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)

Avoided Crossing: Quantum Mechanical “Beam Splitter” (0,1)

ε

2∆

Ener

gy

(1,0)

(1,0)

(0,1)

0

H= ε -ε ∆

∆

“Level velocity”

PLZ

Landau (1932), Zener (1932), Stückelberg (1932), Majorana (1932)

1-PLZ

Some Examples of Landau-Zener Physics

Zewail, Physics Today (1990) Lang, Nature Physics (2008)

Superconducting qubits: Oliver et al., Science (2005), Shevchenko et al., Phys. Rep. (2010)

Spin Physics: The Two Electron Regime

(0,1)

(1,1) (1,2)

(0,2)

VR (mV)

V L (m

V)

S

TO T+ T- j<<kT

(1,1) singlet-triplet splitting:

with U~4 meV, t~20 µeV j=4t2/U=0.4 µeV<<kT

Theory: J~0.3 meV

(0,2) singlet-triplet splitting:

Expt.: J~0.1 to 1 meV

TO T+ T-

S

J~400 µeV

Kyriakidis et al., PRB 66, 035320 (2002) Ashoori et al., PRL 71, 613 (1993)

Double Quantum Dot Energy Level Diagram

(0,1)

(1,1) (1,2)

(0,2) VR (mV)

V L (m

V)

ε

Ener

gy

ε

S

0

(0,2)S

(0,2)S S

EZ=gµBBE

T0

T-

T+

Petta, Marcus et al., Science (2005)

Levy, Phys. Rev. Lett. (2002)

Dynamics of the Coupled Electron-Nuclear Spin System

Loss and DiVincenzo, PRA 57, 120 (1998)

75As, I=3/2, 100% 69Ga, I=3/2, 60% 71Ga, I=3/2, 40%

jjj

e ISbSBeH ,,,0

ββ

ββαγγ

⋅∑+⋅=

Zeeman Hyperfine

SBBeH nuc

⋅+= )( 0γ

Fully polarized nuclei, Bnuc=5.3 T

Unpolarized nuclei, Bnuc~2 mT Khaetskii, Loss, Glazman, PRL 88, 186802 (2002) Paget, Lampel, Sapoval, PRB 15, 5780 (1977)

S •

0B

nucB

TotB

Double Quantum Dot Energy Level Diagram (With Nuclei)

Ener

gy

ε= gate voltage

S

0

T0

T+

(0,2)S

(0,2)S

EZ=gµB(BE+Bnuc)

S

T-

ε > 0 ε < 0

Step 1: Singlet state initialization

Ene

rgy

ε

S

0

T0

T+

(0,2)S

(0,2)S

EZ

S

T-

Petta, Lu, Gossard, Science 327, 669 (2010)

Single Spin Control Driven by Quantum Interference

Spin Singlet State Initialization

(0,1)

(1,1) (1,2)

(0,2) T

S 510e −≈

−= kT

J

S

TPP

VR (mV)

V L (m

V)

M. Atature et al., Science 312, 551 (2006) Petta, Marcus et al., Science (2005)

Levy, Phys. Rev. Lett. (2002)

Step 2: Passage through the beam splitter

Ene

rgy

ε

S

0

T0

T+

(0,2)S

(0,2)S

EZ

S

T-

Ene

rgy

εs

T+

T0 T+

S

Incoherent driving limit: Petta, Taylor, PRL (2008)

Ribeiro, Burkard, PRL (2009) Petta, Lu, Gossard, Science (2010) Ribeiro, Petta, Burkard, PRB (2010)

Single Spin Control Driven by Quantum Interference

Singlet-Triplet Beam Splitter

Ene

rgy

εs

T+

T0 T+

S

Ideal case: PLZ=1/2 maximum contrast, 50%-50% beam splitter

T+

S

ε

Theory: Shimshoni et al., Ann. Phys. (1991) Shevchenko et al., Phys. Rep. (2010)

Stoke’s phase

Step 3: Phase accumulation

φ

−= Z

i φσ2

expU

φ

ε εs

T+ T0

S

Ene

rgy

T+

S Petta, Lu, Gossard, Science 327, 669 (2010)

Single Spin Control Driven by Quantum Interference

Step 4: Interference

Ene

rgy

ε

S

0

T0

T+

(0,2)S

(0,2)S

EZ

S

T-

Ene

rgy

εs

T+

T0 T+

S

PLZ

T+

S Petta, Lu, Gossard, Science 327, 669 (2010)

Single Spin Control Driven by Quantum Interference

Step 5: Spin state measurement

Ene

rgy

ε

S

0

T0

T+

(0,2)S

(0,2)S

EZ

S

T-

Petta, Lu, Gossard, Science 327, 669 (2010)

Single Spin Control Driven by Quantum Interference

(0,1)

(1,1) (1,2)

(0,2)

Ene

rgy

(1,1) (0,2)

S

TO T+ T-

T

S

GQPC GQPC

Singlet measurement

VR (mV)

V L (m

V)

Spin State Measurement (Spin-to-Charge Conversion)

(0,1)

(1,1) (1,2)

(0,2)

Ene

rgy

(1,1) (0,2)

S

TO T+ T-

T

S

GQPC

Triplet measurement

VR (mV)

V L (m

V)

Spin State Measurement (Spin-to-Charge Conversion)

Beam Split Accumulate Phase

Interfere

Ene

rgy

τS (ns) 0 5 10 15 20 25

ε S (m

V)

0.6

PS

1.0

0.8

BE= 100 mT

-1.7

-0.2

Observation of Landau-Zener-Stückelberg Oscillations

ns 6.1==Bg

h

Btheory µ

τ

τ • Fast, Top~1 ns • Local • No Bac needed

Limitations of LZS Interferometry in GaAs Quantum Dots

75As, I=3/2, 100% 69Ga, I=3/2, 60% 71Ga, I=3/2, 40%

• Avoided crossing “gap” governed by BN • T2* governed by BN

Tradeoff between coherence and adiabaticity

Tailored Pulses for Quantum Control “Local Adiabatic Evolution”

References (with Burkard Group): Ribeiro, Petta, Burkard, PRB (2012) Ribeiro, Burkard, Petta, Lu, Gossard, PRL (2013) Ribeiro, Petta, Burkard, PRB (2013)

Two-Transmon Landau-Zener Interferometry

Chris Quintana (2013) Now at UCSB

Spins in GaAs (S-T Qubits) T2* ~ 10 ns, Petta et al. (2005) Techo ~ 1 µs, Petta et al. (2005) T2N ~ 200 µs, Bluhm et al. (2011) T1 ~ 1 ms, Johnson et al. (2005)

Transmon Qubits (cQED) T2* ~ 100 µs, Rigetti et al. (2012) Techo ~ 300 µs, Sears et al. (2012) T1 ~ 70 µs, Rigetti et al. (2012) 1/κ ~ 10 ms, Reagor et al. (2013)

Izmalkov et al., Europhys. Lett. (2004) Oliver et al., Science (2005) Sillanpää et al., PRL (2006) Berns et al., Nature (2008)

Review article: Shevchenko et al., Phys. Rep. (2010)

Cavity Mediated Entanglement Generation Via LZ Interferometry

Theory: Blais et al., PRA (2004); Experiment: Wallraff et al., Nature (2004)

Two Qubit Spectroscopy

Quintana, Petersson, McFaul, Srinivasan, Houck, Petta, PRL (2013)

Two Qubit Landau-Zener Interferometry

From double beam splitter equation: V = 4PLZ(1-PLZ)

Quintana, Petersson, McFaul, Srinivasan, Houck, Petta, PRL (2013)

Single Passage Landau-Zener Transitions

Quintana, Petersson, McFaul, Srinivasan, Houck, Petta, PRL (2013)

Single Passage Entanglement Generation

Fidelity limited by qubit relaxation:

Quintana, Petersson, McFaul, Srinivasan, Houck, Petta, PRL (2013)

Spin Qubit LZS Interferometry

φ U1 U2

U3 Detector

Mirror

Mirror

Entanglement Generation with Superconducting Qubits

Conclusion

Refs: Petta et al., Science (2010); Ribeiro et al., PRB (2013); Ribeiro et al., PRL (2013)

Refs: Petersson et al., Nature (2012); Quintana et al., PRL (2013)

Petta Group

Collaborators: G. Burkard, H. Ribeiro, J. Taylor

Funding:

Postdocs: C. Eichler K. Petersson Grad Students: L. Alegria T. Hazard Y. Liu X. Mi S. Sangtawesin G. Stehlik K. Wang D. Zajac

Undergrads: Z. Atkins J. Cady T. Hartke C. Quintana