Professor Kohei Itoh of Keio University gives a lecture on Silicon Quantum Information Processing.

Lecture includes topics such as:

- Elements of quantum computation
- Nuclear spin coherence in Silicon
- Silicon spintronics

While today’s nanotechnology is mainly concerned with the manipulation of materials at the atomic level, the Itoh group have proceeded one step further with the manipulation of semiconductor nanostructures at the isotopes level.
Silicon, for example, is composed of three stable isotopes ^{28}Si, ^{29}Si and ^{30}Si with the fixed relative abundance given by nature: 92.2% ^{28}Si, 4.7% ^{29}Si and 3.1% ^{30}Si.
In contrast to the widely accepted belief that the perturbation of physical properties of silicon due to differences in isotopes is insignificant,
the Itoh group has successfully shown that the nuclear spin differences (I=1/2 for ^{29}Si, but I=0 for ^{28}Si and ^{30}Si) and the mass difference between the isotopes do matter especially at the nanoscale.
For the first time in the world, the group succeeded in the growth of all three kinds (^{28}Si, ^{29}Si, and ^{30}Si) of isotopically enriched Si bulk crystals [Jpn. J. Appl. Phys. **42**, 6248 (2003)] and Si isotope superlattices
in which alternating layers of different isotopes were formed with nanoscale precision [Appl. Phys. Lett. **83**, 2318 (2003)].
Such structures have been employed to reveal a variety of nanoscale diffusion and chemical reactions [Applied Physics Express, **1**, 021401 (2008),
J. Appl. Phys.**103**, 026101 (2008), Phys. Rev. Lett. **98**, 095901 (2007), etc.] to improve the accuracy of state-of-the-art nano CMOS process simulators that are needed for the development of new silicon integrated circuits.
However, the present proposal concerns the spin related properties of nano-Si that have been revealed by the Itoh group involving both isotope engineering and development of new instruments.

In 2002, the Itoh group proposed a new idea of employing single silicon atom as a bit carrier for processing and storing of information [Phys. Rev. Lett. **89**, 017901 (2002)].
A modified version of the same device concept is shown in Fig. 1 [taken from Itoh’s review, Solid State Comm. **133**, 747 (2005)] in which the nuclear spin orientation and phase of each ^{29}Si represents a bit of information quantum mechanically.
The key is a phosphorus atom attached at the end of the ^{29}Si nuclear spin chain that enables the initialization and read-out of the ^{29}Si nuclear spins.

Towards realization of such a nano silicon quantum device, the Itoh group has performed the following fundamental studies. First, extremely long quantum information retention time of 25 seconds for ^{29}Si
nuclear spins at room temperature was demonstrated experimentally [Phys. Rev. B **71**, 014401 (2005)]. Similarly, spin coherence of electron bound to phosphorus was investigated
to prove the validity of the device shown in Fig. 1 [Phys. Rev. B **70**, 033204 (2004)].
Then, the surface physics of silicon was investigated to prove that it would be possible to fabricate the single wire of ^{29}Si atoms exclusively [J. Appl. Phys. **101**, 081702 (2007), Phys. Rev. Lett. **95**, 106101 (2005), Appl. Phys. Lett. **87**, 031903 (2005)].

The next step was calculation and read-out.
In an eto initialize the device (i.e orient all spins in same direction), optical pumping [Phys. Rev. B **71**, 235206 (2005)]
and dynamic nuclear orientation using phosphorus electron spins [submitted to Phys. Rev. B] have been explored.
Nuclear spin manipulation has been demonstrated by NMR [Phys. Rev. B**68**, 054105 (2003)].
Finally, the read-out of ^{29}Si nuclear spins via ^{31}P nuclear spins and electron spins has been demonstrated
with the combination of extremely high resolution photoluminescence excitation spectroscopy and isotope engineering [J. Appl. Phys. **101**, 081724 (2007), Phys. Rev. Lett. **97**, 227401 (2006)].
Here both optical and electrical read-outs of ensembles of ^{31}P nuclear spins were realized by optical excitation.
More recently, the Itoh group has developed low-magnetic field (B<200G) electrically detected magnetic resonance which allows the formation of entangled Bell states
needed for quantum information processing and the electrical detection of both electron and nuclear spin states. [Phys. Rev. B **80**, 205206 (2009)]
In parallel, efficient initialization schemes of ^{31}P electron and nuclear qubits [Phys. Rev. Lett. **102**, 257401 (2009)] and ^{29}Si nuclear qubits
[Phys. Rev. B **78**, 153201 (2008) and *ibid* **80**, 045201 (2009)], realization of silicon single electron ratchet [Appl. Phys. Lett. **93**, 222103 (2008)],
and growth of isotopically controlled Si and Ge structures for quantum information processing have been achieved [Phys.
Rev. B **79**, 165415 (2009) and phys. status solidi RRL **3**, 61(2009)].

The recent research focus of the Itoh group has been two-fold. One direction is aiming to improve nanometer-sized silicon devices in the next 10 years by nano-diffusion and chemical reaction. The other is aiming for novel quantum spintronic devices which could be commercially viable on a longer timescale.

Fig. 1: Silicon quantum information processor using ^{29}Si nuclear spins as bit carrier and ^{31}P nuclear spin and electron spin to orient and read-out ^{29}Si quantum bits.

The Itoh group has developed EDMR at very low magnetic fields B<200G. At these low fields the ^{31}P nuclear spin of the
phosphorus donor and the corresponding electron spin can form a |↑↓>+|↓↑> superposition Bell state (entanglement)
automatically due to the fact that the hyperfine interaction becomes more dominant than the electron Zeeman interaction as
shown in Fig. 2.

Figure 3 shows the transitions between the Bell and pure states observed for the first time in Si:P using EDMR [Phys. Rev. B 80, 205206 (2009)]. The Itoh group has developed a pulsed EDMR spectrometer in collaboration with Prof Brandt’s group (TU Munich), ideal for these low field studies.

Fig. 2(left): Energy levels of phosphorous electron spin and nuclear spin pairs at low magnetic field (B<200G).

Fig. 3(right): Transitions observed by low B EDMR with irradiation of the different RF frequencies indicated on the side of each spectrum. The transitions correspond to the arrows indicated in Fig.2.