Quantum Emulsion: A Glassy Phase of Bosonic Mixtures in Optical Lattices

We numerically investigate mixtures of two interacting bosonic species with unequal parameters in one-dimensional optical lattices. In large parameter regions full phase segregation is seen to minimize the energy of the system, but the true ground state is masked by an exponentially large number of metastable states characterized by microscopic phase separation. The ensemble of these quantum emulsion states, reminiscent of emulsions of immiscible fluids, has macroscopic properties analogous to those of a Bose glass, namely, a finite compressibility in absence of superfluidity. Their metastability is probed by extensive quantum Monte Carlo simulations generating rich correlated stochastic dynamics. The tuning of the repulsion of one of the two species via a Feshbach resonance drives the system through a quantum phase transition to the superfluid state.

Figure 1

(a) Correlation between the energy and the phase interface in the metastable ensemble. The model parameters are $U_a=J_a$, $U_b=U_{ab}=5J_a$, $J_b=J_a/5$, $⟨n_a⟩=1$, and $n_b=1/2$. Each point is obtained after 1000 thermalization MCSs and 2000 measurement MCSs after cooling at a rate $r=2\times {10}^{-4}$. (b) Density-density correlation function of the $b$ bosons, $C_b(r)=⟨(n_{b,i}-{\overline{n}}_b)(n_{b,i+r}-{\overline{n}}_b)⟩$. (c) Two density snapshots of a long QMC simulation.

Figure 2

(a),(b) Energy versus cooling rate for thermal annealing (Hamiltonian parameters as in Fig. 1). $\Delta T=0.05J_a$ for $L=48$ and $0.02J_a$ for $L=96$. (c) Time schedule in the quantum annealing procedure; in the simulation the time variable is changed in steps of $5\times {10}^{-2}$. [magnetic field (MF)]. (d) Energy versus annealing rate for quantum annealing.

Figure 3

Phases of the $a$ bosons upon tuning the repulsion $U_a$. Upper panel: superfluid fraction ${\rho }_{s,a}$ and compressibility ${\kappa }_a$. Lower panel: coherent fraction $N_a(k=0)$ and inverse correlation length ${\xi }_a^{-1}$. Inset: Sketch of the interaction-assisted resonant tunneling.