[Mathematical symbols can be only approximated here. For the correct
display see the Abstract in the PDF files linked below] This work has
demonstrated that hyperfine decoherence times sufficiently long for
QIP and quantum optics applications are achievable in rare earth ion
centres. Prior to this work there were several QIP proposals using
rare earth hyperfine states for long term coherent storage of optical
interactions [1, 2, 3]. The very long T_1 (~weeks [4]) observed for
rare-earth hyperfine transitions appears promising but hyperfine T_2s
were only a few ms, comparable to rare earth optical transitions and
therefore the usefulness of such proposals was doubtful.
¶
This work demonstrated an increase in hyperfine T_2 by a factor of 7 ×
10^4 compared to the previously reported hyperfine T_2 for
Pr^[3+]:Y_2SiO_5 through the application of static and dynamic
magnetic field techniques. This increase in T_2 makes previous QIP
proposals useful and provides the first solid state optically active
Lamda system with very long hyperfine T_2 for quantum optics
applications.
¶
The first technique employed the conventional wisdom of applying a
small static magnetic field to minimise the superhyperfine interaction
[5, 6, 7], as studied in chapter 4. This resulted in hyperfine
transition T_2 an order of magnitude larger than the T_2 of optical
transitions, ranging fro 5 to 10 ms. The increase in T_2 was not
sufficient and consequently other approaches were required.
¶
Development of the critical point technique during this work was
crucial to achieving further gains in T_2. The critical point
technique is the application of a static magnetic field such that the
Zeeman shift of the hyperfine transition of interest has no first
order component, thereby nulling decohering magnetic interactions to
first order. This technique also represents a global minimum for back
action of the Y spin bath due to a change in the Pr spin state,
allowing the assumption that the Pr ion is surrounded by a thermal
bath. The critical point technique resulted in a dramatic increase of
the hyperfine transition T_2 from ~10 ms to 860 ms.
¶
Satisfied that the optimal static magnetic field configuration for
increasing T_2 had been achieved, dynamic magnetic field techniques,
driving either the system of interest or spin bath were investigated.
These techniques are broadly classed as Dynamic Decoherence Control
(DDC) in the QIP community. The first DDC technique investigated was
driving the Pr ion using a CPMG or Bang Bang decoupling pulse
sequence. This significantly extended T_2 from 0.86 s to 70 s. This
decoupling strategy has been extensively discussed for correcting
phase errors in quantum computers [8, 9, 10, 11, 12, 13, 14, 15], with
this work being the first application to solid state systems.
¶
Magic Angle Line Narrowing was used to investigate driving the spin
bath to increase T_2. This experiment resulted in T_2 increasing from
0.84 s to 1.12 s. Both dynamic techniques introduce a periodic
condition on when QIP operation can be performed without the qubits
participating in the operation accumulating phase errors relative to
the qubits not involved in the operation.
¶
Without using the critical point technique Dynamic Decoherence Control
techniques such as the Bang Bang decoupling sequence and MALN are not
useful due to the sensitivity of the Pr ion to magnetic field
fluctuations. Critical point and DDC techniques are mutually
beneficial since the critical point is most effective at removing high
frequency perturbations while DDC techniques remove the low frequency
perturbations. A further benefit of using the critical point technique
is it allows changing the coupling to the spin bath without changing
the spin bath dynamics. This was useful for discerning whether the
limits are inherent to the DDC technique or are due to experimental
limitations.
¶
Solid state systems exhibiting long T_2 are typically very specialised
systems, such as 29Si dopants in an isotopically pure 28Si and
therefore spin free host lattice [16]. These systems rely on on the
purity of their environment to achieve long T_2. Despite possessing a
long T_2, the spin system remain inherently sensitive to magnetic
field fluctuations. In contrast, this work has demonstrated that
decoherence times, sufficiently long to rival any solid state system
[16], are achievable when the spin of interest is surrounded by a
concentrated spin bath. Using the critical point technique results in
a hyperfine state that is inherently insensitive to small magnetic
field perturbations and therefore more robust for QIP applications.
| Identifer | oai:union.ndltd.org:ADTP/216809 |
| Date | January 2006 |
| Creators | Fraval, Elliot, elliot.fraval@gmail.com |
| Publisher | The Australian National University. Research School of Physical Sciences and Engineering |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | http://www.anu.edu.au/legal/copyrit.html), Copyright Elliot Fraval |
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