Optically Driven Quantum Dot Based Quantum Computation

1. Optically Driven Quantum Dot Based Quantum Computation NSF CENTER - Frontiers of Optical Coherence and Ultrafast Science(FOCUS) NSF Workshop on Quantum Information Processing and Nanoscale Systems. Duncan Steel, Univ. Michigan L.J. Sham, UC-SD Dan Gammon, Naval Research Laboratories ARO/NSA, AFSOR, DARPA, ONR, NSF

2. x- Optically Controlled Spin Optical control of spin: • Use spin as qubit • Use exciton for control and measurement T2 > 1 ms Operation time ~ 10 ps ( p-pulse) T2 / Op. time > 105

3. Requirements to build a QC(Divincenzo Criteria) • Well defined qubits (no extended states) • Initializable • Universal set of quantum gates (highly nonlinear) • Qubit specific measurements • Long coherence time (in excess of 104 operations in the coherence time)

4. InAs GaAs Coupled QD’s [001] Coupled QD’s GaAs 72 nm x 72 nm Cross sectional STM Boishin, Whitman et al. Quantum Dots: The Solid State version of the ion approach The III-V Semiconductor-Optics Approach to QC • Direct bandgap semiconductor allows for optical control • Small effective mass => large Bohr radius => large optical coupling • Ease of doping allows single electron spin manipulation • Epitaxial growth and fabrication technology in place for large scale integration • System is robust against pure dephasing • Optics and electronics easily integrated • Optical manipulation can have clock speeds greater than 10 THz • Adaptive optics allows high speed spatial and temporal pulse shaping taken from R. Notzel

5. The Quantum Toolbox Initialization (optical pumping) Rotations (coherent Raman) Entanglement (ORKKY or Coulomb) Measurement (recycling transitions)

6. Entanglement and two qubit operation • Coherent tunneling provides a kinetic exchange interaction between dots. • A DC bias can be chosen so that kinetic exchange exists only in the optically excited state i.e. only during the laser pulse.[Stinaff et al., Science (2006)] • A theoretical scheme has been worked out for a swap gate using this resonant exchange process[Emary and Sham, Phys. Rev. B (2007)] • Need to determine: • Hamiltonian for two spins • Exchange interactions • Excited state spectrum • Biexciton spectrum • B-field dependence

7. InAs GaAs Coupled QD’s [001] Coupled QD’s GaAs 72 nm x 72 nm Cross sectional STM Boishin, Whitman et al. “Quantum computation with quantum dots” Daniel Loss and David P. DiVincenzo, Phys. Rev. A. 57 p120 (1998) Quantum Dots: Atomic Properties But Better • Larger oscillator strength (x104) • High Q (narrow resonances) • Faster • Designable • Controllable • Integratable with direct solid state photon sources (no need to up/down convert) • Large existing infrastructure for nano-fabrication AFM Image of Al0.5Ga0.5As QD’s formed on GaAs (311)b substrate. Figure taken from R. Notzel

8. PL imaging First layer self-assembly Growth Direction Partial cap with GaAs Indium flush 4 nm Grow GaAs barrier. 2nd layer QD self-assembly BOTTOM QD TOP QD QD PL image Coupled dot spectroscopy Repeat flush and cap Processing for Diode and Optical Mask 2 Intensity (arb. units) QDs 1 Energy -1V EF 0 0V C.B. 900 950 1000 1050 Electric Field PL wavelength (nm) V.B. Schottky diode Sample Development MBE of InAs/GaAs Self-Assembled Dots Microscopy

9. First Demonstration of an all Optically Driven Semiconductor Based Conditional Quantum Logic Gate If ‘a’ is the control bit and ‘b’ is the target bit, the wiring diagram is on the left and the truth table is given by a’ a b b’ Truth Tables based on quantum state probabilities for Ideal and Optically Controlled Quantum Dot (Science ‘03)

10. Anomalous Variation of Beat Amplitude and Phase:The result of spontaneously generated Raman coherence Standard Theory (a) • Plot of beat amplitude and phaseas a function of the splitting. Phys. Rev. Lett. - 2005

11. Fast spin initialization ina single charged quantum dot: theory |T-> |t+>=|3/2> |t->=|-3/2> |T+> H1 H2 - V1 + dark transitions bright transitions |z+>=|1/2> |z->=|1/2> |X+> |X-> Bx If the magnetic field is applied in Faraday geometry, the transition from |t+> (|t->) to |z-> (|z+>) is dipole forbidden transition. So the speed of the spin initialization is limited by the weak decay from |t+> (|t->) to |z-> (|z+>) induced by the heavy-light hole mixing. After the magnetic field is applied in Voigt geometry, the dark transitions become bright. Theory: Theory Phys. Rev. Lett. Jan. 2007

12. Fast spin initialization ina single charged quantum dot: experiment VM absorption map as a function of the applied bias |T-> |T+> I pump V1 H1 H2 V2 0.20 t V1 II 0.15 |X+> |X-> DC(V) s 0.10 t>>s Magnetic Field 0.88T 0.05 Bx 1324.41 1324.53 1324.47 Laser Energy (meV) Blue circle region is transparent due to the laser beam depleting the spin ground states Experiment: Phys. Rev. Lett. Aug. 2007

13. Fast spin initialization ina single charged quantum dot: experiment |T-> |T-> |T+> |T+> re-pump probe probe re-pump V2 V1 H2 V2 V1 H1 s s |X+> |X+> |X-> |X-> absorption (a.u) absorption (a.u) re-pumpoff re-pumpoff H1 V1 H2 V2 recovered absorption re-pump on absorption (a.u) re-pump on absorption (a.u) 1324.44 1234.48 1324.44 1234.48 Laser Energy (meV) Laser Energy (meV)

14. Fast Spin Initialization in a Single Charged QD Demonstrated initialization of the single spin in the lower state to 98% at 1.3 T. Time scale for initialization ~ 0.25 ns. One of the fastest initialization implemented. Equivalent to cooling a spin in ensemble of spins from 4 K to 0.2 K or, equivalently, letting the spin relax to the ground state in a magnetic field of 60 T at 4K. THEORY: C. Emary et al. Phys. Rev. Lett. 98, 047401 (2007). EXPERIMENT: Xiaodong Xu et al. Phys. Rev. Lett. in press (2007).

15. Dressed State Picture The Mollow Absorption Spectrum, AC Stark effect, and Autler Townes Splitting: Gain without Inversion Mollow Spectrum: New physics in absorption Autler Townes Splitting S. H. Autler, C. H. Townes, Phys. Rev. 100, 703 (1955) B. R. Mollow, Phys. Rev. 188, 1969 (1969). B. R. Mollow, Phys. Rev. A. 5, 2217 (1972)..

16. |3> Strong pump Weak probe |2> Power Spectrum of the Rabi Oscillations:Gain without inversionThe Mollow Spectrum of a Single QD Science, August 2007

17. Demonstrates high speed Rabi oscillations in excess of 1.4 GHz with <10 nano-Watts: Dot Switching with ~10-18Joules. 100GHz limit. Achievable with low power diode lasers Enables use of 960 nm band telecom switching technology Impact of the High Speed Rabi experiment

18. Optical control of two dot-spins Current work PRB 07 Two trions with Coulomb interaction Optical RKKY  time    Coulomb  e dot #2 hole    dot #1 dot #2 <=== dot # 1 ===> position Four optical fields Two optical fields e wfs confined to each dot Excited e wf covers both dots Less demand on dot fabrication, more on optics

19. Where’s the Frontier? • Engineering coupled dot system with one electron in each dot with nearly degenerate excited states. • Demonstration of optically induced entanglement • Integration into 2D photonic bandgap circuits • Understanding of decoherence • Possible exploitation of nuclear coupling