Thermodynamics of adiabatically loaded cold bosons in the Mott insulating phase of one-dimensional optical lattices

Abstract

In this work we give a consistent picture of the thermodynamic properties of bosons in the Mott insulating phase when loaded adiabatically into one-dimensional optical lattices. We find a crucial dependence of the temperature in the optical lattice on the doping level of the Mott insulator. In the undoped case, the temperature is of the order of the large onsite Hubbard interaction. In contrast, at a finite doping level the temperature jumps almost immediately to the order of the small hopping parameter. These two situations are investigated on the one hand by considering limiting cases like the atomic limit and the case of free fermions. On the other hand, they are examined using a quasi-particle conserving continuous unitary transformation extended by an approximate thermodynamics for hardcore particles.

Boson Mott Insulators at Finite Temperatures

“…Similar calculations for homogeneous systems with integer filling would yield a much higher temperature [10], since near the center of the Mott lobe the entropy is exponentially suppressed by the finite interaction energy U . In the trapped case, the entropy in fact concentrates around the lobe boundaries, where the generation of excitations is easiest.…”

“…However, actual experiments inevitably take place at finite temperatures, which leads, e.g., to residual number fluctuations. In view of its importance for applications such as the controlled generation of entangled states [1], or the study of quantum magnetism [3], this issue has recently received increasing interest [5,6,7,8,9,10,11,12,13]. In this paper, we first discuss how the phase diagram of a ultracold Bose gas in an optical lattice is modified at finite temperatures.…”

Adiabatic loading of rotating bosons into 1D optical lattice

“…The requirements of this type of loading can be understood from the entropy considerations [16,20]. For the rotating condensate in an optical lattice, the normalized entropy per particle is given by [29] …”

“…Therefore, it is important to consider the entropy-temperature curves under realistic experimental conditions. These curves can be used for analyzing the effect of the optical potential depth and rotation rate on the temperature of the system, and moreover in analyzing the process of loading the rotating condensate into the optical lattice [19,20,21].…”

Finite-temperature coherence of the ideal Bose gas in an optical lattice

“…The question of temperature and critical tempera-ture change during the process of loading an optical lattice with atoms has already received substantial study [22,23,24,25,26,27,28,29]. Unfortunately the problem turns out to be quite complicated in practice.…”