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Physical Review A

Excitation of a single trapped electron by phase-sensitive back-action

P. B. Lerner, P. Tombesi

Published May 1, 1993• 4 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.47.4436

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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.
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.
Limitations on the sensitivity for detecting a weak classical force acting on a harmonic oscillator are imposed by the quantum mechanical properties associated with a "standard" amplitude-and-phase measurement and, classically, by the back reaction noise associated with the finite noise temperature of the amplifier used to process the measurement. These are known as the "standard quantum limit" and the "standard amplifier limit", respectively. We present the theoretical motivation behind the quest to circumvent these limits, and examine a single-transducer back-action evading measurement scheme designed to perform a phase-sensitive coupling to the oscillator, with the concomitant circumvention of the standard amplifier limit via the "squeezing" of amplifier back reaction noise. The applicability of squeezing in the detection of gravitational radiation is explored via the dependence of detection sensitivity on the physical temperature and quality factor of the resonant-bar gravitational radiation antenna, on the noise temperature of the amplifier, and on the squeezing factor of the back-action evading measurement; the success of back-action evasion in improving upon the optimum amplitude-and-phase detection sensitivities depends critically upon these parameters. Using the LSU superconducting dual-cavity accelerometer as a test platform, we present direct evidence for the establishment of a phase-sensitive coupling to an oscillator, along with a variety of indirect corroborating evidence. This data indicates that our phase-sensitive measurement scheme is indeed more sensitive to one component of the oscillator than to the other component. We also present the first evidence for the existence of back-action evasion of amplifier back reaction noise. We show theoretical expectations and experimental results for the dependence of squeezing on: input signal phases, amplitudes, and frequencies; amplifier back reaction levels; background noise; mechanical oscillator frequency; and coherent carrier contribution at the cavity resonance frequency. Squeezing factors of up to fifteen were achieved by our back-action evading measurement scheme.
Detector backaction can be completely evaded when the state of a one-electron quantum cyclotron is detected, but it nonetheless significantly broadens the quantum-jump resonance line shapes from which the cyclotron frequency can be deduced. This limits the accuracy with which the electron magnetic moment can be determined to test the standard model's most precise prediction. A steady-state solution to a master equation, the first quantum calculation for the open quantum cyclotron system, illustrates a method to circumvent the detection backaction upon the measured frequency.
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.