Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system

Kevin A. Fischer1, Rahul Trivedi1, Vinay Ramasesh2, Irfan Siddiqi2, and Jelena Vučković1

1E. L. Ginzton Laboratory, Stanford University, Stanford CA 94305, USA
2Department of Physics, University of California, Berkeley CA 94720, USA

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We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal waveguide modes are a natural basis for characterizing scattering in quantum optics, and afford a powerful technique based on a coarse discretization of time. This overcomes limitations imposed by singularities in the waveguide-system coupling. Moreover, the integrated discretized equations can be faithfully converted to a continuous-time result by taking the appropriate limit. This approach provides a complete solution to the scattered photon field in the waveguide, and can also be used to track system-waveguide entanglement during evolution. We further develop a direct connection between quantum measurement theory and evolution of the scattered field, demonstrating the correspondence between quantum trajectories and the scattered photon state. Our method is most applicable when the number of photons scattered is known to be small, i.e. for a single-photon or photon-pair source. We illustrate two examples: analytical solutions for short laser pulses scattering off a two-level system and numerically exact solutions for short laser pulses scattering off a spontaneous parametric downconversion (SPDC) or spontaneous four-wave mixing (SFWM) source. Finally, we note that our technique can easily be extended to systems with multiple ground states and generalized scattering problems with both finite photon number input and coherent state drive, potentially enhancing the understanding of, e.g., light-matter entanglement and photon phase gates.

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[21] Anita Magdalena Dąbrowska, "Photon counting probabilities of the output field for a single-photon input", Journal of the Optical Society of America B 40 5, 1299 (2023).

[22] Fatih Dinc, İlke Ercan, and Agata M. Brańczyk, "Exact Markovian and non-Markovian time dynamics in waveguide QED: collective interactions, bound states in continuum, superradiance and subradiance", Quantum 3, 213 (2019).

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[24] Victor Rueskov Christiansen, Mads Middelhede Lund, Fan Yang, and Klaus Mølmer, "Jaynes-Cummings interaction with a traveling light pulse", Journal of the Optical Society of America B 41 8, C140 (2024).

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[26] Maryam Khanahmadi and Klaus Mølmer, "Qubit readout and quantum sensing with pulses of quantum radiation", Physical Review A 107 1, 013705 (2023).

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[29] Alexander Holm Kiilerich and Klaus Mølmer, "Input-Output Theory with Quantum Pulses", Physical Review Letters 123 12, 123604 (2019).

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[34] Stephen C. Wein, Jia-Wei Ji, Yu-Feng Wu, Faezeh Kimiaee Asadi, Roohollah Ghobadi, and Christoph Simon, "Analyzing photon-count heralded entanglement generation between solid-state spin qubits by decomposing the master-equation dynamics", Physical Review A 102 3, 033701 (2020).

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[42] Rahul Trivedi, Alex White, Shanhui Fan, and Jelena Vučković, "Analytic and geometric properties of scattering from periodically modulated quantum-optical systems", Physical Review A 102 3, 033707 (2020).

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The above citations are from Crossref's cited-by service (last updated successfully 2024-06-15 09:54:05) and SAO/NASA ADS (last updated successfully 2024-06-15 09:54:06). The list may be incomplete as not all publishers provide suitable and complete citation data.