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Register a new userQuantum phase transition of condensed bosons in optical lattices
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In this paper we study the superfluid-Mott-insulator phase transition of ultracold dilute gas of bosonic atoms in an optical lattice by means of Green function method and Bogliubov transformation as well. The superfluid- Mott-insulator phase transition condition is determined by the energy-band structure with an obvious interpretation of the transition mechanism. Moreover the superfluid phase is explained explicitly from the energy spectrum derived in terms of Bogliubov approach.
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We work out two different analytical methods for calculating the boundary of the Mott-insulator-superfluid (MI-SF) quantum phase transition for scalar bosons in cubic optical lattices of arbitrary dimension at zero temperature which improve upon the seminal mean-field result. The first one is a variational method, which is inspired by variational perturbation theory, whereas the second one is based on the field-theoretic concept of effective potential. Within both analytical approaches we achieve a considerable improvement of the location of the MI-SF quantum phase transition for the first Mott lobe in excellent agreement with recent numerical results from Quantum Monte-Carlo simulations in two and three dimensions. Thus, our analytical results for the whole quantum phase diagram can be regarded as being essentially exact for all practical purposes.
We introduce a theory for the stability of a condensate in an optical lattice. We show that the understanding of the stability-to-ergodicity transition involves the fusion of monodromy and chaos theory. Specifically, the condensate can decay if a connected chaotic pathway to depletion is formed, which requires swap of seperatrices in phase-space.
We present an analytic description of the finite-temperature phase diagram of the Bose-Hubbard model, successfully describing the physics of cold bosonic atoms trapped in optical lattices and superlattices. Based on a standard statistical mechanics approach, we provide the exact expression for the boundary between the superfluid and the normal fluid by solving the self-consistency equations involved in the mean-field approximation to the Bose-Hubbard model. The zero-temperature limit of such result supplies an analytic expression for the Mott lobes of superlattices, characterized by a critical fractional filling.
We investigate the effects of the adiabatic loading of optical lattices to the temperature by applying the mean-field approximation to the three-dimensional Bose-Hubbard model at finite temperatures. We compute the lattice-height dependence of the isentropic curves for the given initial temperatures in case of the homogeneous system i.e., neglecting the trapping potential. Taking the unit of temperatures as the recoil energy, the adiabatic cooling/heating through superfluid (SF) - normal (N) phase transition is clearly understood. It is found that the cooling occurs in SF phase while the heating occurs in N phase and the efficiency of adibatic cooling/heating is higher at higher temperatures. We also explain how its behavior can be understood from the lattice-hight dependence of dispersion relation in each phase. Furthermore, the connection of the adiabatic heating/cooling between the cases with/without the trapping potential is discussed.
In this paper, the quantum phase transition between superfluid state and Mott-insulator state is studied based on an extended Bose-Hubbard model with two- and three-body on-site interactions. By employing the mean-field approximation we find the extension of the insulating lobes and the existence of a fixed point in three dimensional phase space. We investigate the link between experimental parameters and theoretical variables. The possibility to obverse our results through some experimental effects in optically trapped Bose-Einstein Condensates(BEC) is also discussed.
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