Universal Thermometry for Quantum Simulation

Quantum simulation is a highly ambitious program in cold atom research currently being pursued in laboratories worldwide. The goal is to use cold atoms in optical lattices to simulate models for unsolved strongly correlated systems, so as to deduce their properties directly from experimental data. An important step in this effort is to determine the temperature of the system, which is essential for deducing all thermodynamic functions. This step, however, remains difficult for lattice systems at the moment. Here, we propose a method based on a generalized fluctuation-dissipation theorem. It does not rely on numerical simulations and gives a universal thermometry scheme for quantum gas systems including mixtures and spinor gases, provided that the local density approximation is valid.

Figure 1

Demonstration of our scheme. Blue clouds represent $Q$ samples in the repeated experiments. Magenta grids represent the optical lattice. The density of the $i$th sample at position $\mathbf{r}$ is represented as $n^{(i)}(\mathbf{r})$. Azimuthal averaging of $n^{(i)}(\mathbf{r})$ in each sample is done in the region represented by the red ring to obtain $\zeta (\rho )$ and $\eta (\rho )$.

Figure 2

Density profile in the trap. Red dots: Ensemble averaging over 2000 configurations. Blue boxes:LDA. Black crosses: Exact density in the trap.

Figure 3

Compressibility (left) and number fluctuations (right) in the trap. Red dots: averaging over 50 configurations. Black crosses: Exact results in the trap. Blue boxes: LDA.

Figure 4

Linear fit for $\{\mathcal{L}(\rho ),\mathcal{R}(\rho )\}$ to extract $T$. Blue dots are the results of $\mathcal{L}(\rho )$ and $\mathcal{R}(\rho )$ from averaging 50 configurations. Blue straight line is the fitting results. Red straight dashed line represents the real temperature $T=0.1t$.