Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance

TL;DR

This paper demonstrates how to create and control exceptional points in non-Hermitian Hamiltonians of open quantum systems by changing measurement postselection methods, specifically using homodyne detection with a weak laser.

Contribution

It introduces a novel scheme to generate and tune exceptional points in non-Hermitian Hamiltonians through measurement-based postselection in quantum systems.

Findings

Homodyne measurement can induce exceptional points in systems without them.

Different postselections lead to different spectral properties of the non-Hermitian Hamiltonian.

The method allows for controllable engineering of spectral degeneracies in quantum systems.

Abstract

The Exceptional Points (EPs) of non-Hermitian Hamiltonians (NHHs) are spectral degeneracies associated with coalescing eigenvalues and eigenvectors which are associated with remarkable dynamical properties. These EPs can be generated experimentally in open quantum systems, evolving under a Lindblad equation, by postselecting on trajectories that present no quantum jumps, such that the dynamics is ruled by a NHH. Interestingly, changing the way the information used for postselection is collected leads to different unravelings, i.e., different set of trajectories which average to the same Lindblad equation, but are associated with a different NHH. Here, we exploit this mechanism to create and control EPs solely by changing the measurement we postselect on. Our scheme is based on a realistic homodyne reading of the emitted leaking photons with a weak-intensity laser (a process which we call $\beta$-dyne), which we show generates a tunable NHH, that can exhibit EPs even though the system does have any in the absence of the laser. We consider a few illustrative examples pointing the dramatic effects that different postselections can have on the spectral features of the NHH, paving the road towards engineering of EPs in simple quantum systems.