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 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.
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.
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 quantum information processing, unitary transformations are oftentimes used to implement computing tasks.However, unitary transformations are not enough for all situations.Therefore, it is important to explore non-unitary transformations in quantum computing and simulation.Here, we introduce non-unitary transformations by performing singular value decomposition (SVD) on two-photon interference.Through simulation, we show that losses modeled by non-unitary transformation can be perceived as variables to control two-photon interference continuously, and the coincidence statistics can be changed by an appropriate choice of observation basis.The results are promising in the design of integrated optical circuits, providing a way toward fabricating large-scale programmable circuits.
Studying quantum correlations in the presence of loss is of critical importance for the physical modeling of real quantum systems. Here, we demonstrate the control of spatial correlations between entangled photons in a photonic chip, designed and modeled using the singular value decomposition approach. We show that engineered loss, using an auxiliary waveguide, allows one to invert the spatial statistics from bunching to antibunching. Furthermore, we study the photon statistics within the loss-emulating channel and observe photon coincidences, which may provide insights into the design of quantum photonic integrated chips. Published by the American Physical Society 2024