1 / 24

Quantum information processing with electron spins 

Quantum information processing with electron spins . Optics & Spin Physics. Florian Meier and David D. Awschalom. Funding from:. spin manipulation in an extended system spin dynamics in QD’s (one qubit)? spin dynamics in an external B-field el. spin interactions (CNOT)?

Télécharger la présentation

Quantum information processing with electron spins 

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.


Presentation Transcript

  1. Quantum information processing with electron spins  Optics & Spin Physics Florian Meier and David D. Awschalom Funding from:

  2. spin manipulation in an extended system • spin dynamics in QD’s (one qubit)? • spin dynamics in an external B-field • el. spin interactions (CNOT)? • Laser pulse (many photons) for spin read-out or manipulation • single photon as qubit? New questions for optics & spin-physics • optical spin injection • detect spin coherence by time-resolved • Faraday Rotation (TRFR) J.M. Kikkawa and D.D. Awschalom, Nature 397, 139 (1999) • spin manipulation with • optical pulses (fast) J. A. Gupta et al., Science 292, 2412 (2001)

  3. mode 1 QD mode 2 σ1+ Outline • Towards electron interactions (coupled quantum dots): • M. Ouyang and D. D. Awschalom, Science 301, 1074 (2003) [exp.] • F. Meier et al., PRB 69, 195315 (2004) [thy.] • Cavity QED as interface for spin and photon quantum states: • F. Meier and D. D. Awschalom, • cond-mat/0405342. PRB (in press) [thy.]

  4. Universal quantum computing with electron spins requires electron exchange interaction. coupled quantum dots transfer via benzene ring EcA EcB EvB EvA QD B QD A Coupled QD´s • pair of coupled QD´s with one exciton • spin dynamics probed by TRFR • Results: • strong delocalization of spin via conjugated molecule • electron exchange interaction relevant for TRFR

  5. Absorption spectroscopy: • Coupled QD’s with different radii • 1.7 nm (A) and 3.5 nm (B) • Difference in quantum size levels • allows one to selectively address • both QD’s of a coupled pair. • Absorption peaks in the coupled • system are red-shifted. • Consistent with a coherent • delocalization of the electron • or hole over the coupled system. opt. absorption energy Coupled QD‘s: Absorption Molecularly coupled QD’s:

  6. Energy Larmor frequency Coupled QD‘s: TRFR • Faraday rotation: • g-factor size-dependent: distinguish • spin in QD A from spin in QD B. • Pump at low energy: inject • exciton into QD B. • Measure TRFR signal • at varying probe energies: • Find spin in QD A with probability • 10-20% even at T=300 K. EA EB  - B A

  7. absorption and TRFR imply delocalization of electrons • over both coupled QD’s; • transfer probability is of order 10-20% even at room T. • Experimental results: tc EcA EcB where UB Questions for theory: • simple model which explains the exp. features • electron exchange interaction? EvB EvA single-particle energy levels (i) (ii) Coulomb interaction e-h attraction h-h repulsion e-e repulsion transfer of electrons and holes, spin-conserving (iii) el. transfer hole transfer Coupled QD‘s: Theoretical Model

  8. EcA tc EcB EvB EvA Coupled QD‘s: Tunnel matrix elements The only unknown parameters of the model are tc and tv0. Calculate exciton wave functions and eigenenergy: en. red-shift indirect exc. find tc 0.08 eV

  9. mag. sample F dipole transition with operator for  circularly polarized light. TRFR Signal: Theory • FR “macroscopically”: magnetization M • rotates the polarization direction of a • linearly polarized Laser beam. • FR “microscopically”: Because of Pauli blocking, dielectric response • is different for + and -: mathematically: EcB -: transition blocked +: transition allowed EvB +

  10. where • bi-exciton exchange splitting; • probability for el. transfer from QD A to QD B • (QD B to QD A); • EX,A and  energy and linewidth of exciton-transition TRFR in Coupled QD’s: Theory From transition matrix elements to all bi-exciton states, find: • TRFR signal depends on coupling via the transfer probabilities p. • Electron exchange coupling expected to show up in TRFR signal.

  11. TRFR in Coupled QD’s: Results 1. Probability for electron transfer in coupled QD’s: • Obtained with tc calculated from absorption data. • Comparable to exp. spin transfer probability 10%. 2. TRFR signal amplitude as a function of probe energy and Larmor frequ.: theory experiment Reentrant behavior is well reproduced by theory.

  12. =50 meV FR [a.u.] =80 meV =20 meV 2.3 2.4 2.5 E[eV] TRFR: What about Exchange Interaction? 3. Electron exchange interaction is expected to show up in TRFR signal amplitude: Expect several zeroes in F(E). linecut at fixed Larmor frequency Exchange interaction J  20 meV is too small compared to line- width   50 meV !

  13. Coupled QD’s and Quantum Information • Coupled QD’s show strong • delocalization of the electron • wave function; spin is conserved. • Behavior well understood within • a simple theoretical model. • Perspective: Detect electron exchange interaction spectroscopically • or by exchange-governed dynamics.

  14. QD PL σ1+-laser Cavity QED: optical selection rules: • entanglement of atom and cavity • SWAP atom state onto cavity • spin dependent abs. and PL • optical spin-readout QD’s in Cavities: Interface for Spin & Photon Qubits Motivation: Imamoglu, Zoller, Sham, ...: Haroche, Kimble, Walther, ....: atom Can one swap the spin state of a QD onto the cavity mode? • spin-photon entanglement; • spin-photon SWAP gate. Using a 2-mode cavity, can implement

  15. mode 1 y2 QD • QD with excess electron, • Two cavity modes with circular (mode 1) and linear (mode 2) polarization. • Strong coupling. mode 2 σ1+ • QD level scheme (hh or lh valence band maximum); • one spin state of QD is always dark! 2-mode Cavity and QD: The System propagating modes Dynamics if a photon is injected into mode 1? Dynamics depend on

  16. For spin state , transition • to trion state by photon • absorption: σ1+ sz=±1/2 hh jz=-3/2  lh σ1+ or y2 Spin-Photon Entanglement: The Hamiltonian QD with hh (|jz|=3/2) val. band maximum. Possible processes .... (b) Trion decays by photon emission into either 1+ or y2; QD returns to its original spin state. where g1, g2 are coupling constants for modes 1 and 2. (2-mode Jaynes-Cummings model)

  17. Time evolution of y2 σ1+ σ1+ At max. entangled states Spin-Photon Entanglement: Dynamics For g1=g2=g,

  18. propagating modes t[/g] mode 1 y2 Cavity loss is sufficient: mode 2 with σ1+ Liouville operator for cavity loss. Entanglement: Master Equation for Cavity Loss Terminate time evolution here!

  19. cav. loss from mode 2 photon loss into mode 2! For cav. loss from mode 1 t[/g] E inefficient transfer to 2 (linewidth) loss from mode 1 2[g/] Entanglement: Von Neumann Entropy In which direction does the photon leave the cavity for spin state |? Cavity loss terminates coh. evolution exactly after one period. At least one oscillation between cavity modes. Von Neumann entropy as fctn. of 2: Prob. for cavity loss along 2:

  20. F   σ1+ Entanglement: Robustness • How sensitive are the above dynamics to experimental fine-tuning? • Coupling constants g1g2: • QD misalignment by angle : • Detuning  of cavity modes relative to exciton transition: F g1/g2 Resonance condition is crucial!

  21. For spin state , transition • to trion state by photon • absorption: Spin-Photon SWAP: Hamiltonian QD with lh(|jz|=1/2) val. band maximum. Possible processes .... (b) Trion decays by photon emission into either 1+ or z2; QD spin can be flipped! sz=±1/2 σ1+ σ1+ z2 jz=1/2 lh hh Trion couples to two different spin states!

  22. Time evolution of z2 σ1+ σ1+ QD state swapped onto cavity state! At Spin-Photon SWAP: Dynamics For g1=g2=g,

  23. Experimental Implementation • Main challenge: Scheme requires • cavity with • small mode volume of order 3; • high Q-factor,Q>104; • three degenerate modes, which are • not all TE or TM; • QD placed at mode maxima. K. Hennesy et al., APL 83, 3650 (2003) Possible (at least in principle) with defect modes of a photonic crystal.

  24. mode 1 QD mode 2 σ1+ Summary • Spin physics of molecularly coupled QD’s: • delocalization of electron wave function; • dynamics driven by electron exchange • interaction? • QD’s in two-mode cavities: • create spin-photon entanglement; • implement spin-photon SWAP gate; • system robust against experimental • imperfections. y2

More Related