Quantum integrable multi-well tunneling models

Abstract

In this work we present a general construction of integrable models for boson tunneling in multi-well systems. We show how the models may be derived through the Quantum Inverse Scattering Method and solved by algebraic Bethe ansatz means. From the transfer matrix we find only two conserved operators. However, we construct additional conserved operators through a different method. As a consequence the models admit multiple pseudovacua, each associated to a set of Bethe ansatz equations. We show that all sets of Bethe ansatz equations are needed to obtain a complete set of eigenstates.

Efficient trainability of linear optical modules in quantum optical neural networks

“…For few-mode bosonic systems, the structure of exact and high-quality variational ground states of certain quartic Hamiltonians is known [27][28][29][30][31]. The analysis in Proposition 2 can be extended to the case of variational mean field energy estimation of positive quartic Hamiltonians by using higher moments of the Haar measure on the orthogonal group [32].…”

The Yang-Baxter paradox

“…Remark 8. The class of Hamiltonians with the form (12) generalises a class of Hamiltonians introduced in [62]. The classes coincide when A has rank 1.…”

Quantum-classical correspondence of a system of interacting bosons in a triple-well potential

“…When quantum gases, such as chromium or dysprosium, are loaded into triple well potentials [35], dipolar interactions need to be taken into account [35] and they lead to various ground-state phases [35,38]. An integrable version of this dipolar model in one dimension, solvable with the algebraic Bethe ansatz, was derived in [39], and by tilting the potential, this model can be brought to the chaotic domain [40]. The tilt is an additional control parameter that expands the versatility of the model and allows for its possible application as an atomtronic switching device [40] and as a generator of entangled states [41].…”