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QUANTUM TUNNELING OF BOSE-EINSTEIN CONDENSATES IN OPTICAL LATTICES

Fan Wen

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

Abstract In quantum tunneling a particle with energy E can pass through a high potential barrier V(E) due to the wave character of the particle. Bose\|Einstein condensates can display very strong tunneling depending on the structure of the trap, which may be a double\|well or optical lattices. We employed for the first time to our knowledge the periodic instanton method to investigate tunneling of Bose\|Einstein condensates in optical lattices. Our results show that there are two kinds of tunneling in this system, Landau\|Zener tunneling between extended states of the system and Wannier\|Stark tunneling between localized states of the system, and that the latter is 1000 times faster than the former. We also obtain the total decay rate for a wide range of temperature, including classical thermal activation, thermally assisted tunneling and quantum tunneling. Our results agree with experimental data in references[1, 2].Finally, we propose an experimental protocol to observe this new phenomenon in future experiments. periodic instanton, Wannier\|Stark localization, Landau\|Zener tunneling, Wannier\|Stark tunneling

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Abstract In quantum tunneling a particle with energy E can pass through a high potential barrier V(E) due to the wave character of the particle. Bose|Einstein condensates can display very strong tunneling depending on the structure of the trap, which may be a double|well or optical lattices. We employed for the first time to our knowledge the periodic instanton method to investigate tunneling of Bose|Einstein condensates in optical lattices. Our results show that there are two kinds of tunneling in this system, Landau|Zener tunneling between extended states of the system and Wannier|Stark tunneling between localized states of the system, and that the latter is 1000 times faster than the former. We also obtain the total decay rate for a wide range of temperature, including classical thermal activation, thermally assisted tunneling and quantum tunneling. Our results agree with experimental data in references[1, 2].Finally, we propose an experimental protocol to observe this new phenomenon in future experiments. periodic instanton, Wannier|Stark localization, Landau|Zener tunneling, Wannier|Stark tunneling
We investigate the quantum tunneling of Bose-Einstein condensates in optical lattices under gravity in the "Wannier-Stark localization" regime and "Landau-Zener tunneling" regime. Our results agree with experimental data [B. P. Anderson et al., Science 282, 1686 (1998); F. S. Cataliotti et al., Science 293, 843 (2001)]. We obtain the total decay rate which is valid over the entire range of temperatures, and show how it reduces to the appropriate results for the classical thermal activation at high temperatures, the thermally assisted tunneling at intermediate temperatures, and the pure quantum tunneling at low temperatures. We design an experimental protocol to observe this new phenomenon in further experiments.
We review our theoretical advances in quantum tunneling of Bose-Einstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectively, which are the crucial feature of the non-Abelian Josephson effect. When the optical lattices are under gravity, we investigate the quantum tunneling in the “Wannier-Stark localization” regime and “Landau-Zener tunneling” regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At intermediate temperatures, the results of the total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantum tunneling ultimately. And we study the alternating-current and direct-current (ac and dc) photonic Josephson effects in two weakly linked microcavities containing ultracold two-level atoms, which allows for direct observation of the effects. This enables new investigations of the effect of many-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantum tunneling of Bose-Einstein condensates.
We report experimental results on the properties of Bose-Einstein condensates in one-dimensional optical lattices. By accelerating the lattice, we observed Bloch oscillations of the condensate in the lowest band, as well as Landau-Zener (LZ) tunneling into higher bands when the lattice depth was reduced and/or the acceleration of the lattice was increased. The dependence of the LZ tunneling rate on the condensate density was then related to mean-field effects modifying the effective potential acting on the condensate, yielding good agreement with recent theoretical work. We also present several methods for measuring the lattice depth and discuss the effects of the micromotion in the time-orbiting-potential trap on our experimental results.
With considering Bose-Einstein condensates to be confined in a periodic dichromatic optical lattice, Bloch energy band structure and Landau-Zener tunneling behaviors of the first and second band gaps are studied in this paper. It is shown that when the relative phase between the two lattices increases from 0 to π, the width of the first band gap in the Bloch energy band increases, while the width of the second band gap decreases. Meanwhile, it is found that the depth and the relative phase between the two lattices have both an important effect on Landau-Zener tunneling properties.