Research
Superfluidity and Chaos in Bose-Hubbard rings
The essence of superfluidity is the possibility to witness metastable flow states. In the standard classical stability analysis one finds that flow states whose rotation velocity is less than a critical velocity are metastable (”Landau criterion”). We show that the standard Landau superfluidity criteria fail in low-dimensional circuits. We claim that a proper determination of the superfluidity regime-diagram must account for the crucial role of chaos.
The results are novel due to the quantum chaos perspective. In particular we predict drastic differences between 3 site rings and rings that have more than 3 sites. In the former instability of flow states is due to swap of separatrices, while in the latter it has to do with a web of non-linear resonances.
We provide metastability regime diagrams for future hysteresis-type experiments that involve a quench scenario and clarify how phase-space features are reflected in the time dependence of the decay process.
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Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit[arXiv][pdf][PRA 2014] - Superfluidity and Chaos in low dimensional circuits [arXiv] [pdf][Sci-Rep 2015],
- Superfluidity of Bose-Hubbard circuits [arXiv] [pdf] [PRB 2017]
Semiclassical analysis of the Atomtronic quantum interference device
We study the atomtronic quantum interference device, described by a Bose–Hubbard (BH) circuit with a weak link, employing a semiclassical perspective. The introduction of a weak-link allows the reduction of the many-body BH Hamiltonian into the simpler Josephson circuit Hamiltonian, coupled to a Caldeira-Leggett bath. We investigate the viability of the ‘system plus bath’ framework for both rings with few or many sites and find the critical strength of a weak-link, below which the current is diminished.
In addition, we show that in the absence of a weak-link, coherent Rabi oscillations are feasible, with a frequency that is possibly determined by chaos-assistance tunneling, leading to weaker dependence on the number of particles.
Coherent Transport
We find a general expression for the current that flows via a tagged bond of a quantum network from a site (dot) whose potential is varied in time. Our approach allows us to address the adiabatic regime, as well as the slow and fast non-adiabatic regimes, on equal footing. We demonstrate its use in the case of a ring geometry, emphasizing aspects that go beyond the familiar two-level approximation phenomenology, related to the scrambling of the network levels during the sweep process.
