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arXiv:0910.1114 · Physical Review A

Isentropes of spin-1 bosons in an optical lattice

Khan W. Mahmud, G. G. Batrouni, Richard T. Scalettar

Published Mar 17, 2010• 5 citations
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Abstract

We analyze the effects of adiabatic ramping of optical lattices on the temperature of spin-1 bosons in a homogeneous lattice. Using mean-field theory, we present the isentropes in the temperature-interaction strength ($T,{U}_{0}$) plane for ferromagnetic, antiferromagnetic, and zero spin couplings. Following the isentropic lines, temperature changes can be determined during adiabatic loading of current experiments. We show that the heating-cooling separatrix lies on the superfluid-Mott phase boundary with cooling occurring within the superfluid and heating in the Mott insulator and quantify the effects of spin coupling on the heating rate. We find that the mean-field isentropes for low initial entropy terminate at the superfluid--Mott-insulator phase boundary.

DOI
10.1103/physreva.81.033609

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We analyze the effects of adiabatic ramping of optical lattices on the temperature of spin-1 bosons in a homogeneous lattice. Using mean-field theory, we present the isentropes in the temperature-interaction strength (T,U0T,{U}_{0}T,U0​) plane for ferromagnetic, antiferromagnetic, and zero spin couplings. Following the isentropic lines, temperature changes can be determined during adiabatic loading of current experiments. We show that the heating-cooling separatrix lies on the superfluid-Mott phase boundary with cooling occurring within the superfluid and heating in the Mott insulator and quantify the effects of spin coupling on the heating rate. We find that the mean-field isentropes for low initial entropy terminate at the superfluid--Mott-insulator phase boundary.
When atoms are loaded into an optical lattice, the process of gradually turning on the lattice is almost adiabatic. In this paper, we investigate how the temperature changes when going from the gapless superfluid phase to the gapped Mott phase along isentropic lines. To do so we calculate the entropy in the single-band Bose–Hubbard model for various densities, interaction strengths and temperatures in one and two dimensions for homogeneous and trapped systems. Our theory is able to reproduce the experimentally observed visibilities and therefore strongly supports the view that current experiments remain in the quantum regime for the considered lattice depths with low temperatures and minimal heating.
We investigate effects of the adiabatic ramp-up of optical lattices to the temperatures of Bose gases. Applying the mean-field approximation to the three-dimensional Bose-Hubbard model at finite temperatures, we calculate the isentropic curves in the phase diagram against the temperatures and the lattice height. The adiabatic cooling or heating through superfluid-normal phase transition is clearly understood. It is found that the cooling occurs in superfluid phase while the heating occurs in normal phase and the efficiency of adiabatic cooling or heating is higher at higher temperatures. This behavior can be understood from the lattice-height dependence of dispersion relation in each phase. Furthermore, the connection of the adiabatic cooling or heating between the cases with and without the trap potential is addressed.
The superfluid--Mott-insulator transition of spin-2 boson atoms with repulsive interaction in an optical lattice in a magnetic field is presented. By using the mean-field theory, the Mott ground states and phase diagrams of the superfluid--Mott-insulator transition at zero temperature are revealed. An applied magnetic field leads to splitting of some phase boundaries. For all the initial Mott ground states containing multiple spin components, different spin components take on different phase boundaries. It is found that in this system phase boundaries with different magnetization can be moved in different ways by changing only the intensity of the applied magnetic field.
We calculate entropy-temperature curves for interacting bosons in unit filled optical lattices for both homogeneous and harmonically trapped situations, and use them to understand how adiabatic changes in the lattice depth affect the temperature of the system. In a translationally invariant lattice, the zero tunneling limit facilitates a rather detailed analytic description. Unlike the noninteracting bosonic system which is always cooled upon adiabatic loading for low enough initial temperature, the change in the excitation spectrum induced by interactions can lead to heating. Finite tunneling helps to reduce this heating. Finally, we study the spatially inhomogeneous system confined in a parabolic potential and show that the presence of the trap can significantly reduce the final available temperature, due to the nonvanishing superfluid component at the edge of the cloud which is present in trapped systems.
We present a quantitative finite temperature analysis of a recent experiment with Bose-Fermi mixtures in optical lattices, in which the dependence of the coherence of bosons on the interspecies interaction was analyzed. Our theory reproduces the characteristics of this dependence and suggests that intrinsic temperature effects play an important role in these systems. Namely, under the assumption that the ramping up of the optical lattice is an isentropic process, adiabatic temperature changes of the mixture occur that depend on the interaction between bosons and fermions. Matching the entropy of two regimes-no lattice on the one hand and deep lattices on the other-allows us to compute the temperature in the lattice and the visibility of the quasimomentum distribution of the bosonic atoms, which we compare to the experiment.
We investigate strongly correlated spin-1 ultracold bosons with antiferromagnetic interactions in a cubic optical lattice, based on bosonic dynamical mean-field theory. Rich phase diagrams of the system are mapped out at both zero and finite temperature, and in particular the existence of a spin-singlet condensate is established. Interestingly, at finite temperature, we find that the superfluid can be heated into a Mott insulator with even (odd) filling via a first- (second-) order phase transition, analogous to the Pomeranchuk effect in 3He^{3}\mathrm{He}3He. Moreover, for typical experimental setups, we estimate the critical temperature (entropy) for different ordered phases and our results suggest that direct experimental observation of these phases is promising.