Condensed Matter Theory
BoseEinstein condensates: Coherent control by timeperiodic forcing
Contrary to what might be expected on naive grounds, exerting even strong timeperiodic forces on a BoseEinstein 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 "dressedatom picture" known from atomic and molecular physics:Dressing the condensate's matter wave by timeperiodic 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 manybody theory, timedependent 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 MaxPlanckInstitut für Physik komplexer Systeme in Dresden.

We are using spatiotemporal 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
multiphotonlike LandauZener 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).

Together with the experimental group in Pisa, we have
shown that dynamic localization can be observed with BoseEinstein
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 chargedparticle motion in
acdriven periodic potentials. It rests on a forcinginduced effective
renormalization of the nearestneighbor hopping element, which has been
cleanly detected, in a singleparticle 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 timeperiodically forced
condensates not only constitutes key evidence for the validity of the
dressedmatterwave 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.

We have emphasized the conceptual parallels between
"dressed atoms" and "dressed matter waves" by
studying multiphotonlike resonances which occur for matter waves in
strongly shaken optical lattices, and have suggested a scheme for
avoidedlevelcrossing 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.

A paradigmatically important condensedmatter 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 dressedmatterwave approach, we have predicted that
there exists still another, entirely different route to the Mott insulator:
In a timeperiodically 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.

A promising system for studying the combined effects
of manyparticle interaction and timeperiodic 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 condensatefilled double
well gives rise to an analog of photonassisted 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 halfinteger Shapirolike
resonances, and even further such resonances corresponding to other fractions.
Meanwhile, "photon"assisted tunneling of BoseEinstein 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 timeperiodic 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.
Disclaimer Druckversion Martin Holthaus Last modified: Jan 01 2012