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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Multi-Mode Frequency Filtered Photon Correlations of a Driven Three-Level Ladder Atom

Jacob Ngaha, H. J. Carmichael

Published Jun 26, 2023• 0 citations
Publisher

Abstract

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.

DOI
10.1109/cleo/europe-eqec57999.2023.10232177

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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.
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.
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-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.
Multiphoton emitters are a sought-after resource in quantum photonics. Nonlinear interactions between a multilevel atomic system and a coherent drive can lead to resonant two-photon emission, but harvesting light from this process has remained a challenge due to the small oscillator strengths involved. Here we present a study of two-photon resonance fluorescence at microwave frequencies, using a superconducting, ladder-type artificial atom, a transmon, strongly coupled to a waveguide. We drive the two-photon transition between the ground and second-excited states at increasingly high powers and observe a resonance fluorescence peak whose intensity becomes comparable to single-photon emission until it splits into a Mollow-like triplet. We measure photon correlations of frequency-filtered spectral lines and find that while emission at the fundamental frequency stays antibunched, the resonance fluorescence peak at the two-photon transition is superbunched. Our results provide a route towards the realization of multiphoton sources in the microwave domain.
We calculate the second-order correlation function for the atomic fluorescence in the two-photon resonance operation of a driven dissipative Jaynes–Cummings oscillator. We employ a minimal four-level model comprising the driven two-photon transition alongside two intermediate states visited in the dissipative cascaded process, in the spirit of Shamailov et al. (2010). We point to the difference between the output of a JC oscillator exhibiting two-photon blockade and the scattered field of ordinary resonance fluorescence, and discuss the quantum interference effect involving the intermediate states, which is also captured in the axially transmitted light. The spectrum and intensity correlation of atomic emission explicitly reflect the particulars of the cascaded model.