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A number of other problems came up during our work on locking the cavity. The PID had too much gain and so the amplifying circuits needed to be adjusted. The cavity end cap design has a plate that is screwed to the end cap against the back PZT (Fig. 5.9). We believe this plate was ‘rattling’, causing the 17 kHz resonance.

§5.5 Feedback Control of Cavity Resonance 75

SRS

3.7688442 kHz ∆-32.96 deg

1 kHz

Freq. Resp. Phase• 6.25 s

30 kHz -250 deg 250 deg 50 deg/div B Live SRS 18.050252 kHz -50.566 dB 1 kHz

Freq. Resp. Log Mag 6.25 s

30 kHz -80 dB 20 dB 10 dB/div A Live 11/21/05 09:27:11

Figure 5.21: Elliptic band-pass filter transfer function. ‘A Live’ shows the amplitude response, with the maximum suppression at approximately 17 kHz. ‘B Live’ shows the phase response, with a unity gain phase delay of approximatelyπ/2.

source R = 51 load C1=4.7nF R = 2k C3=4.7nF

W

W

76 Optical Noise Reduction

SRS

40.133668 kHz -15.674 dB

100 Hz

Freq. Resp. Log Mag 6.34 s

60 kHz -35 dB 15 dB 5 dB/div A Live SRS 100 Hz -402 mdeg 100 Hz

Freq. Resp. Phase• 6.34 s

60 kHz -180 deg 20 deg 20 deg/div B Live 11/22/05 10:05:04

Figure 5.23: Butterworth low-pass filter transfer function. ‘A Live’ shows the amplitude response, with 3 dB roll-off at approximately 18 kHz and 15 dB supression at 40 kHz. ‘B Live’ is the phase response, showing a smooth, gradual increase in phase delay along the spectrum.

We worked on tightening the back plate, although this had to be done very carefully since uneven tension on the screws tilted the mirror, causing the beam to be clipped by the walls of the cavity. The tightening had to be done while observing the cavity transmission with an infrared camera.

Unfortunately, the Mach-Zehnder interferometer used to analyse the mode cleaner transfer function had been dismantled before we tried to improve the back plate—the transfer function of Fig. 5.20 was measured before the back plate was tightened. It is likely that the first resonance has increased since tightening, possibly to a level higher than can be obtained with a single-PZT actuator (this also means that the elliptic filter in its current configuration is probably not doing very much). The verdict on the push- pull system must remain inconclusive for the time being, since the problems we had with this cavity put us many weeks behind schedule. Now that we could lock it, although not perfectly, we immediately continued on to the main experiment.

paragraph on how well it cleaned the beam, graph of variances at different frequencies against theoretical curve

5.6

Summary

This chapter has described the sources and effects of optical quadrature noise. The re- laxation oscillation of the Mephisto 1064 nm laser was measured with and without the noise-eating circuit. The quantum noise limit for quadrature measurement was calculated. It was shown that resonant cavities offer the ability to mode-clean an impure coherent state. Generally the quadrature variance of a laser will approach the quantum noise limit with increasing modulation frequency. A cavity can speed this approach so that the beam

§5.6 Summary 77

becomes effectively quantum noise limited at a lower frequency. The functional behaviour of the roll-off is determined by the cavity finesse.

To increase the purity of the laser coherent state from the previous generation QKD experiment, a mode cleaning cavity was built by the departmental workshop. The cavity featured the first push-pull actuator built in the department, although results proving the advantage of this design are still inconclusive.

The techniques employed for the subsequent mode-coupling effort are described. The coupling resulted in 96% transmission through the cavity, and a measured finesse of 836±

53, which compared well to the design value of 790.

Mode locking was undertaken with the tilt locking technique, using a departmental PID design. Stable locking was achieved only after numerous iterations of PID circuit component values, principally the elliptic filter design. At this point the quadrature vari- ance was not available, as the remainder of the experiment needed to be running to make this measurement.

Chapter 6

Second Generation CVQKD-SQM

This chapter details the layout, conduct, results and analysis of the second generation SQM experiment. As described in Chapter 5, the Mephisto laser was mode-cleaned with a high finesse optical cavity. The cleaned beam was then used to rebuild the first generation experiment with higher-bandwidth electronics.

Once the experiment was built, the beam was amplitude- and phase-modulated with white noise from Agilent function generators. These were shown to be inadequate for the task and a trial quantum random noise generator was used. Alice’s modulations and Bob’s received signals were simultaneously sampled at 200 Mbps. The data was analysed with a modified version of the analysis and post-selection code used for the first generation experiment. Frequency division multiplexing was introduced into the analysis to counter the effects of nonconstant gain across the spectrum.

6.1

Experimental Design and Methods

The design of the first generation experiment is broadly described in [56] and reported with greater detail in [94]. Apart from the addition of the mode cleaner, detailed in Chapter 5, the experiment remained largely the same. The mixing, locking and modulation techniques described below are unchanged from the first experiment. The distance between Alice and Bob was slightly shorter than in the first experiment (30 cm as opposed to 1 m) due to it being built on a smaller table.

Initially the same detectors were also used. These detectors had a low frequency roll- off from 30 MHz and a nonflat response between 33 and 50 MHz. This response meant it was necessary for the detector transfer function to be characterised and applied to the sampled data.[56] Halfway through the experiment we replaced the detectors with a new design by James Dickson. The new detectors have a flat response to 400 MHz and low frequency roll-off from 10 MHz down. Our characterisation is reported below.

The data acquisition system used in the first generation experiment had a 100 Mbps sample rate. This was replaced with a 200 Mbps system. Thomas rewrote the LabView acquisition programme to improve sampling performance and usability.