Chiral state-conversion without encircling an exceptional point

TL;DR

This paper demonstrates that chiral mode conversion in non-Hermitian systems can occur without encircling an exceptional point, broadening the conditions needed for asymmetric state exchange.

Contribution

It shows that slow parameter variation can induce chiral mode conversion without enclosing an exceptional point, expanding the understanding of non-Hermitian dynamics.

Findings

Mode conversion occurs without encircling an exceptional point.

Asymptotic analysis confirms robustness of the process.

Broadens experimental parameter space for chiral mode conversion.

Abstract

Dynamically varying system parameters along a path enclosing an exceptional point is known to lead to chiral mode conversion. But is it necessary to include this non-Hermitian degeneracy inside the contour for this process to take place? We show that a slow enough variation of parameters, even away from the system's exceptional point, can also lead to a robust asymmetric state exchange. To study this process, we consider a prototypical two-level non-Hermitian Hamiltonian with a constant coupling between elements. Closed form solutions are obtained when the amplification/attenuation coefficients in this arrangement are varied in conjunction with the resonance detuning along a circular contour. Using asymptotic expansions, this input-independent mode conversion is theoretically proven to take place irrespective of whether the exceptional point is enclosed or not upon encirclement. Our results significantly broaden the range of parameter space required for the experimental realization of such chiral mode conversion processes.