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Journal of Optical Technology

Controlling the frequencies of photons emitted by a single quantum dot in a one-dimensional photonic crystal

A I Garifullin, R. Kh. Gainutdinov, Хамадеев Марат Актасович

Published Jun 1, 2024• 2 citations
Publisher

Abstract

Subject of study. A single InAs quantum dot in a one-dimensional photonic crystal based on GaAs is examined. Aim of study. The aim of this study is to develop a method for controlling photon emission frequencies from a single quantum dot within a one-dimensional photonic crystal based on changes in the electromagnetic mass of an electron in the photonic crystal medium. Method. The proposed approach leverages the effect of changing the electromagnetic mass of an electron in the photonic crystal medium, manifesting as corrections to electron energy levels depending on the optical density of the medium. To control this density, the injection of free charge carriers and the quadratic electro-optic Kerr effect are proposed. Main results. The feasibility of in situ control of photon emission frequencies from a quantum dot was demonstrated using quantum transitions between the p- and s-states of a hydrogen-like InAs quantum dot situated in the air voids of a one-dimensional GaAs photonic crystal. This control is achieved through the effect of changing the electromagnetic mass of an electron, as well as tuning the refractive index of the photonic crystal via free charge carrier injection and the electro-optic Kerr effect. Calculations indicate that the photon energy control range available in experiments is limited to several tens of microelectronvolts, restricting practical applicability, and the observed displacement effect is smaller than experimentally recorded values. However, the energy level displacement, influenced by the quantum electrodynamic effect under investigation, exhibits a quadratic dependence on the refractive index of the material forming the photonic crystal. Consequently, the method is expected to scale significantly with increasing optical density. Such photonic crystals could be constructed using metamaterials with a high refractive index. Practical significance. The findings of this study, centered on developing a method for controlling photon emission frequencies from a single quantum dot in a one-dimensional photonic crystal, lay the groundwork for photon-emitter interfaces. These interfaces will incorporate key quantum functionalities, including photonic qubits, single-photon light sources, and nonlinear quantum photon-photon gates.

DOI
10.1364/jot.91.000399

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Subject of study. A single InAs quantum dot in a one-dimensional photonic crystal based on GaAs is examined. Aim of study. The aim of this study is to develop a method for controlling photon emission frequencies from a single quantum dot within a one-dimensional photonic crystal based on changes in the electromagnetic mass of an electron in the photonic crystal medium. Method. The proposed approach leverages the effect of changing the electromagnetic mass of an electron in the photonic crystal medium, manifesting as corrections to electron energy levels depending on the optical density of the medium. To control this density, the injection of free charge carriers and the quadratic electro-optic Kerr effect are proposed. Main results. The feasibility of in situ control of photon emission frequencies from a quantum dot was demonstrated using quantum transitions between the p- and s-states of a hydrogen-like InAs quantum dot situated in the air voids of a one-dimensional GaAs photonic crystal. This control is achieved through the effect of changing the electromagnetic mass of an electron, as well as tuning the refractive index of the photonic crystal via free charge carrier injection and the electro-optic Kerr effect. Calculations indicate that the photon energy control range available in experiments is limited to several tens of microelectronvolts, restricting practical applicability, and the observed displacement effect is smaller than experimentally recorded values. However, the energy level displacement, influenced by the quantum electrodynamic effect under investigation, exhibits a quadratic dependence on the refractive index of the material forming the photonic crystal. Consequently, the method is expected to scale significantly with increasing optical density. Such photonic crystals could be constructed using metamaterials with a high refractive index. Practical significance. The findings of this study, centered on developing a method for controlling photon emission frequencies from a single quantum dot in a one-dimensional photonic crystal, lay the groundwork for photon-emitter interfaces. These interfaces will incorporate key quantum functionalities, including photonic qubits, single-photon light sources, and nonlinear quantum photon-photon gates.
Chapter 1 IntroductionUltimate inhibition of spontaneous emission can be achieved in artificial periodic structures with tailor-made forbidden frequency bands [5].These periodic structures known as photonic crystals consist of different dielectric materials, where the index of refraction varies on length scales comparable to the wavelength of light.Therefore, the periodicity of photonic crystals is about 1000 times as large as that of atomic crystals.Light with specific frequencies is forbidden to propagate along certain directions by wave interference, similarly to Bragg diffraction of x-rays in atomic crystals.Such forbidden frequency ranges are called stopgaps.The larger the contrast of the refractive index between the two materials of a photonic crystal, the more strongly light is influenced, and the broader the stopgaps become.It was predicted in 1987 that an extreme situation may be feasible when light cannot propagate along any direction [6, 7].This situation is called a photonic bandgap.Spontaneous emission is completely inhibited for frequencies inside such a bandgap and, conversely, strongly enhanced for frequencies outside the bandgap.Photonic crystals, therefore, provide an ultimate tool for manipulating with light, which is of extreme interest for scientists and engineers [8, 9].Recent advances in nanotechnology have resulted in ability to synthesize semiconductor structures with dimensions of a few nanometers.Due to the finite sizes, electron-hole pairs (excitons) can be confined in these nanostructures, which leads to discrete excitonic energy levels.The nanocrystals that confine excitons in spherical or circular spaces are known as quantum dots.The discrete structure of the energy levels results in advantageous optical properties of these nanocrystals: narrow and tunable emission spectra.The emission frequencies can be tuned by varying the nanocrystal size: the smaller the size, the higher the emission frequency.These properties make the nanocrystals very promising elementary emitters for new experiments and devices [10, 11]. Outline of the thesisThis thesis describes time-and angle-resolved experiments, in which effects of threedimensional (3D) photonic crystals on spontaneous emission of embedded light sources (quantum dots and dye molecules) were studied.The thesis is organized as follows:In Chapter 2 we review the theoretical basics of the interaction between light and matter.We discuss the factors triggering the process of spontaneous emission and consider in detail the time evolution of the excited state of the emitter that interacts with the quantized 1.
Photonic crystals (PCs) are periodic systems that consist of dielectrics with different refractive indices. Photonic crystals have many potential technological applications. These applications are mainly based on the photonic bang gap effect. However the band gap is not only effect that follows from the periodic changing of the refractive index in the photonic crystal. The periodic change of the photon-matter interaction in photonic crystal medium gives rise to the fact that the mass of an electron in the photonic crystal must differ from its mass in vacuum. Anisotropy of a photonic crystal results in the dependence of the electromagnetic mass correction on the orientation of the electron momentum in a photonic crystal. This orientation dependence in turn gives rise to the significant correction to the transition frequencies in an atom placed in air voids of a photonic crystal. These corrections are shown to be comparable to the atomic optical frequencies. This effect allows one to control the structure of the atomic energy levels and hence to control resonance processes. It can serve as the basis for new line spectrum sources. The effect provides new ways of realization of quantum interference between decay channels that can be important for quantum information science.
Much recent effort has focused on coupling individual quantum emitters to optical microcavities in order to produce single photons on demand, enable single-photon optical switching, and implement functional nodes of a quantum network. Techniques to control the bandwidth and frequency of the outgoing single photons are of practical importance, allowing direct emission into telecommunications wavelengths and "hybrid" quantum networks incorporating different emitters. Here, we describe an integrated approach involving a quantum emitter coupled to a nonlinear optical resonator, in which the emission wavelength and pulse shape are controlled using the intra-cavity nonlinearity. Our scheme is general in nature, and demonstrates how the photonic environment of a quantum emitter can be tailored to determine the emission properties. As specific examples, we discuss a high Q-factor, TE-TM double-mode photonic crystal cavity design that allows for direct generation of single photons at telecom wavelengths (1425 nm) starting from an InAs/GaAs quantum dot with a 950 nm transition wavelength, and a scheme for direct optical coupling between such a quantum dot and a diamond nitrogen-vacancy center at 637 nm.
This thesis presents work on a series of devices for the generation of photonic quantum states based on self-assembled InAs quantum dots, which are among the most technologically mature candidates for practical quantum photonic applications due to their high internal quantum efficiency, narrow linewidth, tunability and straightforward integration with photonic and electric components. The primary results presented concern sources of multi-photon entangled states and single-photon sources with high repetition rate, both of which are crucial components for emerging photonic quantum technologies. First, we propose a scheme for the sequential generation of entangled photon chains by resonant scattering of a laser field on a single charged particle in a cavity-enhanced quantum dot. The charge has an associated spin that can determine the time bin of a photon, allowing for information encoding in this degree of freedom. We demonstrate coherent operations on this spin and realize a proof-of-principle experiment of the proposed scheme by showing that the time bin of a single-photon is dependent on the measured state of the trapped spin. The second main avenue of work investigates the effects of a surface acoustic wave, a mechanical displacement wave confined to the surface of a substrate, on the optical properties of quantum dots. In particular, we exploit the dynamic acoustically-induced tuning of the emission energy to modulate the Purcell effect in a pillar microcavity. Under resonant optical excitation we demonstrate the conversion of the continuous wave laser into a pulsed single-photon stream inheriting the acoustic frequency of 1 GHz as the repetition rate. High resolution spectroscopy reveals the presence of narrow sidebands in the emission spectrum, whose relative intensity can be controlled by the acoustic power and laser detuning. Furthermore, we develop a platform for analogous in-plane experiments by transferring GaAs membranes hosting quantum dots onto LiNbO3 substrates and patterning them into whispering gallery mode optical resonators. In addition to Purcell enhancement and acoustic tuning of the emission, the devices exhibit strong localized mechanical resonances. Finally, we perform initial experiments on the effects of a surface acoustic wave on the spin of a charge trapped in a quantum dot. We integrate acoustic transducers with charge-tunable diodes, where the charge state of the dot can be precisely controlled by an applied bias voltage, and demonstrate the frustration of optical spin pumping by the acoustic wave.
Photonic crystals are periodic systems that consist of dielectrics with different refractive indices. They are designed to act on photons in contrast to semiconductor crystals whose periodicity affects the motion of electrons. Here we consider the interaction of an atomic electron with its own radiation field in the case when the atom is placed in air voids of a photonic crystal and is not in mechanical contact with the vibrational degrees of freedom of the dielectric host. A strong modification of this interaction from that in free space is shown to change the rest mass of the electron, and this has a significant effect on the shift of the atomic energy levels. This shift is investigated by using the example of atomic hydrogen in a high-index-contrast photonic crystal. The found effect may be of interest both from fundamental and practical points of view.
Motivated by developments in quantum information science, much recent effort has been directed toward coupling individual quantum emitters to optical microcavities. Such systems can be used to produce single photons on demand, enable nonlinear optical switching at a single photon level, and implement functional nodes of a quantum network, where the emitters serve as processing nodes and photons are used for long-distance quantum communication. For many of these practical applications, it is important to develop techniques that allow one to generate outgoing single photons of desired frequency and bandwidth, enabling hybrid networks connecting different types of emitters and long-distance transmission over telecommunications wavelengths. Here, we propose a novel approach that makes use of a nonlinear optical resonator, in which the single photon originating from the atom-like emitter is directly converted into a photon with desired frequency and bandwidth using the intracavity nonlinearity. As specific examples, we discuss a high-finesse, TE-TM double-mode photonic crystal cavity design that allows for direct generation of single photons at telecom wavelengths starting from an InAs/GaAs quantum dot with a 950 nm transition wavelength, and a scheme for direct optical coupling of such a quantum dot with a diamond nitrogen-vacancy center at 637 nm.