Spin-qubit dynamics and decoherence Bill Coish Department of - - PowerPoint PPT Presentation
Spin-qubit dynamics and decoherence Bill Coish Department of Physics, McGill University, Montral QC 2013 April 18; INTRIQ Spring Meeting, Bromont, QC Collaborators: McGill: F. Beaudoin, C. Chamberland, B. D'Anjou, S. Chesi, X. (Judy) Wang,
FRQNT
Bill Coish
Department of Physics, McGill University, Montréal QC
Collaborators: McGill: F. Beaudoin, C. Chamberland, B. D'Anjou, S. Chesi, X. (Judy) Wang, ... Sherbrooke: M. Pioro-Ladrière, A. Blais, ...
2013 April 18; INTRIQ Spring Meeting, Bromont, QC
CIFAR
Scalable Platform for QIP?: Single electrons?
V(r) r
encoding:
j"i ! j0i j#i ! j1i
Other ways of “trapping” spin: Semiconductor quantum dots and defects
Self-assembled quantum dots (optical control/readout) `Gated' quantum dots (electrical control/readout) Nitrogen vacancy (NV) centers in diamond (optical control/readout) Donor impurity spin (electrical control/readout)
Scalability: Why electron spins?
Electrons NMR, Charge, etc....
Exchange is local Dipolar, Coulomb interactions long-ranged
Problem: One spin sees many
Many isotopes have non-zero nuclear spin!
Avogadro crystal: Highly pure 28Si
Remove the environmental spins?
Spin of a donor atom in highly pure 28Si behaves almost like it's in 'vacuum' Lifetime of quantum states (nuclear spins):
Silicon
A new quantum silicon race?
Gated Si quantum dots (HRL) Si:SiGe nanowire quantum dots (Harvard) MOSFET (Sandia/Sherbrooke)
Carbon?
12C has no nuclear spin
nanotubes defects in diamond graphene
“Theory of everything” for spins in the solid state
~ E
+
~ I ~ S
~ B
Confined electron
Interactions: s vs. p
+
s-state (electron) p-state (hole)
+
Anything else: NV Center, Nanotubes, graphene,...combination
Electron-spin dynamics: A difficult theoretical problem...
nuclei (quantum dot)
B
Longitudinal fluctuations Transverse fluctuations ('flip-flops')
Hole Spins?
Heavy holes: Fluctuations are purely longitudinal
[Fischer, WAC, Bulaev, Loss, PRB (2008)]
Spin Echo?
Time-reversal of static inhomogeneities
Recent Experiments: Hole-spin Echo
De Greve et al., Nature Physics (2011)
Shorter than for Electrons! BUT: Limited by extrinsic charge noise, not (intrinsic) hyperfine (yet)
Charge noise
Dynamics of x-component not limited by charge noise
XJ Wang, S Chesi, WAC, PRL (2012)
Hole-spin dynamics: Exact solution
Exact analytical solution (messy formula): Decay time decreases for increasing B (dynamics not refocused)
(2D, No strain)
¿ / 1 p B
Exact solution: Larger B
Exact solution: Recurrences (“ESEEM”)
Amplitude:
Motional Averaging!
Method 2: Magnus expansion
Closed-form spin dynamics
nuclear spins Gaussian approximation Short time: (Magnus) XJ Wang, S Chesi, WAC, Phys. Rev. Lett. (2012)
Magnus expansion: Spin echoes in a dynamic environment
B = 0:5 T N = 2000 nuclei
Magnus (dashed red) Exact (solid blue)
Hole spin summary
1/e Decay time XJ Wang, S Chesi, WAC, Phys. Rev. Lett. (2012)
Magnetic-field gradient: Why?
Tokura et al., PRL (2006) Idea 1) Move spin periodically using an electric field in presence of slanting Zeeman field; get an ac magnetic field in the rest frame of the electron. Pioro-Ladrière et al., Nat. Phys. (2008) Idea 2) Couple single spin to the electric-field mode of a stripline resonator Pioro-Ladrière group (Sherbrooke)
Coherence decay with B-field gradient
Single donor spin: Breakdown of Gaussian approximation
Conclusions
Hole spins are robust 'new' qubits? Only a matter of better decoupling/higher B-fields? Magnetic-field gradients may lead to shorter coherence times, but can be controlled with motional averaging.