Abstract Understanding the photon number statistics of a quantum emitter (QE) interacting with complex photonic environments is fundamental to advances in quantum optics and nanophotonics. We introduce a general theoretical framework for calculating the modal photon number density spectrum (MPNDS) in arbitrary dielectric structures with an embedded two-level QE. We validate our approach by investigating a system composed of a two-level QE and a photonic crystal (PhC) slab with an L3 cavity and a waveguide, finding that the MPNDS exhibits significant changes in both waveguide and background radiative channels as the interaction between the QE and modal field transitions from weak coupling to strong coupling. We observe that the number of photons guided along the waveguide shows a strong dependence on the QE’s transition frequency and transition dipole moment, but demonstrates robustness to the transition dipole moment when the transition frequency approaches the waveguide cutoff frequency. Our work allows for the determination and tailoring of light emission characteristics across diverse radiative channels in complex photonic environments.
Abstract Understanding the photon number statistics of a quantum emitter (QE) interacting with complex photonic environments is fundamental to advances in quantum optics and nanophotonics. We introduce a general theoretical framework for calculating the modal photon number density spectrum (MPNDS) in arbitrary dielectric structures with an embedded two-level QE. We validate our approach by investigating a system composed of a two-level QE and a photonic crystal (PhC) slab with an L3 cavity and a waveguide, finding that the MPNDS exhibits significant changes in both waveguide and background radiative channels as the interaction between the QE and modal field transitions from weak coupling to strong coupling. We observe that the number of photons guided along the waveguide shows a strong dependence on the QE’s transition frequency and transition dipole moment, but demonstrates robustness to the transition dipole moment when the transition frequency approaches the waveguide cutoff frequency. Our work allows for the determination and tailoring of light emission characteristics across diverse radiative channels in complex photonic environments.
Photon-mediated coherent interaction determines the decay dynamics of quantum emitters and facilitates on-chip quantum manipulation for quantum information processing. We derive a general formalism to efficiently and flexibly simulate the radiative coupling between two two-level quantum emitters in arbitrary dielectric nanostructures, based on which, the decay dynamics of the two quantum emitters can be obtained. We demonstrate this formalism to investigate the two quantum dots embedded in the photonic crystal L3 cavity. The anticrossing behavior in the evolution spectrum and the vacuum Rabi oscillation in the populations of the two quantum dots can be simulated in both zero and small dot-dot detuning case. Our formalism can serve as a flexible and efficient theoretical tool and may be further developed to handle the cases for different initial states, multiple quantum emitters, and arbitrary metallic nanostructures.
In recent years, Born-Markov master equations based on tracing out the electromagnetic degrees of freedom have been extensively employed in the description of quantum optical phenomena originating from photon-mediated interactions in quantum emitter ensembles. The breakdown of these effective models, built upon assumptions such as ensemble spectral homogeneity, an unstructured photonic density of states, and weak light-matter coupling, has also recently attracted considerable attention. Here, we investigate the accuracy of this well-established framework beyond the most conventional, and extensively explored, spontaneous emission configuration. Specifically, we consider a system comprising two coherently driven and detuned quantum emitters, embedded within a hybrid photonic-plasmonic cavity, formed by a metallic nanorod integrated into a high-refractive-index dielectric microresonator. The local density of photonic states in this structure exhibits a complex frequency dependence, making it a compelling platform for exploring photon-mediated interactions beyond the assumptions above. We benchmark this modeling approach for the quantum dynamics of the emitter pair against exact calculations based on a macroscopic field quantization formalism, providing an illustrative assessment of its validity in significantly structured and dispersive photonic environments. Our analysis reveals four distinct regimes of laser driving and frequency splitting that lead to markedly different levels of accuracy in the effective model.
We present a modal analysis of a popular modeling framework for studying light-matter interaction between quantum emitters and general electromagnetic resonators, in which the active materials are modeled via Lorentzian material responses. The method relies on the Lippmann-Schwinger equation to calculate the complex resonance frequencies of the coupled system based only on a single calculation for the electromagnetic resonator without the active material and without fitting to calculated spectra. As an application example, we consider a recent dielectric cavity design featuring deep subwavelength confinement of light. We find the expected anticrossing of the emitter and cavity resonance frequencies, and comparing with independent reference calculations, we find an extraordinary quantitative agreement with a relative error below one part in ten thousand. To connect with the Jaynes-Cummings model, we relate the classical description of the emitter to the dipole moment in the corresponding quantum optical model. The combined framework therefore enables classical calculations to be used for evaluating the coupling strength entering quantum optical theories in a transparent way. The methodology is expected to be useful in the design and interpretation of ongoing and future experiments and devices involving single-photon sources for quantum information and quantum communication technology.
A photonic crystal, defined as a periodic dielectric structure, can influence the radiation rate of an embedded dipolar emitter. A theory of this effect is developed and the efficiency of a dipolar photonic source is calculated for a realistic three-dimensional crystal. Taking as a starting point the photonic band structure and its associated eigenfields, it is shown that the emission rate is strongly correlated with the density of modes, but also that the density of modes alone cannot explain all features found in the emission spectrum. For an infinite crystal, the computation of the field propagator confirms that the emission rate falls to zero in the frequency range defined by the photonic band gap. The emitter lifetime changes with the dipole location and orientation, leading to a radiation rate enhancement or inhibition according to the direction of the emission. These results may open routes to photonic sources with very high quantum efficiency.
We consider the spontaneous emission of a two-level quantum emitter, such as an atom or a quantum dot, in a modulated time-dependent environment with a photonic band gap. An example of such an environment is a dynamical photonic crystal or any other environment with a band gap whose properties are modulated in time, in the effective mass approximation. After introducing our model of a dynamical photonic crystal, we show that it allows new possibilities to control and tailor the physical features of the emitted radiation, specifically its frequency spectrum. In the weak-coupling limit and in an adiabatic case, we obtain the emitted spectrum and we show the appearance of two lateral peaks due to the presence of the modulated environment, separated from the central peak by the modulation frequency. We show that the two side peaks are not symmetric in height, and that their height ratio can be exploited to investigate the density of states of the environment. Our results show that a dynamical environment can give further possibilities to modify the spontaneous emission features, such as its spectrum and emission rate, with respect to a static one. Observability of the phenomena we obtain is discussed, as well as relevance for tailoring and engineering radiative processes.
Photonic crystals affect the photon emission of embedded emitters due to an altered local density of photon states (LDOS). We review the calculation of the LDOS from eigenmodes in photonic crystals and propose a rate equation model for fluorescent emitters to determine the changes in emission induced by the LDOS. We show how to calculate the modifications of three experimentally accessible characteristics: emission spectrum (spectral redistribution), emitter quantum yield, and fluorescence lifetime. As an example, we present numerical results for the emission of the dye Rhodamine B inside an opal photonic crystal. For such photonic crystals with small permittivity contrast, the LDOS is only weakly modified, resulting in rather small changes. We point out that in experiments, however, usually only part of the emitted light is detected, which can have a very different spectral distribution (e.g., due to a photonic band gap in the direction of detection). We demonstrate the calculation of this detected spectrum for a typical measurement setup. With this reasoning, we explain the previously not fully understood experimental observation that strong spectral modifications occurred, while at the same time only small changes in lifetime were found. With our approach, the mentioned effects can be quantitatively calculated for fluorescent emitters in any photonic crystal.