Jason Petta Physics Department, Princeton University Entanglement Generation Via Landau-Zener Interferometry S T + φ U 1 U 2 U 3 Detector Mirror Mirror Experiment A. Gossard (UCSB) A. Houck H. Lu (UCSB) W. McFaul K. Petersson C. Quintana Theory G. Burkard (Konstanz) H. Ribeiro (Basel) 2 µm g Q
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Entanglement Generation Via Landau-Zener Interferometry · Jason Petta Physics Department, Princeton University Entanglement Generation Via Landau-Zener Interferometry S T + φ U
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Jason Petta Physics Department, Princeton University
Entanglement Generation Via Landau-Zener Interferometry
S
T+
φ U1 U2
U3 Detector
Mirror
Mirror
Experiment A. Gossard (UCSB) A. Houck H. Lu (UCSB) W. McFaul K. Petersson C. Quintana
Theory G. Burkard (Konstanz) H. Ribeiro (Basel)
2 µm
gQ
Spin Qubit Landau-Zener Interferometry
φ U1 U2
U3 Detector
Mirror
Mirror
Entanglement Generation with Superconducting Qubits
Outline
Petta et al., Science (2010); Ribeiro et al., PRB (2013); Ribeiro et al., PRL (2013)
Petersson et al., Nature (2012); Quintana et al., PRL (2013)
DiVincenzo Criteria
• Scalable
• Efficient initialization
• Long decoherence times (T1,T2)
• Universal set of gates
• Readout
0
1
Loss & DiVincenzo Proposal Phys. Rev. A 57, 120 (1998)
• ESR for single spin rotations • Two spin exchange interaction
• “Spin to charge conversion”
• Prepare spin in ground state
Heterostructure grown by: M. P. Hanson and A. C. Gossard, UCSB
40 nm Al0.3Ga0.7As
60 nm Al0.3Ga0.7As
10 nm GaAs cap
50 nm GaAs
GaAs substrate
30 period superlattice 3 nm Al0.3Ga0.7As 3 nm GaAs
δ-doped Si ~4×1012/cm2
800 nm GaAs
not to scale
Charge density~2×1011/cm2 Mobility~2×105 cm2/V·s
0.5 µm
GSR
GSL
GD
x V(
x)
Controlled confinement
Double dot: Elzerman et al., PRB 67, 161308 (2003).
Few electron dots: Ciorga et al., PRB 61, 16315 (2000).
Trapping Single Electrons
Double Quantum Dot Physics
RL,CL RR,CR
VL
RM,CM S D
VR
VR
VL
(0,0) (0,1) (0,2)
(1,0)
(2,0)
(1,1)
(2,1) (2,2)
(1,2)
Double dot review article: van der Wiel et al., RMP 75, 1 (2003)
Charging energy Ec=e2/2C
GD (10
-3 e2/h)
-660 -640 VR (mV)
-670
-650
(M,N) (M,N+1)
(M+1,N) (M+1,N+1)
M, N~20
0
20 V L
(mV)
See also: Petta et al., PRL 93, 186802 (2004), Elzerman et al., PRB 67, 161308 (2003)
x
V(x)
L R
“Charge stability diagram”
0.5 µm
GSR
GSL
GD
R L
T
QPC sensing: Field et al., PRL 70, 1311 (1993)
GD (1
0-3 e
2 /h)
0
50
100
150
-1.05 -1.00 VR (V)
GS
R (e2/h)
0.16
0.20
0.24 dGS
R /dVL (a.u.)
Petta et al., PRL 93, 186802 (2004) Elzerman et al., PRB 67, 161308 (2003)
Single Charge Detection
-5 0 5
-400 VR (mV) -450
-500
-550
V L (m
V)
M, N=0, 1, 2…
(0,0) (0,1)
(1,1) (1,0)
(1,2)
Challenges of Single Spin Control
0
1
• Selectivity- difficult to localize ac magnetic field on a single spin • Speed- require 2-5 mT ac magnetic fields for fast control • Hyperfine interactions- Bac ~ Bnuc • Dissipation- mA currents are not compatible with mK temperatures • Photon assisted tunneling- drives unwanted transitions
Bac
Xiao et al., Nature (2004) Koppens et al., Nature (2006)
Loss & DiVincenzo, PRA (1998)
Ene
rgy
ε
S
0
T0
T+
(0,2)S
(0,2)S
EZ
S
T-
Optical interferometer Quantum dot level diagram
Single Spin Control Driven by Quantum Interference
Petta, Lu, Gossard, Science (2010) Levy, Phys. Rev. Lett. (2002)