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Physical Review A

Observation of the Wannier-Stark fan and the fractional ladder in an accelerating optical lattice

Kirk W. Madison, Martin C. Fischer, Mark G. Raizen

Published Sep 1, 1999• 38 citations
Publisher

Abstract

We report an experimental study of the Wannier-Stark fan and the fractional Wannier-Stark ladder using laser-cooled sodium atoms in an accelerating one-dimensional standing wave of light. We prepare the atoms in the lowest motional band of the optical lattice and then impose a constant acceleration. A weak oscillatory component is added to the acceleration in order to resonantly drive interband transitions, and the number of atoms that remain in the lowest band is measured as a function of the probe frequency. The spectrum is characterized by a ladder of resonances spaced by the atomic Bloch oscillation frequency ${\ensuremath{\omega}}_{B}.$ When an additional, strong ac component at frequency $\ensuremath{\Omega}$ is added, a fractional ladder is observed with a spacing related to the electric matching ratio $\ensuremath{\Omega}/{\ensuremath{\omega}}_{B}.$

DOI
10.1103/physreva.60.r1767

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We report an experimental study of the Wannier-Stark fan and the fractional Wannier-Stark ladder using laser-cooled sodium atoms in an accelerating one-dimensional standing wave of light. We prepare the atoms in the lowest motional band of the optical lattice and then impose a constant acceleration. A weak oscillatory component is added to the acceleration in order to resonantly drive interband transitions, and the number of atoms that remain in the lowest band is measured as a function of the probe frequency. The spectrum is characterized by a ladder of resonances spaced by the atomic Bloch oscillation frequency \ensuremathωB.{\ensuremath{\omega}}_{B}.\ensuremathωB​. When an additional, strong ac component at frequency \ensuremathΩ\ensuremath{\Omega}\ensuremathΩ is added, a fractional ladder is observed with a spacing related to the electric matching ratio \ensuremathΩ/\ensuremathωB.\ensuremath{\Omega}/{\ensuremath{\omega}}_{B}.\ensuremathΩ/\ensuremathωB​.
We report observation of Wannier-Stark ladders with ultracold sodium atoms in an accelerating one-dimensional standing wave of light. Atoms are trapped in a far-detuned standing wave that is accelerated for a controlled duration. A small oscillatory component is added to the acceleration, and the fraction of trapped atoms is measured as a function of the oscillation frequency. Resonances are observed where the number of trapped atoms drops dramatically. The separation between resonant peaks is found to be proportional to the acceleration. We show that this resonant structure can also be understood as a temporal quantum interference effect.
We report the first observation of atomic Wannier-Stark ladders in a potential formed by an accelerating standing wave of light.1 This is a fundamental effect of quantum transport in optical lattices. Wannier-Stark ladder resonances were predicted to occur in the band structure of an electron moving in a periodic lattice with a dc electric field, and have been recently observed in superlattices. Our work is the first spectroscopic study of Wannier-Stark ladders free from complications such as the impurities, lattice vibrations, and multi-particle interactions present in solids.
~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 an experimental study of atomic motion in the Bloch band of a periodic potential. Our system consists of cold sodium atoms in a far detuned standing wave of near resonant light. We prepare the atoms in the lowest motional band, and then impose phase modulation in order to drive interband transitions. We observe Rabi oscillations between the first and second band as a function of modulation intensity and frequency. We also observe damped oscillations of the population as a function of modulation frequency, which are primarily due to a spread in Rabi frequencies over the Bloch band.