Ph.D. Thesis - Physics

pulses would harm the fidelity of the quantum simulation effectively making our classical
controls excessively noisy. The on/off time for these blanking circuits is > 2 µs. The
signal is normally routed automatically from the transmitter boards 1 and 2 to the correct
(high/low) band channel of the first amplifier unit, and likewise from boards 3 and 4 to the
second unit.
All of the outputs from the amplifiers within each band are combined using high-power
combiners before passing through a PIN diode transmit/ receive switch. This switch isolates
these high-power signals from the sensitive receiver preamplifier. The signals are finally
routed to the correct coils of the probe.
When the PIN diode switches are in receive mode, the signals induced in the probe by
the nuclei are passed to high-band and low-band preamplifiers with gain of 35 dB. These
signals are sent to receiver boards in the electronics cabinet that mix the signals down to
audio frequencies and separate them into two quadratures, after which they are also passed
through audio filters (with bandwidth 100 Hz to 256 kHz). The signal is then digitized and
uploaded to the computer. The maximum sampling rate is 1 MHz.
3.4.5 Computer control
A Sun Ultra 10 workstation is the control panel of the spectrometer. Pulse instructions
are sent to the spectrometer using commercial software from Varian. The pulse sequences
themselves are written in C and compiled. One may use a set of low-level commands that
adjust parameters such as pulse duration, phase, and channel number.
It is convenient to use a higher-level language to specify a set of experiments to be
run and to subsequently process the data. Matlab serves this purpose nicely. This affords
a great deal of automation, as a number of experiments can be run for a long period of
time (say, overnight) and then automatically processed later on. For instance, a number of
experiments may be performed and then the final average density matrix calculated.
3.5 Experiment
We chose as our sample 13 C-labeled CHFBr2, the structure of which is shown in Fig. 3-
5. The J-couplings between each nucleus are JHC = 224 Hz, JHF = 50 Hz, and JCF =
−311 Hz. This three-qubit molecule is appropriate for quantum simulations of three modes
and up to three Cooper pairs. We chose to implement two different Hamiltonians, using
two Cooper pairs. The Hilbert space is therefore spanned by |101〉, |110〉, and |011〉.
We implemented two different Hamiltonians: H1, in which Vab = πJHC, Vac = πJHF,
and Vbc = πJCF, and a harder case, H2, in which Vab = πJHC and Vac = Vbc = 0. For
both Hamiltonians, ν1 = 150π Hz, ν2 = 100π Hz, and ν3 = 50π Hz. Although the choice of
Hamiltonians is somewhat arbitrary, they are sufficient to illustrate the impact of control
errors, as H2 requires more refocusing pulses than H1.
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