Mean-Field Dynamics of a Non-Hermitian Bose-Hubbard Dimer

Abstract

We investigate an N-particle Bose-Hubbard dimer with an additional effective decay term in one of the sites. A mean-field approximation for this non-Hermitian many-particle system is derived, based on a coherent state approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in particular, the fixed point structures showing characteristic modifications of the self-trapping transition, are analyzed. The mean-field dynamics is found to be in reasonable agreement with the full many-particle evolution.

Unidirectional nonlinearPT-symmetric optical structures

“…One must also distinguish between closed orbits and those approaching an asymptotic state, as this is in general connected to broken and unbroken PT -symmetry [13]. We note that closely related Bloch dynamics appear in different physical model systems like the ones reported in [24]. Our analysis, indicated that the singularities in z fpd are associated with trajectories that during their evolution, they stay close to the separatrix associated to the critical value χ = 4 (transition between Rabi-oscillations and self-trapping) of the passive system.…”

An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss

“…Another area where the nonlinear Schrödinger dimers occur commonly, comprises the studies of the boson condensation [8,25]. In particular, the nonlinearity (10) describes the mean-field condensate wave function in a symmetric double-well potential in the two-mode approximation [26].…”

“…Originally introduced as a concept in quantum mechanics [1], the idea of PT symmetry has expanded into a wide range of fundamental and applied sciences, most notably photonics [2][3][4], plasmonics [5], quantum optics of atomic gases [6], studies of the Bose-Einstein condensation [7,8], and physics of electronic circuits [9]. The PT -symmetric equations model physical structures with balanced gain and loss.…”

PT-symmetric oligomers: Analytical solutions, linear stability, and nonlinear dynamics

“…This theme has also been considered in the BEC literature and in the context of the so-called leaky Bose-Hubbard dimers (allowing, e.g., the tunneling escape of atoms from one of the wells of a doublewell potential). There, a variant of the model considered below has been self-consistently derived in the mean-field approximation [15] and the correspondence of its classical with the full quantum behavior has been explored [16].…”