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arXiv:cond-mat/0601416 · Physical Review Letters

Unconventional Strongly Interacting Bose-Einstein Condensates in Optical Lattices

Anatoly B. Kuklov

Published Sep 13, 2006• 68 citations
arXivHTMLPDF

Abstract

Feschbach resonances in a non-s-wave channel of two-component bosonic mixtures can induce atomic Bose-Einstein condensates with a nonzero orbital momentum in the optical lattice, if one component is in the Mott insulator state and the other is not. Such non-s-wave condensates break the symmetry of the lattice and, in some cases, time-reversal symmetry. They can be revealed in specific absorption imaging patterns.

DOI
10.1103/physrevlett.97.110405

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Feschbach resonances in a non-s-wave channel of two-component bosonic mixtures can induce atomic Bose-Einstein condensates with a nonzero orbital momentum in the optical lattice, if one component is in the Mott insulator state and the other is not. Such non-s-wave condensates break the symmetry of the lattice and, in some cases, time-reversal symmetry. They can be revealed in specific absorption imaging patterns.
We perform a theoretical study on the recently observed unconventional Bose-Einstein condensations (UBEC) in the high bands of optical lattices. These exotic states are characterized by complex-valued condensate wave functions with nodal points or real-valued wave functions with nodal lines; thus, they are beyond the ``no-node'' theorem of conventional BECs. A quantum phase transition is driven by the competition between the single-particle band and interaction energies. The complex UBECs spontaneously break time-reversal symmetry, exhibiting a vortex-antivortex lattice structure.
We investigate the unconventional Bose-Einstein condensations with the orbital degree of freedom in the three-dimensional cubic optical lattice, which gives rise to various exotic features absent in conventional scalar and spinor Bose-Einstein condensations. Orbital angular momentum moments are formed on lattice sites breaking time-reversal symmetry spontaneously. Furthermore, they exhibit orbital frustrations and develop a chiral ordering selected by the ``order-from-disorder'' mechanism.
Cold atoms in optical lattices provide a unique medium for mimicking effects known from other areas of physics. This is primarily due to a great flexibility and a precise manipulation of the cold atomic system [1–3]. Atoms of a fermionic or bosonic character may be placed in an optical lattice potential whose geometry may be easily controlled by changing polarizations of laser beams. Interactions between atoms may be controlled via magnetic, optical or microwave Feshbach resonances [4, 5] as well as via changing the depth of the optical lattice. The latter modifies primarily the tunneling between lattice sites, enabling e.g. the superfluid-Mott insulator quantum phase transition in the optical realization of the Bose-Hubbard model as proposed by Jaksch and Zoller [6] and subse
An important new development in the field of ultracold atomic gases is the study of the properties of these gases in a so-called optical lattice. An optical lattice is a periodic trapping potential for the atoms that is formed by the interference pattern of a few laser beams. A reason for the interest in these systems is that the effects of the interatomic interactions can be strongly enhanced. More specifically, it has been shown in a beautiful experiment by Greiner et al. in 2002 that by loading a Bose-Einstein condensate into an optical lattice it is possible for the system to undergo a quantum phase transition to a new quantum phase of matter, the so-called Mott insulator phase. Within this Mott insulator phase each lattice site is occupied by exactly one atom. This makes the Mott insulator phase especially well suited for applications in the field of quantum computation and quantum information processing. We have theoretically investigated the above mentioned quantum phase transition and our formalism allows for a description of the Mott insulator phase at nonzero temperatures. Another important experimental development in the field of ultracold atomic gases is the use of Feshbach resonances to control the interatomic interactions. Such a resonance occurs whenever two colliding atoms form a long-lived molecule for some time. The crucial point of a Feshbach resonance is that the above mentioned molecule has a magnetic moment that is not equal to twice the magnetic moment of the atom. As a consequence the energy difference between the two atoms and the molecule and hence the interactions between the atoms can be controlled by using an external magnetic field. By combining these two techniques, i.e, by trapping ultracold atomic gases in an optical lattice and by tuning a magnetic field near a Feshbach resonance there can be a new quantum phase transition between two superfluid phases. We gave derived the the theory for the description of these Feshbach resonances in optical lattices and applied it to various systems. To be a bit more precise, if we tune the external magnetic field such that the energy difference between a molecule and two atoms is sufficiently negative, then the gas consists of a Bose-Einstein condensate of molecules. In contrast, if the energy difference is large enough and positive we have a gas that consists primarily of a Bose-Einstein condensate of atoms. It turns out that these two limits are separated by an Ising-like quantum phase transition. By using atomic Bose gases near a Feshbach resonance detailed experimental studies which test the theoretical predictions of the statistical and dynamical properties of these quantum phase transitions can be made.
In the context of Gross-Pitaevskii theory, we investigate the unconventional Bose-Einstein condensations in the two-species mixture with ppp-wave symmetry in the second band of a bipartite optical lattice. An imaginary-time propagation method is developed to numerically determine the ppp-orbital condensation. Different from the single-species case, the two-species boson mixture exhibits two nonequivalent complex condensates in the intraspecies-interaction-dominating regime, exhibiting the vortex-antivortex lattice configuration in the charge and spin channels, respectively. When the interspecies interaction is tuned across the SU(2) invariant point, the system undergoes a quantum phase transition toward a checkerboardlike spin-density wave state with a real-valued condensate wave function. The influence of lattice asymmetry on the quantum phase transition is addressed. Finally, we present a phase-sensitive measurement scheme for experimentally detecting the unconventional Bose-Einstein condensation in our model.