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NSF CENTER - Frontiers of Optical Coherence and Ultrafast Science (FOCUS) Optically Driven Quantum Dot Based Quantum Computation 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 Optically Controlled Spin x- Optical control of spin: – Use spin as qubit T2 > 1 ms Operation time ~ 10 ps ( p-pulse) T2 / Op. time > 105 – Use exciton for control and measurement 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) The III-V Semiconductor-Optics Approach to QC Quantum Dots: The Solid State version of the ion approach • 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 GaAs InAs Coupled QD’s Coupled QD’s 72 nm x 72 nm GaAs Cross sectional STM Boishin, Whitman et al. The Quantum Toolbox Initialization (optical pumping) Measurement (recycling transitions) Rotations (coherent Raman) Entanglement (ORKKY or Coulomb) Entanglement and two qubit operation 1. Coherent tunneling provides a kinetic exchange interaction between dots. 2. 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)] 3. 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: 1. 2. 3. 4. 5. Hamiltonian for two spins Exchange interactions Excited state spectrum Biexciton spectrum B-field dependence “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 nanofabrication • • • • • • GaAs InAs Coupled QD’s Coupled QD’s AFM Image of Al0.5Ga0.5As QD’s formed on GaAs (311)b substrate. Figure taken from R. Notzel 72 nm x 72 nm GaAs Cross sectional STM Boishin, Whitman et al. Sample Development Intensity (arb. units) MBE of InAs/GaAs Self-Assembled Dots First layer self-assembly Partial cap with GaAs Indium flush Grow GaAs barrier. 2nd layer QD self-assembly TOP QD PL imaging BOTTOM QD QD PL image 2 1 0 900 950 1000 1050 PL wavelength (nm) Repeat flush and cap Coupled dot spectroscopy Microscopy QDs EF Growth Direction 4 nm 0V C.B. V.B. -1V Schottky diode Energy Processing for Diode and Optical Mask Electric Field 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 b a’ b’ a a’ b b’ 0 0 1 1 0 1 0 1 0 0 1 1 0 1 1 0 Truth Tables based on quantum state probabilities for Ideal and Optically Controlled Quantum Dot Ideal Truth Table Physical Truth Table 1 1 1 1 1 1 0.9 1 0.9 0.8 0.8 0.8 0.7 0.63 0.7 0.6 0.67 0.6 Population 0.5 Population 0.5 0.4 0.4 0.3 0 0.2 0 0 |10> 0 0 0 |00> |01> Input States |11> 0 0 0.1 0.3 0 0 0 |10> 0 0 |01> Output States |00> 0 0.2 0 0.1 (Science ‘03) 0 0 0.13 0.17 |11> 0.06 0.11 0.14 0 |00> |11> 0 0.2 0.09 |01> |10> Input State |10> |01> Output State |00> |11> Anomalous Variation of Beat Amplitude and Phase: The result of spontaneously generated Raman coherence Bea t ampli tude (a.u .) Standard Theory (a) (a) 0 20 40 Spl itti ng ( meV) • Plot of beat amplitude and phase as a function of the splitting. Phys. Rev. Lett. - 2005 Fast spin initialization in a single charged quantum dot: theory |T-> |t+>=|3/2> + dark |t->=|-3/2> transitions - |T+> V1 H1 H2 bright transitions |z+>=|1/2> |z->=|1/2> |X+> |X-> 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. Bx After the magnetic field is applied in Voigt geometry, the dark transitions become bright. Theory: Theory Phys. Rev. Lett. Jan. 2007 Fast spin initialization in a single charged quantum dot: experiment VM absorption map as a function of the applied bias |T-> |T+> I pump V1 V1 0.20 t 0.15 |X+> H1 H2 V2 II |X-> s 0.10 t>>s Magnetic Field 0.88T 0.05 Bx 1324.41 1324.47 Laser Energy (meV) 1324.53 Blue circle region is transparent due to the laser beam depleting the spin ground states Experiment: Phys. Rev. Lett. Aug. 2007 Fast spin initialization in a single charged quantum dot: experiment |T-> |T+> re-pump V1 H2 probe V2 V1 V2 H1 s |X+> |X+> |X-> absorption (a.u) |X-> re-pump off H2 re-pump on 1324.44 1234.48 Laser Energy (meV) re-pump off V1 V2 recovered absorption absorption (a.u) absorption (a.u) re-pump probe s absorption (a.u) |T-> |T+> H1 re-pump on 1324.44 1234.48 Laser Energy (meV) 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). The Mollow Absorption Spectrum, AC Stark effect, and Autler Townes Splitting: Gain without Inversion Dressed State Picture 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).. Power Spectrum of the Rabi Oscillations: Gain without inversion The Mollow Spectrum of a Single QD |3> Weak probe Strong pump |2> Science, August 2007 Impact of the High Speed Rabi experiment • 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 Optical control of two dot-spins Current work PRB 07 Two trions with Coulomb interaction Optical RKKY time e Coulomb dot #2 hole dot #1 dot #2 position Four optical fields e wfs confined to each dot Less demand on dot fabrication, more on optics <=== dot # 1 ===> Two optical fields Excited e wf covers both dots 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