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Photonics

Quantum Interference of Spontaneous Emission and Coherent Population Trapping for a Quantum Emitter Embedded Within a Two-Dimensional Photonic Crystal

Vassilios Yannopapas, Emmanuel Paspalakis

Published Oct 22, 2025• 0 citations
Publisher

Abstract

We investigate the phenomenon of quantum interference in spontaneous emission pathways for a quantum emitter embedded in a two-dimensional photonic crystal composed of a square lattice of dielectric cylindrical rods. Using a V-type three-level system as a model, we demonstrate that the anisotropic Purcell effect inherent in such photonic structures can amplify quantum interference to its theoretical maximum, where the degree of interference p reaches unity. This results in the complete suppression of spontaneous emission for one polarization (directional suppression) and the emergence of coherent population trapping without the need for external coherent fields. By employing density matrix formalism, we derive analytical expressions for the population dynamics and identify conditions for indefinite or long-lived excited-state population. Our findings can find application in quantum technologies, including high-precision atomic clocks, magnetometry, and quantum information processing.

DOI
10.3390/photonics12111041

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We investigate the phenomenon of quantum interference in spontaneous emission pathways for a quantum emitter embedded in a two-dimensional photonic crystal composed of a square lattice of dielectric cylindrical rods. Using a V-type three-level system as a model, we demonstrate that the anisotropic Purcell effect inherent in such photonic structures can amplify quantum interference to its theoretical maximum, where the degree of interference p reaches unity. This results in the complete suppression of spontaneous emission for one polarization (directional suppression) and the emergence of coherent population trapping without the need for external coherent fields. By employing density matrix formalism, we derive analytical expressions for the population dynamics and identify conditions for indefinite or long-lived excited-state population. Our findings can find application in quantum technologies, including high-precision atomic clocks, magnetometry, and quantum information processing.
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Studying the spontaneous emission of a V-type three-level atom embedded in a photonic crystal (PC) by fractional calculus, we found that the atomic excited states in the anisotropic PC can be expressed as a superposition of four dressed states analytically. Through detuning two allowed atomic transition energies with respect to the photonic band edge, the coupling between these two transitions leads to three dynamic regimes, namely non-Markovian decay, damped quantum interference and quantum interference, classified by the numbers of contributed bounded dressed states. From the degree of quantum interference of two atomic transitions, we found the energy exchange between the atom and PC reservoir is the lowest as the excited states become degenerate but with maximum quantum interference when the atom is prepared at one of the excited states. The results also show that excited states prefer to stay out of phase at all detuning energy except for near degenerate. Therefore, we can control the spontaneous emission rate not only by the amount of detuning frequencies but also the relative phase of initial states.
We study theoretically the emergence of an anisotropic Purcell factor in random two-dimensional fractal aggregates of nanoparticles. These nanoparticles can either be metallic nanoparticles made of silver, which exhibit surface plasmon resonances, or high-index dielectric nanoparticles like silicon, which possess optical Mie resonances. To calculate the spontaneous emission rates of a quantum emitter, we utilize the electromagnetic Green’s tensor within the framework of the coupled-dipole method. Our findings reveal that the Purcell factor exhibits spatial variations, with certain regions, referred to as hot spots, displaying high values for dipoles oriented within the plane of the fractal aggregate, while dipoles oriented vertically to the aggregate have values close to unity. This anisotropy in the Purcell factor leads to significant quantum interference effects in the spontaneous emission paths of multi-level quantum emitters. As a consequence of this quantum interference, we demonstrate the occurrence of population trapping in a V-type quantum emitter embedded within a fractal aggregate of nanoparticles which cannot otherwise take place if the emitter is placed in vacuum.
We describe the spontaneous emission properties of an M-type five-level atom embedded in a photonic crystal (PC), which is coherently driven by two external laser fields. It leads to two types of quantum interference: reservoir-induced interference and laser-induced interference. Considering different detunings of atomic transition frequencies from band edges, we reveal some interesting phenomena such as spectral-line enhancement, spectral-line suppression, spectral-line narrowing, reservoir-induced cancellation of spontaneous emission and the appearance of dark lines, which originate from the quantum interference effects and the control of external laser fields. These investigations suggest possible applications in quantum optics, optical communications and in the fabrication of novel optoelectronic devices.
The spontaneous emission from a V-type three-level atom embedded in an isotropic photonic crystal with dynamic photonic band edge is studied. We consider the situation where the atom interacts with all possible radiation modes, and calculate numerically the evolution of atomic population without using Markov approximation. The calculation method can be used in related researches. In the present paper, we mainly discuss the effects of modulation parameters and the quantum interference on spontaneous emission when the band edge is modulated with step function or triangle function. We hope that the results can contribute to the applications in the dynamic photonic crystal environment in controlling the spontaneous emission via the quantum interference. The results show that in the step-modulated situation, the number of the photon-atom bound dressed states after the modulation has happened depends on atomic transition frequencies and the band edge frequency at that time, and is identical to the one in the unmodulated situation with the same parameters. The long-time evolution of the atomic population is affected by the time when the modulation happens. Depending on the system initial state, after the modulation has happened, the quantum interference can weaken the probability amplitude components corresponding to the photon-atom bound dressed states, and cause the upper-level population to decay quickly from a great value to a value near zero; or on the contrary, it can strengthen the bound dressed states, and make the upper levels retain a high population. In the modulated situation with trigonometric functions, after long enough time, the total upper-level population presents a decaying quasi-periodic oscillation behaviour. And the evolution of the total upper-level population tends to synchronize with the modulation, so the frequency of the quasi-periodic oscillation is approximately equal to the modulation frequency. But, the quantum interference can destroy the synchronization under some conditions. The decay rate of the total upper-level population is affected by the modulation frequency, and also by the initial state of the system and the angle between two dipole moment because of the quantum interference.