Loss was typically considered a nemesis to optics, which should always be avoided or compensated. On the other hand, gain would be a valuable asset, allowing for mitigating losses and increasing the signal power. However, research has blurred those boundaries, demonstrating that their role can not be simply categorized this way. For instance, loss gives access to nonlinear eects in linear devices, and linear gain introduce additional noise to a quantum system. Undeniably, their role in quantum optics can not be ignored, and this is the path this Ph.D. dissertation follows. First, a general method to compute the input-output relations in any lossy linear N-port device is presented. The method, based on the singular value decomposition (SVD), allows for the analysis of quantum interference in the device and, at the same time, provides an intuitive picture of its classical operation principle. The method's applicability is demonstrated by using dierent reciprocal and nonreciprocal devices. In particular, using this SVD-based procedure to analyze quantum interference in a Wilkinson power divider (WPD) reveals interesting physics in the device. It is theoretically demonstrated that WPDs grant access to coherent perfect absorption (CPA) quantum state transformations in CPA networks with a smaller footprint and a reduced number of elements, which might contribute to reducing the size and complexity of optical networks. Additionally, numerical simulations suggest that WPDs can be designed in a pure silicon-on-insulator platform by taking advantage of radiative losses. Balanced gain-loss optical systems are also investigated. In particular, a method that identies the photonic quantum eigenmodes of the spatial evolution in coupled gain-loss waveguides is proposed, indicating that the associated statistics could be measured using standard detection techniques. Therefore, the noise generation in dierent coupled waveguides is studied, emphasizing its relation with the linear or nonlinear nature of the gain/loss mechanism. The existence of phase transition points in the eigenvalue/eigenvector structure, the possibility of gain and loss mechanisms of different nature to compensate for each other, and the nontrivial properties of the system's uctuations are some of the outcomes of the presented study, thus contributing to a better understanding of non-Hermitian quantum systems. Last but not least, relevant results on scattering theory are presented. The generalized optical theorem is used to derive upper bounds on the cross-polarized backscattering cross-section of systems integrated with a ground plane. Moreover, viable strategies to design these backscatterers based on highly-directive scattering systems are identified.
Loss was typically considered a nemesis to optics, which should always be avoided or compensated. On the other hand, gain would be a valuable asset, allowing for mitigating losses and increasing the signal power. However, research has blurred those boundaries, demonstrating that their role can not be simply categorized this way. For instance, loss gives access to nonlinear eects in linear devices, and linear gain introduce additional noise to a quantum system. Undeniably, their role in quantum optics can not be ignored, and this is the path this Ph.D. dissertation follows. First, a general method to compute the input-output relations in any lossy linear N-port device is presented. The method, based on the singular value decomposition (SVD), allows for the analysis of quantum interference in the device and, at the same time, provides an intuitive picture of its classical operation principle. The method's applicability is demonstrated by using dierent reciprocal and nonreciprocal devices. In particular, using this SVD-based procedure to analyze quantum interference in a Wilkinson power divider (WPD) reveals interesting physics in the device. It is theoretically demonstrated that WPDs grant access to coherent perfect absorption (CPA) quantum state transformations in CPA networks with a smaller footprint and a reduced number of elements, which might contribute to reducing the size and complexity of optical networks. Additionally, numerical simulations suggest that WPDs can be designed in a pure silicon-on-insulator platform by taking advantage of radiative losses. Balanced gain-loss optical systems are also investigated. In particular, a method that identies the photonic quantum eigenmodes of the spatial evolution in coupled gain-loss waveguides is proposed, indicating that the associated statistics could be measured using standard detection techniques. Therefore, the noise generation in dierent coupled waveguides is studied, emphasizing its relation with the linear or nonlinear nature of the gain/loss mechanism. The existence of phase transition points in the eigenvalue/eigenvector structure, the possibility of gain and loss mechanisms of different nature to compensate for each other, and the nontrivial properties of the system's uctuations are some of the outcomes of the presented study, thus contributing to a better understanding of non-Hermitian quantum systems. Last but not least, relevant results on scattering theory are presented. The generalized optical theorem is used to derive upper bounds on the cross-polarized backscattering cross-section of systems integrated with a ground plane. Moreover, viable strategies to design these backscatterers based on highly-directive scattering systems are identified.
Modeling quantum interference in the presence of dissipation is a critical aspect of quantum technologies. Including dissipation into the model of a linear device enables for assesing the detrimental impact of photon loss, as well as for studying dissipation-driven quantum state transformations. However, establishing the input-output relations characterizing quantum interference at a general lossy N-port network poses important theoretical challenges. Here, we propose a general procedure based on the singular value decomposition (SVD), which allows for the efficient calculation of the input-output relations for any arbitrary lossy linear device. In addition, we show how the SVD provides an intuitive description of the principle of operation of linear optical devices. We illustrate the applicability of our method by evaluating the input-output relations of popular reciprocal and nonreciprocal lossy linear devices, including devices with singular and nilpotent scattering matrices. We expect that our procedure will motivate future research on quantum interference in complex devices, as well as the realistic modelling of photon loss in linear lossy devices.
Modeling quantum interference in the presence of dissipation is a critical aspect of quantum technologies. Including dissipation into the model of a linear device enables for assessing the detrimental impact of photon loss, as well as for studying dissipation-driven quantum state transformations. However, establishing the input-output relations characterizing quantum interference at a general lossy N-port network poses important theoretical challenges. Here, we propose a general procedure based on the singular value decomposition (SVD), which allows for the efficient calculation of the input-output relations for any arbitrary lossy linear device. In addition, we show how the SVD provides an intuitive description of the principle of operation of linear optical devices. We illustrate the applicability of our method by evaluating the input-output relations of popular reciprocal and nonreciprocal lossy linear devices, including devices with singular and nilpotent scattering matrices. Our method also enables the analysis of quantum interference in large lossy networks, as we exemplify with the study of an N-port epsilon-near-zero (ENZ) hub. We expect that our procedure will motivate future research on quantum interference in complex devices, as well as the realistic modelling of photon loss in linear lossy devices.
Quantum coherence, quantum decoherence, and photon number reduction are coexistent in linear lossy optical systems. However, how these three elements combine together to determine the evolution of the quantum light remains unclear. Here, based on singular value decomposition (SVD), we propose the theory of deterministic photon-loss subspace (DPLS) for quantum interferences in lossy systems. By performing an SVD of scattering matrices with singular values either 0 or 1, a series of completely lossy and lossless input modes are first defined. According to n_1,...,n_i photons in the first,..., i-th lossy modes, the Hilbert space of the input states can be decomposed into a set of orthogonal subspaces H_((n_1,...,n_i ))^in, i.e., deterministic photon-loss subspaces (DPLSs). When the concept of DPLS is established, the input state can be projected onto these DPLSs. In each DPLS, the photons in lossy modes will be completely dissipated, while those in lossless modes experience a unitary evolution. The output state is a statistical mixture of the evolved outcomes of all projections, since decoherence is a concurrent process. Then, based on the DPLS theory, we not only revisited Anti-HOM interference and the distillation of quantum states, but also demonstrate a robust W-state generation for various input states in a three-port lossy system with one-dimensional DPLSs. Through investigating the loss-induced subspace structure of the system, our general theory for analyzing quantum state evolution in lossy systems explicitly reveals the interplay among quantum coherence, quantum decoherence, and photon number reduction. By engineering the loss, the constructed DPLSs can be used to precisely control quantum interferences in dissipative systems, with potential applications in quantum state preparation, quantum logic operations, and other quantum information processes.
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.
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.
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.