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arXiv:2011.08136 · Review of Scientific Instruments

Switchable damping for a one-particle oscillator

Xing Fan, S. E. Fayer, T. G. Myers, Benedict Sukra, Geev Nahal, G. Gabrielse

Published Feb 1, 2021• 4 citations
arXivHTMLPDF

Abstract

The possibility to switch the damping rate for a one-electron oscillator is demonstrated for an electron that oscillates along the magnetic field axis in a Penning trap. Strong axial damping can be switched on to allow this oscillation to be used for quantum nondemolition detection of the cyclotron and spin quantum state of the electron. Weak axial damping can be switched on to circumvent the backaction of the detection motion that has limited past measurements. The newly developed switch will reduce the linewidth of the cyclotron transition of one-electron by two orders of magnitude.

DOI
10.1063/5.0038005

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The possibility to switch the damping rate for a one-electron oscillator is demonstrated for an electron that oscillates along the magnetic field axis in a Penning trap. Strong axial damping can be switched on to allow this oscillation to be used for quantum nondemolition detection of the cyclotron and spin quantum state of the electron. Weak axial damping can be switched on to circumvent the backaction of the detection motion that has limited past measurements. The newly developed switch will reduce the linewidth of the cyclotron transition of one-electron by two orders of magnitude.
Electronic feedback is used to self-excite the axial oscillation of a single electron in a Penning trap. Large, stable, easily detected oscillations arise even in an anharmonic potential. Amplitudes are controlled by adjusting the feedback gain, and frequencies can be made nearly independent of amplitude fluctuations. Quantum jump spectroscopy of a perpendicular cyclotron motion reveals the absolute temperature and amplitude of the self-excited oscillation. The possibility to quickly measure parts per billion frequency shifts could open the way to improved measurements of e(-), e(+), p, and (-)p magnetic moments.
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.
Fock states of a oneelectron cyclotron oscillator have been produced and observed nondestructively The states are longlived because spontaneous emission is inhib ited by a factor of using the modied radiation eld of a cylindrical Penning trap Direct nondestructive observation is achieved with a magnetic gradient that is ten times larger than previously possible allowing the states to be resolved with high signaltonoise ratio Quantum jumps up to the n cyclotron level have been observed The potential line broadening from the increased magnetic cou pling is avoided because we have lowered the temperature to which electrons can be cooled by nearly two orders of magnitude to as low as \t mK This is the rst time a trapped elementary particle has been cooled below K At these low temperatures the cyclotron oscillator is completely cooled to its ground state Detection of the electron signal is made possible by a lowpower transistor that was developed in collaboration with condensedmatter colleagues Applications include
A quantum cyclotron is one trapped electron or positron that occupies only its lowest cyclotron and spin states. A master equation is solved for a driven quantum cyclotron with a QND (quantum nondemolition) coupling to a detection oscillator in thermal equilibrium, the latter making this an open quantum system. The predicted rate of a cyclotron and spin quantum jumps as a function of drive frequency, for a small coupling between the detection motion and its thermal reservoir, differs sharply from what has been predicted and used for past measurements. The calculation suggests a ten times more precise electron magnetic moment measurement is possible, as needed to investigate current differences between the most precise prediction of the standard model of particle physics, and the most accurate measurement of a property of an elementary particle.
With a superposition of static electric and magnetic fields, a Penning trap can confine a single electron indefinitely. A weak coupling of the electron to its environment makes the system ideal for precision measurements but renders detection of the electron’s motion difficult. In order to measure fundamental properties of an electron, we employ a Penning trap cooled by a dilution refrigerator. This experimental setup requires extremely low-noise and low-power cryogenic amplifiers for detection of the electron’s axial motion. We design and demonstrate new amplifiers, resulting in a significant decrease of the axial temperature and in an improved signal to noise ratio. We use feedback to cool the axial motion and to self-excite the axial motion for continuous monitoring of the axial frequency. These techniques for cooling and measuring the axial frequency may contribute to an improved measurement of the electron g factor, a more stringent CPT test in leptons, and a more precise measurement of the proton-electron mass ratio.