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arXiv:0809.1032 · Physical Review Letters

Avoided-Level-Crossing Spectroscopy with Dressed Matter Waves

André Eckardt, Martin Holthaus

Published Dec 12, 2008• 57 citations
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Abstract

We devise a method for probing resonances of macroscopic matter waves in shaken optical lattices by monitoring their response to slow parameter changes, and show that such resonances can be disabled by particular choices of the driving amplitude. The theoretical analysis of this scheme reveals far-reaching analogies between dressed atoms and time periodically forced matter waves.

DOI
10.1103/physrevlett.101.245302

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We devise a method for probing resonances of macroscopic matter waves in shaken optical lattices by monitoring their response to slow parameter changes, and show that such resonances can be disabled by particular choices of the driving amplitude. The theoretical analysis of this scheme reveals far-reaching analogies between dressed atoms and time periodically forced matter waves.
We suggest to view ultracold atoms in a time-periodically shifted optical lattice as a 'dressed matter wave', analogous to a dressed atom in an electromagnetic field. A possible effect lending support to this concept is a transition of ultracold bosonic atoms from a superfluid to a Mott-insulating state in response to appropriate "dressing" achieved through time-periodic lattice modulation. In order to observe this effect in a laboratory experiment, one has to identify conditions allowing for effectively adiabatic motion of a many-body Floquet state.
Motivated by recent experimental progress achieved with ultracold atoms in kilohertz-driven optical lattices, we provide a theoretical discussion of mechanisms governing the response of a particle in a cosine lattice potential to strong forcing pulses with smooth envelope. Such pulses effectuate adiabatic motion of a wave packet's momentum distribution on quasienergy surfaces created by spatiotemporal Bloch waves. Deviations from adiabaticity can then be deliberately exploited for exerting coherent control and for reaching target states which may not be accessible by other means. As one particular example, we consider an analog of the $\ensuremath{\pi}$ pulses known from optical resonance. We also suggest adapting further techniques previously developed for controlling atomic and molecular dynamics by laser pulses to the coherent control of matter waves in shaken optical lattices.
We study the evolution of bosons in a periodically driven optical lattice during a slow change of the driving amplitude. Both the regime of high-frequency and low-frequency driving are investigated. In the low-frequency regime, resonant absorption of energy is observed. In the high-frequency regime, the dynamics is compared to a system with an effective Hamiltonian in which the atoms are ``dressed'' by the driving field. This ``dressing'' can dramatically change the amplitude and sign of the effective tunneling. A particular focus of this study is the investigation of the time scales necessary for the evolving quantum state to follow almost adiabatically to the ground state of the effective many-body system.
The tunneling properties of a quantum system of matter waves inside a periodic potential can be dramatically changed if the potential is driven back and forth. Similarly to an atom in a strong radiation field, the matter waves inside the strongly driven potential are "dressed" and acquire new properties. In this paper, the authors have demonstrated that such dressed matter waves can be coherently and adiabatically loaded and controlled in one, two and three dimensional strongly driven optical lattices. In the driven lattices the tunneling probability and the tunneling phase between adjacent lattice sites become a function of the driving parameters. The regimes in which the driving parameters can be changed without exciting the system have been identified, thus allowing coherent and adiabatic following. This coherent control is then used in order to reversibly induce the superfluid-Mott insulator phase transition by changing the the driving strength.
Coherent directed quantum transport of ultracold rubidium atoms in an optical realization of a quantum rocking ratchet is investigated experimentally. By changing parameters of the underlying periodic modulations we resolve transport resonances in the mean momentum of a dilute atomic Bose-Einstein condensate. These resonances are attributed to the avoided crossings between Floquet eigenstates which are widely separated on the energy scale. By increasing the amplitude of the drive we observe a theoretically predicted bifurcation of a single-peak resonance into a doublet. Our results prove the feasibility of fine experimental control over nonequlibrium, coherent quantum transport in ac-driven optical lattices