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Optomechanical systems are rapidly becoming one of the most promising platforms for observing quantum behaviour, especially at the macroscopic level. Moreover, thanks to their state-of-the-art methods of fabrication, they may now enter…
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides…
Nonlinear optical effects provide a natural way of light manipulation and interaction, and form the foundation of applied photonics -- from high-speed signal processing and telecommunication, to ultra-high bandwidth interconnects and…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
Nonlinear spectroscopy is a cornerstone of quantum science, providing unique access to multi-point correlations, quantum coherence, and couplings that are invisible to linear methods. However, classical simulation of these phenomena is…
Although classical nonlinear dynamics suggests that sufficiently strong nonlinearity can sustain oscillations, quantization of such model typically yields a time-independent steady state that respects time-translation symmetry and thus…
We explore the potential of direct spectroscopy of ultra-narrow optical transitions of atoms localized in an optical cavity. In contrast to stabilization against a reference cavity, which is the approach currently used for the most highly…
Nonlinearity is a key resource in both classical and quantum signal processing. Nonlinear nanomechanical elements have found applications ranging from sensing to computing, while networks of nonlinear resonators, as well as nonlinearly…
Approximating functions by a linear span of truncated basis sets is a standard procedure for the numerical solution of differential and integral equations. Commonly used concepts of approximation methods are well-posed and convergent, by…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
We investigate optical nonlinear interactions in a dynamic environment by studying generation of photons in spontaneous parametric down conversion inside a nonlinear cavity where the optical path length is periodically modulated in time. We…
Systems of coupled cavity modes have the potential to provide bright quantum optical states of light in a highly versatile manner. Microring resonators for instance are highly scalable candidates for photon sources thanks to CMOS…
We create classical (non-quantum) dynamic data structures supporting queries for recommender systems and least-squares regression that are comparable to their quantum analogues. De-quantizing such algorithms has received a flurry of…
Optical parametric oscillators are widely-used pulsed and continuous-wave tunable sources for innumerable applications, as in quantum technologies, imaging and biophysics. A key drawback is material dispersion imposing the phase-matching…
Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…
Non-linearities are a key feature allowing non-classical control of quantum harmonic oscillators. However, when non-linearities are strong, designing protocols for control is often difficult, placing a barrier to exploiting these properties…
In this letter, we investigate the quantum optical properties of driven-dissipative nonlinear systems in a cascade configuration. We show that pumping a nonlinear system with a state having a noncoherent statistics, can improve the…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Herewe investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…