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arXiv:1201.6286 · Physical Review A

Wave-function-renormalization effects in resonantly enhanced tunneling

Niels Lörch, Francesco Vincenzo Pepe, Hans Lignier, D. Ciampini, R. Mannella, O. Morsch, E. Arimondo, Paolo Facchi A, Giuseppe Florio, Saverio Pascazio, Sandro Wimberger

Published May 3, 2012• 13 citations
arXivHTMLPDF

Abstract

We study the time evolution of ultracold atoms in an accelerated optical lattice. For a Bose-Einstein condensate with a narrow quasimomentum distribution in a shallow optical lattice the decay of the survival probability in the ground band has a steplike structure. In this regime we establish a connection between the wave-function-renormalization parameter $Z$ introduced by P. Facchi, H. Nakazato, and S. Pascazio [Phys. Rev. Lett. 86, 2699 (2001)] to characterize nonexponential decay and the phenomenon of resonantly enhanced tunneling, where the decay rate is peaked for particular values of the lattice depth and the accelerating force.

DOI
10.1103/physreva.85.053602

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We study the time evolution of ultracold atoms in an accelerated optical lattice. For a Bose-Einstein condensate with a narrow quasimomentum distribution in a shallow optical lattice the decay of the survival probability in the ground band has a steplike structure. In this regime we establish a connection between the wave-function-renormalization parameter ZZZ introduced by P. Facchi, H. Nakazato, and S. Pascazio [Phys. Rev. Lett. 86, 2699 (2001)] to characterize nonexponential decay and the phenomenon of resonantly enhanced tunneling, where the decay rate is peaked for particular values of the lattice depth and the accelerating force.
We study the time evolution of a Bose-Einstein condensate in an accelerated optical lattice. When the condensate has a narrow quasimomentum distribution and the optical lattice is shallow, the survival probability in the ground band exhibits a steplike structure. In this regime we establish a connection between the wave-function renormalization parameter ZZZ and the phenomenon of resonantly enhanced tunneling.
Summary form only given.We report the observation of short-time deviation from exponential decay in a quantum tunneling experiment. Our system consists of ultracold sodium atoms that are trapped in an accelerating periodic optical potential created by a standing wave of light. Atoms can escape the wells via quantum tunneling, and the number that remain is measured as a function of interaction time for a fixed value of the well depth and acceleration. To study tunneling in this system, sodium atoms are first trapped and cooled in a magneto-optical trap. The trapping beams as well as the magnetic field gradient are then turned off, and an accelerating far-detuned standing wave of light is turned on. A three-step acceleration is implemented to measure the loss due to tunneling. Once the final velocity is reached, the potential is turned off and the atomic fluorescence is imaged after a free drift time. We have measured the survival probability and found that the initial survival probability is flat and then crosses over to an exponential decay. The intermediate stage is characterized by a time-dependent loss rate. To analyze the short-time tunneling probability and the approach to exponential decay, we use a simple model of the band structure with a single (trapped) band separated by a bandgap from a free particle state. We find an analytic expression for the survival probability that is quadratic for the first few microseconds of evolution, with a crossover to exponential decay at long times. We show that this crossover time is related to the tunneling time. We also identify a new parameter regime where coherent oscillations of the survival probability are seen.
We study the tunneling decay of a Bose-Einstein condensate from tilted optical lattices within the mean-field approximation. We introduce a method to calculate ground and excited resonance eigenstates of the Gross-Pitaevskii equation, based on a grid relaxation procedure with complex absorbing potentials. This algorithm works efficiently in a wide range of parameters where established methods fail. It allows us to study the effects of the nonlinearity in detail in the regime of resonant tunneling, where the decay rate is enhanced by resonant coupling to excited unstable states.
We study the formation and collision-aided decay of an ultracold atomic Bose-Einstein condensate in the first excited band of a double-well two-dimensional optical lattice with weak harmonic confinement in the perpendicular zzz direction. This lattice geometry is based on an experiment by Wirth et al. [Nat. Phys. 7, 147 (2010)]. The double well is asymmetric, with the local ground state in the shallow well nearly degenerate with the first excited state of the adjacent deep well. We compare the band structure obtained from a tight-binding model with that obtained numerically using a plane-wave basis. We find the tight-binding model to be in quantitative agreement for the lowest two bands, in qualitative agreement for the next two bands, and inadequate for even higher excited bands. The bandwidths of the excited bands are much larger than the harmonic-oscillator energy spacing in the zzz direction. We then study the thermodynamics of a noninteracting Bose gas in the first excited band. We estimate the condensate fraction and critical temperature Tc{T}_{c}Tc​ as functions of the lattice parameters. For typical atom numbers, the critical energy kBTc{k}_{B}{T}_{c}kB​Tc​, with kB{k}_{B}kB​ the Boltzmann constant, is larger than the excited bandwidths and harmonic-oscillator energy. Using conservation of total energy and atom number, we show that the temperature increases after the lattice transformation. Finally, we estimate the time scale for a two-body collision-aided decay of the condensate as a function of the lattice parameters. The decay involves two processes, the dominant one in which both colliding atoms decay to the ground band, and the second involving excitation of one atom to a higher band. For this estimate, we have used tight-binding wave functions for the lowest four bands and numerical estimates for higher bands. The decay rate rapidly increases with lattice depth, but close to the critical temperature, it stays smaller than the tunneling rate between the sss and ppp orbitals in adjacent wells.
The nonlinear Landau—Zener tunneling and nonlinear Rabi oscillations of Bose—Einstein condensate (BEC) with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters (i.e., the modulation amplitude and frequency) and the strength of periodic potential.