Related papers: Driving Quantum Systems with Superoscillations
Band-limited functions can oscillate locally at an arbitrarily fast rate through an interference phenomenon known as superoscillations. Using an optical pulse with a superoscillatory envelope we experimentally break the temporal…
Superoscillations are band-limited functions that can oscillate faster than their fastest Fourier component. These functions (or sequences) appear in weak values in quantum mechanics and in many fields of science and technology such as…
A function f is said to possess superoscillations if, in a finite region, f oscillates faster than the shortest wavelength that occurs in the Fourier transform of f. I will discuss four aspects of superoscillations: 1. Superoscillations can…
In ordinary circumstances the highest frequency present in a wave is the highest frequency in its Fourier decomposition. It is however possible for there to be a spatial or temporal region of the wave which locally oscillates at a still…
A remarkable phenomenon of superoscillations implies that electromagnetic waves can locally oscillate in space or time faster than the fastest spatial and temporal Fourier component of the entire function. This phenomenon allows to focus…
Superoscillation is a counterintuitive phenomenon for its mathematical feature of ``faster-than-Fourier", which has allowed novel optical imaging beyond the diffraction limit. In this article, we introduce a superoscillating quantum control…
Super-oscillation is a counter-intuitive phenomenon describing localized fast variations of functions and fields that happen at frequencies higher than the highest Fourier component of their spectra. The physical implications of the effect…
Quantum systems can show qualitatively new forms of behavior when they are driven by fast time-periodic modulations. In the limit of large driving frequency, the long-time dynamics of such systems can often be described by a…
It has been found that functions can oscillate locally much faster than their Fourier transform would suggest is possible - a phenomenon called superoscillation. Here, we consider the case of superoscillating wave functions in quantum…
Surprisingly, differentiable functions are able to oscillate arbitrarily faster than their highest Fourier component would suggest. The phenomenon is called superoscillation. Recently, a practical method for calculating superoscillatory…
We report the discovery of super resonance--a new regime of resonant behavior in which a mode's out-of-phase response persists far beyond its classical bandwidth. This effect emerges from a coiled phononic structure composed of a locally…
Superoscillatory wave forms, i.e., waves that locally oscillate faster than their highest Fourier component, possess unusual properties that make them of great interest from quantum mechanics to signal processing. However, the more…
The phenomenon of superoscillation, where band limited signals can oscillate over some time period with a frequency higher than the band limit, is not only very interesting but it also seems to offer many practical applications. The first…
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing…
Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechanical operators as a weak value, where the preselected state…
Superoscillating functions, i.e., functions that locally oscillate at a rate faster than their highest Fourier component, are of interest for applications from fundamental physics to engineering. Here, we develop a new method which allows…
We consider an optomechanical system that is composed of a mechanical and an optical mode interacting through a linear and quadratic optomechanical dispersive couplings. The system is operated in an unresolved side band limit with a high…
It is widely recognized that a physical system can only respond to a periodic driving significantly when the driving frequency matches the normal mode frequency of the system, which leads to resonance. Off-resonant phenomena are rarely…
Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to…
We experimentally show that the response of a quantum-chaotic system can display resonance lines sharper than the inverse of the excitation duration. This allows us to discriminate two neighboring frequencies with a resolution nearly 40…