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 March 29, 2011, Aussois, France

Motivation  Coherent control of anchored qubits – spins of carriers.  Coherent control of flying qubits – polarization of photons.  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)

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

Polarization – Poincare’ sphere H V Poincare sphere Stokes parameters Information can be encoded in the photon’s polarization state. 4 measurements are required to determine the full polarization state of light: a 2x2 density matrix

Selection rules for optical transitions in semiconductor QDs 7 h e e e e e e e e e e e e e e e e e e e e e ~0.3 eV ~0.05 eV ~1.25 eV

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 GaAs 1.5 monolayer InAs (PCI) 2nm GaAs GaAs h emission due to radiative recombination S Off resonance excitation P

Two electrons (holes) non-interacting spin states: Electrons (holes) singlet state: Electrons (holes) triplet states: Spin interaction of charge carriers S T0T0 T -1(-3) T +1(+3) Total spin: e-e (h-h) exchange ~5meV Energy S Non- radiatively Spin blockaded 30 (15) meV

Bright Exciton Dark Exciton Isotropic electron-hole exchange Anisotropic electron-hole exchange Δ 0 ≈ 0.3meV Δ 1 ≈ 0.03meV Δ 2 ≈ 0.001meV Non interacting V H Quantum dot e-h pair (exciton) states Dark exciton : Ground- state, Optically inactive, quantum two level system

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

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

1 st pulse 2 nd pulse V H H V 0  θ 2A/I 0 P0(θ,)P0(θ,) 1 st pulse

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

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

Time resolved, two-photon PL measurement XX 0 TT, X 0 P excitation  t [ps] E [eV] XX 0 T3 XX 0 T0 X -1 XX 0 X0X0 X +1 XX 0 XX 0 T0 55 [10 3 counts/min] [integated Counts/min] XX 0 T3 X0X0

Quasi-resonantResonant

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 " (arXiv: v1 [quant-ph]28 Sep 2010), PRL 2011.

Technion – Israel Institute of Technology Physics Department and Solid State Institute 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

Summary: