Bosonic molecules in a lattice: Unusual fluid phase from multichannel interactions

We show that multichannel interactions significantly alter the phase diagram of ultracold bosonic molecules in an optical lattice. Most prominently, an unusual fluid region intervenes between the conventional superfluid and the Mott insulator. In it, number fluctuations remain but phase coherence is suppressed by a significant factor. This factor can be made arbitrarily large, at least in a two-site configuration. We calculate the phase diagram using complementary methods, including Gutzwiller mean-field and density-matrix renormalization group calculations. Although we focus on bosonic molecules without dipolar interactions, we expect multichannel interactions to remain important for dipolar interacting and fermionic molecules.

Figure 1

Nonreactive molecules in a lattice: Hamiltonian and results for two sites. (a) A molecule tunnels into an adjacent singly occupied site to create one of several two-particle states $|2_{\alpha }\rangle$ with energy $U_{\alpha }$ where $\alpha$ labels possible channels. The corresponding matrix element is $-t{O}_{\alpha }$, where $t$ is the single-molecule tunneling rate. (b–d) Number fluctuations $\sigma$ and halved coherence $C/2$. (b) Single channel, as for simple atoms. (c) Two channels ($U_2={10}^4{U}_1$, $O_1=0.22$, $O_2=0.97$) illustrate two major modifications to the phase diagram: (i) a wide intermediate range (shaded) of $t/U_1$ where coherence is significantly suppressed even though number fluctuations are near their large-$t$ values and (ii) suppressed number fluctuations at the boundary between the intermediate and the large-$t$ regions. (d) Results for three channels ($U_2={10}^2{U}_1$, $U_3={10}^4{U}_1$, $O_1=0.32$, $O_2=0.55$, $O_3=0.77$).

Figure 2

Coherence $C_{10,20}$, number fluctuations, and density of a 1D chain as a function of $t/U_1$ for Gutzwiller mean-field theory (left) and DMRG ($L=30$, right) for one channel and two channels, (top to bottom), and cuts at $\mu =0.5$. Parameters are $U_2={10}^4{U}_1$ and $O_2=0.89$. Contour lines are spaced in intervals of 0.05 for $C$ and $\sigma$, and 0.067 for density. Note that the Mott lobe tilts upwards as $O_1$ is decreased, and the presence of the coherence plateau in the two-channel plot. This opacity ratio is at the limit of what our numerical calculations can handle, hence the jagged number fluctuations in the DMRG cut (see text for details).

Figure 3

Effects of changing $O_{\alpha }$ on (a) number fluctuations and (b) coherence, illustrated by solving two molecules on two sites with two-channel interactions. The ratio $O_2/O_1$ is doubled each step.

Figure 4

Effect of random distribution of $O_{\alpha }\mathrm{s}$ and $U_{\alpha }\mathrm{s}$. (a) Parametric plots of coherence versus number fluctuations for two-molecule, two-site, five-channel model. We plot 1000 curves, each from parameters sampled from a physically realistic distribution described in the text. (b) Same as (a) for $L=15$ chain with $\langle n\rangle =1$, calculated using DMRG. (c) Same as (a), but with 100 channels. In all cases, there are strong deviations from the single-channel result (bottom solid line).