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arXiv:1501.01799 · Physical Review A

Optimization of photon correlations by frequency filtering

Alejandro González-Tudela, Elena del Valle, Fabrice P. Laussy

Published Apr 6, 2015• 50 citations
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Abstract

Photon correlations are a cornerstone of quantum optics. Recent works [E. del Valle, New J. Phys. 15, 025019 (2013); A. Gonzalez-Tudela et al., New J. Phys. 15, 033036 (2013); C. Sanchez Mu\~noz et al., Phys. Rev. A 90, 052111 (2014)] have shown that by keeping track of the frequency of the photons, rich landscapes of correlations are revealed. Stronger correlations are usually found where the system emission is weak. Here, we characterize both the strength and signal of such correlations, through the introduction of the ``frequency-resolved Mandel parameter.'' We study a plethora of nonlinear quantum systems, showing how one can substantially optimize correlations by combining parameters such as pumping, filtering windows and time delay.

DOI
10.1103/physreva.91.043807

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Photon correlations are a cornerstone of quantum optics. Recent works [E. del Valle, New J. Phys. 15, 025019 (2013); A. Gonzalez-Tudela et al., New J. Phys. 15, 033036 (2013); C. Sanchez Mu~noz et al., Phys. Rev. A 90, 052111 (2014)] have shown that by keeping track of the frequency of the photons, rich landscapes of correlations are revealed. Stronger correlations are usually found where the system emission is weak. Here, we characterize both the strength and signal of such correlations, through the introduction of the ``frequency-resolved Mandel parameter.'' We study a plethora of nonlinear quantum systems, showing how one can substantially optimize correlations by combining parameters such as pumping, filtering windows and time delay.
A theory of correlations between N photons of given frequencies and detected at given time delays is presented. These correlation functions are usually too cumbersome to be computed explicitly. We show that they are obtained exactly through intensity correlations between two-level sensors in the limit of their vanishing coupling to the system. This allows the computation of correlation functions hitherto unreachable. The uncertainties in time and frequency of the detection, which are necessary variables to describe the system, are intrinsic to the theory. We illustrate the power of our formalism with the example of the Jaynes-Cummings model, by showing how higher order photon correlations can bring new insights into the dynamics of open quantum systems.
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.
The violation of the Cauchy-Schwarz and Bell inequalities ranks among the major evidence of the genuinely quantum nature of an emitter. The conventional theoretical approaches associate operators with spectral lines to study correlations between photons from real-state transitions. Instead, we use a formalism that studies directly correlations between the physical reality---the photons---with no prejudice as to their origin. This allows us to extend photon correlations to all frequencies in all the possible windows of detection and to reveal landscapes of two-photon correlations that delineate regions of quantum emission, i.e., where classical inequalities are violated. We show that quantum correlations are rooted in the joint emission of two photons involving virtual states of the emitter instead of, as previously assumed, cascaded transitions between real states. As a result, correlations can be optimized in a process akin to distillation by keeping only the emission which is quantum and filtering out that which is not.
Accessing complete information about the emission from any quantum-optical systems requires tools capable of a frequency-resolved characterization of multi-photon transitions that would go beyond the standard g(2) correlation measurements. This is particularly important when analyzing systems which exhibit strong nonlinear response with multiple emission pathways. In this work, we calculate and analyze in details correlations of light emitted from two such canonical nonlinear optical systems, one incorporating Kerr nonlinear medium, and another exhibiting optomechanical coupling between light and quantized motion of a generic mechanical oscillator. We compare their single- and two-photon emission characteristics by employing a recently developed framework that allows us to calculate the frequency-resolved g(2) correlations between emitted photons with two arbitrary frequencies. Our analysis shows a rich landscape of bunching and antibunching associated with multi-photon emission events, and reveals the distinctive temporal characteristics of such processes. This new understanding provides a new asset to characterize and exploit nonlinear phenomena in Kerr and optomechanical systems in future experiments.
We summarise the main results that follow from our theory of frequency- and time-resolved photon correlations, which provides exact computations in nontrivial systems. We illustrate the theory with original results as interesting cases can be picked up from the endless configurations that abound in any quantum optical system. In particular, we compare our exact results with previous approximations, upgrade correlations to the case of photon bundles as otherwise no clear physical picture emerge, highlight the interest of measuring away from the peaks in rich landscapes of correlations and emphasize the joint time and frequency aspect of our theory.