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Emergent quantum probability from full quantum dynamics and the role of energy conservation

Abstract We propose and study a toy model for the quantum measurements that yield the Born's rule of quantum probability. In this model, the electrons interact with local photon modes and the photon modes are dissipatively coupled with local photon reservoirs. We treat the interactions of the electrons and photons with full quantum mechanical description, while the dissipative dynamics of the photon modes are treated via the Lindblad master equation. By assigning double quantum dots setup for the electrons coupling with local photons and photonic reservoirs, we show that the Born's rule of quantum probability can emerge directly from microscopic quantum dynamics. We further discuss how the microscopic quantities such as the electron-photon couplings, detuning, and photon dissipation rate affect the quantum dynamics. Surprisingly, in the infinite long time measurement limit, the energy conservation already dictates the emergence of the Born's rule of quantum probability. For finite-time measurement, the local photon dissipation rate determines the characteristic time-scale for the completion of the measurement, while other microscopic quantities affect the measurement dynamics. Therefore, in genuine measurements, the measured probability is determined by both the local devices and the quantum mechanical wavefunction.

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Semiclassical theory of frequency combs generated by parametric modulation of optical microresonators

Abstract An optical microresonator, which parameters are periodically modulated in time, can generate optical frequency comb (OFC) spectral resonances equally spaced by the modulation frequency. Significant recent progress in realization of OFC generators based on the modulation of microresonator parameters boosted interest to their further experimental development and theoretical understanding of underlying phenomena. However, most of theoretical approaches developed to date were based on the lumped parameter models which unable to evaluate, analyse, and optimize the effect of spatial distribution of modulation inside microresonators. Here we develop the multi-quantum semiclassical theory of parametrically excited OFCs which solves these problems. As an application, we compare OFCs which are resonantly or adiabatically excited in a racetrack microresonator (RTM) and a SNAP (Surface Nanoscale Axial Photonics) bottle microresonator (SBM). The principal difference between these two types of microresonators consists in much slower propagation speed of whispering gallery modes along the SBM axis compared to the speed of modes propagating along the RTM waveguide axis. We show that, due to this difference, similar OFCs can be generated by an SBM with a much smaller size compared to that of the RTM. Based on the developed theory, we analytically express the OFC spectrum of microresonators through the spatial distribution of modulated parameters and optimize this distribution to arrive at the strongest OFCs generated with minimum power consumption.

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