For a non-interacting many particle Bose system whose energy operator is diagonal in the number of occupation operators [Formula: see text] upper bounds on the thermal averages [Formula: see text] are obtained. These bounds lead to the proof of Bose–Einstein condensation for finite values of the inverse temperature β and for chemical potential μ=0. Finally for μ<0, in the case of a generalization of the studied model system, the property of Local Gaussian Domination for the grand canonical partition function is proved.For a non-interacting many particle Bose system whose energy operator is diagonal in the number of occupation operators [Formula: see text] upper bounds on the thermal averages [Formula: see text] are obtained. These bounds lead to the proof of Bose–Einstein condensation for finite values of the inverse temperature β and for chemical potential μ=0. Finally for μ<0, in the case of a generalization of the studied model system, the property of Local Gaussian Domination for the grand canonical partition function is proved.

International Journal of Modern Physics BJan 30, 20023 citations

Unconventional Bose-Einstein condensation in a system with two species of bosons in the p -orbital bands in an optical lattice

Jhih-Shih You, I-Kang Liu, Daw-Wei Wang +2 more

In the context of Gross-Pitaevskii theory, we investigate the unconventional Bose-Einstein condensations in the two-species mixture with $p$ -wave symmetry in the second band of a bipartite optical lattice. An imaginary-time propagation method is developed to numerically determine the $p$ -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.In the context of Gross-Pitaevskii theory, we investigate the unconventional Bose-Einstein condensations in the two-species mixture with $p$-wave symmetry in the second band of a bipartite optical lattice. An imaginary-time propagation method is developed to numerically determine the $p$-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.

arXiv:1508.02914Physical Review AMay 23, 20164 citations

Bose-Einstein Condensation in Quantum Lattice Model

Tosizumi Aoki

Journal of the Physical Society of JapanFeb 15, 19922 citations

In the context of Gross-Pitaevskii theory, we investigate the unconventional Bose-Einstein condensations in the two-species mixture with

p

-wave symmetry in the second band of a bipartite optical lattice. An imaginary-time propagation method is developed to numerically determine the

p

-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.