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Spatial Propagation and Characterization of Quantum States of Light in Integrated Photonic Devices

David Barral

Published Nov 23, 2015• 0 citations
OpenAlex

Abstract

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.

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Spatial Propagation and Characterization of Quantum States of Light in Integrated Photonic Devices

David Barral

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.

•Nov 23, 2015•1 citation

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Integrated optical quantum circuits based on photonic waveguiding structures are increasingly gaining attention as a possible solution for scalable quantum technologies with important applications to quantum simulations. Quantum communication provides secure information transmission, but the distance over which quantum states of light can be distributed without significant disturbance is limited due to inescapable losses and noise in optical elements. Loss is the greatest challenge facing the implementation of integrated photonic technologies, and it is inescapable in experimental reality. In recent years there is a rise of interest in structures with spatially inhomogeneous losses. Light propagation in waveguiding structures with spatially distributed sections of loss can be used for implementation of quantum plasmonic circuits, which are able to strongly confine light to sub-wavelength dimensions, as well as for parity-time (PT) symmetric structures, with phase transition associated with PT-symmetry breaking, which opens new possibilities for light manipulation. The PhD thesis contains research on the controllable classical and quantum dynamics of optical frequency conversion processes in quadratically nonlinear photonic integrated circuites in the presence of losses. Namely, I discuss spontaneous parametric down-conversion (SPDC), sum-frequency generation (SFG) and optical parametric amplification (OPA) in nonlinear structures governed by non-Hermition Hamiltonians. I explore the fundamental features of multi-photon generation in integrated nonlinear waveguides. I have been shown that arrays of coupled nonlinear waveguides can serve as a robust integrated platform for the generation of entangled photon states with nonclassical spatial correlations through spontaneous parametric down-conversion (SPDC), and that the operation of such quantum circuit is tolerant even to relatively high losses. Furthermore, I have studied the bi-photon multimode quantum emission tomography in waveguide structures with spatially inhomegeneous losses. The PhD thesis also covers the research on the effect of these losses in waveguide couplers possessing parity-time (PT) symmetry. I have identified an anti-PT spectral symmetry of a parametric amplifier based on those couplers. Finally, I describe the single-photon conversion to a photon pair, and identify opportunities for the efficient enhancement of this process.

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This thesis work covers both classical and quantum aspects of nonlinear propagation of photons in nanophotonic Silicon waveguides. The work has been carried out within the framework of the project SIQURO, which aims to bring the quantum world into integrated photonics by using the Silicon platform and, therefore, permitting in a natural way the integration of quantum photonics with electronics. The research towards on chip bright quantum sources of photon pairs has been done by investigating Multi Modal Four Wave Mixing in micrometer-size waveguides, thus exploiting the large third order nonlinearity of Silicon. The possibility to induce second order nonlinearities by straining its unit cell has been also analyzed through the study of the electro-optic effect. This has been done with the aim to promote Silicon as a platform for the integration of quantum sources of entangled photons based on Spontaneous Parametric Down Conversion. New quantum interference effects have been reported in a free space unbalanced Mach Zehnder interferometer asymmetrically excited by colour entangled photon pairs. Innovative designs of integrated quantum circuits have been proposed, which extend the capabilities of the quantum circuits demonstrated so far and provide additional functionalities. This work represents a step forward to the realization of self subsistent integrated devices for quantum enhanced measurement, quantum computation and quantum crypthography.

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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.
We present the main theoretical results on spatial propagation of quantum light in nonlinear waveguiding devices together with a few applications. We show that the quantization of the classical momentum provides a consistent quantum mechanical formulation of both the linear and the nonlinear quantum light propagation in waveguiding devices. The momentum operator allows us to derive the correct spatial Heisenberg's equations for the forward and backward absorption and emission operators and consequently to analyze the spatial propagation in the multimode optical-field strength space. For that purpose we use the Feynman's path integral method in order to derive the quantum spatial optical propagators of different nonlinear waveguiding devices and accordingly to calculate the spatial propagation of the optical-field strength probability amplitude of quantum states in these nonlinear devices. Likewise, we present a preliminary and heuristic formulation of quantum dissipation in order to take into account the losses under spatial quantum propagation in lossy nonlinear waveguiding devices. It must be stressed that these optical-field strength probabilities have the advantage of being measured by homodyne techniques and therefore their theoretical analysis is of a remarkable interest in the optical characterization of quantum states obtained under linear and nonlinear propagation in waveguiding devices.
A quantum mechanical analysis of the guided light in integrated photonics waveguides is presented. The analysis is made starting from one-dimensional (1D) guided vector modes by taking into account the modal orthonormalization property on a cross section of an optical waveguide, the vector structure of the guided optical modes and the reversal-time symmetry in order to quantize the 1D vector modes and to derive the quantum momentum operator and the Heisenberg equations. The results provide a quantum-consistent formulation of the linear and nonlinear quantum light propagations as a function of forward and backward creation and annihilation operators in integrated photonics. As an illustration, an application to an integrated nonlinear directional coupler is given, that is, both the nonlinear momentum and the Heisenberg equations of the nonlinear coupler are derived.
A quantum analysis of the generalized polarization properties of multimode non-stationary states based on their optical field-strength probability distributions is presented. The quantum generalized polarization is understood as a significant confinement of the probability distribution along certain regions of a multidimensional optical field-strength space. The analysis is addressed to quantum states generated in multimode linear and nonlinear waveguiding (integrated) photonic devices, such as multimode waveguiding directional couplers and waveguiding parametric amplifiers, whose modes fulfill a spatial modal orthogonality. In particular, the generalized polarization degree of coherent, squeezed and Schrödinger’s cat states is analyzed.
Integrated optical quantum circuits based on photonic waveguiding structures are increasingly gaining attention as a possible solution for scalable quantum technologies with important applications to quantum simulations. Quantum communication provides secure information transmission, but the distance over which quantum states of light can be distributed without significant disturbance is limited due to inescapable losses and noise in optical elements. Loss is the greatest challenge facing the implementation of integrated photonic technologies, and it is inescapable in experimental reality. In recent years there is a rise of interest in structures with spatially inhomogeneous losses. Light propagation in waveguiding structures with spatially distributed sections of loss can be used for implementation of quantum plasmonic circuits, which are able to strongly confine light to sub-wavelength dimensions, as well as for parity-time (PT) symmetric structures, with phase transition associated with PT-symmetry breaking, which opens new possibilities for light manipulation. The PhD thesis contains research on the controllable classical and quantum dynamics of optical frequency conversion processes in quadratically nonlinear photonic integrated circuites in the presence of losses. Namely, I discuss spontaneous parametric down-conversion (SPDC), sum-frequency generation (SFG) and optical parametric amplification (OPA) in nonlinear structures governed by non-Hermition Hamiltonians. I explore the fundamental features of multi-photon generation in integrated nonlinear waveguides. I have been shown that arrays of coupled nonlinear waveguides can serve as a robust integrated platform for the generation of entangled photon states with nonclassical spatial correlations through spontaneous parametric down-conversion (SPDC), and that the operation of such quantum circuit is tolerant even to relatively high losses. Furthermore, I have studied the bi-photon multimode quantum emission tomography in waveguide structures with spatially inhomegeneous losses. The PhD thesis also covers the research on the effect of these losses in waveguide couplers possessing parity-time (PT) symmetry. I have identified an anti-PT spectral symmetry of a parametric amplifier based on those couplers. Finally, I describe the single-photon conversion to a photon pair, and identify opportunities for the efficient enhancement of this process.
This thesis work covers both classical and quantum aspects of nonlinear propagation of photons in nanophotonic Silicon waveguides. The work has been carried out within the framework of the project SIQURO, which aims to bring the quantum world into integrated photonics by using the Silicon platform and, therefore, permitting in a natural way the integration of quantum photonics with electronics. The research towards on chip bright quantum sources of photon pairs has been done by investigating Multi Modal Four Wave Mixing in micrometer-size waveguides, thus exploiting the large third order nonlinearity of Silicon. The possibility to induce second order nonlinearities by straining its unit cell has been also analyzed through the study of the electro-optic effect. This has been done with the aim to promote Silicon as a platform for the integration of quantum sources of entangled photons based on Spontaneous Parametric Down Conversion. New quantum interference effects have been reported in a free space unbalanced Mach Zehnder interferometer asymmetrically excited by colour entangled photon pairs. Innovative designs of integrated quantum circuits have been proposed, which extend the capabilities of the quantum circuits demonstrated so far and provide additional functionalities. This work represents a step forward to the realization of self subsistent integrated devices for quantum enhanced measurement, quantum computation and quantum crypthography.