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 NSF CENTER - Frontiers of Optical Coherence and Ultrafast Science (FOCUS) ARO/NSA, AFSOR, DARPA, ONR, NSF

Optically Controlled Spin Optical control of spin: –Use spin as qubit –Use exciton for control and measurement T 2 > 1  s Operation time~ 10 ps (  -pulse) T 2 / Op. time> 10 5 x-x-

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 10 4 operations in the coherence time)

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 InAs GaAs Cross sectional STM Boishin, Whitman et al. Coupled QD’s [001] 72 nm x 72 nm taken from R. Notzel Quantum Dots: The Solid State version of the ion approach

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

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.Hamiltonian for two spins 2.Exchange interactions 3.Excited state spectrum 4.Biexciton spectrum 5.B-field dependence

Quantum Dots: Atomic Properties But Better Larger oscillator strength (x10 4 ) 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 InAs GaAs Cross sectional STM Boishin, Whitman et al. Coupled QD’s [001] 72 nm x 72 nm AFM Image of Al0.5Ga0.5As QD’s formed on GaAs (311)b substrate. Figure taken from R. Notzel “Quantum computation with quantum dots” Daniel Loss and David P. DiVincenzo, Phys. Rev. A. 57 p120 (1998)

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

Truth Tables based on quantum state probabilities for Ideal and Optically Controlled Quantum Dot (Science ‘03) 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’ bb’

Anomalous Variation of Beat Amplitude and Phase: The result of spontaneously generated Raman coherence (a) Standard Theory Plot of beat amplitude and phase  as a function of the splitting. Phys. Rev. Lett

Fast spin initialization in a single charged quantum dot: theory After the magnetic field is applied in Voigt geometry, the dark transitions become bright. 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. |z->=|1/2>|z+>=|1/2> |t+>=|3/2> |t->=|-3/2> ++ -- dark transitions |T+> |T-> V1 H1H2 bright transitions BxBx |X+> |X-> Theory: Theory Phys. Rev. Lett. Jan. 2007

Fast spin initialization in a single charged quantum dot: experiment Blue circle region is transparent due to the laser beam depleting the spin ground states  t >>  s BxBx VM absorption map as a function of the applied bias pump |T+> |T-> |X+> |X-> ss tt V1 I H1V II H2 Magnetic Field 0.88T DC(V) Laser Energy (meV) Experiment: Phys. Rev. Lett. Aug. 2007

Fast spin initialization in a single charged quantum dot: experiment Laser Energy (meV) re-pump off re-pump on H2 V2 re-pump off Laser Energy (meV) V1 H1 re-pump on recovered absorption absorption (a.u) ss re-pump H2V2 probe |T+> |X+> |X-> |T-> ss re-pump H1V1 probe |T+> |X+> |X-> |T-> V1 V2

Fast Spin Initialization in a Single Charged QD THEORY: C. Emary et al. Phys. Rev. Lett. 98, (2007). EXPERIMENT: Xiaodong Xu et al. Phys. Rev. Lett. in press (2007). 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.

The Mollow Absorption Spectrum, AC Stark effect, and Autler Townes Splitting: Gain without Inversion Autler Townes Splitting Mollow Spectrum: New physics in absorption 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).. Dressed State Picture

Power Spectrum of the Rabi Oscillations: Gain without inversion The Mollow Spectrum of a Single QD |2> |3> Strong pump Weak probe 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 ~ Joules. 100GHz limit. Achievable with low power diode lasers Enables use of 960 nm band telecom switching technology

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

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