Related papers: Time-frequency as quantum continuous variables
We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum…
Conventional optical synthesis, the manipulation of the phase and amplitude of spectral components to produce an optical pulse in different temporal modes, is revolutionizing ultrafast optical science and metrology. These technologies rely…
We review the physical phenomena that arise when quantum mechanical energy levels are modulated in time. The dynamics resulting from changes in the transition frequency is a problem studied since the early days of quantum mechanics. It has…
We develop a mathematical framework for quantum time transfer based on commuting families of Hamiltonians and synchronization observables. The synchronization subspace is defined as the kernel of a difference operator between local clocks,…
A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…
The complex Fourier transform of the two-point correlator of the energy spectrum of a quantum system is known as the spectral form factor (SFF). It constitutes an essential diagnostic tool for phases of matter and quantum chaos. In black…
The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for…
We demonstrate a high-dimensional mode-sorter for single photons based on a multi-output quantum pulse gate, which we can program to switch between different temporal-mode encodings including pulse modes, frequency bins, time bins, and…
The nonstationary nature of signals and nonlinear systems require the time-frequency representation. In time-domain signal, frequency information is derived from the phase of the Gabor's analytic signal which is practically obtained by the…
Temporal-spectral modes of light provide a fundamental window into the nature of atomic and molecular systems and offer robust means for information encoding. Methods to precisely characterize the temporal-spectral state of light at the…
Quantum optics plays a crucial role in developing quantum computers on different platforms. In photonics, precise control over light's degrees of freedom, including discrete variables (polarization, photon number, orbital angular momentum)…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
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,…
Two systems for a charged particle are studied, the first one when it is under the effect of a constant electric field, and the second one when it is under the effect of a constant electromagnetic field. For both systems, it is possible to…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
Time-varying media, characterized by dynamic or spacetime-modulated constitutive parameters such as permittivity and permeability, have recently emerged as a transformative paradigm for advanced wave control, transcending the constraints…
The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…
We argue that the account of Reference Frames quantum properties must change the standard space-time picture accepted in Quantum Mechanics. If RF is connected with some macroscopic solid object then its free quantum motion - wave packet…
We provide a Hilbert space approach to quantum mechanics where space and time are treated on an equal footing. Our approach replaces the standard dependence on an external classical time parameter with a spacetime-symmetric algebraic…
We generalize the concepts of Internal Time Superoperator, its associated non unitary similarity transformations and Liapounov variables, to quantum systems with diagonal singularity, and we give a constructive proof of the existence of…