aiqbench analysis
This paper advances quantum optics theory by deriving time-closed solutions for trilinear bosonic systems using a perturbative expansion in field amplitudes, offering superior convergence over standard BCH methods in high-gain regimes. The approach provides rigorous higher-order corrections essential for analyzing entanglement detection and squeezing limits in parametric amplification and frequency generation processes.
Weak-Field Expansion: A Time-Closed Solution of Quantum Three-Wave Mixing
arXiv:2603.29869v3 Announce Type: replace Abstract: We present a systematic derivation of the Heisenberg evolution of a trilinear bosonic Hamiltonian system in presence of a strong drive beyond the standard approximation of a classical, undepleted driving field. We employ a perturbative expansion of the Hamiltonian propagator in orders of the input field amplitudes, as opposed to the standard Baker-Campbell-Hausdorff (BCH) expansion of the propagator in orders of time. Our method automatically provides time-closed expressions; and converges considerably faster than BCH, especially in the regime of high parametric gain because the small parameter it uses is natural to the problem. We obtain the well-known quantum solution for optical parametric amplification of down-conversion simply as the first order of the expansion, and present the rigorous procedure to derive higher order corrections one by one. To demonstrate the utility of higher corrections, we discuss the 2nd order correction to the pump field as an ideal detector of time-energy entanglement in parametric down-conversion. We also use the 3rd order correction to calculate the limits on the achievable squeezing with parametric amplification and on the fidelity of quantum state-transfer from one optical mode to another with sum/difference frequency generation, due to the quantum properties of the strong driving field.
Abstract:We present a systematic derivation of the Heisenberg evolution of a trilinear bosonic Hamiltonian system in presence of a strong drive beyond the standard approximation of a classical, undepleted driving field. We employ a perturbative expansion of the Hamiltonian propagator in orders of the input field amplitudes, as opposed to the standard Baker-Campbell-Hausdorff (BCH) expansion of the propagator in orders of time. Our method automatically provides time-closed expressions; and converges considerably faster than BCH, especially in the regime of high parametric gain because the small parameter it uses is natural to the problem. We obtain the well-known quantum solution for optical parametric amplification of down-conversion simply as the first order of the expansion, and present the rigorous procedure to derive higher order corrections one by one. To demonstrate the utility of higher corrections, we discuss the 2nd order correction to the pump field as an ideal detector of time-energy entanglement in parametric down-conversion. We also use the 3rd order correction to calculate the limits on the achievable squeezing with parametric amplification and on the fidelity of quantum state-transfer from one optical mode to another with sum/difference frequency generation, due to the quantum properties of the strong driving field.
arXiv:2603.29869 [quant-ph]
(or arXiv:2603.29869v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2603.29869 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 287 words
