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Quantum Electronics and Laser Science Conference

Dynamical Bloch band suppression in an optical lattice

Martin C. Fischer, Kirk W. Madison, Roberto B. Diener, Qian Niu

Published Jan 20, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qels.1999.807604

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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.
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 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.
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. Since optical lattices can be used to investigate both classical energy band transport and the corresponding quantized states, they are ideal for studying the classical-quantum correspondence. Here, we investigate this correspondence for cold sodium atoms in a one-dimensional optical lattice along the x-direction and a three-dimensional harmonic trap. The energy versus crystal momentum dispersion relation for the lowest energy band of the optical lattice, together with the harmonic potential, define an effective Hamiltonian that we use to calculate classical atom paths. When a symmetry axis of the harmonic trap is aligned with the optical lattice, the atoms follow stable trajectories similar to Bloch oscillations But tilting this symmetry axis away from the optical lattice direction induces a transition to strongly chaotic dynamics.
We analyse a laser assisted sympathetic cooling scheme for atoms within the lowest Bloch band of an optical lattice. This scheme borrows ideas from sub-recoil laser cooling, implementing them in a new context in which the atoms in the lattice are coupled to a Bose–Einstein condensate (BEC) reservoir. In this scheme, excitation of atoms between Bloch bands replaces the internal structure of atoms in normal laser cooling, and spontaneous emission of photons is replaced by creation of excitations in the BEC reservoir. We analyse the cooling process for many bosons and fermions, and obtain possible temperatures corresponding to a small fraction of the Bloch band width within our model. This system can be seen as a novel realisation of a many-body open quantum system.