Ultra-Cooled Atomic Reservoir as a High-Precision Sensor of Electric Signals

An atomic reservoir has been built, tested, and characterized in order to be used as a highly precise detector of electric signals arriving at the trapping electrodes. Our system consists of a single laser-cooled $^{40}$Ca$^+$ ion stored in a trap with rotational symmetry, where the performance is observed through the axial motion of the ion, equivalent to an underdamped harmonic oscillator. Thus, the results are achievable either in Paul or Penning traps. We have found that, for an ion oscillator temperature of $T_{scriptsize{rm radial}} leq 2.9(7)$ mK ($omega_r =2pi times 54$ kHz) and $T_{scriptsize{rm axial}}leq 9.6(2.4)$ mK ($omega_z =2pi times 108$ kHz), the atomic reservoir is sensitive to a time-varying electric field providing a force of $5.32(5)$ neV/$mu $m. We have also measured a quality factor $Q=7750(90)$, and a decay constant $gamma_z=88(2)$ s$^{-1}$. By sweeping the trap frequencies, this method can be applied to determine the strength of any oscillating charge. Moreover, the eigenfrequencies of any charged particle stored in an adjacent trap, regardless of its mass, charge, or polarity, can be probed and monitored by coupling its low-amplitude axial motion with the atomic reservoir. The time scale of the measurement will depend on the control of the phase of the ion motion, which can be neglected in the quantum regime.