Deterministic Coherent Writing and Control of the Dark Exciton Spin using Short Single Optical Pulses Ido Schwartz, Dan Cogan, Emma Schmidgall, Liron Gantz, Yaroslav Don and David Gershoni The Physics Department and the Solid State Institute, Technion Israel Institute of Technology Haifa, Israel Technion Israel Institute of Technology Frisno 13, March 1, 015, Aussois, France
Overview Three main experimental results: 1. Deterministic, all-optical excitation of a quantum-dot confined dark exciton (DE). Coherent writing of its spin state using single polarized picosecond pulse. 3. Coherent control of the DE spin state using a picosecond optical pulse This talk: Qubits in quantum dots Deterministic DE generation and spin writing DE life and coherence times Coherent control of the DE spin state Schwartz et al. Phys Rev X 5, 011009 (015). Featured in Nature Materials 14, 60 (015).
Semiconductor Quantum Dots self assembled dots
Advantages of Quantum Dots Live forever Easily incorporated into microcavities and devices Easily accessed optically and electronically Level separation compatible with fast optics (picoseconds) Can be easily charged and discharged Disadvantages: Every dot is different (size, structure, location) Coupled to their solid state environment (phonons)
From Spin to Polarization Orbital angular momentum ( 0) and spin (1/) Non-Resonant Excitation Resonant Excitation σ Orbital angular momentum ( ±1) and spin (±1/) aligned :±3/ Discrete set of energy levels Photon Polarization Exciton Spin State 3 + 1 σ + Dark Exciton + Randomized Photon does carrier not spin alter electon spin. Conduction band Empty of electrons Photon emission Due to recombination of e-h pair Valence band full of electrons (no holes) Benny et al. PRL (011).
Dark Excitons in Quantum Dots Energy Non interacting Bright Exciton = + = σ + σ 3 1 1 3 1 + = = Dark Exciton 3 1 3 1 1 Isotropic electron-hole exchange Δ 0 300μeV Anisotropic electron-hole exchange a Δ 1 34μeV Δ 1.4μeV s a s σ σ σ + V + σ + H A long-lived two-level system. A qubit? Poem et al. Nature Physics 6, 993-997 (010).
DiVincenzo criteria for QIP: Fortschr. Phys. 48 77 (000) We need to find some quantum property of a scalable physical system in which to encode our bit of information (qubit). It should Live long enough to enable performing computation. Initial state preparation. Setting the state of the qubits to zero before each new computation. Isolation from the environment to maintain the quantum nature of the qubit - reducing the effects of decoherence. Gate implementation. Manipulation of the states of individual qubits with reasonable precision, and inducing interactions between them in a controlled way. The gate operation time must be much shorter than the decoherence time (allow error corrections) Readout. It must be possible to measure the final state of our qubits once the computation is finished, to obtain the output of the computation.
Other Quantum Dot Qubits System Lifetime Coherence Time No Field B Field No Field B Field Initalization Electron Spin <1µs 1 10s of ms 1 1-10 ns 1 Few µs 1 Optical pumping (ns) Hole Spin 1 µs Few ms 1-0 ns 10s of µs Optical pumping (ns) Bright Exciton 1 ns 3 Same >10 ns 3 Same Polarized pulse (ps) Dark Exciton >1µs 4 >100 ns 4 Polarized pulse (ps) Charged Optically qubits: active: Sensitive Short lifetime to electrostatic fluctuations. 1 See Bracker et al. PRL (005), Press et al. Nature (008), Berezovski et al. Science (008),Greilich et al. Nat. Phys. (009 ) and others. See De Greve et al. Nat. Phys. (011), Godden et al. PRL (01), Fras et al. PRB (011) and others. 3 See Benny et al. PRL (011) and others. 4 See Schwartz et al. PRX (015)
The Dark Exciton Bloch Sphere ψ = As + Ba ψ () t = s iωt + e a a = ( ) / 1.3µ ev T = π / ω = h/ 3.1ns
Heralding and Probing the DE Spin State I(t) CO No absorption. No Absorption Biexciton biexciton Emission Resonance emission. t CROSS σ + S = ( + ) / +> -> A = ( ) / I. Schwartz et al. Phys Rev X 5, 011009 (015).
Spectroscopy of the DE Low intensity M. Zielinski et al. Phys Rev B 91 085403 (015).
Rabi Oscillations and Spin Rotation e> g> g> i e π e> g> e ω 0 g> = δ = ω = ω 0 = 0 δ ω ω 0 0 Pulse Area A= A=ππ g-e g+e Rabi oscillations: g> = empty dot g e> = DE Change pulse area by varying laser intensity
Rabi Oscillations s> a> δ = ω ω 0 0 Pulse Area A=π iϕ a >+ e s > s = + a> + Spin rotation: Direction determined by polarization Angle determined by detuning a = Y. Kodriano et al. PRB 85, 41304(R) (01). S. Economou and T. Reinecke PRL 99, 17401 (007)
DE Rabi Oscillations Pulse width 50ns Rep rate 1 MhZ Deterministic writing of the DE!
Direct Measurement of the DE Lifetime Pump (H) Probe Probe Probe τ DE 1.1 μs
Life and Coherence Time of the Dark Exciton Lifetime Coherence Coincidences Coincidences Autocorrelation of the biexciton emission line under D-polarized CW resonant excitation
Coherence of the Dark Exciton Rep rate 76MHz Detector Start Timer polarizer T * 100nsec polarizer Detector Stop
Controlling the DE Spin State Bloch Sphere Pulse Sequence ( + ) / 0 Control (ps) Pump Probe ( ) / I(t) t
Controlling the Dark Exciton Spin Control (ps, H) R) Pump (H) Probe (R) ( + ) / ( ) /
Writing the spin of the bright exciton by one short optical pulse 1 H i V = R + ( R - L ) 0 X =34µev V> H> H> i 1 ( ) ( + ) Poincare sphere T = =1ps V> Bloch sphere H X 0 V Energy (ev)
Writing the spin of the bright exciton with one optical pulse α R + β L 0 X =34µev H> V> H> i 1 ( ) ( + ) Poincare sphere Y. Benny, et al. " Phys. Rev. Lett. 106, 040504, (011). V> Bloch sphere H X 0 V Energy (ev)
Technion Israel Institute of Technology Physics Department and Solid State Institute
Writing the spin of the dark exciton by one ps optical pulse BE-DE mixing induced by the QD assymmetry Bright Exciton Dark Exciton M. Zielinski et al. Phys Rev B 91 085403 (015). Unpolarized DE quasi resonance
Coherent Writing the Dark Exciton spin State by a Single Picosecond-long Optical Pulse Polarization degree P( θφ, )
Summary The dark exciton is a neutral, long-lived, physical two-level system: Lifetime: longer than 1 µs Coherence time ( ):* T longer than 100 ns No magnetic field, without spin echo! We demonstrate: Deterministic photogeneration of the DE. Control of the DE state by a picosecond pulse - 6 and 5 orders of magnitude faster than its lifetime and coherence time, respectively. Coherent writing by a single polarized picosecond pulse Consequently, the dark exciton is an excellent solid state spin qubit.
Prof. David Gershoni Emma Schmidgall Dan Cogan Liron Gantz Ido Schwartz Thank you for your attention!