March 29 2011 Aussois France David Gershoni The

March 29, 2011, Aussois, France David Gershoni The Physics Department, Technion-Israel Institute of Technology, Haifa, 32000, Israel and Joint Quantum Institute, NIST and University of Maryland, USA Technion – Israel Institute of Technology Physics Department and Solid State Institute

Motivation q. Coherent control of anchored qubits – spins of carriers. q. Coherent control of flying qubits – polarization of photons. q. Semiconductor Quantum dots provide a unique stage for controlling the interactions between both type of qubits, and they are compatible with the technology of light sources and detectors.

Outline • Two level system: Spin and Light Polarization • Introduction to energy levels and optical transitions in SCQDs • The bright and dark excitons as matter two level systems – Writing the exciton spin state by a polarized light pulse tuned into excitonic resonances. – Reading its spin state by a second polarized light pulse, resonantly tuned into biexcitonic resonances. – Manipulating its spin state by a third polarized and/or detuned pulse.

Two level system and the Bloch Sphere classical bit (0 or 1)– quantum bit (qubit – Bloch sphere)

• Jones vector: • General solution to Maxwell equations for the direction of the electric field vector of a photon is an ellipse Linear Circular Technion – Israel Institute of Technology, Physics Department and Solid State Institute Elliptical 5

Polarization – Poincare’ sphere Poincare sphere Stokes parameters 4 measurements are required to determine the full polarization state of light: a 2 x 2 density matrix V H Information can be encoded in the photon’s polarization state.

Selection rules for optical transitions in semiconductor QDs ~1. 25 e. V e e e 7 e e h e e e e ~0. 05 e. V e ~0. 3 e. V

STM (scanning tunneling microscope) images self assembled dots Not all the same, but live forever and can be put into high Q - microcavities, easily

Single Quantum Dot - Photoluminescence 2 nm Ga. As 1. 5 monolayer In. As (PCI) Ga. As Off resonance excitation P S h emission due to radiative recombination

Spin interaction of charge carriers • Two electrons (holes) non-interacting spin states: 30 (15) me. V Total spin: • Electrons (holes) singlet state: on tively N ia rad Energy S S • Electrons (holes) triplet states: Spin blockaded T+1(+3) T-1(-3) T 0 e-e (h-h) exchange ~5 me. V

Quantum dot e-h pair (exciton) states Non interacting Isotropic electron-hole exchange Anisotropic electron-hole exchange Bright Exciton Δ 1 ≈ 0. 03 me. V H Δ 0 ≈ 0. 3 me. V Dark Exciton Dark exciton: Ground- state, Optically inactive, quantum two level system V Δ 2 ≈ 0. 001 me. V

The dark exciton’s advantages • Its lifetime is long – comparable to that of a single electron or hole. • It is neutral and therefore less sensitive than charged particles to fluctuating electric fields. • Due to its fine structure and smaller g-factor, it is more protected than the electron or hole from fluctuating magnetic fields, especially where no external magnetic field is applied. as an in-matter qubit But how can it be addressed? E. Poem et al. , Nature Physics ( November 2010)

Biexciton excitation spectrum P S S P 0 XS We can generate any of these biexciton spin states by tuning the energy and polarization of the laser.

Experimental setup Polarizing beam splitter First monochromator and CCD camera/Detector Spectral Two channel arbitrary polarization rotator Filter H V Second monochromator And detector Beam combiner Second pulse laser He Objective First pulse laser Sample Delay line

2 A/ I 0 2 nd pulse V H 1 st pulse 0 θ P 0(θ, )

‘Writing’ the spin with the 1 st photon. A ∆=30µev S A Poincare sphere Bloch sphere S

‘Reading’ the spin with the 2 nd photon Poincare I(XX 0) Bloch

Dt [ps] [103 counts/min] Time resolved, two-photon PL measurement XX 0 TT, X 0 P excitation XX 0 T 0 XX 0 [integated Counts/min] XX 0 T 3 XX 0 T 0 XX 0 T 3 X-1 XX 0 5 E [e. V] X 0 X+1

Quasi-resonant Resonant

Conclusions so far… • We demonstrate for the first time that the exciton spin can be ‘written’ in any arbitrary coherent superposition of its symmetric and anti-symmetric spin eigenstates by an elliptically polarized short laser pulse. • We showed that by tuning a second polarized laser pulse to a biexcitonic resonance, the exciton spin can be faithfully ‘readout’. • Y. Benny, et al, "Coherent optical writing and reading of the exciton spin state in single quantum dots " (ar. Xiv: 1009. 5463 v 1 [quant-ph]28 Sep 2010), PRL 2011.

March 31, 2011, Aussois, France E. Poem, Y. Kodriano, Y. Benny, C. Tradonsky, N. H. Lindner, J. E. Avron and D. Galushko The Physics Department and The Solid State Institute, Technion-Israel Institute of Technology, Haifa, 32000, Israel B. D. Gerardot and P. M. Petroff Materials Department, University of California Santa Barbara, CA, 93106, USA Technion – Israel Institute of Technology Physics Department and Solid State Institute

Summary: •