The Uncertainty of the Electromagnetic Field of a Particle

D. Rodríguez-Méndez, Shahen Hacyan, Rocío Jáuregui

Szabolcs Hack, Béla Gábor Pusztai, Krisztina Joós +3 more

We investigate the dynamics of a charged particle interacting with a multimode quantized electromagnetic field and obtain an analytic solution for the full electron--field system. This framework enables the calculation of position expectation values and uncertainties for arbitrary wave packets and field states, allowing us to identify quantum corrections to the corresponding classical motion. While the corrections to the position expectation value are weak and largely insensitive to the quantum state of the field, the wave packet broadening exhibits a pronounced dependence on the field state. In particular, the quantum uncertainty of the radiation is directly imprinted onto the spatial uncertainty of the particle. We illustrate these effects for Gaussian wave packets interacting with coherent, Fock, and squeezed states, including bright squeezed vacuum. The interaction with a finite-duration laser pulse is also analyzed as a multimode example. Our results provide a transparent analytic route toward understanding how quantum fluctuations of light influence electron dynamics in strong-field settings.

Peter H. Handel

Most sensors traduce various environmental, industrial, or laboratory parameters into electrical signals. Quantum sensing pushes this to the ultimate limit of achievable sensitivity, detectivity, resolution, and stability. Quantum mechanics sets these limits through the uncertainty principle. It causes the ubiquitous 1/f noise, as we show here for LiNbO3. Quantum 1/f theory, known as the quantum theory of the fundamental 1/f noise phenomenon, is a new aspect of quantum mechanics, that governs the nonlinear interaction of particle and field, introducing the new notions of "physical cross sections" (PCS) and "physical process rates" (PPR). These contain the fundamental macroscopic quantum 1/f fluctuations. They yield the usually defined PCS and PPR with infrared radiative corrections, when the expectation value is taken over the low-frequency photon states of negative entropy. The physical charged particle, such as an electron, contains both the bare particle and its electromagnetic field. The latter is in a coherent state, where the phase of the electromagnetic field oscillators is determined. Heisenberg’s uncertainty principle then requires that the energy must be uncertain, leading to nonstationary states describing the particle. The particle’s resulting fractional current fluctuations in large devices always have the spectrum 2α/πf, where α=1/137 is the fine structure constant.