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arXiv:2405.03900 · Physical Review A

Multimode array filtering of resonance fluorescence

Jacob Ngaha, A. S. Parkins, H. J. Carmichael

Published Aug 16, 2024• 5 citations
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Abstract

We present a frequency-filtering method for measuring and calculating frequency-filtered photon correlations. This method is a cavity-based system we call the multimode array filter, which consists of an array of tunable single-mode cavities that are equally spaced in frequency. By introducing a mode-dependent phase modulation, we produce a near rectangular frequency response, allowing us to increase the filter bandwidth---and thus the temporal response---without sacrificing frequency isolation. We model the frequency filtering using a cascaded quantum open systems approach which completely neglects any back-action of the filter onto the source system. This allows us to derive a closed set of operator moment equations for source and filter system operators, thus providing an extremely efficient method to calculate frequency-filtered first- and second-order correlation functions. We demonstrate this filtering method by applying it to a resonantly driven two-level atom. We present examples of frequency-filtered power spectra to demonstrate the improved frequency isolation of the multimode array filter over the single-mode filter. We then present results for the single-mode and multimode array filtered second-order auto- and cross-correlation functions. These are compared against expressions derived in the secular approximation. The improved frequency isolation of the multimode array filter allows us to investigate new regimes of frequency-filtered photon correlations, such as two-photon leapfrog processes, and the effect of vanishing bandwidth on filtered autocorrelation functions.

DOI
10.1103/physreva.110.023719

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We present a frequency-filtering method for measuring and calculating frequency-filtered photon correlations. This method is a cavity-based system we call the multimode array filter, which consists of an array of tunable single-mode cavities that are equally spaced in frequency. By introducing a mode-dependent phase modulation, we produce a near rectangular frequency response, allowing us to increase the filter bandwidth---and thus the temporal response---without sacrificing frequency isolation. We model the frequency filtering using a cascaded quantum open systems approach which completely neglects any back-action of the filter onto the source system. This allows us to derive a closed set of operator moment equations for source and filter system operators, thus providing an extremely efficient method to calculate frequency-filtered first- and second-order correlation functions. We demonstrate this filtering method by applying it to a resonantly driven two-level atom. We present examples of frequency-filtered power spectra to demonstrate the improved frequency isolation of the multimode array filter over the single-mode filter. We then present results for the single-mode and multimode array filtered second-order auto- and cross-correlation functions. These are compared against expressions derived in the secular approximation. The improved frequency isolation of the multimode array filter allows us to investigate new regimes of frequency-filtered photon correlations, such as two-photon leapfrog processes, and the effect of vanishing bandwidth on filtered autocorrelation functions.
Resonance fluorescence and photon correlations are areas that have long been studied, and are integral to the field of quantum optics. Recently frequency filtered photon correlations and the method of frequency filtering have had a surge of interest [1]–[4]. In this work we develop a novel method of calculating frequency filtered photon correlations by coupling the atomic fluorescence - in this case, from a three-level ladder type atom [5], [6] - into an array of single-mode cavity filters. This coupling, modelled with an open cascaded systems approach [7], [8] is entirely unidirectional, allowing us to derive a closed set of coupled moment equations for the filter source operators. This provides an extremely efficient method for calculating frequency filtered second-order correlation functions.
Frequency-resolved quantum correlation of resonance fluorescence is investigated in a two-atom radiating system. In this quantum radiating system, only one atom is driven by a laser field, and the spontaneous transition of the undriven atom resonates with one of the Rabi sidebands of the driven atom. A single-mode empty cavity is applied to serve as a Lorentzian filter to output the superbunched fluorescent photon pairs when its frequency is tuned to halfway between the central peak and one of the side peaks. In the case of large filter width, two-photon correlation signal and its physical correspondence can be bridged analytically in our approach. It reveals that this superbunching effect turns out to be the constructive quantum interference between a pair of coupled two-photon cascaded transitions. Ulteriorly, it is the consequence of the modulations of the unfiltered dressed-state transition amplitudes by the filter. Our analytical formalism also shows that, although the dipole-dipole interaction is usually weak, the interatomic coherence caused by this weak perturbation can also play a crucial role in breaking through the superbunching limit obtained from a single two-level atom in the same parameter regime. In addition to being a treasurable quantum pump to probe into the target quantum system, it is also found in our investigation that this superbunched fluorescence can serve as a promising quantum response in detecting this weak perturbation in the interior of the quantum source. A general case is also considered when the two-atom radiating system is monitored by two filter-detector monitoring systems. It is found that this filtered strong quantum correlation can be maintained even though the two photons are spatially separated.
Abstract Frequency-resolved photon statistics of resonance fluorescence generated from a two-level system driven by a strong laser field and a weak laser field with equal frequencies are studied. The frequency resolution of fluorescent radiation is described by quantum filtering dynamics, which is simulated theoretically by two single-mode quantum optical cavities with tunable frequencies to scan the incident fluorescent radiation. By calculating the two-photon intensity–intensity correlation functions in terms of the cavity modes, we demonstrate that two-color strong correlations of resonance fluorescence can be generated not only between the opposite sidebands, but also between the central band and one of the sidebands: although both sidebands are broadened due to the perturbation of the weak laser field on the strong-field dressed atom. We emphasize that these properties are in contrast to the conventional case of the standard single-atom Mollow triplet. Moreover, if the resonance frequencies of the two filtering cavities are tuned appropriately, broadband two-color strong correlations are predicted, and the physical origin is revealed from the perspective of quantum interference of photon emission dynamics. This can be considered as a feasible scheme for the design of broadband non-classical light sources, and may be beneficial to the quantum precise detection of atomic and molecular dynamics via quantum optical spectroscopy.
Frequency-filtered photon correlations have been proven to be extremely useful in grasping how the detection process alters photon statistics. Harnessing the spectral correlations also permits refinement of the emission and unraveling of previously hidden strong correlations in a plethora of quantum-optical systems under continuous-wave excitation. In this work, we investigate such correlations for time-dependent excitation and develop a methodology to compute efficiently time-integrated correlations, which are at the heart of the photon-counting theory, and subsequently apply it to analyze the photon emission of pulsed systems. By combining this formalism with the —which facilitates frequency-resolved correlations—we demonstrate how spectral filtering enhances single-photon purity and suppresses multiphoton noise in time-bin-encoded quantum states. Specifically, filtering the central spectral peak of a dynamically driven two-level system boosts temporal coherence and improves the fidelity of time-bin entanglement preparation, even under conditions favoring multiphoton emission. These results establish spectral filtering as a critical tool for tailoring photon statistics in pulsed quantum light sources.
Frequency-resolved correlation (FRC) is investigated in fluorescent emission radiated from a $\mathrm{\ensuremath{\Lambda}}$-type atomic system by employing weak coupling regime between quantum emitter and cavities, in which each cavity substituting a Lorentzian filter is assumed to pass through only one fluorescent photon at a time so that the analytical discussions for time orderings can be carried out in a truncated Hilbert space with single-excitation state for each cavity mode. In the limit of bad cavity (large passband width of filter) and short delay, the conditional time ordering amplitudes are introduced with the help of conditioned dressed atom-photon states prepared by preselection to probe into the effect of preferential screening for time orderings of filter-detector systems. Meanwhile, the past quantum state formalism is also applied in FRC to further excavate their collective monitoring effect. Based on the obtained two-mode correlation signals, it is found that, in nonresonant two-photon cascaded processes, bunching and antibunching can appear in two opposite detection orderings, respectively, and can be switched. The physical origin is explored that the two different transition amplitudes of emitted photons from a common spectral band of resonance fluorescence are responsible for opposite time orderings, thus, the imbalance between two complementary time orderings can be enhanced, which is impossible to achieve in resonance fluorescence of two-level atoms. This mechanism is embodied in the conditional time ordering amplitudes produced by this detection theory of cavity modes.
In the framework of the signal processing approach to single-atom resonance fluorescence with spectral resolution, we diagrammatically derive an analytical formula for arbitrary-order spectral correlation functions of the scattered fields that pass through Fabry-Perot interferometers. Our general expression is then applied to study correlation signals in the limit of well separated spectral lines of the resonance fluorescence spectrum. In particular, we study the normalized second-order temporal intensity correlation functions in the case of the interferometers tuned to the components of the spectrum and obtain interferential corrections to the approximate results derived in the secular limit. In addition, we explore purely spectral correlations and show that they can fully be understood in terms of the two-photon cascades down the dressed state ladder.