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Optically Driven Spins in Semiconductor Quantum Dots. Duncan Steel - Lecture 2. DPG Physics School 2010 on "Nano-Spintronics" .

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## Optically Driven Spins in Semiconductor Quantum Dots

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**Optically Driven Spins in Semiconductor Quantum Dots**Duncan Steel - Lecture 2 DPG Physics School 2010 on "Nano-Spintronics"**The qubit for real systems is the electron or hole spin:**The key to optically driven quantum computing in semiconductors is the negatively charged exciton (trion) in a quantum dot |1> |1> |0> |0> Electronic Spin Qubit Optical Bloch Vector Qubit Semiconductor Quantum Coherence Engineering Successful coherent optical manipulation of the optical Bloch vector necessary to manipulate the spin vector**The electron spin vector**AlGaAs (GaAs) GaAs (InAs) AlGaAs (GaAs) |1> |0>**The electron spin vector**AlGaAs (GaAs) GaAs (InAs) AlGaAs (GaAs) l |1> |0>**The electron spin vector**AlGaAs (GaAs) GaAs (InAs) AlGaAs (GaAs) l |1> |0>**The electron spin vector**Long coherence time AlGaAs (GaAs) GaAs (InAs) AlGaAs (GaAs) |1> |0>**Raman coherence oscillates at frequency of the Zeeman**splitting due to electron in-plane g-factor and decays with time. • Circularly polarized pump pulse creates coherent superposition of spin up and down state. Optical Excitation of Spin Coherence:Two-photon stimulated Raman**Single Electron Spin Coherence:Raman Quantum Beats**Charged Exciton System X - CNOS (a. u.) G G Neutral Exciton System X G G hgs (meV) T2* >10 nsec at B=0 Phys. Rev. Lett. - 2005**Anomalous Variation of Beat Amplitude and Phase**Standard Theory (a) (b) • Plot of beat amplitude and phaseas a function of the splitting.**Anomalous Variation of Beat Amplitude and Phase**Standard Theory (a) • Plot of beat amplitude and phaseas a function of the splitting.**Spontaneously Generated Coherence (SGC)**Trion G G • Coupling to electromagnetic vacuum modes can create coherence* !! • Modeled in density matrix equations by adding a relaxation term: • Normally forbidden in atomic systems or extremely weak.**Anomalous Variation of Beat Amplitude and Phase:The result**of spontaneously generated Raman coherence Standard Theory (a) • Plot of beat amplitude and phaseas a function of the splitting. Phys. Rev. Lett. - 2005**Two-Photon Spin Rabi**Trion Trion Laser Pulse**Phase Gate - Demonstration of Geometric Phase (Aharonov &**Anandan) Optical Control of Trion Optical Bloch Vector Optical Control of Spin Bloch Vector**Demonstration of the Phase Control**• Modulation effect clearly seen • Frequency of the modulations depends on the strength of the CW field • Phase change after modulation points consistent with theory for 0.2, 5 and 10 mW scans • Action of CW field can be likened to a spin phase gate**Dressed State Picture**The Mollow Absorption Spectrum, AC Stark effect, and Autler Townes Splitting: Gain without Inversion Mollow Spectrum: New physics in absorption Autler Townes Splitting 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)..**Power Spectrum of the Rabi Oscillations:Gain without**inversionThe Mollow Spectrum of a Single QD |3> |2> Weak probe Strong pump X. Xu, B. Sun, P. R. Berman, D.G. Steel, A. Bracker, D. Gammon, L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science, 317 p 929 (2007).**Probe Abosorption as a**Function of the Pump Intensity (on resonance) Pump intensity (Io=0.03w/cm ) 2 50 Io 40 Io 30 Io 20 Io 10 Io 5 Io 0 Io 321594 321591 Probe Frequency (GHz) Autler-Townes Splitting in a Single Quantum Dot Dressed state Picture |b(N)> |1> } WR |3> |a(N)> |b(N-1)> } WR |2> |a(N-1)> Absorption (a.u.) 1 Rabi Splitting (GHz) 0 8 0 4 Pump Field Strength( )**Probe Absorption as a Function of Pump Frequency Detuning**Theoretical Plot Experimental Data Pump Detuning (GHz) Pump Intensity 30Io 1.7 0.6 Absorption (a.u.) 0.3 0.0 -0.3 -0.6 -1.7 0 -5.0 -2.5 2.5 5.0 321594 321591 Probe Frequency (GHz) Probe Detuning (G units)**|T->**|T-> |T+> H1 V2 Wp Wd V2 V1 H1 H2 |X+> |X+> |X-> |X-> Bx V1 H1 H2 V2 -8 8 0 -3 -3 0 Laser Detuning (GHz) Laser Detuning (G units) Thy Physical Model of the Dark State Experiment The Quartet Transition Pattern Theoretical plot of the CPT including electron spin dephasing B=1.32 T 1 DT/T (10-4) 0**The Observation of the Coherent Population Trapping of an**Electron Spin |T-> Wd/2p(GHz) 1 1.38 H1 V2 Ωp Ωd 0 1 1.26 |X+> 0 |X-> 1 0.83 DT/T (10-4) 0 1 0.78 0 1 0.56 0 0 0 5 -5 0 Probe Detuning (GHz) The probe absorption spectrum scanning across transition H1 Solide lines are the fits, which yield electron spin T2* of 4 ns. Nature - Physics, 2008**Probing Dynamic Nuclear Spin**Polarization by Dark State Spectroscopy Probe absorption spectra by varying the laser scan rate |T-> Ωpump Ωprobe h e e e e |X+> |X-> Large trion excitation (absorption) is favored Dynamic control of nuclear field Broadened & rounded trion peak (Dark state position reflect Zeeman Splitting) Scan direction dependence: hysteresis & dark state shift**Time Dependent Probe Absorption Spectrum**Ωpump Ωprobe h e e e e B=2.6 T |T-> |X+> |X->**Time Dependent Probe Absorption Spectrum**Laser frequency parked here Partial backward scan Ωpump Ωprobe h e e e e |T-> Stable configuration: maximum trion excitation (absorption) |X+> |X->**Time Dependent Probe Absorption Spectrum**Ωpump Ωprobe h e e e e |T-> Dark State is a meta-stable state for nuclear field |X+> |X->**Trion Induced Dynamic Nuclear Spin Polarization**anisotropic hyperfine from hole |T> nuclear Zeeman << trion linewidth Flip up rate: Flip down rate: Whichever increases rt dominates! DNP rate Nuclear field dynamics:**Dynamic Nuclear Spin Polarization Induced Spectral Servo**Probe laser frequency Two photon detuning Absorption Nuclear field Probe detuning ( = 2-ph detuning - nuclear field )**Numerical Simulation Results : Slow Scan**Experiment Theory Nuclear field dynamics: Parameters: Nuclear T1**Numerical Simulation Results : fast Scan**Experiment Theory Parameters: Nuclear T1 Microscopic theory: Weng Yang et al., Q14.00002; http://arxiv.org/abs/1003.3072**Nuclear Field Locking Effect**Stable configurations for DNP Metastable configurations DNP rate: Two-photon detuning Nuclear field locked to stable value**Dynamic Nuclear Spin Feedback Suppresses Fluctuations**Nuclear field self-focus to stable value DNP by trion Nuclear field unstable against DNP Stable-config nuclear field locked to frequencies CW laser excitation Single QD arbitrary nuclear spin config Medium trion excitation 2-photon resonance shifts Nuclear spin fluctuation C. Latta et al., Nature Phys. 5, 758 (2009) Ivo T. Vink et al, Nature Phys. 5, 764 (2009) Maximum trion excitation**Suppression of Nuclear Field Inhomogeneous Broadening**• More enhancement on spin T2* with larger pump strength larger pump larger slope in tighter locking Pump intensity 40 60 70 90 20 spin T2* peak-to-dip ratio Absorption Probe detuning**Suppression of Nuclear Field Inhomogeneous Broadening**Thermal value Ωpump Ωprobe h e e e e • Spin decoherence rate extracted from dip-to-peak ratio |T-> • T2* extended well above thermal value |X+> • Deficiency: locking position changes with probe scan |X->**Coherent Spin Manipulations without Hyperfine Induced**Dephasing Pump 1 >> Pump 2 >> Probe (fixed freq) (fixed freq) (freq scan) • Pump 1 +pump 2 locks nuclear field to a constant value • Pump 1 + probe measures spin T2***Three Beam Measurement**Clean line shape Spin decoherence rate ~ 1 MHz, reduced by a factor of 400 Xu, X. et al., Nature59, 1105 (2009)**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.**Semiconductor Nano-Optics:An Interdisciplinary Collaboration**Dan Gammon Naval Research Lab Lu Sham UC-San Diego Paul Berman Luming Duan Roberto Merlin U. Mich.**Outstanding Graduate Students****• Nicolas Bonadeo (graduated) • Jeff Guest (graduated) • Gang Chen (graduated) • Todd Stievater (graduated) • Anthony Lenihan (graduated) • Elizabeth Tabak (graduated) • Elaine Li (graduated) • Gurudev Dutt (graduated) • Jun Cheng (graduated) • Yanwen Wu (graduated) • Qiong Huang (graduated) • Xiaodong Xu • Erik Kim • Katherine Smirl • Bo Sun • John Schaible • Vasudev Lai **Alberto Amo - Autonoma University of Madrid

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