The experimental setup used for the quantum computing related experi- ments is shown in Fig. 5.2. Light from a highly stabilised dye-laser was steered toward a Mach-Zehnder interferometer. The first beam-splitter in this interferometer is a piece of uncoated glass. This resulted in most of the light going into one particular arm. This arm, the ‘sample arm’, contained two acousto-optic modulators (AOMs) in series followed by the sample. The ‘reference arm’ was empty except for a polarisation rotator followed by a polariser. These two elements were used to provide continuous attenuation to the light in the reference arm and enabled the intensity of this reference arm to be reduced to a suitable level for the detector.
Not shown in Fig. 5.2 is the auxiliary optical beam. This was taken off one of the zeroth order beams of the first AOM in the sample beam, passed through an AOM. This auxiliary beam was then steered through into
5.2 Experimental setup 115
AOM Crystal
Figure 5.3:The different beams generated by the second AOM to address thecontroland
targetanti-holes deflected by differing amounts as they are deflected. The geometry shown
was used to counteract this. The angle between the two beams has been exaggerated and without the lens, the two beams would only just be resolved by the time the light had propagated to the cryostat. Very good overlap between the beams could be achieved because of this.
the spare output port of the interferometer. Because of the layout of the experiment on the optical table this was the easiest way to assure that the auxiliary beam and the main experimental beam overlap in the sample. It was decided to make the auxiliary beam quite wide at the sample to make achieving this overlap easier.
The use of two acousto-optic modulators resulted in a total attenuation of the light of > 100 db when turned off. The first AOM was driven with a 90 MHz signal and the first order diffraction on the low frequency side left unblocked. For the experiments involving only one anti-hole, the second AOM was driven with a 80 MHz signal and the first order diffraction taken on the high frequency side. This resulted in the light reaching the sample being 10 MHz lower than that in the reference arm. When the two beams were combined on the exit beam-splitter of the interferometer, a 10 MHz beat on the light was produced. When the light from each arm is mode-matched and of the same intensity, the resulting amplitude modulation on the signal from the detector will have 100% depth. If care was taken adjusting the positions of the lenses and aligning the beams modulation depths of >95% were obtained. Typically a modulation depth of>80% was used.
As well as shifting the frequency, AOMs deflect the light an amount pro- portional to the modulating frequency. So that the beams that were used to address each anti-hole were well overlapped, the lens that focused the light on to the sample was arranged such that it imaged the second AOM. It was this AOM that was used to shift the frequency of the beam to address differ- ent anti-holes. The geometry is shown in Fig. 5.3. A 60 cm lens was placed upstream of the interferometer and this was used to alter the position of the beam waist relative to the AOM. This was used to vary the position of the beam waist relative to the sample.
While the interferometer was aligned for the target beam, the mode matching was sufficient to see beat signals at the detector due to the control beam.
The physics of how the detection scheme operates is described in Sec. 4.4. In summary, the amplitude and phase of the coherent emission produced in the same mode as the exciting laser beam provides a direct measurement of the ensemble average of the Pauli operators hXi and hYi. Generally mea- surements were made on the target anti-hole. The coherent emission from the target anti-hole produces a 10 MHz beat signal when combined with the light from the reference arm of the interferometer. This beat signal was passed through a 10 MHz band pass filter with a bandwidth of approximately 3 MHz. This filtered signal was then amplified and passed into a Mini-Circuits MIQA- 10D detector [148]. This detector has two outputs which give the amplitude of the component of the input signal that is both in phase and in quadrature with a supplied 10 MHz local oscillator signal. A block diagram of the de- tector is shown in Fig. 5.4. Assuming the interferometer is rigid, the phase of the 10 MHz beat signal is given by the phase of the light in the sample arm. Thus, the output of the IQ detector gives the amplitude and phase of the light coming from the sample arm of the interferometer. The resulting system was shot noise limited and has previously enabled photon echoes con- taining as few as 400 photons [141] to be observed. The IQ detector could only operate at 10 MHz which meant that it could only monitor the target anti-hole easily. When measurements of the other anti-hole were required, the roles of the two anti-holes could be reversed. Both a simple amplitude detector and recording the beat signal raw were also used at times, but not for any of the results presented here.
Over the short timescales of an experimental shot (hundreds of microsec- onds) the phase noise from the interferometer was small <5◦ but in some cases significant. Over longer periods, such as the time between shots, the effect of the phase noise from the interferometer was total. As the pulses used to drive the atoms saturated the detection system, a weak phase reference pulse was applied after the experimental shot in situations where phases of the emission from the ions relative to the laser were required.
A photon echo obtained with this detection system is shown in Fig. 2.7 on page 44.
5.2.1
Ultra-high resolution laser
As has been mentioned above, the homogeneous linewidths of the optical transitions are extremely narrow. To make full use of these long coherence
5.2 Experimental setup 117 90 Signal IN In Phase OUT In Quadrature OUT Local Oscillator
Figure 5.4: Block diagram showing the operation of the IQ detector.
times, a laser that is phase stable for at least a similar length of time is required. This is a very strict criterion and it was fortunate that such a laser was indeed available. The criterion of phase coherence times for the laser was not met by many of the labs RF sources (even some reputedly designed for NMR) even though the frequencies of oscillation were seven orders of magnitude smaller. Achieving such stability in a system that contains what is essentially a jet of antifreeze in the optical path is truly remarkable. The laser has been developed by Dr. Matthew Sellars and various co-workers at the Laser Physics Centre, at ANU.
This laser is discussed in detail elsewhere [149, 150], so only a brief de- scription is given here.
The laser is a modified Coherent 699 ring dye laser. If the laser was perfectly mechanically stable it would have a linewidth of approximately 2 Hz [151]. However the motion of various parts of the laser, in particular the dye jet cause frequency jitter and active stabilisation is required to obtain a reasonable linewidth. In its unmodified form the frequency control elements used consist of a galvo-driven Brewster plate and cavity mirror mounted on a piezoelectric-electric stack. The Brewster plate is used to correct for slow fluctuations (DC up to around 100 Hz) and the piezoelectric-stack is used for faster fluctuations. The error signal for the commercial control system is generated from the side of a transmission peak of a low finesse near-confocal cavity. This cavity has a free spectral range of approximately 1 GHz. The laser linewidth achieved by the commercial stabilisation system
is approximately 2 MHz.
An investigation of the frequency noise of this laser showed significant frequency jitter over timescales much faster than the 2 kHz bandwidth of the commercial frequency stabilisation system [150].
The frequency reference for the improved stabilisation system was custom- made by the CSIRO. The spacer for the cavity 50 cm long tube of “zerodur”, was suspended by wires and surrounded by a heat-shield. The temperature of the heat-shield was actively stabilised at approximately 313 K. The whole assembly placed in a vacuum chamber to help this. The error signal for the laser frequency was generated by the Pound-Drever method [152].
The bandwidth of the stabilisation system was improved by improve- ments to the servo electronics. An electro-optic modulator was added to the laser cavity to provide frequency corrections over faster timescales than those possible using the piezoelectric-driven mirror.
When optimised the resulting stability was better than 200 Hz over timescales of 0.2 s [149].