Related papers: Superoscillations: Realisation of quantum weak val…
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…
Arguments from scale physics, augmented by numerical and analytical investigations, are used to consider the probability and the detectability of superoscillations in generic functions. The detectability is defined as the fraction of the…
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…
We show that it is possible to construct spectrally lower bound limited functions which can oscillate locally at an arbitrarily low frequency. Such sub-oscillatory functions are complementary to super-oscillatory functions which are…
It is usually believed that a function whose Fourier spectrum is bounded can vary at most as fast as its highest frequency component. This is in fact not the case, as Aharonov, Berry and others drastically demonstrated with explicit counter…
We report a method for constructing bandpass functions that approximate a given analytic function with arbitrary accuracy over a finite interval. A corollary is that bandpass functions can be obtained that oscillate arbitrarily slower than…
Superoscillations are a phenomenon where a band-limited wave may locally oscillate faster than its highest Fourier component. They are a product of destructive interference between the wave's constituent harmonics. In this article, we…
We present a new scheme to detect and visualize oscillations of a single quantum system in real time. The scheme is based upon a sequence of very weak generalized measurements, distinguished by their low disturbance and low information…
The LSND and MiniBoone seeming anomalies in neutrino oscillations are usually attributed to physics beyond the Standard model. It is, however, possible that they may be an artefact of the theoretical treatment of particle oscillations that…
Weak measurement is a standard measuring procedure with two changes: it is performed on pre- and post-selected quantum systems and the coupling to the measuring device is weakened. The outcomes of weak measurements, ``weak values'' are very…
Quantum measurements are described as instantaneous projections in textbooks. They can be stretched out in time using weak measurements, whereby one can observe the evolution of a quantum state as it heads towards one of the eigenstates of…
The outcomes of a series of measurements, made on a quantum system, form a sequence of random events which occur in a particular order. The system, together with a meter or meters, can be seen as following the paths of a stochastic network…
Quantum light is considered to be one of the key resources of the coming second quantum revolution expected to give rise to groundbreaking technologies and applications. If the spatio-temporal and polarization structure of modes is known,…
The weak values and weak measurement formalism were initially limited to pure states, which were later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be…
Nanomechanical oscillators are at the heart of ultrasensitive detectors of force, mass and motion. As these detectors progress to even better sensitivity, they will encounter measurement limits imposed by the laws of quantum mechanics. For…
The concept of superbandwidth refers to the fact that a band-limited signal can exhibit, locally, an increase of its bandwidth, i.e., an effective bandwidth greater than that predicted by its Fourier transform. In this work, we study the…
We further develop the concept of supergrowth [Jordan, Quantum Stud.: Math. Found. $\textbf{7}$, 285-292 (2020)], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function being higher than its…
We construct a signal from "almost" pure oscillations within some low frequency band. We construct it to produce a superoscillation with frequency above the nominal band limit. We find that indeed the required high frequency is produced but…
In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time…
Besides their stunning physical properties which are unmatched in a classical world, squeezed states of electromagnetic radiation bear advanced application potentials in quantum information systems and precision metrology, including…