Quantum holonomy in the Lieb-Liniger model

Abstract

We examine a parametric cycle in the N -body Lieb-Liniger model that starts from the free system and goes through Tonks-Girardeau and super-Tonks-Girardeau regimes and comes back to the free system. We show the existence of exotic quantum holonomy, whose detailed workings are analyzed with the specific sample of two-and three-body systems. The classification of eigenstates based on clustering structure naturally emerges from the analysis.

Adiabatic cycles in quantum systems with contact interactions

“…During the cycle, we vary an additional wall adiabatically, while the interparticle interaction is kept fixed. This is in contrast to the scheme described in [4,5], where the interaction strength between Bose particles is an effective adiabatic parameter. In this study, we suppose that the wall is described by a δ-function shaped potential [6][7][8].…”

“…Such a population inversion can be induced even by an adiabatic cycle, which can be obtained with an extension of the adiabatic process that connects Tonks-Girardeau and super-Tonks-Girardeau gases both to weaker repulsive and weaker attractive regime. The repetitions of this adiabatic cycle transform the ground state of non-interacting bosons into their higher excited states and achieve the population inversion [5]. This is counterintuitive, since there is no external field to drive the final state of the bosons away from the initial state.…”

Adiabatic excitation of a confined particle in one dimension with a variable infinitely sharp wall

“…Another exam-ple C Y involves an insertion, a flip, and a removal of the wall. The eigenspace permutation induced by C Y resembles the one found in the Lieb-Liniger model [17], where all eigenspaces are excited at a time [18].…”

“…In this cycle, the strength of the two-body contact interaction of Bose particles is varied from zero to ∞, then is changed from ∞ to −∞ suddenly, and is finally increased from −∞ to zero. The adiabatic cycle excites the system consists of the Bose particles [18].…”

Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops

“…Namely, under the presence of such an exotic quantum holonomy, the initial and final states of an adiabatic cycle belong to different eigenspaces. The exotic quantum holonomy has been studied both in one-body [5][6][7][8][9][10] and in many-body systems [11]. Applications of the exotic quantum holonomy to quantum state manipulation and adiabatic quantum computation [12] were also proposed [5,6,13].…”