Abstract
An exactly solved bosonic tunneling model is studied along a line of the coupling parameter space, which includes a quantum phase boundary line. The entire energy spectrum is computed analytically, and found to exhibit multiple energy-level crossings in a region of the coupling parameter space. Several key properties of the model are discussed, which exhibit a clear dependence on whether the particle number is even or odd. Principal among these is a number-parity effect in the quantum dynamics.
Highlights
The symmetric two-site Bose–Hubbard model has been studied widely for some time [1,2,3,4,5,6]
We investigate some further consequences of number parity in the remaining sections
There is no supersymmetry point in the coupling parameter space when N is odd. One example where this particular parity property has a striking manifestation is in the study of quantum dynamics
Summary
The symmetric two-site Bose–Hubbard model has been studied widely for some time [1,2,3,4,5,6]. It is checked that, up to the inclusion of an N-dependent term, U maps Hamiltonians between the phase-locking and self-trapping phases, while Hamiltonians in the Josephson phase are mapped back to the Josephson phase under the action of U This shows that there is a one-toone correspondence between the energy spectra in phaselocking and self-trapping phases. Hamiltonians on the line γ = λ, or equivalently Ω = k/2, are invariant under the action of U Along this line, which includes the boundary between the phase-locking and self-trapping phases, analytic expressions for the entire energy spectrum can be obtained, as we describe below
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