Direct Tunneling Delay Time Measurement in an Optical Lattice

Abstract

We report on the measurement of the time required for a wave packet to tunnel through the potential barriers of an optical lattice. The experiment is carried out by loading adiabatically a Bose-Einstein condensate into a 1D optical lattice. A sudden displacement of the lattice by a few tens of nanometers excites the micromotion of the dipole mode. We then directly observe in momentum space the splitting of the wave packet at the turning points and measure the delay between the reflected and the tunneled packets for various initial displacements. Using this atomic beam splitter twice, we realize a chain of coherent micron-size Mach-Zehnder interferometers at the exit of which we get essentially a wave packet with a negative momentum, a result opposite to the prediction of classical physics.

Phase transition kinetics for a Bose Einstein condensate in a periodically driven band system

“…As we have the same time-averaged Bose-Hubbard Hamiltonian (4) for all ν, the nucleation time is found to vary only rather weakly with the driving frequency. This behavior is expected to change for ν∼ν c where ν c corresponds to the center of mass oscillation frequency (see appendix C) [26]. Spanning the interval 0<ν<ν c , we could nucleate staggered states only for a frequency ν below ∼ν c /2 (see figure 3(b) with V 0 =2.6E L and ν c =8.1kHz, and appendix D), which defines experimentally the range of validity of the single band approximation.…”

“…Our experiments were realized on our rubidium-87 BEC machine that relies on a hybrid (magnetic and optical) trap [26]. The pure BEC of 10 5 atoms in the F=1, m F =−1 state is loaded in a horizontal 1D optical lattice (lattice spacing d=532 nm) by superposing two counterpropagating lasers.…”

Coherent backscattering and forward-scattering peaks in the quantum kicked rotor

“…Second, the fluctuations observed in position outside the CBS and CFS peaks are also significantly reduced because the different channels induce an additional averaging washing out the effects of the correlations of the pseudo-disorder at long times. This is particularly apparent in Figure 8, which shows the time evolution of a wave packet in the space of positions for a set of parameters which is experimentally accessible [65], namely e = 2.89, K = 6, ε = 0.8, and ω 2 = 2π 64 25 . With these parameters, the effective Heisenberg time is τ o ≈ T = 25.…”

“…One can however bypass this bottleneck by performing a phase space rotation (as explained below), converting hereby the spatial structures of the CBS and CFS peaks into well-defined, and more easily measurable signatures in the momentum distribution. Such a method has been recently experimentally demonstrated [65]. …”

“…Its phase space distribution is a periodic pattern, along the x-axis, of lines parallel to the p-axis. If we turn on the standing wave during a quarter of the pendulum period T r , the wave packet will start to move and go down the harmonic wells until it reaches its minima at the time when the standing wave is switched off [65].…”