Toward sub-Kelvin resistive cooling and non destructive detection of trapped non-neutral electron plasma

Abstract

A resonant circuit tuned to a particular frequency of the motion of charged particles stored in a Penning trap and connected to a low noise amplifier allows, at the same time, cooling and non destructive detection of the particles. Its use is widely diffused when single or few particles are stored near the centre of a hyperbolic Penning trap. We present a consistent model that predicts the shape of the induced signal when the tuned circuit is used to detect and cool the axial motion of a cold non neutral plasma stored in an open-ended cylindrical Penning trap. The model correctly accounts for the not negligible axial plasma size. We show that the power spectrum of the signal measured across the tuned circuit provides information about the particle number and insights about the plasma temperature. We report on the design of a HEMT-based cryogenic amplifier working at 14.4 MHz and 4.2 K and the results of the noise measurements. We have measured a drain current noise in the range from 6 to 17 pA/ √ Hz, which corresponds to an increase of the tuned circuit equivalent temperature of at maximum 0.35 K. The cryogenic amplifier has a very low power consumption from few tens to few hundreds of µW corresponding to a drain current in the range 100-800 µA. An additional contribution due to the gate noise has been identified when the drain current is below 300 µA; above that value an upper limit of the increase of the equivalent tuned circuit temperature due to this contribution of 0.02 K has been obtained. These features make the tuned circuit connected to this amplifier a promising device for detecting and cooling the axial motion of an electron plasma when the Penning trap is mounted inside a dilution refrigerator.

Levitated electromechanics: all-electrical cooling of charged nano- and micro-particles

“…A similar calculation for the parallel RLC circuit yields the same result for the friction rate. This resonant enhancement of friction is in agreement with the damping rate observed for trapped atomic ions and electrons [33,34]. Note that the series adiabatic friction rate ( 6) is equal to the parallel on-resonance damping rate (8).…”

“…where we introduced the effective resistance R eff [28,34]. For a series RLC circuit R eff = Q 2 f R, while for parallel it reads R eff = ω z LQ f , with the circuit quality factor…”

“…The dissipation of energy across R is accompanied by heating due to Johnson-Nyquist noise [28,33,34], modeled as a white voltage-noise source V R of width Circuit diagram for the feedback control of charged particle motion. The motion of the particle induces a voltage U across the effective resistance R eff .…”

“…The dissipation of energy across R is accompanied by heating due to Johnson-Nyquist noise [28,33,34], modeled as a white voltage-noise source V R of width…”

Electric trapping and circuit cooling of charged nanorotors

“…The motional energy of a charged particle can be reduced by coupling it to a series or parallel RLC circuit through dissipation in the resistor [45][46][47][48][49][50][51][52]. The present section demonstrates how this resistive cooling can dampen the combined rotational-translational state of a nanoparticle and provides the resulting damping rates in the quasi-adiabatic and on-resonance limits.…”