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Strongly-driven nonlinear optical processes such as spontaneous parametric down-conversion and spontaneous four-wave mixing can produce multiphoton nonclassical beams of light which have applications in quantum information processing and…
Excited states of molecules lie in the heart of photochemistry and chemical reactions. The recent development in quantum computational chemistry leads to inventions of a variety of algorithms that calculate the excited states of molecules…
In this work we develop an open quantum system view of the parametric approximation, which allows us to obtain systematic perturbative corrections to it. We consider the Jaynes-Cummings model with dissipation, assuming that the field is in…
We study theoretically an array of two-level qubits moving relative to a one-dimensional waveguide. This motion can be implemented mechanically or simulated via the modulation of the couplings between the qubits and the waveguide. When the…
We present second-order molecular cluster perturbation theory (MCPT(2)), a linear scaling methodology to calculate arbitrarily large systems with explicit calculation of individual wavefunctions in a coupled-cluster framework. This new…
Despite recent progress in nonlinear optics in wavelength-scale resonators, there are still open questions on the possibility of parametric oscillation in such resonators. We present a general approach to predict the behavior and estimate…
The U(1,1) and U(2) transformations realized by three-mode interaction in the respective parametric approximations are studied in conditional measurement, and the corresponding non-unitary transformation operators are derived. As an…
Two-dimensional (2D) spectroscopy combines high temporal and spectral resolution, allowing the observation of ultrafast energy transfer and the separation of homogeneous and inhomogeneous broadening. Typically, 2D spectroscopy is dominated…
Quantum phase estimation (QPE) of the eigenvalues of a unitary operator on a target quantum system is a crucial subroutine in various quantum algorithms. Conventional QPE is often expensive to implement as it requires a large number of…
Nonlinear optics underpins quantum photonics by enabling the generation and control of quantum states of light. We present new applications of optical resonators as mode selectors in nonlinear processes. First, we show that cavity-enhanced…
Optical parametric amplification is a second-order nonlinear process whereby an optical signal is amplified by a pump via the generation of an idler field. It is the key ingredient of tunable sources of radiation that play an important role…
In this paper we introduce a numerical method for nonlinear parabolic PDEs that combines operator splitting with deep learning. It divides the PDE approximation problem into a sequence of separate learning problems. Since the computational…
The problem of estimating a generic phase-shift experienced by a quantum state is addressed for a generally degenerate phase shift operator. The optimal positive operator-valued measure is derived along with the optimal input state. Two…
We present the constructon and detailed analysis of highly-optimized self-refocusing pulse shapes for several rotation angles. We characterize the constructed pulses by the coefficients appearing in the Magnus expansion up to second order.…
Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual…
We propose two algorithms for discrete-time parameter estimation, one for time-varying parameters under persistent excitation (PE) condition, another for constant parameters under no PE condition. For the first algorithm, we show that in…
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the…
Multi-photon quantum interference is the underlying principle for optical quantum information processing protocols. Indistinguishability is the key to quantum interference. Therefore, the success of many protocols in optical quantum…
The investigation of the first-order quantum phase transition (QPT) is far from clarity in comparison to that of the second-order or continuous QPT, in which the order parameter and associated broken symmetry can be clearly identified and…
We introduce a technique for calculating the density operator time evolution along the lines of Heisenberg representation of quantum mechanics. Using this technique, we find the exact solution for the quantum evolution of two and three…