Fundamental Investigations of Quantum and Bandlimited Systems

Abstract

We look at three different kinds of systems, requiring quantum to classical description. The first system is a quantum harmonic oscillator in general Gaussian states undergoing continuous position and momentum measurements. We look at the stochastic evolution of the system conditioned on measurement outcomes. Adopting the CDJ (Chantasri-Dressel-Jordan; Chantastri et al. 2013) stochastic path integral formalism to such continuous variable systems, we characterize the statistics of simultaneous position and momentum measurements. We also find the optimal set of readouts and optimal evolution under monitoring. Simulated stochastic trajectories confirm our analytical findings. Finally, we provide a framework to find the optimal paths and conditions for optimal control for general continuously monitored systems. Our results are relevant for cooling and state preparation of macroscopic resonators.

Next, we consider type II superconductors. When the magnetic field applied on a type II superconductor is between its two critical fields, magnetic flux vortices, also called fluxons, develop. Our work proposes a refrigeration mechanism utilizing the flow of fluxons. In a corbino-like geometry, the fluxons are circulated in a loop along a magnetic field gradient. The fluxons then extract heat from a cold reservoir and dump it in a hot reservoir, thus achieving refrigeration. We characterize the figures of merit of the refrigerator, such as the coefficient of performance and the cooling power. We also optimize the performance of the refrigerator. Such refrigeration techniques can help implement local cooling in circuit-QED experiments.

Finally, we look at superoscillatory/supergrowing optical fields for superresolution imaging in diffraction-limited classical optical systems. Superoscillation/supergrowth refers to a bandlimited function locally oscillating/growing at a rate faster than its highest Fourier component. Superoscillatory optical field spots have been utilized for superresolution imaging, but intense sidelobes lead to poor imaging quality. Our work shows that supergrowing regions can have exponentially higher intensities than superoscillatory regions, mitigating the issue of sidelobes. We also prescribe algorithms to reconstruct subwavelength objects from their images with superoscillatory/supergrowing optical fields. Finally, we provide a robust framework for approximating arbitrary functions in a finite interval by a bandlimited function. Our results are relevant for imaging.