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SPIE Quantum Nanophotonics

Statistical properties of light emitted by active media embedded on a microcavity system

Juan Gonzalez, Herbert Vinck Posada, Diego N. Bernal-García

Published Sep 11, 2018• 0 citations
Publisher

Abstract

In this paper, we study the statistical properties of light generated by two different types of quantum emitters embedded in an optical micro-cavity. These emitters are a single quantum dot (QD) and an artificial molecule (AM), which is made by two interacting QDs. The study of the statistical properties is done by means of the second-order correlation function, which can be calculated using the elements of the density matrix operator. Some non-Hamiltonian processes are considered such as incoherent pumping of photons, spontaneous emission, decay in leaky modes, phonon assistance to the main QD, and phonon assistance to the tunnelling mechanism. The effect of each one of those mechanisms in the emission properties of the system is analysed for a certain range of parameters. As a result, we observe that the tunnelling mechanism, as well as the phonon assistance mechanism to the main QD, are processes that can favour anti-bunching in the emitted photons. For the tunnelling phonon assistance, we find that these mechanisms attest against the non-classical character of the photons, changing its statistics by increasing the value of the second-order correlation function. However, the effect of the three mechanisms acting together on the system is a net diminish of the second-order correlation function, in comparison with the same system when all the mechanisms are turned off.

DOI
10.1117/12.2321699

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In this paper, we study the statistical properties of light generated by two different types of quantum emitters embedded in an optical micro-cavity. These emitters are a single quantum dot (QD) and an artificial molecule (AM), which is made by two interacting QDs. The study of the statistical properties is done by means of the second-order correlation function, which can be calculated using the elements of the density matrix operator. Some non-Hamiltonian processes are considered such as incoherent pumping of photons, spontaneous emission, decay in leaky modes, phonon assistance to the main QD, and phonon assistance to the tunnelling mechanism. The effect of each one of those mechanisms in the emission properties of the system is analysed for a certain range of parameters. As a result, we observe that the tunnelling mechanism, as well as the phonon assistance mechanism to the main QD, are processes that can favour anti-bunching in the emitted photons. For the tunnelling phonon assistance, we find that these mechanisms attest against the non-classical character of the photons, changing its statistics by increasing the value of the second-order correlation function. However, the effect of the three mechanisms acting together on the system is a net diminish of the second-order correlation function, in comparison with the same system when all the mechanisms are turned off.
We study the dynamics of a quantum dot embedded in a three-dimensional microcavity in the strong coupling regime in which the quantum dot exciton has an energy close to the frequency of a confined cavity mode. Under the continuous pumping of the system, the confined electron and hole can recombine either by spontaneous emission through a leaky mode or by stimulated emission of a cavity mode that can escape from the cavity. The numerical integration of a master equation including all these effects gives the dynamics of the density matrix. By using the quantum regression theorem, we compute the first- and second-order coherence functions required to calculate the photon statistics and the spectrum of the emitted light. Our main result is the determination of a range of parameters in which a state of cavity modes with Poissonian or sub-Poissonian (nonclassical) statistics can be built up within the microcavity. Depending on the relative values of pumping and rate of stimulated emission, either one or two peaks close to the excitation energy of the dot and/or to the natural frequency of the cavity are observed in the emission spectrum. The physics behind these results is discussed.
In this thesis three different approaches to control the quantum statistics in nanoscopic devices are investigated. In the first part of the thesis, mechanical oscillations in solid state devices are manipulated by an external laser to show bistabilities, coherent amplification, and enhanced damping. The dynamics is controlled by the frequency of the external laser. This study is performed in a semiclassical approximation, where expectation values of operators are factorized. These effects are used to show the similarities and differences between optomechanical systems and phonon cavities. In the regime of coherent amplification of phonons the theoretical description is extended to a fully quantum mechanical model. This reveals additional resonances due to collective processes that can be addressed via the frequency of the external laser. In the second part, a quantum light source is considered for manipulation of the emission statistics of a second quantum optical system serving as target. A Jaynes-Cummings system is used as a source that may be tuned from nonclassical to thermal emission via the pump strength. The target consists of a cavity with two emitters. The nature of the imprinted statistics is studied by higher order correlation functions. The resulting statistics deviates strongly from thermal, coherent or antibunched statistics. The third part considers coherent self feedback with time-delay, which is motivated by classical Pyragas control. The finite time delay is used as control parameter. The matrix product state evolution in the picture of the quantum stochastic Schrödinger equation is employed as a systematic way of dealing with quantum self-feedback. In this thesis, the approach is extended to include higher order terms in the time evolution operator. This is done systematically so that arbitrary order can be included enabling faster numerical evaluation. This extension of the matrix product state evolution method allows to investigate efficiently the emission statistics of a single mode cavity containing two emitters. It is shown that feedback can enhance antibunching in the light field while also counter-intuitively increasing the number of emitted photons at the same time. Expressing the time evolution operator as a sum of sparse matrices allows to include time dependent Hamiltonians in an efficient manner. Considering the pulsed excitation of a two level emitter, it is demonstrated that emission statistics may be tuned via feedback. This allows to switch between single photon emission and enhanced two photon emission.
We theoretically investigate the photon statistics in a cavity quantum electrodynamics system of a single quantum dot (QD) coupled to photonic molecule. Our previous work [Wen Zhang et.al, Phys. Rev. A 89, 043832 (2014)] has shown that QD-bimodal cavity system can generate ultrastrongly sub-Poissonian light by regulating the ratio between driving strengths of two cavity modes. Here we study two coupled single-mode nanocavities with a QD coupling to one of them as a photonic molecule system. Statistical character of photon emission is presented by evaluating the zero-delay secondorder correlation function g2(0). When both cavities with/without QD are driven, the sub-Poissonian character can be optimized by regulating the ratio between driving strengths of each cavities. We also present the dependences of other system parameters on the photon statistics. The physical mechanism of both effects is to optimize the combination of super-Poissonian and coherent light which results in sub-Poissonian light generation. As a result g2(0) can be reduced up to several orders of magnitude compared with the QD coupled one-mode-cavity system.
There exists a growing interest in the properties of the light generated by hybrid systems involving a mesoscopic number of emitters as a means of providing macroscopic quantum light sources. In this work, the quantum correlations of the light emitted by a collection of emitters coupled to a generic optical cavity are studied theoretically using an effective Hamiltonian approach. Starting from the single-emitter level, we analyze the persistence of photon antibunching as the ensemble size increases. Not only is the photon blockade effect identifiable, but photon antibunching originated from destructive interference processes, the so-called unconventional antibunching, is also present. We study the dependence of these two types of negative correlations on the spectral detuning between cavity and emitters, as well as its evolution as the time delay between photon detections increases. Throughout this work, the performance of plasmonic nanocavities and dielectric microcavities is compared: despite the distinct energy scales and the differences introduced by their respectively open and closed character, the bunching and antibunching phenomenology presents remarkable similarities in both types of cavities.
An important result from quantum optics and condensed matter physics is the use of radiation-matter interaction to produce light with specific characteristics. In this work, we study a nonstationary atom-cavity system and characterize the physical properties of the emitted light. In particular we deal with a Fabry-Perot cavity with a moving mirror which has an embedded two-level system. The study of the statistical properties is done by means of the second-order correlation function with zero delay, which allows to classify the light emitted by the physical system in three different statistical regimes (Poissonian, sub-Poissonian and super-Poissonian) depending on the relationship between the variance and the mean of the photon number distribution. Therefore, in a range of parameters for which the extraction of excitations from the quantum vacuum is evident, we find that the non-classicality of the emitted light depends strongly on the relationship between the radiation-matter coupling constant and the frequency of modulation of the length of the cavity.
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.