# Non-Hermitian dynamics without dissipation in quantum systems

## TL;DR

This paper introduces methods to achieve non-Hermitian dynamics in quantum systems without dissipation, enabling new applications in quantum sensing, entanglement, and topological phenomena using parametric driving.

## Contribution

It presents routes to realize unconditional non-Hermitian dynamics in non-dissipative quantum systems via quadratic bosonic Hamiltonians that break particle number conservation.

## Key findings

- Non-Hermitian dynamics can be achieved without dissipation in quantum systems.
- Mappings from non-Hermitian to Hermitian Hamiltonians are explored.
- Applications include quantum sensing, entanglement, and topological effects.

## Abstract

Models based on non-Hermitian Hamiltonians can exhibit a range of surprising and potentially useful phenomena. Physical realizations typically involve couplings to sources of incoherent gain and loss; this is problematic in quantum settings, because of the unavoidable fluctuations associated with this dissipation. Here, we present several routes for obtaining unconditional non-Hermitian dynamics in non-dissipative quantum systems. We exploit the fact that quadratic bosonic Hamiltonians that do not conserve particle number give rise to non-Hermitian dynamical matrices. We discuss the nature of these mappings from non-Hermitian to Hermitian Hamiltonians, and explore applications to quantum sensing, entanglement dynamics and topological band theory. The systems we discuss could be realized in a variety of photonic and phononic platforms using the ubiquitous resource of parametric driving.