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arXiv:1803.00620

Photon correlations in both time and frequency

Juan Camilo López Carreño, Elena del Valle, Fabrice P. Laussy

Published Mar 1, 2018• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1803.00620

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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.
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.
We discuss two-photon physics, taking for illustration the particular but topical case of resonance fluorescence. We show that the basic concepts of interferences and correlations provide at the two-photon level an independent and drastically different picture than at the one-photon level, with landscapes of correlations that reveal various processes by spanning over all the possible frequencies at which the system can emit. Such landscapes typically present lines of photon bunching and circles of antibunching. The theoretical edifice to account for these features rests on two pillars: (i) a theory of frequency-resolved photon correlations and (ii) admixing classical and quantum fields. While experimental efforts have been to date concentrated on correlations between spectral peaks, strong correlations exist between photons emitted away from the peaks, which are accessible only through multi-photon observables. These could be exploited for both fundamental understanding of quantum-optical processes as well as applications by harnessing these unsuspected resources. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.
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.
Abstract. We apply our recently developed theory of frequency-filtered and time-resolved N-photon correlations [1] to study the two-photon spectra of a variety of systems of increasing complexity: single mode emitters with two limiting statistics (one harmonic oscillator or a two-level system) and the various combinations that arise from their coupling. We consider both the linear and nonlinear regimes under incoherent excitation. We find that even the simplest systems display a rich dynamics of emission, not accessible by simple single photon spectroscopy. In the strong coupling regime, novel two-photon emission processes involving virtual states are revealed. Furthermore, two general results are unraveled by two-photon correlations with narrow linewidth detectors: i) filtering induced bunching and ii) breakdown of the semi-classical theory. We show how to overcome this shortcoming in a fully-quantized picture. PACS numbers: 42.50.Ar,42.50.Lc,05.10.Gg,42.25.Kb,42.79.Pw ar X iv
Introduction We have now prepared the way for a quantum treatment of problems that are of interest in optics. We have examined some basic properties of the quantized field and have explored the coherent-state representation and some of its virtues. Until now our discussions have been essentially formal; we have not concerned ourselves with what is actually measured in the laboratory, nor with questions concerning the interactions of the quantized field with other systems. In the following sections we shall turn our attention to some of the quantum field theoretic quantities that are of particular interest in quantum optics and are of significance in the measurement of the field. Our discussions in this chapter will still be somewhat formal, in that we shall not yet come to grips with the problem of the interaction of the field with the apparatus. That problem will be tackled in Chapter 14. For the moment we shall continue to oversimplify and treat the field as a free field. However, within the idealized context of the free field we shall examine some of the questions encountered in measurements in quantum optics. We shall see that normally ordered correlations play a dominant role and examine some of their properties. Anti-normally ordered correlations will be seen to arise in much less common and less useful measurements of the field. We shall also examine the sense in which a photon may be said to be localized in a measurement in which a photoelectric emission is registered.
We propose an alternative formulation of the sensor method presented in Phys. Rev. Lett. 109, 183601 (2012) for the calculation of frequency-filtered and time-resolved photon correlations. Our approach is based on an algebraic expansion of the joint steady state of quantum emitter and sensors with respect to the emitter-sensor coupling parameter $\ensuremath{\epsilon}$. This allows us to express photon correlations in terms of the open quantum dynamics of the emitting system only and ensures that computation of correlations are independent on the choice of a small value of $\ensuremath{\epsilon}$. Moreover, using time-dependent perturbation theory, we are able to express the frequency- and time-resolved second-order photon correlation as the addition of three components, each of which gives insight into the physical processes dominating the correlation at different time scales. We consider a bioinspired vibronic dimer model to illustrate the agreement between the original formulation and our approach.