Ph.D. Thesis - Physics

A fit of the resulting curve returns the initial energy of the ion, provided that the laser
detuning and intensity are well-known. The detuning and saturation parameter (related to
the intensity) are plugged into the fit function, such that E0 is the only free parameter. The
derivation of this formula is presented in the theoretical paper cited above. An experiment
is repeated several times to get a good curve. Since heating is a stochastic process, the ion
heats up by a different amount each time, and averaging is required to get a good value for
the average heating rate.
9.3 Measurements
In this section we present the data for one experimental run, bringing in the wire from a
far distance (D > 4 mm) to D = 0.6 mm from the trapped ion. At each wire position,
compensation was done and the vertical compensation voltage was recorded, the vertical
and horizontal secular frequencies were recorded, and a heating rate measurement was
performed.
For all the measurements in this section, the trap drive frequency was Ω/(2π) =
14.74 MHz, with a drive voltage of Vrf ≈ 200 V. The center of the trap was set at ground,
and the voltages on the other electrodes that yielded a compensated trap were between -10
and 10 V.
Vertical compensation
Two compensation voltages, called H and V , were varied as the wire is brought in. Each
is a linear combination of the voltages on several of the dc electrodes, with H changing
primarily the electric field in the ˆx direction, and V changing the field in the ˆy direction.
Of the two, only V changes appreciably, since the wire is moving vertically down onto the
ion, with a small offset (≈50 µm) for imaging the ion. The vertical wire positions are
plotted in Fig. 9-7. We see that there is a monotonic but nonlinear dependence on the wire
position. It is possible that the dc charge on the wire changes during the course of the
experiment, either by discharging or by picking up stray charged particles from the (small)
ambient pressure or photoelectrons induced by laser scatter.
Secular frequencies
We plot here in Fig. 9-8 the secular frequency measurements for the same set of wire
positions as above. Only the horizontal (ωˆx) and vertical (ωˆy) frequencies are plotted.
The secular frequencies fit well to a 1/D 2 dependence, as displayed in Fig. 9-9. The
equations are ωˆy/ (2π) = 0.124/D 2 + 1.63 and ωˆx/ (2π) = 0.121/D 2 + 1.44, where ωˆy and
ωˆx are the vertical and horizontal frequencies measured in 10 6 s −1 and d is the ion-wire
distance measured in mm. 1.63 and 1.44 MHz are the values of ωˆy and ωˆx, respectively,
when the wire is effectively at D = ∞, and is not influencing the trap at all.
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