well as a function of time. The second way we study tunneling is to create atomic wave-packets within the wells and to observe their motion as they oscillate. The wave-packets are created by diabatically displacing the trapped atoms in either position or momentum space. Tunneling occurs when the wave-packets run against barriers provided by the maxima of the trapping potential.