Thermally induced coherence in a Mott insulator of bosonic atoms

Naively, one may think that increasing temperature causes quantum coherence to decrease. Using finite-temperature perturbation theory and exact calculations for the strongly correlated bosonic Mott insulating state, we show a practical counterexample that can be explored in optical lattice experiments: the short-range coherence of the Mott insulating phase can increase substantially with increasing temperature. We demonstrate that this phenomenon originates from thermally produced defects that can tunnel with ease. Since the near-zero temperature coherence properties have been measured with high precision, we expect these results to be verifiable in current experiments.

Figure 1

Schematic of processes that lead to short-range coherence. (a) Gapped tunneling: particle-hole formation caused by tunneling $J$ but costing the gap energy $U$. (b, c) Gapless tunneling: thermal defects can tunnel without energy cost.

Figure 2

Nearest-neighbor coherence. (a) Perturbative treatment: full $c_1^{(1)}$ (solid line), gapped $c_1^{(1a)}$(dashed line), and gapless $c_1^{(1b)}$ (dash-dotted line) results for $\mu =1.5U$. Perturbative (black) [Eqs. (7) and (8)] and simple analytic (yellow/grey) [Eqs. (9) and (10)] results. (b) Variation with chemical potential and comparison of perturbative (solid line) and exact (dots) results for a 1D lattice. $\mu =1.25U$ (black), $1.5U$ (red/grey), and $1.75U$ (green/light grey). Inset: comparison of full perturbative results (solid line) against exact calculations (dots) near the phase boundary $\mu =1.95U$ (blue/dark grey), $1.05U$ (red/light grey). Other parameters: $J=0.01U$ and $\mathrm{n̄}=2$.

Figure 3

Nearest-neighbor coherence along $x$. Homogeneous case (independent of dimensionality) with $\mu =0.8U$ (black dots). Inhomogeneous 1D case for $\mu =0.8U$ (green/light grey line) and $0.5U$ (blue/dark grey dotted line). Inhomogeneous 2D case for $\mu =0.8U$ (red/grey dashed line). Other parameters: $J/U=8.35\times {10}^{-3}$, $\mu$ values such that $\mathrm{n̄}=1$ at trap center, ${}^{87}\mathrm{Rb}$ atoms in a $410$-nm-period lattice, and harmonic trap frequency of $\omega =2\pi \times 40$ Hz.