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Physical Review A

1-bit memory using one electron: Parametric oscillations in a Penning trap

Ching-Hsiang Tseng, Daphna G. Enzer, G. Gabrielse, Fred L. Walls

Published Mar 1, 1999• 19 citations
Publisher

Abstract

The parametric oscillation of a single trapped electron is studied and used to measure enhanced spontaneous emission. Hysteresis in this motion provides a 1-bit memory to store information about excitations made with the electron ``in the dark.'' The time dependence and stability criteria for the parametric excitation are examined. The cyclotron motions for one and two electrons are also studied.

DOI
10.1103/physreva.59.2094

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The parametric oscillation of a single trapped electron is studied and used to measure enhanced spontaneous emission. Hysteresis in this motion provides a 1-bit memory to store information about excitations made with the electron ``in the dark.'' The time dependence and stability criteria for the parametric excitation are examined. The cyclotron motions for one and two electrons are also studied.
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.
Quantum jumps between Fock states of a one-electron oscillator reveal the quantum limit of a cyclotron accelerator. The states live for seconds when spontaneous emission is inhibited by 140 within a cylindrical Penning trap cavity. Averaged over hours the oscillator is in thermal equilibrium with black-body photons in the cavity. At 80 mK, quantum jumps occur only when resonant microwave photons are introduced into the cavity, opening a route to improved measurements of the magnetic moments of the electron and positron. The temperature demonstrated is about 60 times lower than the 4.2 K temperature at which charged elementary particles were previously stored. Implications for the production of cold antihydrogen are discussed.
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.
A one-electron qubit would offer a new option for quantum information science, including the possibility of extremely long coherence times. One-quantum cyclotron transitions and spin flips have been observed for a single electron in a cylindrical Penning trap. However, an electron suspended in a planar Penning trap is a more promising building block for the array of coupled qubits needed for quantum information studies. The optimized design configurations identified here promise to make it possible to realize the elusive goal of one trapped electron in a planar Penning trap---a substantial step toward a one-electron qubit.
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.
The hysteresis curve of the bistable cyclotron motion of a single electron in a magnetic field driven by external microwave radiation is obtained by only varying the phase of a phase-sensitive back-action-evading experimental setup. Thus the steady-state solution of the cyclotron motion includes two branches which could be switched by only changing the phase of the device. This effect is of particular interest as an example of the influence of the noise properties of the measurement apparatus on a microscopic system subjected to measurement.