Photon number density operatoriE^⋅A^

Hawton, Margaret; Melde, T.

doi:10.1103/physreva.51.4186

Cited by 14 publications

(22 citation statements)

References 10 publications

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“…The number operator i D (−) · A (+) /2 + H.c. was shown previously to be the zeroth component of a four-vector obtained by contraction of the second rank EM field tensor with the four-potential (φ, A) [36]. This demonstates that the biorthonormal basis is of value for comparison with the existing literature.…”

Section: Photon Wave Mechanicsmentioning

confidence: 51%

“…The electric field wave function used in [2,5] or RS vectors in [1,18] by themselves do not provide a basis, and this is the root of the criticism of [2] made in [3]. The 2-photon wave function (36) is symmetric in agreement with [1,2].…”

Section: Wave Functionmentioning

confidence: 99%

“…ν with the 4-potential as F µν * A ν gives a 4-vector [36]. Thus n (1/2) , j (1/2) is a 4-vector and photon density is its zeroth component.…”

Section: Photon Wave Mechanicsmentioning

confidence: 99%

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Photon wave mechanics and position eigenvectors

Hawton

2007

Phys. Rev. A

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One and two photon wave functions are derived by projecting the quantum state vector onto simultaneous eigenvectors of the number operator and a recently constructed photon position operator [Phys. Rev A 59, 954 (1999)] that couples spin and orbital angular momentum. While only the Landau-Peierls wave function defines a positive definite photon density, a similarity transformation to a biorthogonal field-potential pair of positive frequency solutions of Maxwell's equations preserves eigenvalues and expectation values. We show that this real space description of photons is compatible with all of the usual rules of quantum mechanics and provides a framework for understanding the relationships amongst different forms of the photon wave function in the literature. It also gives a quantum picture of the optical angular momentum of beams that applies to both one photon and coherent states. According to the rules of qunatum mechanics, this wave function gives the probability to count a photon at any position in space.

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Section: Photon Wave Mechanicsmentioning

confidence: 51%

Section: Wave Functionmentioning

confidence: 99%

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Photon wave mechanics and position eigenvectors

Hawton

2007

Phys. Rev. A

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“…Both A µ ∂ ν A µ = (A µ ∂ ct A µ , A µ ∇A µ ) and A µ F µν = (A · E/c, A × B) multiplied by iǫ 0 c/ are candidates for the four-current density, F µν = ∂ µ A ν −∂ ν A µν being the Faraday tensor. The properties of an operator of the form iA ν F νµ were investigated in [50]. The Coulomb gauge condition ∇ · A = 0 is not Lorentz invariant, but A µ can be chosen to transform as a Lorentz four-vector up to an extra term that maintains the Coulomb gauge in all frames of reference [18].…”

Section: Photonsmentioning

confidence: 99%

Maxwell meets Reeh–Schlieder: The quantum mechanics of neutral bosons

Hawton

Debierre

2017

Physics Letters A

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We find that biorthogonal quantum mechanics with a scalar product that counts both absorbed and emitted particles leads to covariant position operators with localized eigenvectors. In this manifestly covariant formulation the probability for a transition from a one-photon state to a position eigenvector is the first order Glauber correlation function, bridging the gap between photon counting and the sensitivity of light detectors to electromagnetic energy density. The position eigenvalues are identified as the spatial parameters in the canonical quantum field operators and the position basis describes an array of localized devices that instantaneously absorb and re-emit bosons.

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“…Since the electric and magnetic field operators form the second rank tensor F µν = ∂ µ A ν − ∂ ν A µ , contraction with the four-potential A µ in the Lorenz gauge gives the four-vector J µ = F µν A ν . The positive frequency four-flux operator was derived in [10]. Using the Coulomb gauge in vacuum for simplicity [10] gives…”

Section: Photonsmentioning

confidence: 99%

Photon location in spacetime

Hawton¹

2012

Phys. Scr.

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The NewtonWigner basis of orthonormal localized states is generalized to orthonormal and relativistic biorthonormal bases on an arbitrary hyperplane in spacetime. This covariant formalism is applied to the measurement of photon location using a hypothetical 3D array with pixels throughout space turned on at a fixed time and a timelike 2D photon counting array detector with good time resolution. A moving observer will see these detector arrays as rotated in spacetime but the spacelike and timelike experiments remain distinct.

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Photon number density operatoriE^⋅A^

Cited by 14 publications

References 10 publications

Photon wave mechanics and position eigenvectors

Photon wave mechanics and position eigenvectors

Maxwell meets Reeh–Schlieder: The quantum mechanics of neutral bosons

Photon location in spacetime

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