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Physical Review A

Observation of Rabi oscillations between Bloch bands in an optical potential

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

Published Oct 1, 1998• 57 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.58.r2648

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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.
Dynamical Bloch band suppression is observed for the first time, using cold sodium atoms in a far detuned standing wave of light. This system has well-defined Bloch bands as its energy spectrum, which are modified dynamically by imposing a strong phase modulation of the standing wave. The atoms are prepared in the lowest band, and the spectrum is mapped out by introducing a weak spectroscopic probe that drives transitions between the modified bands. Dynamical suppression of the bands is observed at a critical value of the modulation strength, and is well supported by a full quantum mechanical analysis that goes beyond the single-band and tight-binding approximations.
We demonstrate spatial Rabi oscillations in optical waveguide arrays. Adiabatic transitions between extended Floquet-Bloch modes associated with different bands are stimulated by periodic modulation of the photonic lattice in the propagation direction. When the stimulating modulation also carries transverse momentum, the transition becomes indirect, equivalent to phonon-assisted Rabi oscillations. In solid state physics such indirect Rabi oscillations necessitate coherent phonons and hence they have never been observed. Our experiments suggest that phonon-assisted Rabi oscillations are observable also with Bose-Einstein condensates, as well as with other wave systems-where coherence can be maintained for at least one period of the Rabi oscillation.
The early quantum theory of electrical conductivity in crystal lattices by Bloch and Zener [1,2] led to the striking prediction that a homogeneous static electric field induces an oscillatory rather than uniform motion of the electrons. These so-called Bloch oscillations have never been observed in natural crystals because the scattering time of the electrons by the lattice defects is much shorter than the Bloch period. In semiconductor superlattices the larger spatial period leads to a much shorter Bloch period (,600 fs) and Bloch oscillations have recently been observed through the emission of THz radiation by the electrons [3]. Here we present Bloch oscillations of atoms in the fundamental energy band of a periodic optical potential. We directly measure the atomic momentum distribution evolving in time under the influence of a constant inertial force for various potential depths. We experimentally observe oscillation periods in the millisecond range as well as positive and negative effective masses. Bloch oscillations are a pure quantum effect which can be explained in a simple one-dimensional model. The periodicity of the lattice (period d) leads to a band structure (Fig. 1) of the energy spectrum of the particle and the corresponding eigenenergies Ensqd and eigenstates jn, ql (Bloch states) are labeled by the discrete band index n and the continuous quasimomentum q; Ensqd and jn, ql are periodic functions of q with period 2pyd and q is conventionally restricted to the first Brillouin zone g2pyd, pydg [4]. Under the influence of a constant external force F, weak enough not to induce interband transitions, a given Bloch state jn, qs0dl evolves (up to a phase factor) into the state jn, qstdl according to qstd ­ qs0d 1 Ftyh . (1) This evolution is periodic with a period tB ­ hyjFjd corresponding to the time required for the quasimomentum to scan a full Brillouin zone. The mean velocity in jn, qstdl
Summary form only given. We report the observation of dynamical suppression of Bloch bands due to an AC field. Our system consists of laser-cooled atoms in an optical lattice, rather than electrons in a superlattice. The main advantage of our system is the long coherence times, limited only by residual spontaneous scattering. In our experiment we trap neutral sodium atoms in the lowest band of a one-dimensional optical lattice. We then modulate the position of the potential to realize both an intense AC field and a weak spectroscopic probe in order to directly observe band suppression.
We show theoretically that the dynamics of cold atoms in the lowest-energy band of a stationary optical lattice can be transformed and controlled by a second, weaker, periodic potential moving at a constant speed along the axis of the stationary lattice. The atom trajectories exhibit complex behavior, which depends sensitively on the amplitude and speed of the propagating lattice. When the speed and amplitude of the moving potential are low, the atoms are dragged through the static lattice and perform drifting orbits with frequencies an order of magnitude higher than that corresponding to the moving potential. Increasing either the speed or amplitude of the moving lattice induces Bloch-like oscillations within the energy band of the static lattice, which exhibit complex resonances at critical values of the system parameters. In some cases, a very small change in these parameters can reverse the atom's direction of motion. In order to understand these dynamics we present an analytical model, which describes the key features of the atom transport and also accurately predicts the positions of the resonant features in the atom's phase space. The abrupt controllable transitions between dynamical regimes, as well as the associated set of resonances, provide a mechanism for transporting atoms between precise locations in a lattice, as required for using cold atoms to simulate condensed matter or as a stepping stone to quantum information processing. The system also provides a direct quantum simulator of acoustic waves propagating through semiconductor nanostructures in sound analogs of the optical laser (saser).