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arXiv:1311.0516 · Physical Review Letters

Probing the Combined Electromagnetic Local Density of Optical States with Quantum Emitters Supporting Strong Electric and Magnetic Transitions

Dongfang Li, Sinan Karaveli, Sébastien Cueff, Wenhao Li, Rashid Zia

Published Nov 28, 2018• 27 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.121.227403

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Nano Letters•Apr 18, 2013•41 citations
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.
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.
Mie resonances in dielectric particles can increase the local optical density of states (LDOS) associated with either electric or magnetic transition rates in nearby quantum emitters without ohmic losses. Their rather large quality factors compensate their low field confinement as compared to the plasmon resonances of metallic nanostructures for which nonradiative decay channels dominate. We show theoretically that near-infrared quadrupolar magnetic resonances in silicon particles can preferentially promote magnetic versus electric radiative deexcitation in trivalent erbium ions at 1.54 $\ensuremath{\mu}$m. The distance dependent interaction between magnetic (electric) dipole emitters and induced magnetic or electric dipoles and quadrupoles is derived analytically and compared to quasiexact full-field calculations based on Mie theory. We discuss how near-field coupling between nearby particles can further enhance the magnetic LDOS and compensate for the weak refractive index contrasts between dielectric particles and a typical host matrix for the lanthanide ions.
Abstract We provide a pedagogical introduction to the concept of the local density of optical states (LDOS), illustrating its application to both the classical and quantum theory of radiation. We show that the LDOS governs the efficiency of a macroscopic classical antenna, determining how the antenna’s emission depends on its environment. The LDOS is shown to similarly modify the spontaneous emission rate of a quantum emitter, such as an excited atom, molecule, ion, or quantum dot that is embedded in a nanostructured optical environment. The difference between the number density of optical states, the LDOS, and the partial LDOS is elaborated and examples are provided for each density of states to illustrate where these are required. We illustrate the universal effect of the LDOS on emission by comparing systems with emission wavelengths that differ by more than 5 orders of magnitude, and systems whose decay rates differ by more than 5 orders of magnitude. To conclude we discuss and resolve an apparent difference between the classical and quantum expressions for the spontaneous emission rate that often seems to be overlooked, and discuss the experimental determination of the LDOS.
Engineering the local density of states with nanophotonic structures is a powerful tool to control light-matter interactions via the Purcell effect. At optical frequencies, control over the electric field density of states is typically used to couple to and manipulate electric dipole transitions. However, it is also possible to engineer the magnetic density of states to control magnetic dipole transitions. In this work, we experimentally demonstrate the optical magnetic Purcell effect using a single rare earth ion coupled to a nanophotonic cavity. We engineer a new single photon emitter, Er3+^{3+}3+ in MgO, where the electric dipole decay rate is strongly suppressed by the cubic site symmetry, giving rise to a nearly pure magnetic dipole optical transition. This allows the unambiguous determination of a magnetic Purcell factor Pm=1040±30P_m=1040 \pm 30Pm​=1040±30. We further extend this technique to realize a magnetic dipole spin-photon interface, performing optical spin initialization and readout of a single Er3+^{3+}3+ electron spin. This work demonstrates the fundamental equivalence of electric and magnetic density of states engineering, and provides a new tool for controlling light-matter interactions for a broader class of emitters.
The long lifetime of lanthanide emitters can present a challenge for conventional pump-based modulation schemes, where the maximum switching speed is limited by the decay time of the excited state. However, spontaneous emission can also be controlled through the local optical environment. Here, we demonstrate a direct modulation scheme enabled by dynamic control of the local density of optical states (LDOS). Specifically, we exploit the LDOS differences between electric and magnetic dipole transitions near a metal mirror and demonstrate that rapid nanometer-scale mirror displacements can modulate the emission spectra of trivalent europium ions within their excited state lifetime. The dynamic LDOS modulation presented here can be readily extended to faster optical modulation schemes and applied to other long-lived emitters to control the direction, polarization, and spectrum of spontaneous emission at sublifetime scales.