Theory of Electrons in Solids Lu J' Sham, University of California San Diego, DMR 0403465

1
Theory of Electrons in SolidsLu J. Sham,
University of California San Diego, DMR 0403465
Fig. 1 Nuclear bath trajectories
How the electron spin coherence is lost and
restored

• An electron is confined in a semiconductor
  quantum dot. The directions of its spin pointing
  up or down along a magnetic field constitute 0 or
  1 of a bit of information. The quantum state of
  the electron spin can be in a superposition of
  its up and down states. This possibility of being
  in two states at the same time is the root of the
  power of quantum information or computer.
• Coherence is a measure of the capacity of
  such superposition. Maintaining coherence for a
  long enough time to do a useful series of
  operations is a fundamental element in the
  quantum computer.
• The most stubborn cause of disturbance of
  the electron coherence is the bath of millions of
  nuclear spins in the dot. Decoherence arises out
  of the quantum schizophrenia of the nuclear spins
  to follow the electron spin up state with one
  collective trajectory and the electron spin down
  state with another (blue and red curves of Fig.
  1).
• By switching the roles of the electron up
  and down states, the nuclear schizophrenic paths
  follow the new master states. By a concatenated
  sequence of electron flips (Fig. 2), the nuclear
  multitude may be coaxed back into a single
  collective state, restoring the electron
  coherence. Fig. 3(a) shows the increase of
  coherence time with flips. Note the magnifying
  factor of the true time for the l-th level.

spin flip at time ?
flip at 3?
Fig. 2 Flip sequences
coherence
decoherence
Fig. 3 (a) Coherence (b) Deviation from ideal
2
Theory of Electrons in SolidsLu J. Sham,
University of California San Diego, DMR 0403465

• Supplementary Notes
• The theory of decoherence of an electron spin in
  contact with a bath of nuclear spins is given by
  Yao, Liu Sham (cond-mat/0508441, Phys. Rev. B
  to be published). The technical term for the
  schizophrenia of the nuclear bath is
  entanglement. If the superposition of the
  electron spin up (u) and down (d) states is
  represented by ud, the state including the
  nuclear spins is initially (ud)N, N for the
  collective nuclear state. The contact between the
  electron and the nuclear path causes the nuclear
  spin states to split, thus, (uBdR). This
  schizophrenia disrupts the coherence between the
  u and d states. The nuclear state is termed
  collective, because of the mutual interaction, as
  in mass hysteria.
• Note that the herding of the millions of nuclear
  spins is done by flipping a single electron spin,
  a very economical method. The concatenated
  sequences are built by induction. (Yao, Liu
  Sham, cond-mat/0604634, submitted for
  publication.) The first line in Fig. 2 represents
  a simple flip of the electron spin from up to
  down and vice versa the second line is a two
  flip sequence made up of the first one and then
  its reverse the third one is the concatenation
  of the second sequence and its reverse and so
  on. The coherence scale is set from 1 to 0, 1
  being perfect and 0 being totally incoherent,
  like a classical coin. To compare the coherence
  with one and two electron spin flips, the red and
  dotted blue curves in Fig. 3 (a), remember that
  the coherence of the blue curve is at twice the
  flip time, i.e. one needs to stretch out the blue
  curve horizontally by a factor of two. To compare
  the fifth concatenated sequence with the first,
  one needs to stretch out its curve (green dots) a
  factor of 32 horizontally. The high coherence
  plateau lasts a very long time indeed compared
  with the optical operation time of about 10 ps
  (or about 100 million operations during high
  coherence).

3
Theory of Electrons in SolidsLu J. Sham,
University of California San Diego, DMR 0403465

• Education
• Applied Quantum Mechanics for undergraduates and
  graduates entering into quantum technology
• I have been building and teaching a course suited
  to the future needs of a quantum engineer, with
  an online self-test on mathematics preparation
  and remedial action and a selection of topics
  more immediate to the needs than a standard
  quantum course.
• http//physicscourses.ucsd.edu/lsham

• Education and Human Resource
• Wang Yao, graduated Ph.D. 6/25/06, solid state
  cavity QED and single electron spin decoherence
  and recovery for quantum computing. Now
  postdoctoral at U. of Texas, Austin.
• Parin Dalel, a new graduate student with
  industrial experience and several patents,
  educates the group on classical computers and
  scalability. His research applies the information
  theory approach to issues in spintronics and
  quantum computation. His education program may be
  an experimental paradigm for interdisciplinary
  research to further quantum technology.
• Semion Saikin, postdoctoral, quantum information
  in solids and decoherence of electron spin due to
  a mesoscopic ensemble of nuclear spins.

Outreach Contact with industry to explore
possible technological applications of our ideas
in spintronics and quantum computing, through
UCSD Office of Technology Transfer and California
Institute of Telecommunication and Information
Technology.