Slow Thermalization between a Lattice and Free Bose Gas

Using a 3D spin-dependent optical lattice, we study thermalization and energy exchange between two ultracold Bose gases, one of which is strongly correlated and bound to the lattice and another that is free from the lattice potential. Disruption of interspecies thermalization is revealed through measurements of condensate fraction after the lattice is superimposed on the parabolic confining potential. By selectively heating the lattice-bound species and measuring the rate of heat transfer to the free state, suppression of energy exchange is observed. Comparison with a Fermi’s golden rule prediction confirms that this effect is caused by a dispersion mismatch that reduces the phase space available for elastic collisions. This result has critical implications for methods proposed to cool strongly correlated lattice gases.

Figure 1

Schematic of the spin-dependent lattice potential. The $|1⟩$ atoms (blue spheres centered at lattice minima) are lattice bound, while the $|0⟩$ atoms (red spheres offset from lattice minima) do not experience the lattice potential. Confinement of both species is provided by a 1064 nm crossed-dipole trap (orange lines, $t1$ and $t2$). The spin-dependent lattice is formed by three pairs of counterpropagating 790 nm laser beams (red lines, $l1$, $l2$, and $l3$). Each pair consists of beams with orthogonal linear polarizations (indicated by dashed arrows for $l{1}_a$ and $l{2}_b$).

Figure 2

Top: condensate fraction versus lattice depth for each species. Blue circles (red squares) are for the $|1⟩$ ($|0⟩$) atoms. Each point is averaged over 9–15 experimental runs; the error bars represent the standard error in the mean. For data shown as circles, $N_0/N$ was measured after turning off the lattice potential in less than 50 ns. For data shown as triangles, $N_0/N$ was measured after band mapping in $100\mu \mathrm{s}$, which may overestimate the condensate fraction and underestimate temperature [26]. Bottom: temperature inferred from the measured $N_0/N$ and number of atoms; the statistical uncertainty $T$ is less than 6%. Mixed Mott insulator and superfluid phases exist (at zero temperature) in the lattice for $s\gtrsim 13$. For the predictions shown as dashed lines (upper red for $|0⟩$, lower blue for $|1⟩$), interspecies thermalization is assumed to be absent, and entropy is conserved separately for each component. The solid line assumes interspecies thermal equilibrium.

Figure 3

(a) Condensate fraction for the $|0⟩$ component after dephasing versus hold time for $s=4$. Each point is the average of 10 experimental runs, and the error bars show the standard error of the mean. (b) Temperature inferred for the $|0⟩$ component from the data in (a) (circles) and from a measurement when the lattice atoms are not dephased (diamonds). The solid line is a linear fit to data taken after dephasing and with $t_{\mathrm{hold}}=0–12\mathrm{ms}$ (solid circles), while the dashed line is a linear fit to the control data (diamonds) for all $t_{\mathrm{hold}}$. (c) Control data for the heating rate. The black diamonds show $\dot{T}$ when the lattice atoms are not dephased, and the red squares show $\dot{T}$ when no lattice atoms are present. For comparison, the calculated heating rate for the $|0⟩$ atoms from spontaneous emission driven by the lattice laser beams is $0.02\mathrm{nK}/\mathrm{ms}\times s[E_R]$, which is consistent with the measured heating rates at low $s$ within 1.5 times the standard error.

Figure 4

Energy exchange rate for different lattice potential depths, all in the superfluid regime of the Bose-Hubbard model. Each point is derived from a fit to data at constant $s$, such as the solid line in Fig. 3b; the error bars are the fit uncertainty. The lines show a FGR calculation of the energy exchange rate $\dot{E}$. The scale has been adjusted so that $\dot{E}$ and $\dot{T}$ coincide at $s=4$ since these quantities are proportional.