Critical temperature of noninteracting bosonic gases in cubic optical lattices at arbitrary integer fillings

We have shown that the critical temperature of a Bose-Einstein condensate to a normal phase transition of noninteracting bosons in cubic optical lattices has a linear dependence on the filling factor, especially at large densities. The condensed fraction exhibits a linear power law dependence on temperature in contrast to the case of ideal homogeneous Bose gases.

Figure 1

The solution of Eq. (11) $t_c^0\left(\nu \right)$ (a) shown as symbols, and the dimensionless critical temperature, $T_c^0/J$, (b) of ideal cubic optical lattice versus the filling factor $\nu$ in realistic dimensions $d=1,2,3$. The dashed lines in panel (a) show the asymptotics of $t_c^0\left(\nu \right)$ given by (14).

Figure 2

The condensed fraction $n_0$ vs reduced temperature $t=T/T_c^0$, as an exact solution of Eq. (19) for $d=3$ and different values of $\nu$. The thick solid line corresponds to the IHB gas.

Figure 3

The total energy per site in units $T_c^0$ vs reduced temperature $t=T/T_c^0$, for $d=3$ and different values of $\nu$. The thick solid line corresponds to the IHB gas.

Figure 4

The same as in Fig. 3 but for the heat capacity, $C_v/N_s$. It seen that at high filling factors, $\nu \ge 10$, the $C_v/N_s$ becomes constant at $T\ge 0.1T_c^0$

Figure 5

The same as in Fig. 3 but for the entropy per particle, $S/N$. It is seen that $t^{3/2}$ power law does not hold even at $\nu =1$.