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

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Semiconductor Quantum Coherence Engineering |0> |1> |0> |1> Optical Bloch Vector Qubit Electronic Spin Qubit Successful coherent optical manipulation of the optical Bloch vector necessary to manipulate the spin vector 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

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The electron spin vector GaAs AlGaAs |0> |1> (GaAs) (InAs)

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GaAs AlGaAs (GaAs) (InAs) |0> |1> The electron spin vector

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GaAs AlGaAs (GaAs) (InAs) |0> |1> The electron spin vector

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GaAs AlGaAs (GaAs) (InAs) Long coherence time |0> |1> The electron spin vector

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Optical Excitation of Spin Coherence: Two-photon stimulated Raman Circularly polarized pump pulse creates coherent superposition of spin up and down state. Raman coherence oscillates at frequency of the Zeeman splitting due to electron in-plane g- factor and decays with time.

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CNOS (a. u.) Single Electron Spin Coherence: Raman Quantum Beats X - X Charged Exciton System Neutral Exciton System T 2 * >10 nsec at B=0 h s ( eV) Phys. Rev. Lett. - 2005

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Anomalous Variation of Beat Amplitude and Phase (a)(b) Standard Theory Plot of beat amplitude and phase as a function of the splitting.

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(a) Standard Theory Anomalous Variation of Beat Amplitude and Phase Plot of beat amplitude and phase as a function of the splitting.

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Spontaneously Generated Coherence (SGC) Trion 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.

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Anomalous Variation of Beat Amplitude and Phase: The result of spontaneously generated Raman coherence (a) Standard Theory Plot of beat amplitude and phase as a function of the splitting. Phys. Rev. Lett. - 2005

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Two-Photon Spin Rabi Trion Laser Pulse

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Initialization

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Phase Gate - Demonstration of Geometric Phase (Aharonov & Anandan) Optical Control of Spin Bloch Vector Optical Control of Trion Optical Bloch Vector

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Coherent Generation of a Geometrical Phase

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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

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The Mollow Absorption Spectrum, AC Stark effect, and Autler Townes Splitting: Gain without Inversion Autler Townes Splitting Mollow Spectrum: New physics in absorption 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).. Dressed State Picture

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Power Spectrum of the Rabi Oscillations: Gain without inversion The Mollow Spectrum of a Single QD |2> |3> Strong pumpWeak probe 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).

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Autler-Townes Splitting in a Single Quantum Dot Absorption (a.u.) |2> |1> |3> | (N-1)> (N-1) | (N)> (N) } R Dressed state Picture Rabi Splitting (GHz) 0 1 Pump Field Strength( ) 04 8 Probe Frequency (GHz) 321591 321594 0 I o 10 I o 20 I o 30 I o 40 I o 50 I o 5 I o Probe Abosorption as a Function of the Pump Intensity (on resonance) Pump intensity (I o =0.03w/cm ) 2

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Probe Absorption as a Function of Pump Frequency Detuning Experimental Data Theoretical Plot Probe Frequency (GHz) 321591 321594 Probe Detuning units 0 -2.5-5.0 2.55.0 -1.7 -0.6 -0.3 0.0 0.3 1.7 0.6 Pump Detuning (GHz) Pump Intensity 30I o Absorption (a.u.)

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Thy Physical Model of the Dark State Experiment V1 V2 H1H2 Laser Detuning (GHz) 0 -8 8 |X+> |X-> BxBx |T+> |T-> V1 V2 H1H2 DT/T (10 -4 ) 0 1 |T-> |X+> |X-> H1V2 WpWp WdWd Laser Detuning (G units ) 0 -3-3 -3-3 Theoretical plot of the CPT including electron spin dephasing B=1.32 T The Quartet Transition Pattern

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The Observation of the Coherent Population Trapping of an Electron Spin |T-> |X+> |X-> H1V2 ΩpΩp ΩdΩd The probe absorption spectrum scanning across transition H1 Solide lines are the fits, which yield electron spin T 2 * of 4 ns. 5 DT/T (10 -4 ) W d /2 p (GHz) 0 0.56 0.78 0.83 1.26 1.38 Probe Detuning (GHz) 0 -5 0 0 1 0 1 0 1 0 1 0 1 Nature - Physics, 2008

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Probing Dynamic Nuclear Spin Polarization by Dark State Spectroscopy ee h ee Ω probe Ω pump |T-> |X-> |X+> Broadened & rounded trion peak Large trion excitation (absorption) is favored Scan direction dependence: hysteresis & dark state shift (Dark state position reflect Zeeman Splitting) Dynamic control of nuclear field Probe absorption spectra by varying the laser scan rate

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B=2.6 T Time Dependent Probe Absorption Spectrum e e h ee Ω probe Ω pump |T-> |X-> |X+>

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Laser frequency parked here Partial backward scan Stable configuration: maximum trion excitation (absorption) Time Dependent Probe Absorption Spectrum e e h ee Ω probe Ω pump |T-> |X-> |X+>

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Time Dependent Probe Absorption Spectrum e e h ee Ω probe Ω pump |T-> |X-> |X+> Dark State is a meta-stable state for nuclear field

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anisotropic hyperfine from hole Flip up rate: Flip down rate: Whichever increases t dominates! nuclear Zeeman << trion linewidth DNP rate Trion Induced Dynamic Nuclear Spin Polarization |T> Nuclear field dynamics:

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Probe laser frequency Nuclear field Absorption Probe detuning ( = 2-ph detuning - nuclear field ) Two photon detuning Dynamic Nuclear Spin Polarization Induced Spectral Servo

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Experime nt Theor y Parameters: Nuclear T 1 Nuclear field dynamics: Numerical Simulation Results : Slow Scan

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Experime nt Theor y Parameters: Nuclear T 1 Numerical Simulation Results : fast Scan Microscopic theory: Weng Yang et al., Q14.00002; http://arxiv.org/abs/1003.3072

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Stable configurations for DNP DNP rate: Two-photon detuning Metastable configurations Nuclear field locked to stable value Nuclear Field Locking Effect

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Dynamic Nuclear Spin Feedback Suppresses Fluctuations Stable-config nuclear field locked to frequencies Nuclear field unstable against DNP CW laser excitation Nuclear field self-focus to stable value Nuclear spin fluctuation 2-photon resonance shifts Single QD arbitrary nuclear spin config Medium trion excitation Maximum trion excitation DNP by trion C. Latta et al., Nature Phys. 5, 758 (2009) Ivo T. Vink et al, Nature Phys. 5, 764 (2009)

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Probe detuning Absorption –More enhancement on spin T 2 * with larger pump strength larger pump larger slope in tighter locking Pump intensity 20 40607090 spin T 2 * peak-to-dip ratio Suppression of Nuclear Field Inhomogeneous Broadening

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–Spin decoherence rate extracted from dip-to-peak ratio –Deficiency: locking position changes with probe scan –T 2 * extended well above thermal value Thermal value e e h ee Ω probe Ω pump |T-> |X-> |X+> Suppression of Nuclear Field Inhomogeneous Broadening

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Coherent Spin Manipulations without Hyperfine Induced Dephasing –Pump 1 + pump 2 locks nuclear field to a constant value –Pump 1 + probe measures spin T 2 * Pump 1 >> Pump 2 >> Probe (fixed freq) (fixed freq) (freq scan)

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Spin decoherence rate ~ 1 MHz, reduced by a factor of 400 Three Beam Measurement Clean line shape Xu, X. et al., Nature 59, 1105 (2009)

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Wheres 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.

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Semiconductor Nano-Optics: An Interdisciplinary Collaboration Dan Gammon Naval Research Lab Lu Sham UC-San Diego Paul Berman Luming Duan Roberto Merlin U. Mich.

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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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