Historical research guide · 0672 · 2019
Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States
Wayne Cheng-Wei Huang · Herman Batelaan
In one minute
Stochastic electrodynamics — SED — is the classical theory in which the vacuum’s zero-point field is a real random electromagnetic field and particles are ordinary charges being shaken by it. Its record is remarkable: it reproduces the retarded van der Waals force, the ground state of the harmonic oscillator, Landau diamagnetism, the Planck blackbody spectrum and the Debye specific-heat law exactly. Wayne Cheng-Wei Huang and Herman Batelaan set out to find the edge of that record and built the sharpest test yet. Two counter-propagating laser pulses split a trapped oscillator’s ground state into two well-separated wavepackets — a squeezed Schrödinger cat state that stands in for the two slits of the double-slit experiment. Through the whole excitation the classical and quantum calculations track each other, energy for energy. When the packets swing back together, the quantum calculation shows interference fringes while the SED simulation of thirty thousand particles reproduces only their smooth outline. The authors read this as SED behaving like the decoherence limit of quantum mechanics.
Connection
The zero-point field of chapter 2 is real physics in every formulation; what this paper marks is the exact place where its classical version stops tracking quantum behaviour, and it names the missing ingredient — the Fourier relation between position and momentum — as the target for anyone building the bridge. That is chapter 1’s discipline at its best: a computable prediction that two pictures cannot both satisfy.
From the source
Stochastic electrodynamics, in which particles are classical charges driven by a real random zero-point electromagnetic field, is in exact agreement with quantum mechanics for a long list of systems: the retarded van der Waals force, the ground-state distribution of harmonic oscillators, Landau diamagnetism, the Planck spectrum of blackbody radiation and the Debye specific-heat law for solids, with parametric interaction also giving discrete excitation spectra in excellent agreement.Section 1, Introduction
Two counter-propagating dichromatic laser pulses exert a spatially modulated Kapitza-Dirac force whose difference frequency, tuned to twice the oscillator’s resonance, parametrically excites a ground-state harmonic oscillator into a squeezed Schrödinger cat state — a superposition of two macroscopically distinct, displaced squeezed states that serves as the harmonic-oscillator analogue of the left-slit-plus-right-slit electron state.Sections 2 and 3, Equations (4), (5) and (8)
Through the excitation itself the classical and quantum treatments agree: the ensemble average of the SED oscillator energy and the expectation value of the quantum energy stay overlapped for most of the pulse, and the two energy distributions have similar width and average value even though the quantum one is discrete and the classical one continuous.Section 3, Figure 3a and 3b
When the two wavepackets recombine after a quarter of the oscillator period, interference fringes appear in the quantum probability distribution but not in the SED distribution, which captures only the outline as if the coherence between the packets had been lost; the fringe spacing follows two pi times the reduced Planck constant divided by the mass, the resonant frequency and the packet separation, which mimics the double-slit diffraction formula.Section 3, Figure 4a and 4b; Section 4
The authors’ reading of the difference is structural: position and momentum are independent dynamical variables in stochastic electrodynamics, whereas the canonical commutation relation makes them a Fourier pair in quantum mechanics, so SED may be seen as the decoherence limit of quantum mechanics rather than a rival to it — and on that basis they predict that an SED calculation of electron double-slit diffraction, if ever carried out, will not show fringes.Section 4, Discussion and Conclusions
Any mechanism or theoretical operation that restores the Fourier relation between position and momentum in stochastic electrodynamics, or that deteriorates it in quantum mechanics, would be the proper decoherence theory bridging the two — which the authors name as the open problem their result leaves standing.Section 4, final paragraph
The way in
https://doi.org/10.3390/atoms7020042How to cite it
Wayne Cheng-Wei Huang, Herman Batelaan (2019) Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States doi:10.3390/atoms7020042