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Physical Review A

Quantum transport of atoms in an optical lattice

Paul M. Visser, Gerard Nienhuis

Published Nov 1, 1997• 15 citations
Publisher

Abstract

Quantum-mechanical transport of atoms in an optical lattice in one dimension is described in an exactly solvable model. The atoms are tightly bound and they are sufficiently cooled so that they are restricted only to the lowest Bloch band in a single adiabatic potential. The coherent spreading of an atomic wave packet by tunneling is counteracted by the localizing effect of photon emission that accompanies optical pumping. The time evolution of the quasimomentum distribution, the coherence length, and the spatial width of the atomic state are evaluated analytically. These quantities depend strongly on the statistics of photon emissions.

DOI
10.1103/physreva.56.3950

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Quantum-mechanical transport of atoms in an optical lattice in one dimension is described in an exactly solvable model. The atoms are tightly bound and they are sufficiently cooled so that they are restricted only to the lowest Bloch band in a single adiabatic potential. The coherent spreading of an atomic wave packet by tunneling is counteracted by the localizing effect of photon emission that accompanies optical pumping. The time evolution of the quasimomentum distribution, the coherence length, and the spatial width of the atomic state are evaluated analytically. These quantities depend strongly on the statistics of photon emissions.
The quantum-mechanical transport properties of cold atoms in an optical lattice are described in terms of an analytically tractable model. The atoms are cooled down to the lowest energy band in the periodic optical potential, in the tight- binding limit. The transport mechanisms are coherent tunneling through potential barriers, and momentum recoil at optical pumping. Expressions are obtained for the time-dependent population distributions over the energy eigenstates and over localized states. These expressions are modified in the presence of a dark atomic state, that is uncoupled to the field.
Optical lattices are formed when cold atoms get trapped in the periodic array of optical potential wells created by a number of traveling light waves. Exact periodicity is guaranteed when the number of traveling waves exceeds the number of dimensions by no more than one. We present a few simple exactly solvable models for the transport of atoms over a lattice in the tight-binding limit. One model concerns the spreading of an atom by tunneling through the barriers and by momentum recoil induced by optical pumping. Another model gives results for the amplitude of Bloch oscillations, which occur when a uniform is added to the periodic potential. Finally the dissipative spreading of the quasimomentum due to optical pumping is modeled.
We have performed experiments using a three-dimensional Bose-Einstein condensate of sodium atoms in a one-dimensional optical lattice to explore some unusual properties of band structure. In particular, we investigate the loading of a condensate into a moving lattice and find nonintuitive behavior. We also revisit the behavior of atoms, prepared in a single quasimomentum state, in an accelerating lattice. We generalize this study to a cloud whose atoms have a large quasimomentum spread, and show that the cloud behaves differently from atoms in a single Bloch state. Finally, we compare our findings with recent experiments performed with fermions in an optical lattice.
Recent work in atom optics has led to enormous progress in the study of quantum chaos and has addressed a broad range of problems in quantum transport, traditionally studied in the context of condensed matter physics. This issue brings together the various researchers working in the border domain between atom optics and solid state physics and focuses on atomic motion in light fields in a regime that is dominated by quantum effects. The topics discussed in this issue include: • quantum effects of atomic motion in light fields; • quantum chaos in time dependent lattices; • tunnelling in stationary or time-dependent lattices; • Wannier-Stark ladder and Bloch oscillations; • atomic band structures; • many-body effects on transport in optical lattices; • effects of decoherence on quantum transport; • weak and dynamical localization. At this point we take the opportunity to express our gratitude to the authors of the papers of this issue and the reviewers for their efforts in preparing and ensuring the high quality of the state of the art presentation.
We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After first preparing localized atomic wave functions in an optical lattice through a Mott insulating phase, we place each atom in a superposition of two internal spin states. Then state selective optical potentials are used to split the wave function of a single atom and transport the corresponding wave packets in two opposite directions. Coherence between the wave packets of an atom delocalized over up to seven lattice sites is demonstrated.
Atomic quantum systems such as atomic clocks or qubits with cold atoms in tweezer arrays have attracted enormous interests both in academia and industry. In this work, we report a theoretical study and experimental demonstration of quantum tunneling of atoms in 1D optical lattices with decoherence. In such decoherence process, the expansion of atomic wave packet is suppressed and resonance spectrum is broadened. In this regime, as the decoherence rate L or the modulation time t increases, the evolution of atomic wave packets transitions from coherent tunneling to classical diffusion. We propose a detection method to fast evaluate the degree of decoherence in such systems. Our work benefits the study of decoherence properties of precision measurements based on optical lattice.