Due to the rapid progress in atomic physics and quantum optics over the last twenty years, it has become possible to cool atoms down to extremely low temperatures. In these regimes, the atoms can no longer be considered as classical particles, but their quantum nature has to be taken fully into account. So far, the most spectacular milestone in these developments has been the experimental realization of Bose-Einstein condensation in atomic gases in 1995, which has spawned a vast amount of exciting further activities. From a theoretical point of view, the study of ultracold atomic gases is particularly attractive as the interactions between the particles are very weak. This makes them amenable to a much simpler and detailed description than it is possible for other comparable systems, e.g., of solid-state physics.

If you are not familiar with this fascinating and flourishing field, that has been awarded the Nobel Prizes in Physics in 1997 and 2001, the following reviews might provide a good starting-point:

W. Ketterle, D. M. Stamper-Kurn, and D. S. Durfee, Making, probing and understanding Bose-Einstein condensates
F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases

Many further links can be found at the Georgia Southern University.

In our group, we have studied various aspects of the quantum-statistical and dynamical behavior of ultracold quantum gases and, in particular, Bose-Einstein condensates. Work by our group members in this area is listed below.

Superradiant scattering from Bose-Einstein condensates

We have developed a theoretical description of superradiant light scattering from Bose-Einstein condensates. Our approach is based on the Maxwell-Schrödinger equations describing the coupled dynamics of matter-wave and optical fields and relies on two main concepts: the semiclassical description of the field dynamics which allows to study long-time effects and the inclusion of spatial propagation effects. In this way, we are able to reproduce and explain many of the characteristic features observed in the MIT experiments of Inouye et al., Science 285, 571 (1999), and Schneble et al., Science 300, 475 (2003), such as the shape of the atomic side-mode distributions for forward and backward scattering, the spatial asymmetry between forward and backward side modes, and the depletion of the condensate center observed for forward scattering. Furthermore, our theory also allows to obtain further detailed insights into the system dynamics which would be difficult to obtain experimentally.

O. Zobay and Georgios M. Nikolopoulos, Phys. Rev. A 73, 013620 (2006)
O. Zobay and Georgios M. Nikolopoulos, Phys. Rev. A 72, 041604(R) (2005)

Critical properties of interacting Bose gases

The renormalization group is not only a powerful tool for describing the universal characteristics of phase transitions, but it can also be applied to study the non-universal thermodynamic behavior beyond mean-field theory. We have developed a method by which thermodynamic properties of a weakly interacting Bose gas can be investigated. This approach not only allows us to examine the behavior of a homogeneous, three-dimensional gas across the phase transition to Bose condensation [6-9], but makes it also possible to include effects of external trapping potentials. With this method, we have studied in detail the critical properties of Bose gases in harmonic and general power-law potentials [3-5].

In combination with results from variational perturbation theory [2], this research has provided a deeper understanding of how an increasingly inhomogeneous potential suppresses critical fluctuations and changes nonperturbative into perturbative physics: the critical properties of homogeneous Bose gases are dominated by long wavelength critical fluctuations which have to be described nonperturbatively, whereas condensation in sufficiently inhomogeneous, e.g., harmonic, potentials can be treated perturbatively. Studying the critical properties of Bose gases in general power-law potentials allows to smoothly interpolate between these limits.

O. Zobay, Phys. Rev. A 73, 023616 (2006)
O. Zobay, G. Metikas, and H. Kleinert, Phys. Rev. A 71, 043614 (2005)
O. Zobay, G. Metikas, and G. Alber, Phys. Rev. A 69, 063615 (2004)
O. Zobay, J. Phys. B 37, 2593 (2004)
G. Metikas, O. Zobay, and G. Alber, Phys. Rev. A 69, 043614 (2004)
G. Metikas, O. Zobay, and G. Alber, J. Phys. B 36, 4595 (2003)
G. Metikas and G. Alber, J. Phys. B 35, 4223 (2002)
G. Alber and G. Metikas, Appl. Phys. B 73, 773 (2001)
G. Alber, Phys. Rev. A 63, 023613 (2001)

From matter-wave bubbles to two-dimensional atom trapping: Bose-Einstein condensates in field-induced adiabatic potentials

We have developed a method to create two-dimensional trapping as well as atomic shell, or bubble, states for a Bose-Einstein condensate initially prepared in a conventional magnetic trap. The scheme relies on the use of time-dependent, radio frequency-induced adiabatic potentials which we show to form a versatile and robust tool to generate novel trapping potentials. The shell states take the form of thin, highly stable matter-wave bubbles and can serve as stepping-stones to prepare atoms in highly-excited trap eigenstates or to study "collapse and revival phenomena." The creation of matter-wave bubbles requires gravitional effects to be compensated for. However, in our scheme gravitation can also be exploited to provide a route to two-dimensional atom trapping. We investigated the loading process for such a trap and examined experimental conditions under which a 2D condensate may be prepared.
Our proposed scheme has recently been realized by a number of experimental groups.

O. Zobay and B. M. Garraway, Phys. Rev. A 69, 023605 (2004)
O. Zobay and B. M. Garraway, Phys. Rev. Lett. 86, 1195 (2001)

Time-dependent tunneling and nonlinear Landau-Zener effect of Bose-Einstein condensates

We have investigated the influence of atomic interactions on time-dependent tunneling processes of Bose-Einstein condensates. In a variety of contexts the relevant condensate dynamics can be described by a Landau-Zener equation modified by the appearance of nonlinear contributions. Based on this equation we have studied how the interactions modify the tunneling probability. In particular, we found that for certain parameter values, due to a nonlinear hysteresis effect, complete adiabatic population transfer is impossible however slowly the resonance is crossed. Our results also indicate that the interactions can cause significant increase as well as decrease of tunneling probabilities that should be observable in currently feasible experiments.

O. Zobay and B. M. Garraway, Phys. Rev. A 61, 033603 (2000)

Creation of gap solitons in Bose-Einstein condensates

Solitons are localized wave packet that propagate without dispersion. In the context of Bose-Einstein condensates, one can distinguish between bright and dark solitons. The latter corresponds to minima of the condensate wave function, whereas the former refer to maxima. In BECs with repulsive atomic interactions (which are studied in most experiments), only dark solitons arise in a natural way.

However, by taking additional measures it is nevertheless possible to create bright solitons. Motivated by the analogy to conventional nonlinear optics, we have devised a method to launch bright gap solitonlike structures in condensates confined in optical traps. Their formation relies on the dynamics of the atomic internal ground states in two far-off-resonance counterpropagating left- and right-circularly polarized laser beams. The soliton motion can be controlled by suitable additional optical and magnetic fields. As an illustration we have discussed a nonlinear atom-optical Mach-Zehnder interferometer based on gap solitons.

S. Pötting, O. Zobay, P. Meystre, and E. M. Wright, J. Mod. Opt. 47, 2653 (2000)
O. Zobay, S. Pötting, P. Meystre, and E. M. Wright, Phys. Rev. A 59, 643 (1999)