Maximal localizability of photons (original) (raw)
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Frontiers in Photonics
The classical free-space solutions of Maxwell’s equations for light propagation in one dimension include wave packets of any shape that travel at the speed of light. This includes highly-localised wave packets that remain localised at all times. Motivated by this observation, this paper builds on recent work by Southall et al. [J. Mod. Opt. 68, 647 (2021)] and shows that a local description of the quantised electromagnetic field, which supports such solutions and which must overcome several no-go theorems, is indeed possible. Starting from the assumption that the basic building blocks of photonic wave packets are so-called bosons localised in position (blips), we identify the relevant Schrödinger equation and construct Lorentz-covariant electric and magnetic field observables. In addition we show that our approach simplifies to the standard description of quantum electrodynamics when restricted to a subspace of states.
Localization of One-Photon States
Physical Review Letters, 1997
Single photon states with arbitrarily fast asymptotic power-law fall-off of energy density and photodetection rate are explicitly constructed. This goes beyond the recently discovered tenth power-law of the Hellwarth-Nouchi photon which itself superseded the long-standing seventh powerlaw of the Amrein photon.
Why photons cannot be sharply localized
Physical Review A, 2009
Photons cannot be localized in a sharply defined region. The expectation value of their energy density and the photon number density can only be approximately localized, leaving an exponential tail. We show that one may sharply localize either electric or magnetic (but not both) footprints of photons, and only momentarily. In the course of time evolution this localization is immediately destroyed. However, the coherent states, like their classical counterparts, can be localized without any limitations. The main tool in our analysis is a set of space-dependent photon creation and annihilation operators defined without any reference to the mode decomposition.
Physics Letters A, 1993
We show that there is only one operator having some minimal properties enabling it to be a one photon position operator. These properties are stated, and the solution is shown to be the photon position operator proposed by Pryce. This operator has non-commuting components. Nevertheless, it is shown that one can find states localized with an arbitrary precision.
Photon position operators and localized bases
Physical Review A, 2001
We extend a procedure for construction of the photon position operators with transverse eigenvectors and commuting components [Phys. Rev. A 59, 954 (1999)] to body rotations described by three Euler angles. The axial angle can be made a function of the two polar angles, and different choices of the functional dependence are analogous to different gauges of a magnetic field.
Photon localization barrier can be overcome
Optics Communications, 2005
In contradistinction to a widespread belief that the spatial localization of photons is restricted by a power-law falloff of the photon energy density, I. Bialynicki-Birula [Phys. Rev. Lett. 80, 5247 (1998)] has proved that any stronger -up to an almost exponential -falloff is allowed. We are showing that for certain specifically designed cylindrical one-photon states the localization is even better in lateral directions. If the photon state is built from the so-called focus wave mode, the falloff in the waist cross-section plane turns out to be quadratically exponential (Gaussian) and such strong localization persists in the course of propagation.
Angular momentum and the geometrical gauge of localized photon states
Physical Review A, 2005
Localized photon states have non-zero angular momentum that varies with the non-unique choice of a transverse basis and is changed by gauge transformations of the geometric vector potential a. The position operator must depend on the choice of gauge, but a complete gauge transformation of a physically distinct state has no observable effects. The potential a has a Dirac string singularity that is related to an optical vortex of the electric field.
Extreme nonlocality with one photon
2009
Quantum nonlocality is typically assigned to systems of two or more well separated particles, but nonlocality can also exist in systems consisting of just a single particle, when one considers the subsystems to be distant spatial field modes. Single particle nonlocality has been confirmed experimentally via a bipartite Bell inequality. In this paper, we introduce an N-party Hardy-like proof of impossibility of local elements of reality and a Bell inequality for local realistic theories for a single particle superposed symmetrical over N spatial field modes (i.e. a N qubit W state). We show that, in the limit of large N, the Hardy-like proof effectively becomes an all-versus nothing (or GHZ-like) proof, and the quantum-classical gap of the Bell inequality tends to be same of the one in a three-particle GHZ experiment. We detail how to test the nonlocality in realistic systems.
A simple geometrical interpretation of the photon position operator
2021
It is shown that the photon position operator ~̂ X with commuting components introduced by Margaret Hawton can be written in the momentum representation as ~̂ X = i ~̂ D, where ~̂ D is a flat connection in the tangent bundle T (R \ {(0, 0, k3) ∈ R : k3 ≥ 0}) over R \ {(0, 0, k3) ∈ R : k3 ≥ 0} equipped with the Cartesian structure. Moreover, ~̂ D is such that the tangent 2-planes orthogonal to the momentum are parallelly propagated with respect to ~̂ D and, also, ~̂ D is an anti-Hermitian operator with respect to the scalar product 〈Ψ|Ĥ−2s|Φ〉. The eigenfunctions Ψ ~ X(~x) of the position operator ~̂ X are found.