Condensed Matter Theory

Bose-Einstein condensates: Coherent control by time-periodic forcing

Contrary to what might be expected on naive grounds, exerting even strong time-periodic forces on a Bose-Einstein condensate by shaking its trapping potential with kHz frequencies does not necessarily lead to uncontrolled excitations, and hence to the condensate's destruction. Rather, careful selection of the parameters of the driving force enables one to create new quantum states with properties which differ signifcantly from those of the respective unforced system. The situation encountered here is, in many respects, reminiscent of the "dressed-atom picture" known from atomic and molecular physics:

Dressing the condensate's matter wave by time-periodic forcing allows one to equip the system with properties which the unforced, "bare" matter wave did not have.

We study the emerging novel mechanisms for quantum state engineering with mesoscopic matter waves, employing combinations of techniques adapted from many-body theory, time-dependent quantum mechanics, and nonlinear dynamics.

Part of this research is performed in collaboration with the experimental BEC group in Pisa, Italy, headed by E. Arimondo and O. Morsch. We also interact strongly with our former group member A. Eckardt, who is now at the Max-Planck-Institut für Physik komplexer Systeme in Dresden.

Quasienergy surfaces for a driven optical lattice

  • We are using spatio-temporal Bloch waves for the theoretical description of ultracold atoms in driven optical lattices; such states embody both the spatial periodicity of the lattice and the temporal periodicity of the driving force on equal footing. The response of atomic wave packets to pulses with deliberately shaped amplitudes then can be regarded as adiabatic motion on quasienergy surfaces, with multiphoton-like Landau-Zener transitions occurring at their avoided crossings. This approach enables one to transfer many concepts developed for the coherent control of molecular dynamics by laser radiation to the coherent control of matter waves in shaken optical lattices. For details, see
    Phys. Rev. A 84, 063617 (2011),
    Phys. Rev. B 84, 054301 (2011),
    Phys. Rev. A 81, 063612 (2010).

Inhibition of spreading due to quasienergy band collapse

  • Together with the experimental group in Pisa, we have shown that dynamic localization can be observed with Bose-Einstein condensates in strongly shaken optical lattices, in perfect agreement with the theoretical prediction. The concept of dynamic localization had been developed much earlier in the context of charged-particle motion in ac-driven periodic potentials. It rests on a forcing-induced effective renormalization of the nearest-neighbor hopping element, which has been cleanly detected, in a single-particle setting, by M. Oberthaler's group in Heidelberg [E. Kierig et al., Phys. Rev. Lett. 100, 190405 (2008)]. Moreover, the Pisa group has provided evidence for this renormalization with dilute condensates in driven optical lattices [H. Lignier et al., Phys. Rev. Lett. 99, 220403 (2007)]. The realization of dynamic localization with time-periodically forced condensates not only constitutes key evidence for the validity of the dressed-matter-wave approach, but also suggests systematic ways of quasienergy band engineering.
    See Phys. Rev. A 79, 013611 (2009) for details.
    A synopsis of this work has appeared in Physics - spotlighting exceptional research.

Quasienergy spectrum for dressed matter waves

  • We have emphasized the conceptual parallels between "dressed atoms" and "dressed matter waves" by studying multiphoton-like resonances which occur for matter waves in strongly shaken optical lattices, and have suggested a scheme for avoided-level-crossing spectroscopy in such systems. Quite interestingly, some resonances can be disabled by proper choices of the driving amplitude, thus leading to further tools for coherent control.
    See Phys. Rev. Lett. 101, 245302 (2008) for details.

Driving-induced superfluid-insulator transition

  • A paradigmatically important condensed-matter phenomenon, which reflects the competition between delocalization due to tunneling and localization due to interaction, is the quantum phase transition from a superfluid to a Mott insulator. As known from the pioneering experiment by M. Greiner et al. [Nature 415, 39 (2002)], this transition occurs with ultracold atoms in an optical lattice upon increasing the lattice depth. Exploiting the dressed-matter-wave approach, we have predicted that there exists still another, entirely different route to the Mott insulator: In a time-periodically driven optical lattice with fixed depth, the driving amplitude decides whether the system is superfluid, or in a Mott insulator state. This prediction has now been confirmed experimentally by the Pisa group [A. Zenesini et al., Phys. Rev. Lett. 102, 100403 (2009)]; thus furnishing the very first example of coherent control over a quantum phase transition.
    See Phys. Rev. Lett. 95, 260404 (2005) for details.

Photon-assisted BEC tunneling

  • A promising system for studying the combined effects of many-particle interaction and time-periodic forcing is provided by a driven bosonic Josephson junction, which constitutes a natural extension of the system realized by the Heidelberg group [M. Albiez et al., Phys. Rev. Lett. 95, 010402 (2005)]. We have shown that periodic modulation of such a condensate-filled double well gives rise to an analog of photon-assisted tunneling, with distinct signatures of the interparticle interaction visible in the amount of particles transferred from one well to the other. In particular, under experimentally accessible conditions there are half-integer Shapiro-like resonances, and even further such resonances corresponding to other fractions. Meanwhile, "photon"-assisted tunneling of Bose-Einstein condensates in optical lattices has been detected by the Pisa group [C. Sias et al., Phys. Rev. Lett. 100, 040404 (2008)].
    See Phys. Rev. Lett. 95, 200401 (2005) for details.

Taken together, the results obtained in these joint experimental and theoretical efforts strongly indicate that time-periodic forcing offers unprecedented possibilities for coherent control of mesoscopic matter waves.

This work is supported by the Deutsche Forschungsgemeinschaft under grant No. HO 1771/6.

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