A Revisit on the Concepts of Spin Relaxation and Decoherence Time

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A Revisit on the Concepts of Spin Relaxation and
Decoherence Time

• Zheng Yisong
• Department of Physics, Jilin University
• Collaborators
• Prof. Wang Xiangrong,
• Department of Physics, Hong Kong
• University of Science Technology.
• Yin Sun, Ph.D Student, HKUST.

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Magnetic Resonance
Solid State Quantum Computation
Spintronics

• Spin (Dynamic evolution)
• Spin relaxation and decoherence

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Outline

• To clarify the concepts of the spin relaxation
  and decoherence times for a single spin and a
  spin ensemble.
• To discuss the different roles of the
  environmental field components on the spin
  relaxation and docoherence.

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Bloch equation Phys.Rev.70,460(1946),
104,563(1956)

• A spin ensemble is subjected to a magnetic field
• The spin polarization(magnetization) is described
  as

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Two phenomenological Parameters T1and T2 T1 is
the time for the longitudinal magnetization to
reach equilibrium. The Spin Relaxation time
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T2 is the time for an ensemble of transverse
spins initially precessing in phase to lose their
phase due to the fluctuations of the precessing
frequencies. The Spin dephasing time
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Solid state quantum computation involves the
single spin manipulation

• D. Loss et al PRA 57, 120 (1998),
• B. E. Kane, Nature 393, 133 (1998)

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Spin ensemble
Single spin
How to define
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Two level systems ½ Spin
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(1)
(3)
(2)
Summation is over different measurements on the
same spin.
(3)
(2)
(1)
Summation is over different spins
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Characterize the longitudinal relaxation and
transverse decoherence of a single spin, which
are dertermined by the fluctuation of the
environmental field in the temporal domain.
Characterize the longitudinal relaxation and
transverse decoherence of the total spin
ensemble, which are dertermined by the
fluctuation of the environmental field both in
the spatial and temporal domain.
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A example to show the substantial difference
between
Condition
Single Spin
A spin ensemble
A pseudo relaxation time
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The difference between and PRL
88, 186802 (2002).
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A discussion about the roles of the diagonal and
off-diagonal couplings on the spin relaxation and
decoherence.
Time-correlation of the fluctuating environmental
field
The higher frequency modes give the smaller
contributions to the fluctuating environmental
field
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The modes near Rabi resonance are important.
B
Spin relaxation can be suppressed by increasing
the external magnetic field.
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The role of diagonal coupling
The root-mean-square change of phase is given by
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We have clarified the conceptional difference of
the spin relaxation and decoherence times between
a single particle spin and an ensemble of spins.
Conclusion
Only the modes in the vicinity of Rabi resonance
of the off-diagonal fluctuating field give a
dominant contribution for the longitudinal spin
relaxation time. A sufficiently high steady
magnetic field can result in a very long spin
relaxation time.
The spin decoherence time is mainly determined by
the diagonal fluctuating field. Unlike the case
of spin relaxation, the fast and slow
fluctuations of the diagonal field are both
importance to affect the spin decoherence time.
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Thank you for your attention