Many-body quantum effects of ultracold atoms

May 2006.

The study of many-body quantum nature of ultracold atoms is a challenging problem of the fundamental physics. The many-body quantum effects become important in the systems of low dimensionality, the systems with strict symmetry constraints, degeneracy, or strong interaction. Examples include low-dimensional gases, condensates of spinor atoms, rapidly rotating condensates, condensates with strong atom-atom interaction, and ultracold atoms confined in double-well potentials or optical lattices. To explore many-body quantum effects in the systems with degeneracy, one can employ the second-quantization theory for coupled multiple modes. That is, the systems are treated as an ensemble of discrete quantized particles rather than continuous fields. Within the second quantization formalism, the systems of multiple coupled modes obey Hubbard-like Hamiltonians, and some many- body quantum phenomena including entanglement and squeezing, dynamics and collapse and revival, and quantum phase transition in these models have been investigated.

(a) Bosons in a strongly trimerized Kagomé lattice can be reduced to three site Bose-Hubbard rings. (b) Combining a proper two dimensional harmonic potential with the Kagomé lattice, triple-well potential can be generated; (c) three-site state.

The theory group at the Australian National University explores the subtle many-body quantum effects in the systems of ultracold atoms to determine the ways for their control. Recently, Dr. Chaohong Lee proposed a robust scheme of the Mach-Zehnder interferometer based on many-body states in Bose-Josephson junctions [Phys. Rev. Lett. 97, 150402 (2006)]. In this proposal, he has demonstrated how the combination of nonlinear and many-body quantum effects can be used to realize a Heisenberg-limited Mach-Zehnder interferometry. Very recently, the group analyzed how the classical discrete vortices melt under the action of quantum fluctuations and the first results have just been published [C. Lee, T. Alexander, and Yu.S. Kivshar, Phys. Rev. Lett. 97, 180406 (2006)]. In particular, they studied the phase coherence and the effects of quantum fluctuations on vortices and revealed that the breakdown of these coherent structures through quantum fluctuations accompanies the superfluid-insulator crossover.