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Annual Meeting Optical Society of America

QND measurements and wave function collapse in penning traps

Irene Marzoli, Paolo Tombesi

Published Jan 1, 1993• 0 citations
Publisher

Abstract

The attained precision of measurements in Penning traps is so high that, for light particles, the relativistic corrections are detectable. Thus, the coupling among the various motions of the trapped particle is provided by the relativistic shift of the mass. A parallel LCR circuit interacting with the elastically bound particle represents the measurement device. The measurement is performed by monitoring the resonance frequency of the spectral function of the output voltage.

DOI
10.1364/oam.1993.wxx.4

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The attained precision of measurements in Penning traps is so high that, for light particles, the relativistic corrections are detectable. Thus, the coupling among the various motions of the trapped particle is provided by the relativistic shift of the mass. A parallel LCR circuit interacting with the elastically bound particle represents the measurement device. The measurement is performed by monitoring the resonance frequency of the spectral function of the output voltage.
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We have developed and applied a novel method for the precise determination of small frequency differences of particle motions inside a Penning trap. In the present case, the frequency differences on the order of 100 mHz at motional frequencies on the order of 1 MHz are used to determine the spin state of an electron bound in a hydrogen-like ion. This novel technique measures the integrated phase difference of the particles' motions relative to an excitation with a well-defined phase. Thereby, the Fourier-limit for frequency measurements based on Fourier-analyses of detection signals can be overcome.
We present a thorough analysis of the electronic detection of charged particles, confined in a Penning trap, via image charges induced in the trap electrodes. Trapping of charged particles in an electrode structure leads to frequency shifts, which are due to image charge and space charge effects. These effects are of importance for Penning trap experiments which involve high charge densities or require high precision in the motional frequencies. Our analysis of image charges shows that only (higher order) odd powers of the particle displacement lead to induced charge differences, giving rise to a signal. This implies that, besides the centre-of-mass frequency of a trapped particle cloud, also higher order individual particle frequencies induce a signal, which can be picked up by an electronic detection circuit attached to the trap electrodes. We also derive analytic expressions for the image charge and space charge induced frequency shifts and perform simulations of space charge effects. In relation to this, we discuss the consequences of the shifted particle frequencies for resistive cooling of the particle motion.
We propose a scheme for quantum-logic spectroscopy of an electron or positron in a Penning trap. An electron or positron in a spectroscopy trap is coupled to a remote logic electron or positron via a wire to achieve motional entanglement. By separating the two traps, one can significantly improve magnetic field homogeneity, microwave characteristics, and detection sensitivity. The proposed scheme will improve the measurement precision of the electron's and positron's magnetic moments and charge-to-mass ratios, enabling precise tests of the standard model of particle physics.