We experimentally demonstrated that the lifetime of quantum emitters with strongly mixed electric dipole (ED) and magnetic dipole (MD) transitions can directly probe the combined electromagnetic local density of optical states. OCIS codes: (250.0250) Optoelectronics; (260.2510) Fluorescence; (260.3160) Interference. Purcell effect shows the spontaneous decay rate of a quantum emitter depends on its local density of optical states (LDOS), which indicates that the spontaneous decay rate can be selectively enhanced or suppressed by properly engineering its local optical environment. As demonstrated in Drexhage's pioneering experiments, the electric LDOS oscillates as a function of the separation distance between the emitter and metal-dielectric interface (red line in Fig. 1(a)), thus leading to the measurable oscillations of corresponding lifetimes (red line in Fig. 1(b)). The lifetime oscillations refer to the enhancement and suppression of spontaneous decay rate of light emitters at varied locations. In the literature, the fitting to the oscillations has been employed to infer quantum efficiency of light emitters. However, these oscillations are not a fundamental nature of electromagnetic mode density. The measured electric LDOS using the common purely ED or ED-dominant emitters is only the projection of the combined electromagnetic LDOS onto an isotropic electric dipole (Fig. 1(a)). In the past decade, the magnetic light matter interaction has drawn great attention thanks to the advance of metamaterials. In addition to those magnetic resonators (e.g., split-ring resonators and parallel nanorods), strong MD transitions exist as well in transition-metal and lanthanide ions [1]. In order to probe the combined electromagnetic LDOS, strongly mixed ED-MD emitters are required to access to electric and magnetic LDOS simultaneously. Here we experimentally investigated the lifetimes of two strongly mixed ED-MD emitters: divalent nickel ions in magnesium oxide (Ni 2+ :MgO) and trivalent erbium ions in yttrium oxide (Er 3+ :Y 2 O 3) [2]. Staircaselike samples with 44 distinct regions (i.e., with varied spacer thicknesses d and/or top interfaces) were fabricated for the two quantum emitters, respectively. Time-dependent photoluminence was then measured for all distinct areas of the samples to extract the corresponding lifetimes. The measured lifetime of the mixed ED-MD emitter does not solely depend on electric or magnetic LDOS, but rather follows the combined electromagnetic LDOS. Almost no lifetime oscillations was observed in the measured lifetimes of 3 T 2 → 3 A 2 transitions in Ni 2+ :MgO, as shown in Fig. 1(c) (black dots). This is further confirmed by a technologically and scientifically important emitter Er 3+ :Y 2 O 3. Of great interest, the complex electronic levels of Er 3+ make it support both purely ED transitions (4 S 3/2 → 4 I 15/2) at visible regime and strongly mixed ED-MD transitions (4 I 13/2 → 4 I 15/2) at telecom wavelengths [3]. The measured lifetime of strongly mixed ED-MD transitions 4 I 13/2 → 4 I 15/2 in Er 3+ :Y 2 O 3 at telecom wavelengths follows the combined electromagnetic LDOS. In contrast, the measured lifetime of the purely ED transitions at visible regime (4 S 3/2 → 4 I 15/2) originating from the same Er 3+ emitters solely depends on the electric LDOS. The extracted MD contributions from the theoretical fitting of measured lifetimes match the results obtained by the recently developed energy-momentum spectroscopy [3,4]. The findings here show that, for emitters with strongly mixed ED-MD transitions as well as characterized quantum efficiency and bulk lifetime, a single lifetime measurement can probe the combined electromagnetic LDOS at the point of interest in a complex optical system, such as metamaterials, epsilon-near-zero materials, and topological photonics.
We experimentally demonstrate that the radiative decay rate of a quantum emitter is determined by the combined electric and magnetic local density of optical states (LDOS). A Drexhage-style experiment was performed for two distinct quantum emitters, divalent nickel ions in magnesium oxide and trivalent erbium ions in yttrium oxide, which both support nearly equal mixtures of isotropic electric dipole and magnetic dipole transitions. The disappearance of lifetime oscillations as a function of emitter-interface separation distance confirms that the electromagnetic LDOS refers to the total mode density, and thus similar to thermal emission, these unique electronic emitters effectively excite all polarizations and orientations of the electromagnetic field.
Summary form only given. Although it is often assumed that all light-matter interactions at optical frequencies are mediated by electric dipole transitions, strong optical-frequency magnetic dipoles do exist. In fact, we see magnetic dipole emission every day from the many lanthanide ions (such as erbium, europium, and terbium) that help to illuminate everything from fluorescent lighting to telecom fiber amplifiers. Higher-order processes such as magnetic dipole and electric quadrupole transitions also play an important part in the light emission from transition metal ions and semiconductor quantum dots. Nevertheless, most applications have overlooked the device implications of these electric-dipole-forbidden transitions throughout the visible and near-infrared regime, and their contributions to many important emitters have not been fully characterized.In this presentation, we will experimentally characterize the "forbidden" transitions in a range of solid-state emitters and investigate their applications and implications for nanophotonics. We will examine the electric dipole approximation commonly used to describe light-matter interactions and discuss naturally occurring systems that exhibit higher-order magnetic dipole and electric quadrupole emission. We will illustrate how these nanoscale quantum transitions can provide both a new way to probe magnetic light-matter interactions and a new degree of design freedom for active electronic and photonic devices. Specifically, we will demonstrate how the different symmetries of multipolar transitions can be exploited to identify, quantify, and control light emission, even at sub-lifetime scales. Despite similar radiation patterns, magnetic and electric dipole emitters have different symmetries with respect to polarization and phase. Thus, in an inhomogeneous environment, we can tailor interference effects and the local density of optical states to selectively enhance either electric or magnetic dipole emission [1,2]. To examine the scope of such higher-order transitions, we will present quantum mechanical calculations that identify all the magnetic dipole and electric quadrupole emission lines in the trivalent lanthanide series in the visible to near-infrared spectrum [3]. Then, we will present an energyand momentum-resolved spectroscopy technique to directly quantify the electric and magnetic dipole contributions from any mixed transition. [4] Using energy-momentum spectroscopy, we will experimentally examine the higher order transitions in lanthanide ions [4,5], transition metal ions [6], and epitaxial quantum dots [7]. If time permits, we will then show how the symmetry differences between magnetic and electric dipoles can be used to address specific electronic states [6] and to dynamically tune emission spectra at sub-lifetime-scales [8].
The electromagnetic-vacuum-field fluctuations are intimately linked to the process of spontaneous emission of light. Atomic emitters cannot probe electric- and magnetic-field fluctuations simultaneously because electric and magnetic transitions correspond to different selection rules. In this Letter we show that semiconductor quantum dots are fundamentally different and are capable of mediating electric-dipole, magnetic-dipole, and electric-quadrupole transitions on a single electronic resonance. As a consequence, quantum dots can probe electric and magnetic fields simultaneously and can thus be applied for sensing the electromagnetic environment of complex photonic nanostructures. Our study opens the prospect of interfacing quantum dots with optical metamaterials for tailoring the electric and magnetic light-matter interaction at the single-emitter level.
Abstract The radiative transition probability is a fundamental property for optical transitions. Extensive research, theoretical and experimental, has been conducted to establish the relation between the photonic environment and electric dipole (ED) transition probabilities. Recent work shows that the nanocrystal (NC)-cavity model accurately describes the influence of the refractive index n on ED transition rates for emitters in NCs. For magnetic dipole (MD) transitions, theory predicts a simple n3 dependence. However, experimental evidence is sparse and difficult to obtain. Here we report Eu3+-(with distinct ED+MD transitions) and Gd3+-(MD transitions) doped β-NaYF4 NC model systems to probe the influence of n on ED and MD transition probabilities through luminescence lifetime and ED/MD intensity ratio measurements. The results provide strong experimental evidence for an n3 dependence of MD transition probabilities. This insight is important for understanding and controlling the variation of spectral distribution in emission spectra by photonic effects.