Photon wave functions, wave-packet quantization of light, and coherence theory

By Brian J. Smith, Michael G. Raymer. 2007

190 citations recorded by the source corpus.

The monochromatic Dirac and polychromatic Titulaer–Glauber quantized field theories (QFTs) of electromagnetism are derived from a photon-energy wave function in much the same way that one derives QFT for electrons, i.e., by quantization of a single-particle wave function. The photon wave function and its equation of motion are established from the Einstein energy–momentum–mass relation, assuming a local energy density. This yields a theory of photon wave mechanics (PWM). The proper Lorentz-invariant single-photon scalar product is found to be non-local in coordinate space, and is shown to correspond to orthogonalization of the Titulaer–Glauber wave-packet modes. The wave functions of PWM and mode functions of QFT are shown to be equivalent, evolving via identical equations of motion, and completely describe photonic states. We generalize PWM to two or more photons, and show how to switch between the PWM and QFT viewpoints. The second-order coherence tensors of classical coherence theory and the two-photon wave functions are shown to propagate equivalently. We give examples of beam-like states, which can be used as photon wave functions in PWM, or modes in QFT. We propose a practical mode converter based on spectral filtering to convert between wave packets and their corresponding biorthogonal dual wave packets.

Subfields: Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/e410a069c3ec234adfedb17e17005b6faa6a0139

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Alexander I. Lvovsky
2. Michael G. Raymer
3. Claude Fabre
4. Nicolas Treps
5. E. Bimbard
6. Nitin Jain
7. A. MacRae

In Electrical and Electronic Engineering

1. Claude Fabre
2. Michael G. Raymer
3. Alexander I. Lvovsky
4. Nicolas Treps

Citations in the corpus

• Modes and states in quantum optics (2019, background): “There is therefore an exact mapping between a single-photon quantum state |1 : f〉 and the corresponding spatiotemporal mode amplitude f(r, t), so that it is often convenient to consider f as the ”wave function” of the single photon (Smith and Raymer, 2007).”
• Continuous-variable optical quantum-state tomography (2009, methodology): “This is consistent with the adoption of a definition for a photon’s spatial wave function Sipe, 1995; Bialynicki-Birula, 1996; Smith and Raymer, 2007 , in which the Schrödinger equation is replaced by the Maxwell equations since a photon cannot be strictly localized in space, some subtleties must…”