Nonreciprocal dynamics of exceptional points in pseudo-Hermitian systems under artificial gauge field

Abstract The exploration of nonreciprocal dynamics carries substantial significance in both the field of quantum information processing and the domain of topological photonics. Here, we propose a quadruple-well system for generating nonreciprocity through the utilization of laser-assisted tunneling, wherein the generic principles governing the process can induce both purely real and complex asymmetric coupling mechanisms between adjacent wells. The complex asymmetric tunneling amplitudes induce an artificial gauge field that is equivalent to the Aharonov–Bohm phase experienced by charged particles in a magnetic field. The inclusion of purely real asymmetric tunneling amplitudes introduces pseudo-Hermiticity into the system. We explicitly delineate the conditions for the phase transitions of the system, transitioning from the parity–time ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">PT</mml:mi> </mml:mrow> </mml:mrow> </mml:math> )-symmetric phase to the spontaneously broken <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">PT</mml:mi> </mml:mrow> </mml:mrow> </mml:math> -symmetric phase, along with the corresponding exceptional points (EPs). We then conduct a comprehensive investigation of the intriguing nonreciprocal dynamics both near and at the EPs, yielding notably distinct analytical results across all parametric regions. Furthermore, we demonstrate the tunability of nonreciprocal transport by manipulating the pseudo-Hermiticity and artificial gauge field, thereby enabling the reversal of the nonreciprocal directionality. Our study exhaustively elucidates the profound mechanisms underlying the interplay between pseudo-Hermiticity and artificial gauge fields on nonreciprocal dynamics, with potential implications for the design of innovative quantum nonreciprocal devices.