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Laser & Photonics Review

Photon Statistics: Conventional and Unconventional Photon Statistics (Laser Photonics Rev. 14(6)/2020)

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

Published Jun 1, 2020• 5 citations
Publisher

Abstract

Similar to interferences in classical optics that can combine two waves to produce no output or more output than input, multiphoton interferences can produce, for instance, anti-bunched light by admixing squeezed (bunched) and laser (uncorrelated) light. The general case of quantum-field interferences, that can be self- or externally realized in coherently driven quantum sources, leads to a classification of conventional and unconventional photon statistics, as discussed by Elena del Valle and co-workers in article number 1900279.

DOI
10.1002/lpor.202070032

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Similar to interferences in classical optics that can combine two waves to produce no output or more output than input, multiphoton interferences can produce, for instance, anti-bunched light by admixing squeezed (bunched) and laser (uncorrelated) light. The general case of quantum-field interferences, that can be self- or externally realized in coherently driven quantum sources, leads to a classification of conventional and unconventional photon statistics, as discussed by Elena del Valle and co-workers in article number 1900279.
Abstract The photon statistics emitted by a large variety of light‐matter systems under weak coherent driving can be understood, to lowest order in the driving, in the framework of an admixture of (or interference between) a squeezed state and a coherent state, with the resulting state accounting for all bunching and antibunching features. One can further identify two mechanisms that produce resonances for the photon correlations: i) conventional photon blockade describes cases that involve a particular quantum level or set of levels in the excitation/emission processes with interferences occurring to all orders in the photon numbers, while ii) unconventional photon blockade describes cases where the driving laser is far from resonance with any level and the interference occurs for a particular number of photons only, yielding stronger correlations but only for a definite number of photons. Such an understanding and classification allows for a comprehensive and transparent description of the photon statistics from a wide range of disparate systems, where optimum conditions for various types of photon correlations can be found and realized.
Abstract In quantum optics, the second-order correlation function g (2)(τ) characterizes the photon statistics of a state of light and can be used to distinguish between its classical or quantum nature. In this article, we study a simple setup which offers the possibility to generate quantum states of light with very small g (2)(0), a signature of strong anti-bunched light. This can be achieved by mixing on a beamsplitter a coherent state with a nonclassical state, such as a squeezed state, and even with a bunched state (g (2)(0) > 1) such as a Schrödinger cat state. We elucidate the interference mechanism generating such strong anti-bunching and relate it to the unconventional photon blockade. We also detail how this effect can be applied to detect weakly squeezed states of light.
Photon correlations, as measured by Glauber's nthn\mathrm{th}nth-order coherence functions g(n){g}^{(n)}g(n), are highly sought to be minimized and/or maximized. In systems that are coherently driven, so-called blockades can give rise to strong correlations according to two scenarios based on level repulsion (conventional blockade) or interferences (unconventional blockade). Here, we show how these two approaches relate to the admixing of a coherent state with a quantum state such as a squeezed state for the simplest and most recurrent case. The emission from a variety of systems, such as resonance fluorescence, the Jaynes-Cummings model, or microcavity polaritons, as a few examples of a large family of quantum optical sources, are shown to be particular cases of such admixtures, that can further be doctored up externally by adding an amplitude- and phase-controlled coherent field with the effect of tuning the photon statistics from exactly zero to infinity. We show how such an understanding also allows to classify photon statistics throughout platforms according to conventional and unconventional features, with the effect of optimizing the correlations and with possible spectroscopic applications. In particular, we show how configurations that can realize simultaneously conventional and unconventional antibunching bring the best of both worlds: huge antibunching (unconventional) with large populations and being robust to dephasing (conventional).
Photon anti-bunching, measured via the Hanbury-Brown-Twiss experiment, is one of the key signatures of quantum light and is tied to sub-Poissonian photon number statistics. Recently, it has been reported that photon anti-bunching or conditional sub-Poissonian photon number statistics can be obtained via second-order interference of mutually incoherent weak lasers and heralding based on photon counting [Phys. Rev. A92, 033855 (2015)10.1103/PhysRevA.92.033855; Opt. Express24, 19574 (2016)10.1364/OE.24.019574; https://arxiv.org/abs/1601.08161]. Here, we report theoretical analysis on the limits of manipulating conditional photon statistics via interference of weak lasers. It is shown that conditional photon number statistics can become super-Poissonian in such a scheme. We, however, demonstrate explicitly that it cannot become sub-Poissonian, i.e., photon anti-bunching cannot be obtained in such a scheme. We point out that incorrect results can be obtained if one does not properly account for seemingly negligible higher-order photon number expansions of the coherent state.
Statistical and quantum optics provides a clear, up-to-date and comprehensive introduction to the recent field of modern optics dealing with coherence and fluctuations of light. The first two chapters discuss the statistical frame work needed for later part of the book followed by systematic account of coherence theory with a detailed discussed on photon statistics. Description of quantum theory of coherence is preceded by a introductory chapter on field quantization. A detailed description of non-classical light highlighted by phenomena of anti-bunching, Sub-Poissonian statistics, production and detection of squeezed light and coherent state follows. Next is the discussion on E-P-R paradox on reality, locality and completeness of quantum mechanics bringing out clearly the importance of Bell's inequalities. The concluding two chapters put forward forcefully the new fundamental concepts based on quantum superposition and entanglement leading to two photon interference, quantum cryptography and teleportation.
Laser light possesses perfect coherence, but cannot be attenuated to single photons via linear optics. An elegant route to convert laser light into single photons is based on photon blockade in a cavity with a single atom in the strong coupling regime. However, the single-photon purity achieved by this method remains relatively low. Here we propose an interference-based approach where laser light can be transformed into single photons by destructively interfering with a weak but super-bunched incoherent field emitted from a cavity coupling to a single quantum emitter. We demonstrate this idea by measuring the reflected light of a laser field which drives a double-sided optical microcavity containing a single artificial atom-quantum dot (QD) in the Purcell regime. The reflected light consists of a superposition of the driving field with the cavity output field. We achieve the second-order autocorrelation g2(0)=0.030+-0.002 and the two-photon interference visibility 94.3%+-0.2. By separating the coherent and incoherent fields in the reflected light, we observe that the incoherent field from the cavity exhibits super-bunching with g2(0)=41+-2 while the coherent field remains Poissonian statistics. By controlling the relative amplitude of coherent and incoherent fields, we verify that photon statistics of reflected light is tuneable from perfect anti-bunching to super-bunching in agreement with our predictions. Our results demonstrate photon statistics of light as a quantum interference phenomenon that a single QD can scatter two photons simultaneously at low driving fields in contrast to the common picture that a single two-level quantum emitter can only scatter (or absorb and emit) single photons. This work opens the door to tailoring photon statistics of laser light via cavity or waveguide quantum electrodynamics and interference.