We analyze time-of-flight absorption images obtained with dilute Bose-Einstein con-densates released from shaken optical lattices, both theoretically and experimentally. We argue that weakly interacting, ultracold quantum gases in kilohertz-driven op
tical potentials constitute equilibrium systems characterized by a steady-state distri-bution of Floquet-state occupation numbers. Our experimental results consistently indicate that a driven ultracold Bose gas tends to occupy a single Floquet state, just as it occupies a single energy eigenstate when there is no forcing. When the driving amplitude is sufficiently high, the Floquet state possessing the lowest mean energy does not necessarily coincide with the Floquet state connected to the ground state of the undriven system. We observe strongly driven Bose gases to condense into the former state under such conditions, thus providing nontrivial examples of dressed matter waves.
Matter waves can be coherently and adiabatically loaded and controlled in strongly driven optical lattices. This coherent control is used in order to modify the modulus and the sign of the tunneling matrix element in the tunneling Hamiltonian. Our fi
ndings pave the way for studies of driven quantum systems and new methods for engineering Hamiltonians that are impossible to realize with static techniques.
The time it takes a quantum system to complete a tunneling event (which in the case of cross-barrier tunneling can be viewed as the time spent in a classically forbidden area) is related to the time required for a state to evolve to an orthogonal sta
te, and an observation, i.e., a quantum mechanical projection on a particular basis, is required to distinguish one state from another. We have performed time-resolved measurements of Landau-Zener tunneling of Bose-Einstein condensates in accelerated optical lattices, clearly resolving the steplike time dependence of the band populations. The use of different protocols enabled us to access the tunneling probability, in two different bases, namely, the adiabatic basis and the diabatic basis. The adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic one to the freeparticle momentum eigenstates. Our findings pave the way towards more quantitative studies of the tunneling time for LZ transitions, which are of current interest in the context of optimal quantum control and the quantum speed limit.
By moving the pivot of a pendulum rapidly up and down one can create a stable position with the pendulums bob above the pivot rather than below it. This surprising and counterintuitive phenomenon is a widespread feature of driven systems and carries
over into the quantum world. Even when the static properties of a quantum system are known, its response to an explicitly time-dependent variation of its parameters may be highly nontrivial, and qualitatively new states can appear that were absent in the original system. In quantum mechanics the archetype for this kind of behaviour is an atom in a radiation field, which exhibits a number of fundamental phenomena such as the modification of its g-factor in a radio-frequency field and the dipole force acting on an atom moving in a spatially varying light field. These effects can be successfully described in the so-called dressed atom picture. Here we show that the concept of dressing can also be applied to macroscopic matter waves, and that the quantum states of dressed matter waves can be coherently controlled. In our experiments we use Bose-Einstein condensates in driven optical lattices and demonstrate that the many-body state of this system can be adiabatically and reversibly changed between a superfluid and a Mott insulating state by varying the amplitude of the driving. Our setup represents a versatile testing ground for driven quantum systems, and our results indicate the direction towards new quantum control schemes for matter waves.
We present our experimental investigations on the subject of nonlinearity-modified Bloch-oscillations and of nonlinear Landau-Zener tunneling between two energy bands in a rubidium Bose Einstein condensate in an accelerated periodic potential. Nonlin
earity introduces an asymmetry in Landau-Zener tunneling. We also present measurements of resonantly enhanced tunneling between the Wannier-Stark energy levels for Bose-Einstein condensates loaded into an optical lattice.
