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arXiv:2102.01169 · Journal of Lightwave Technology

Quantum Projectors Implemented With Optical Directional Couplers in Ion-Exchanged Glasses

Xesús Prieto-Blanco, Carlos Montero-Orille, Jesús Liñares, Héctor González-Núñez, Daniel Balado

Published Jul 7, 2022• 5 citations
arXivHTMLPDF

Abstract

Ion-exchanged glass as a platform for quantum photonics is proposed. Quantum projectors are implemented with integrated optical directional couplers fabricated by ion-exchange K$^+$/Na$^+$in soda-lime glass. We consider devices composed of concatenated directional couplers which implement$N$-dimensional quantum projective measurements, and concomitantly the production of 1-qudit states. The fundamental units of these devices are 2 × 2 directional couplers that are experimentally studied in order to obtain, through an optical characterization, empiric relationships between fabrication and optical parameters of such couplers. Likewise, a two-dimensional quantum projector is demonstrated so that projective measurements are obtained for the states of basesX(diagonal) andY(circular).

DOI
10.1109/jlt.2022.3189206

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Ion-exchanged glass as a platform for quantum photonics is proposed. Quantum projectors are implemented with integrated optical directional couplers fabricated by ion-exchange K+^++/Na+^++in soda-lime glass. We consider devices composed of concatenated directional couplers which implementNNN-dimensional quantum projective measurements, and concomitantly the production of 1-qudit states. The fundamental units of these devices are 2 × 2 directional couplers that are experimentally studied in order to obtain, through an optical characterization, empiric relationships between fabrication and optical parameters of such couplers. Likewise, a two-dimensional quantum projector is demonstrated so that projective measurements are obtained for the states of basesX(diagonal) andY(circular).
Abstract We show that photonic quantum circuits for implementing arbitrary SU(N) transformations can be made using only synchronous directional couplers. These simple elements provide both beam splitting and phase shifting so that, under a proper concatenation of such elements, unitary transformations of arbitrary dimension can be implemented. The circuits made in this way are robust and controllable, because only one type of element is used and the technology involved in their fabrication is very mature. We present several examples of original passive photonic circuits intended for quantum projective measurements and quantum state generation due to their interest in photonic quantum technology for quantum key distribution systems. Likewise, we have designed, fabricated, and characterized, on an ion-exchanged glass platform, different couplers, which form the basic elements or building blocks of these passive circuits highly compatible with optical fibres.
In this dissertation we introduce a quantum theory of propagation of light in integrated photonic devices. The necessity of this theory is justi ed due to the conceptual and formal inconsistencies the Hamiltonian theory presents when dealing with propagation problems. Taking into account the orthonormalization property and the modal norms, we carry out a canonical quantization of the ux of Momentum and derive Heisenberg equations. We apply it to coupling devices with di erent features of the refractive index: inhomogeneities, nonlinear response and losses; like N N linear and nonli- near directional couplers and spontaneous parametric down conversion and spontaneous four wave mixing-based nonlinear inhomogeneous waveguides. Likewise, we introduce the optical eld-strength space and the amplitude probability distributions in this representation, and by means of a spatial- type Lagrangian theory we derive by path integration propagators in this space for di erent-media based devices. In this way we solve the propagation for discrete and continuous variables. Next, we present a new method of characterization of quantum states introducing a generalized quantum polarization, based on the con nement in particular regions of the optical eld space of the probability distributions of quantum states. Likewise, we propose a consistent polarization degree, a gure which measures how di erent a state is from a full unpolarized one, showing its application to the characterization of various examples of stationary and dynamic quantum states. The last aim of this dissertation is to measure quantum states of light propagating in integrated photonic devices. We designe a versatile and relia- ble electro-optic integrated device to accomplish this goal. This device allows carrying out any SU(2) unitary transformation and is able to be nested as well, allowing its extension to SU(N) transformations. Likewise, it outper- forms other current schemes based on pasive directional couplers due to its ability to reduce the e ect produced by fabrication errors, a very important fact when complex circuits are involved. We perform simulations and show possible applications. In summary, in this thesis we develop tools to design and simulate the performance of photonic devices, as well as propose a characterization me- thod for quantum states propagating within, with interest in the conti- nuously growing eld of integrated quantum photonics.
In this dissertation we introduce a quantum theory of propagation of light in integrated photonic devices. The necessity of this theory is justified due to the conceptual and formal inconsistencies the Hamiltonian theory presents when dealing with propagation problems. Taking into account the orthonormalization property and the modal norms, we carry out a canonical quantization of the flux of Momentum and derive Heisenberg equations. We apply it to coupling devices with different features of the refractive index: inhomogeneities, nonlinear response and losses; like N × N linear and nonli- near directional couplers and spontaneous parametric down conversion and spontaneous four wave mixing-based nonlinear inhomogeneous waveguides. Likewise, we introduce the optical field-strength space and the amplitude probability distributions in this representation, and by means of a spatial- type Lagrangian theory we derive by path integration propagators in this space for different-media based devices. In this way we solve the propagation for discrete and continuous variables. Next, we present a new method of characterization of quantum states introducing a generalized quantum polarization, based on the confinement in particular regions of the optical field space of the probability distributions of quantum states. Likewise, we propose a consistent polarization degree, a figure which measures how different a state is from a full unpolarized one, showing its application to the characterization of various examples of stationary and dynamic quantum states. The last aim of this dissertation is to measure quantum states of light propagating in integrated photonic devices. We designe a versatile and relia- ble electro-optic integrated device to accomplish this goal. This device allows carrying out any SU(2) unitary transformation and is able to be nested as well, allowing its extension to SU(N) transformations. Likewise, it outper- forms other current schemes based on pasive directional couplers due to its ability to reduce the effect produced by fabrication errors, a very important fact when complex circuits are involved. We perform simulations and show possible applications. In summary, in this thesis we develop tools to design and simulate the performance of photonic devices, as well as propose a characterization me- thod for quantum states propagating within, with interest in the conti- nuously growing field of integrated quantum photonics.
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Very recently, the interest for quantum technologies by the scientific community and industry has strongly increased. Different types of implementations have been proposed as a practical implementation for a quantum bit. In particular, quantum photonics is a strong candidate for such applications. We are interested in using single photons and single spins in diamond as a solid state host matrix (nanodiamonds or membranes). Integration of nanosources of light is currently a major bottleneck preventing the realisation of all-photonic chips for quantum technologies and nanophotonics applications. Ideally, one needs optical circuitry, on-chip photodetection and on-chip generation of quantum states of light (single photons, entangled photons…). Our recent work on a new platform for quantum photonics using integrated optics can offer an easier and robust way to create compact quantum circuits that can be on chip and scalable. In this context, the coupling between waveguides and single photon emitters is critical. The goal of our research is to efficiently couple single photon emitters with a new platform made of optical glass waveguides. These waveguides are based on the so-called ion-exchange glass technology and is know in the photonics industry for quite some time but has never been used in the context of quantum technologies. Efficient light-matter interface is of primordial importance in this system. To achieve this goal, several paths are undertaken such as the use of dielectric and plasmonic structuration in order to increase the light interaction with the waveguide or to develop fabrication techniques to insert the emitters directly inside the guide (for nanodiamonds). We will show what is our current state of the art for placing single emitters at the right place on our optical waveguides made of ion-exchange in glass and in particular what can be done to improve our first promising results in order to get near unity coupling between the optical bus and single photon emitters. We will show first results with semiconductor nanocrystals (NCs) but also using nitrogen-vacancy and silicon-vacancy defects in nanodiamond. The very first step in of our approach consists in the design of the structured waveguide using electromagnetic FDTD. We demonstrated that it is possible to achieve more than 90% coupling. In practice, before using coloured centres in diamond, we started working with CdSe/ZnS semiconductor nanocrystals. So far, we use straight waveguides defined to be single modes at the nominal wavelength of the emission line of the nanoemitters. The positioning of nanoemitters is still a challenge to be achieved. We developed an original technique based on photopolymerisation of light where the nanocrystals are grafted into a light sensitive polymer and can be placed at adequate positions.
This paper reviews recent advances in integrated waveguide circuits, lithographically fabricated for quantum optics. With the increase in complexity of realizable quantum architectures, the need for stability and high quality nonclassical interference within large optical circuits has become a matter of concern in modern quantum optics. Using integrated waveguide structures, we demonstrate a high performance platform from which to further develop quantum technologies and experimental quantum physics using single photons. We review the performance of directional couplers in Hong-Ou-Mandel experiments, together with inherently stable interferometers with controlled phase shifts for quantum state preparation, manipulation, and measurement as well as demonstrating the first on-chip quantum metrology experiments. These fundamental components of optical quantum circuits are used together to construct integrated linear optical realizations of two-photon quantum controlled logic gates. The high quality quantum mechanical performance observed at the single photon level signifies their central role in future optical quantum technologies.