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Conference on Lasers and Electro-Optics

Nonexponential decay in atomic tunneling

K.W. Hadison, Martin C. Fischer, Qian Niu, Mark G. Raizen

Published Nov 27, 2002• 0 citations
Publisher

Abstract

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.

DOI
10.1109/iqec.1998.680069

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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 observe quantum tunneling of cold sodium atoms from an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. For sufficiently large values of the acceleration, we observe an exponential decay in the number of atoms that remain trapped as a function of the interaction time. We show that this loss is due to quantum tunneling, and compare the decay rates with Landau-Zener theory. We also observe oscillations in the tunneling rate as a function of the acceleration which are due to quantum interference effects.
~Received 30 October 1996! We observe quantum tunneling of cold sodium atoms from an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. For sufficiently large values of the acceleration, we observe an exponential decay in the number of atoms that remain trapped as a function of the interaction time. We show that this loss is due to quantum tunneling, and compare the decay rates with Landau-Zener theory. We also observe oscillations in the tunneling rate as a function of the acceleration which are due to quantum interference effects. @S1050-2947~97!50702-5# PACS number~s!: 03.75.Be, 32.80.Pj, 42.50.Vk Tunneling in the center-of mass motion of atoms should become an important process at the low temperatures that are now achieved with laser cooling. This can appear, for example, as a loss mechanism for atoms confined in an optical lattice constructed from interfering beams of light. While atomic motion in these structures has become an active area of research @1,2#, tunneling has been obscured by spontaneous scattering @3#. An alternative atom optics system where tunneling can be significant has appeared in our efforts to develop a cold atomic beam for interferometry. Our approach has been to launch laser-cooled atoms in the potential created by an accelerating, far-detuned, standing wave of light. This system was previously used to study Wannier-Stark ladders @4# and Bloch oscillations @5#. The results reported in this Rapid Communications provide an observation of tunneling in atom optics, and the high degree of experimental control has enabled a quantitative comparison with theory. We consider atomic motion in an accelerating standing wave of light. For sufficiently large detuning from atomic resonance, the atoms remain in their internal ground state and experience an effective one-dimensional potential given by V0cos@2kL(x2at 2 /2)#, where k L52p/l L is the wave number, and a is the acceleration of the standing wave @6#. The well depth V0 is the amplitude of the optical dipole potential. It is proportional to the laser intensity and inversely proportional to detuning from atomic resonance. We neglect variations of the potential in the two transverse directions, which is justified for beams that are sufficiently
We report the first observation of the quantum Zeno and anti-Zeno effects in an unstable system. Cold sodium atoms are trapped in a far-detuned standing wave of light that is accelerated for a controlled duration. For a large acceleration the atoms can escape the trapping potential via tunneling. Initially the number of trapped atoms shows strong nonexponential decay features, evolving into the characteristic exponential decay behavior. We repeatedly measure the number of atoms remaining trapped during the initial period of nonexponential decay. Depending on the frequency of measurements we observe a decay that is suppressed or enhanced as compared to the unperturbed system.
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.