Transport of atoms in a quantum conveyor belt

Abstract

We have performed experiments using a 3D-Bose-Einstein condensate of sodium atoms in a 1D optical lattice to explore some unusual properties of band-structure. In particular, we investigate the loading of a condensate into a moving lattice and find non-intuitive behavior. We also revisit the behavior of atoms, prepared in a single quasimomentum state, in an accelerating lattice. We generalize this study to a cloud whose atoms have a large quasimomentum spread, and show that the cloud behaves differently from atoms in a single Bloch state. Finally, we compare our findings with recent experiments performed with fermions in an optical lattice.PACS numbers: 03.75. Lm, 32.80.Qk An optical lattice is a practically perfect periodic potential for atoms, produced by the interference of two or more laser beams. An atomic-gas Bose-Einstein condensate (BEC)[1, 2] is a coherent source of matter waves, a collection of atoms, all in the same state, with an extremely narrow momentum spread. Putting such atoms into such a potential provides an opportunity for exploring a quantum system with many similarities to electrons in a solid state crystal but with unprecedented control over both the lattice and the particles. In particular we can easily control the velocity and acceleration of the lattice as well as its strength, making it a variable "quantum conveyor belt". This allows us to explore situations that are difficult or impossible to achieve in solid state systems. The results are often remarkable and counterintuitive. For example atoms that are being carried along by a moving optical lattice are left stationary when the still-moving lattice is turned off, in apparent violation of the law of inertia.A few experiments have studied quantum degenerate atoms in moving optical lattices [3,4,5,6]. Bragg diffraction of a Bose condensate is a special case of quantum degenerate atoms in a moving lattice [7]. Here, using a Bose-Einstein condensate and a moving lattice, we achieve full control over the system, in particular its initial quasimomentum and band index as well as its subsequent evolution. We also show the difference in behavior when the atom sample has a large spread of quasimomenta, as compared with the narrow quasimomentum distribution of a coherent BEC.Our lattice is one-dimensional along the x axis, produced by the interference of two counter-propagating laser beams, each of wave-vector k = 2π/λ (λ ≈ 589 nm is the wavelength of the laser beams). This results in a sinusoidal potential, V sin 2 kx, with a spatial period We will use Bloch theory, emphasizing the single particle character of the problem. An overview of Bloch theory, as it applies to this one dimensional system, is supplied in reference [3]. Briefly, the wave function of the atoms in the lattice can be decomposed into the Bloch eigenstates u n,q (x)e iqx characterized by a band index n and a quasimomentum q, defined in the rest frame of the lattice. The eigenenergies of the system, E n (q), as well as the eigenstates are periodic in q with a periodicity 2h...

Response of a particle in a one-dimensional lattice to an applied force: Dynamics of the effective mass

“…In many experiments that study the motion of cold atoms in optical lattices, the measured variable is the velocity of the wavepacket rather than its acceleration [3][4][5][6][7][8]. In Figure 5 we show a plot of the velocity for the same parameters as Figure 4.…”

“…In * fduque@physics.utoronto.ca these systems a constant force can be introduced by accelerating the lattice uniformly so that the atoms experience an inertial force in the lattice frame. Many experiments with ultracold atoms have been carried out to examine interesting phenomena caused by the band structure in one-dimensional optical lattices [3][4][5][6][7][8]. Here we discuss the possibility of detecting the oscillatory behaviour of the expectation value of the acceleration in ultracold atoms in a one-dimensional optical lattice when an inertial force is suddenly applied.…”

Long-time nonlinear dynamical evolution forP-band ultracold atoms in an optical lattice

“…There are many other methods preparing a BEC in the P-band quantum state [4,[17][18][19][20], but normally the loading time is tens of milliseconds. Our method has the merit of rapid generation of the quantum state in the P-band.…”

Quantum Stripe Ordering in Optical Lattices

“…In optical lattices, pioneering experiments on orbital physics have been recently carried out by Browaeys et. al [7] by accelerating the lattice of bosons, and by Kohl et. al [8] by using fermionic Feshbach resonance.…”