Melting of Discrete Vortices via Quantum Fluctuations

We consider nonlinear boson states with a nontrivial phase structure in the three-site Bose-Hubbard ring, quantum discrete vortices (or $q$ vortices), and study their “melting” under the action of quantum fluctuations. We calculate the spatial correlations in the ground states to show the superfluid-insulator crossover and analyze the fidelity between the exact and variational ground states to explore the validity of the classical analysis. We examine the phase coherence and the effect of quantum fluctuations on $q$ vortices and reveal that the breakdown of these coherent structures through quantum fluctuations accompanies the superfluid-insulator crossover.

Figure 1

Schematic diagrams. (a) Bosons in a strongly trimerized Kagomé lattice [10] can be reduced to three-site Bose-Hubbard rings. (b) Combining a proper two-dimensional harmonic potential with the Kagomé lattice, a triple-well potential can be generated; (c) three-site state.

Figure 2

Spatial correlations vs $U/T$.

Figure 3

Fidelities between the variational and exact ground states vs $U/T$ for different $N$.

Figure 4

Quantum adiabatic evolution of $q$ vortices with $N=6$ from the linear to the nonlinear limit. (a) and (b) correspond to the cases of $L=3k$ and $L=3k\pm 1$, respectively.

Figure 5

Quantum fluctuations for the vortex states vs the ratio $U/T$ for different values of $N$.