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arXiv:quant-ph/9707012 · Physical Review A

Measuring the cyclotron state of a trapped electron

Stefano Mancini, Paolo Tombesi

Published Oct 1, 1997• 6 citations
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Abstract

We propose the cyclotron state retrieval of an electron trapped in a Penning trap by using different measurement schemes based on suitable modifications of the applied electromagnetic fields, and exploiting the axial degree of freedom as a probe. A test for the matter-antimatter symmetry of the quantum state is proposed.
DOI
10.1103/physreva.56.3060

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•Jan 1, 2007•0 citations
The quantum non-demolition measurement of the cyclotron excitations of an electron trapped in a Penning trap is shown to be accessible, with the modern technology, by only considering the coupling between the axial and the cyclotron motions induced by the relativistic correction to the electron's mass. It is shown that such a measurement is possible only when the spin state of the electron is preassigned and the wave function will then collapse into a Fock state. When this is not the case the wave function of the electron will collapse into an entangled state.
A single electron in a quantum cyclotron yields new measurements of the electron magnetic moment, given by g/2 = 1.00115965218073(28)[0.28 ppt], and the fine structure constant, α −1 = 137.035999084(51)[0.37 ppb], both significantly improved from prior results. The static magnetic and electric fields of a Penning trap confine the electron, and a 100 mK dilution refrigerator cools its cyclotron motion to the quantum-mechanical ground state. A quantum nondemolition measurement allows resolution of single cyclotron jumps and spin flips by coupling the cyclotron and spin energies to the frequency of the axial motion, which is self-excited and detected with a cryogenic amplifier. The trap electrodes form a high-Q microwave resonator near the cyclotron frequency; coupling between the cyclotron motion and cavity modes can inhibit spontaneous emission by over 100 timesthe free-space rate and shiftthe cyclotron frequency, a systematic effect that dominated the uncertainties of previous g-value measurements. A cylindrical trap geometry creates cavity modes with analytically calculable couplingsto cyclotron motion. Two independent methods use the cyclotron damping rate of an electron plasma or of the single electron itself as probes of the cavity mode structure and allow the identification ofthe modes by their geometries and couplings, the quantification of an offset between the mode and electrostatic centers, and the reduction of the cavity shift uncertainty to sub-dominant levels. Measuring g at four magnetic fields with cavity shifts spanning thirty times the final g-value uncertainty provides a check on the calculated cavity shifts. Magnetic field fluctuations limit the measurement of g by adding a noise-model dependence to the extraction of the cyclotron and anomaly frequencies from their resonance lines; the relative agreement of two line-splitting methods quantifies a lineshape model uncertainty. New techniques promise to increase field stability, narrow the resonance lines, and accelerate the measurement cycle. The measured g allows tests for physics beyond the Standard Model through searches for its temporal variation and comparisons with a “theoretical” g-value calculated from quantum electrodynamics and an independently measured fine structure constant.