[Paper Review] Strong Purcell enhancement of an optical magnetic dipole transition

Sebastian P. Horvath, Christopher M. Phenicie+10 more|arXiv (Cornell University)|Jul 6, 2023

Quantum optics and atomic interactions4 citations

TL;DR

This paper demonstrates strong Purcell enhancement of an optical magnetic dipole (MD) transition in a single Er³⁺ ion embedded in a MgO host crystal, leveraging cubic site symmetry to suppress electric dipole decay and isolate the MD transition. Using a nanophotonic cavity with a small magnetic mode volume (Vₘ = 0.068 μm³), the authors achieve a magnetic Purcell factor of Pₘ = 1040 ± 30, unambiguously attributing the enhancement to the MD channel, and further realize a spin-photon interface for optical spin initialization and readout.

ABSTRACT

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, Er$^{3+}$ 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 $P_m=1040 \pm 30$. We further extend this technique to realize a magnetic dipole spin-photon interface, performing optical spin initialization and readout of a single Er$^{3+}$ 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.

Motivation & Objective

• To demonstrate strong Purcell enhancement of an optical magnetic dipole transition in the visible to near-infrared range, a regime where electric dipole transitions typically dominate.
• To engineer a single-photon emitter with a nearly pure magnetic dipole transition by exploiting cubic site symmetry in Er³⁺:MgO, minimizing competing electric dipole decay pathways.
• To unambiguously identify and quantify magnetic density of states engineering in the optical domain using a nanophotonic cavity with a small magnetic mode volume.
• To establish a functional spin-photon interface based on the cavity-enhanced magnetic dipole transition for optical initialization and readout of a single Er³⁺ electron spin.

Proposed method

• Engineering Er³⁺:MgO as a single-photon emitter with a nearly pure magnetic dipole transition by leveraging the cubic site symmetry of the host crystal, which suppresses electric dipole decay.
• Using a nanophotonic cavity with a small magnetic mode volume (Vₘ = 0.068 μm³) to enhance the local magnetic density of states and induce Purcell enhancement.
• Measuring the fluorescence and absorption spectra of individual Er³⁺ ions and comparing them with a crystal field model to confirm the magnetic dipole nature of the transition.
• Calculating the magnetic dipole matrix element and transition rate using a Hamiltonian that includes crystal field and spin-orbit coupling, yielding a predicted MD decay rate of 43.23 s⁻¹ and a lifetime of 23.1 ms.
• Evaluating competing decay pathways, including electric dipole (ED) and electric quadrupole (EQ), to rule out ED contributions as the source of observed Purcell enhancement.
• Performing optical spin initialization and readout using the cavity-enhanced MD transition to characterize the ground state spin structure, lifetime, and coherence time of the single Er³⁺ spin.

Experimental results

Research questions

• RQ1 Can strong Purcell enhancement be achieved for an optical magnetic dipole transition in a solid-state system with minimal electric dipole contamination?
• RQ2 To what extent can the magnetic density of states in a nanophotonic cavity be engineered to enhance magnetic dipole emission?
• RQ3 Can a single Er³⁺ ion in a MgO host crystal serve as a nearly pure magnetic dipole emitter due to cubic site symmetry?
• RQ4 Is the observed Purcell enhancement in the cavity predominantly due to magnetic dipole emission, and can this be unambiguously distinguished from electric dipole or higher-order contributions?
• RQ5 Can the cavity-enhanced magnetic dipole transition be used to implement a functional spin-photon interface for optical control and measurement of a single electron spin?

Key findings

• The Er³⁺:MgO system exhibits a nearly pure magnetic dipole transition at 1540.48 nm due to cubic site symmetry, which strongly suppresses electric dipole decay.
• The magnetic Purcell factor was experimentally measured as Pₘ = 1040 ± 30, demonstrating strong enhancement of the magnetic dipole emission rate in a nanophotonic cavity.
• The measured Purcell factor agrees well with theoretical predictions for a pure magnetic dipole emitter, ruling out significant contributions from electric dipole decay (less than 10%).
• The electric quadrupole decay rate was estimated to be negligible (1.72 × 10⁻⁵ s⁻¹), confirming it does not contribute meaningfully to the observed enhancement.
• The cavity-enhanced magnetic dipole transition enabled optical initialization and readout of a single Er³⁺ electron spin, allowing determination of its ground state spin structure and coherence time.
• The results establish the fundamental equivalence of electric and magnetic density of states engineering in the optical domain and open new pathways for using magnetic dipole transitions in quantum technologies.