Non-Hermiticity in quantum nonlinear optics through symplectic transformations

• URL: http://arxiv.org/abs/2310.04523v1
• Date: Fri, 6 Oct 2023 18:41:46 GMT
• Title: Non-Hermiticity in quantum nonlinear optics through symplectic transformations
• Authors: Ross Wakefield, Anthony Laing, and Yogesh N. Joglekar
• Abstract summary: We show that second-quantised Hermitian Hamiltonians on the Fock space give rise to non-Hermitian effective Hamiltonians. We create a quantum optical scheme for simulating arbitrary non-unitary processes by way of singular value decomposition.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Over the past decade classical optical systems with gain or loss, modelled by non-Hermitian parity-time symmetric Hamiltonians, have been deeply investigated. Yet, their applicability to the quantum domain with number-resolved photonic states is fundamentally voided by quantum-limited amplifier noise. Here, we show that second-quantised Hermitian Hamiltonians on the Fock space give rise to non-Hermitian effective Hamiltonians that generate the dynamics of corresponding creation and annihilation operators. Using this equivalence between $\mathcal{PT}$-symmetry and symplectic Bogoliubov transformations, we create a quantum optical scheme comprising squeezing, phase-shifters, and beam-splitters for simulating arbitrary non-unitary processes by way of singular value decomposition. In contrast to the post-selection scheme for non-Hermitian quantum simulation, the success probability in this approach is independent of the system size or simulation time, and can be efficiently Trotterised similar to a unitary transformation.

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