Electron-ion correlation histograms

The electron-ion correlation histogram displays the relative time difference ∆t until a sub- sequent ion pulse is detected in the opposite ion-CEM after observing an electron pulse in thee−-CEM (fig. 5.3(b)). In fig. 5.4, a sample electron-ion correlation histogram of measured time differences∆tfor an accelerating voltage of∆Uacc= 3.8 kVis shown12. In the histogram, all electron arrivals are arranged to be situated att= 0. The strong temporal correlation of the photoelectron-ion pair from the photoionisation of neutral atoms is displayed by the pro- nounced correlation peak at∆t= 388.5 nsin the correlation histogram. The correlation peak

11

Assuming sufficient laser power for the ionisation transition ω2i, the trapped neutral atom in the future

combined setup will be photoionised within nanoseconds. Due to this triggered photoionisation of a quasi- resting single atom target, also the individual flight timesti,ecan be observed.

12_{The single measurement in fig. 5.4 corresponds to a relative position of (x = 1.2 mm, y = −0.4 mm) in}

0 500 2 1500 4 2000 6 1000 8 3 ion incidences [10 ] Dt [ns] 0 360 380 400 420 8 6 4 2 0 (a) (b) Dt correlation peak 2 3 4 5 ion incidences 1 0 0 4 8 12 16 20 correlation peak Dt [µs]

Figure 5.4:(a) Sample electron-ion correlation histogram of measured time differences∆t be- tween electron and 87_{Rb-ion detections (fig. 5.3(b)) for an accelerating voltage of ∆U}

acc = 3.8 kV. The histogram displays a pronounced correlation peak from photoionisation at ∆t = 388.5 ns. Inset: Zoom of the correlation peak with Gaussian fit (red curve). (b) Baseline zoom of the histogram in (a), showing correlated ion counts from 0−5 and for relative arrival time differences∆tfrom0up to20µs. Apart the correlation peak at∆t= 388.5 nsfrom photoioni- sation, no second correlation peak can be identified.

exhibits a Gaussian shape with a narrow temporal spread13 of ∆tfwhm = 8.5 ns (fig. 5.4(a), inset). The prominent correlation peak in the electron-ion correlation histogram represents a clear signature of the photoionisation of neutral atoms in the ionisation volume in between the CEMs. In contrast to that, without photoionisation14only a flat baseline plateau of ion inci- dences without any correlation peak is observed in the corresponding correlation histogram. In this case, the electron-ion correlations are merely random distributed in the histogram, similar to the distribution of arrival times as depicted in fig. 5.4(b) for values of∆t >1µs.

Coincidence time window

The number of coincidences Nc from photoionisation of neutral atoms can be deduced from the electron-ion correlation histograms. Particularly, it is derived from the specific temporal position and shape of the correlation peak in the histograms. To determine the exact number of coincidences in contrast to any uncorrelated events (accidental coincidences,Nac), first a fixed coincidence time window∆tc has to be chosen. The integrated number of electron-ion correlations in the chosen window ∆tc reflects the total number of coincidencesNc (fig. 5.5). This number will be used to determine the absolute efficiency of the CEM detectors in the efficiency calibration measurements (see section 5.4).

For the photoionisation calibration measurements of this thesis, the coincidence time win- dow∆tcstarts20ns before the center of the Gaussian correlation peak and ends80ns after it (fig. 5.5). The length of the coincidence time window is explicitly chosen to be∆tc= 100ns. By temporal width, the time window thus encloses the entire photoionisation correlation peak together with an additional dead time window following the peak. This follows as the dead time of the discriminator unit of twmt = 80 ns prevents the CEMs from possible multiple

13

The full width at half maximum∆tfwhmof the Gaussian peak corresponds to a single standard deviation of

1σ= 3.6 ns.

14_{For example, photoionisation does not occur if only one of the two laser beam sources or even no laser beam}

5.2. Electron-ion correlation measurements WMT dead time 1 10 2 10 ion incidences 300 400 500 600 700 3 10 4 10 coincidence window Dt [ns]

Figure 5.5:Zoom of the histogram in fig. 5.4(a), in logarithmic representation. Despite the fitted Gaussian correlation peak, some late87_{Rb-ion arrivals occur within the chosen coincidence} window of ∆tc = 100 ns(shaded area). In comparison, the integral dead time (80 ns) of the used discriminator unit for single pulse counting is shown.

counting of single physical incidences in pulse counting mode caused by cable ringing or ion feedback at the end of the CEM detector (see section 3.4). The particular choice of the asym- metric, extended coincidence window ∆tc thus results from the presence of a few late ion detections (fig. 5.5; values from 400−600ns) compared to the entirely random distributed background of accidental incidences (fig. 5.4(b); ∆t >1µs). Independent measurements with

different pulse processing circuitry show that these late ion detections are indeed physical in- cidences, and are not an artifact of any subsequent pulse processing electronics. Consequently, the coincidence time window has also to include some of these late ion counts15.

Measurement of correlated photoelectron-ion incidences and data acquisition

In the experiment, the single countsNi,eand the background counts Nbi,be at the CEMs are measured alternating with 100 Hz. The single counts Ni,e include the correlated events from photoionisation while the additional measurement of the background counts Nbi,be without photoionisation allows a refined background correction. Experimentally, the measurement of the single and background counts is performed by switching16the laser beam of the excitation transition (λ12 = 780 nm; fig. 4.1(a)) on and off by means of an acousto-optical modulator (AOM). In contrast to that, the laser beam of the ionising transition (λ2i = 473 nm) is continuously operated during an entire measurement series.

For the pulse processing and data acquisition, the single ion and electron incidences at the CEMs are postprocessed in a custom-made timestamp unit [236], or with a digital storage oscilloscope17. Electron-ion correlation histograms are then generated from the data sets by cross-correlating the temporal arrivals of the individual electron and ion incidences. The 15_{Additionally, the independent measurements suggest that also the late ion detections after the coincidence}

window end at∆t >468.5 nsare physical incidences (fig. 5.5). Theoretically, the chosen coincidence time window may therefore be extended even further, counting the full contribution of observed late ion arrivals (up to∆t= 600 ns). However, these physical incidences are not covered by the dead timetwmt= 80 nsof

the comparator unit anymore. As a conservative estimation therefore, only a coincidence time window of

∆tc= 100ns up to∆t= 468.5 nsis chosen. 16

The duration of a single measurement cycle is10ms. The red laser beam is thus turned on/off for an equal time period of5ms each per single cycle (fig. 5.6(a), inset).

17

0.10 0.15 0.20 ion incidences [100 ns] 0.05 (a) 0 0 1 2 3 4 5 Dt [ms] t [ms] I 0 5 I12 tp 10 0 15 0.10 0.15 0.20 ele. incidences [100 ns] 0.05 (b) 0 0 1 2 3 4 5 Dt [ms]

Figure 5.6:Trigger-ion correlations (a) and trigger-electron correlations (b) per100 nstime bin. The histograms correlate the relative arrival time of ion and electron incidences relative to the trigger of the photoionisation pulse at t = 0 (inset, (a)). Within the entire photoionisation sequence(∆t= 5 ms; green box, inset), the arrival of the electron and ion incidences are merely stochastic at the respective CEM. Consequently, the photoionisation of neutral atoms out of the thermal background of the UHV occurs random during a photoionisation sequence.

number of coincidencesNc for the calibration measurements is thus subsequently determined from the correlation histograms generated with these devices. For the data acquisition how- ever, in particular the timestamp unit represents an outstanding alternative as it additionally allows to assign each single electron or ion incidence an individual timetag corresponding to its arrival time at the respective CEM. This enables not only to cross-correlate individual electron-ion incidences, but to reconstruct the full temporal evolution of the observed counts Ni,e andNbi,be during the entire measurement.

One should further note that the photoionisation of neutral atoms itself out of the thermal background in the UHV occurs completely stochastic within the photoionisation sequence of tp = 5 ms during a single measurement cycle of 10 ms(fig. 5.6, inset). In fig. 5.6, the relative temporal arrival of ion and electron incidences for the photoionisation sequence (∆t= tp =

5 ms; green box, inset) is depicted after switching the red laser on for photoionisation. The histograms of the relative arrivals for ions and electrons are shown for several accumulated photoionisation sequences of tp. Neither for the ion or the electron incidences, any preferred relative arrival time for the incidences according to the switching on of the red laser beam (trigger at ∆t= 0) can be identified. This leaves the photoionisation of neutral atoms out of the thermal background of the UHV temporally random during a photoionisation sequence.