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arXiv:1901.09030 · Laser & Photonics Review

Conventional and Unconventional Photon Statistics

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

Published May 14, 2020• 104 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1002/lpor.201900279

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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.
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).
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.
Photon blockades are traditionally classified into conventional and unconventional types, depending on distinct physical mechanisms. Regarding the cavity decay rate κ, the conventional photon blockade takes place under strong nonlinearity condition (g>κ), whereas the unconventional photon blockade occurs in the regime of weak nonlinearity (g<κ). We here propose how to derive an optimal condition for photon blockade utilizing a two-photon Jaynes-Cummings model. Under this condition, the equal-time second-order correlation function reaches its minimum, leading to photon antibunching in both conventional and unconventional photon blockade regimes (g>κ and g<κ), even in g∼κ. This characteristic is termed universal photon blockade. By comparing it with the conventional and the unconventional photon blockades in the weak-driving limit, the advantages of universal photon blockade are revealed. Our proposal paves an avenue towards the future study of photon blockades and has potential applications in generating antibunched photons.
We investigate the photon statistics of an ensemble of coherently driven non-interacting two-level atoms in the weak driving regime. As it turns out, the system displays unique emission characteristics that are strongly in contrast to the emission of classical oscillating dipoles. By deriving the second-order autocorrelation function, we show that extraordinary two-photon correlations are obtained, ranging from strong antibunching to superbunching. These features are enhanced by disorder in the emitter positions, and the control parameter is the number of excitations in the system. We observe the appearance of bunching and antibunching when the light is scattered by the atoms predominantly coherently, i.e., mimicking classical Rayleigh scattering, whereas thermal photon statistics is obtained when the light is scattered via spontaneous decay, a well-known quantum effect. The underlying mechanism is the interplay between coherent scattering, which exhibits spatial fluctuations due to interference, and dissipation in the form of isotropic spontaneous decay.
We explore a method for achieving photon blockade (PB) through a two-photon Jaynes-Cummings (JC) model that includes both cavity and atom drivings. Analytical expressions for the steady state are derived to calculate photon-number distribution and correlation functions. Based on this analysis, we establish the theoretical conditions required for generating PB by controlling both drivings and propose a scheme to identify conventional photon blockade (CPB) and unconventional photon blockade (UPB) by analyzing the second- and third-order correlation functions. We validate our findings through numerical simulations conducted in an artificial atom system. We discuss two cases, one in which the transition frequency of the two-level atom is in two-photon resonance with the cavity frequency and the other in which it is off-resonance. We observe a significant interplay between CPB and UPB effects in the resonant case. In the off-resonance case, we demonstrate that UPB can be achieved by manipulating the strengths of atom driving and cavity driving to satisfy a specific relationship while meeting the requirements for optimal detuning relations. This work provides essential insights into controlling the PB effect using the two-photon JC model with both the atom and cavity drivings.
Photon blockade, in analogy to Coulomb's or phonon blockades, is a phenomenon when a single photon in a nonlinear cavity blocks the transmission of a second photon. This effect can occur in Kerr-type systems driven by a laser due to strong nonlinear photon-photon interactions. We predict the occurrence of higher-order photon blockades where the transmission of more than two photons is effectively blocked by single- and two-photon states. This photon blockade can be achieved by tuning the frequency of the laser driving field to be equal to the sum of the Kerr nonlinearity and the cavity resonance frequency. We refer to this phenomenon as two-photon blockade or two-photon state truncation via nonlinear scissors, and can also be interpreted as photon-induced tunneling. We also show that, for a driving-field frequency fulfilling another resonance condition and for higher strengths of the driving field, even a three-photon blockade can occur but less clearly than in the case of single- and two-photon blockades. We demonstrate how various photon blockades can be identified by analyzing photon-number correlations, coherence and entropic properties, Wigner functions, and spectra of squeezing. We show that two- and three-photon blockades can, in principle, be observed in various cavity and circuit quantum electrodynamical systems for which the standard single-photon blockade was observed without the need of using higher-order driving interactions or Kerr media exhibiting higher-order nonlinear susceptibility.