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The purpose of this paper is to study metrics suitable for assessing uncertainty of power spectra when these are based on finite second-order statistics. The family of power spectra which is consistent with a given range of values for the…
The variance of the number of particles in a set is an important quantity in understanding the statistics of non-interacting fermionic systems in low dimensions. An exact map of their ground state in a harmonic trap in one and two…
The points where diffraction orders emerge or vanish in the propagating spectrum of periodic non-Hermitian systems are referred to as scattering thresholds. Close to these branch points, resonances from different Riemann sheets can…
The Heisenberg limit provides a fundamental bound on the achievable estimation precision with a limited number of $N$ resources used (e.g., atoms, photons, etc.). Using entangled quantum states makes it possible to scale the precision with…
The standard cosmological model, known as the LambdaCDM model, has been successful in many respects, but it has some significant discrepancies, some of which have not been resolved yet. In measuring the Hubble-Lematre parameter, there is an…
A central feature of quantum metrology is the possibility of Heisenberg scaling, a quadratic improvement over the limits of classical statistics. This scaling, however, is notoriously fragile to noise. While for some noise types it can be…
The downscaling of optical systems to the micro and nano-scale results in very compliant systems with nanogram-scale masses, which renders them susceptible to optical forces. Here we show a specially designed resonant structure for enabling…
In this paper we review the Heisenberg uncertainty principle in a discrete setting and, as in the classical uncertainty principle, we give it a dynamical sense related to the discrete Schr\"odinger equation. We study the convergence of the…
Microring optical modulators are being explored extensively for energy-efficient photonic communication networks in future high-performance computing systems and microprocessors, because they can significantly reduce the power consumption…
The dark photon is a well-motivated candidate of dark matter due to its potential to open the window of new physics beyond the Standard Model. A fundamental mass-range-sensitivity dilemma is always haunting the dark photon searching…
We are concerned with describing the structure of the set of points in the unit interval which, when subjected to rotation by irrational alpha modulo one, for all finite portions of the orbit contain at least as many points in the bottom…
Performant on-chip spectrometers are important for advancing sensing technologies, from environmental monitoring to biomedical diagnostics. As device footprints approach the scale of the operating wavelength, previously strategies,…
We show that when a microsphere is illuminated by an evanescent wave, the optical forces on- and off- whispering gallery mode (WGM) resonance can differ by several orders of magnitude. Such size selective force allows one to selectively…
The Heisenberg uncertainty principle imposes a fundamental restriction in quantum mechanics, stipulating that measuring one observable completely erases the information on its conjugate one, thereby preventing simultaneous measurements of…
The subject under study is an open subsystem of a larger linear and conservative system and the way in which it is coupled to the rest of system. Examples are a model of crystalline solid as a lattice of coupled oscillators with a finite…
Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…
The Heisenberg uncertainty principle is one of the most famous features of quantum mechanics. However, the non-determinism implied by the Heisenberg uncertainty principle --- together with other prominent aspects of quantum mechanics such…
Quantum phase transitions are often embodied by the critical behavior of purely quantum quantities such as entanglement or quantum fluctuations. In critical regions, we underline a general scaling relation between the entanglement entropy…
We consider entanglement-assisted frequency estimation by Ramsey interferometry, in the presence of dephasing noise from spatiotemporally correlated environments.By working in the widely employed local estimation regime, we show that even…
A general quantum limit to the sensitivity of particle position measurements is derived following the simple principle of the Heisenberg microscope. The value of this limit is calculated for particles in the Rayleigh and Mie scattering…