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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> |0> Optical Bloch Vector Qubit |0> Semiconductor Quantum Coherence Engineering Successful coherent optical manipulation of the optical Bloch vector necessary to manipulate the spin vector |1> Electronic Spin Qubit The electron spin vector AlGaAs (GaAs) GaAs (InAs) AlGaAs (GaAs) |0> |1> The electron spin vector AlGaAs (GaAs) GaAs (InAs) AlGaAs (GaAs) l |0> |1> The electron spin vector AlGaAs (GaAs) GaAs (InAs) AlGaAs (GaAs) l |0> |1> The electron spin vector Long coherence time AlGaAs (GaAs) GaAs (InAs) AlGaAs (GaAs) |0> |1> 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 gfactor and decays with time. Single Electron Spin Coherence: Single Charged Exciton Raman Quantum Beats Charged Exciton System X- Neutral Exciton System CNOS (a. u.) G G Ensemble Charged Excitons Single Neutral Exciton X Phys. Rev. Lett. - 2005 500 1000 1500 2000 2500 Delay (ps) hgs (meV) G 0 G T2* >10 nsec at B=0 Anomalous Variation of Beat Amplitude and Phase Standard Theory (a) • Plot of beat amplitude and phase as a function of the splitting. (b) Anomalous Variation of Beat Amplitude and Phase Standard Theory (a) • Plot of beat amplitude and phase as 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 phase as a function of the splitting. Phys. Rev. Lett. - 2005 Two-Photon Spin Rabi Trion Laser Pulse Trion ˆ X ˆ Rotations with a nd Y Zˆ Precession y Initialization x y x 0 2 0 Rx Rz R x 0 2 2 R y R z R x R z 2 2 Phase Gate - Demonstration of Geometric Phase (Aharonov & Anandan) Tz Optical Control of Trion Optical Bloch Vector Z Z Optical Control of Spin Bloch Vector Fo r 0 the state v ecto r fo r th e sp in , th e trio n 2 xˆ rotatio n transfo rm s Uˆ 0 1 ˆ w here U 0 0 to 0 ˆ and U C z C z 1 C z C z Coherent Generation of a Geometrical Phase 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 The Mollow Absorption Spectrum, AC Stark effect, and Autler Townes Splitting: Gain without Inversion Dressed State Picture 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 inversion The 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). Autler-Townes Splitting in a Single Quantum Dot Dressed state Picture |1> |2> 30 Io 20 Io 10 Io 5 Io 0 Io 321594 321591 Probe Frequency (GHz) |3> |b(N)> |a(N)> |b(N-1)> 40 Io Rabi Splitting (GHz) Absorption (a.u.) Probe Abosorption as a Function of the Pump Intensity (on resonance) Pump intensity (Io=0.03w/cm2) 50 Io |a(N-1)> 1 0 0 4 Pump Field Strength(1 / Io 8 ) } WR } WR Probe Absorption as a Function of Pump Frequency Detuning Theoretical Plot Experimental Data Pump Detuning (GHz) Absorption (a.u.) Pump Intensity 30Io 1.7 0.6 0.3 0.0 -0.3 -0.6 -1.7 321591 321594 Probe Frequency (GHz) -5.0 -2.5 0 2.5 5.0 Probe Detuning Gunits Thy Physical Model of the Dark State Experiment |T-> |T-> |T+> H1 Wp V2 V1 H1 V2 Wd H2 |X+> |X+> |X-> |X-> Bx D arkstate DT/T (10-4) The Quartet Transition Pattern V1 H1 H2 V2 1 W p X Wd X W 2p W 2d Theoretical plot of the CPT including electron spin dephasing B=1.32 T 0 -8 0 Laser Detuning (GHz) 8 -3 -3 0 Laser Detuning (G units) The Observation of the Coherent Population Trapping of an Electron Spin 1 0 1 The probe absorption spectrum scanning across transition H1 Wd/2p(GHz) 1.38 1.26 |T-> DT/T (10-4) 0 1 0.83 p 0 1 0.78 V2 d |X+> 0 1 H1 |X-> Solide lines are the fits, which yield electron spin T2* of 4 ns. 0.56 0 0 0 -5 0 Probe Detuning (GHz) 5 Nature - Physics, 2008 Ωpump |X+> Ωprobe Relative Absorption x 10 ehe |T-> -4 Probing Dynamic Nuclear Spin Polarization by Dark State Spectroscopy 3 Probe absorption spectra by varying the laser scanforward rate Black: Red: backward 2 1 e e |X-> 0 319074 319077 Probe Frequency (GHz) Broadened & rounded trion peak Scan direction dependence: hysteresis & dark state shift Large trion excitation (absorption) is favored Dynamic control of nuclear field (Dark state position reflect Zeeman Splitting) Time Dependent Probe Absorption Spectrum B=2.6 T ehe |T-> Ωpump |X+> e Ωprobe e |X-> Time Dependent Probe Absorption Spectrum Laser Partialfrequency backwardparked scan here ehe |T-> Ωpump |X+> e Ωprobe e |X-> Stable configuration: maximum trion excitation (absorption) Time Dependent Probe Absorption Spectrum Relative Abs. x 10 -4 (e) (f) L R 1.5 R L D 0 319083 319089 Probe Frequency (GHz) ehe |T-> Ωpump |X+> e Ωprobe e |X-> D 0 300 Time (S) 600 Dark State is a meta-stable state for nuclear field Trion Induced Dynamic Nuclear Spin Polarization anisotropic hyperfine from hole |T> Z Sh Ik nuclear Zeeman << trion linewidth Flip up rate: Flip down rate: f Z h S I k f Z h k S I i i 2 t ,i t , f t t 2 t ,i t , f t t Whichever increases t dominates! Nuclear field dynamics: d dt DNP rate g N a t t t t Dynamic Nuclear Spin Polarization Induced Spectral Servo Two photon detuning Nuclear field Absorption Probe laser frequency Probe detuning ( = 2-ph detuning - nuclear field ) Numerical Simulation Results : Slow Scan Experime nt Theor y Nuclear field dynamics: d dt g N a t t Parameters: g N 1.5 s 1 a 2.4 (M H z) 3 Nuclear T1 ~ sec Ah ~ 3 m eV Numerical Simulation Results : fast Scan Experime nt Theor y Parameters: g N 0.4 s 1 a 50 (M H z) 3 Nuclear T1 ~ sec Ah ~ 20 m eV Microscopic theory: Weng Yang et al., Q14.00002; http://arxiv.org/ab Nuclear Field Locking Effect Metastable configurations Stable configurations for DNP t DNP rate: t t pum p Two-photon detuning Nuclear field locked to stable value W pum p 2 prob ( pum p probe ) Dynamic Nuclear Spin Feedback Suppresses Fluctuations DNP by trion Nuclear field self-focus to stable value Nuclear field unstable against DNP Single QD arbitrary nuclear spin config CW laser excitation Medium trion excitation 2-photon resonance shifts C. Latta et al., Nature Phys. 5, 758 (2009) Maximum trion excitation Nuclear spin fluctuation Stable-config nuclear field locked to frequencies Suppression of Nuclear Field Inhomogeneous Broadening More enhancement on spin T2* with larger pump strength larger pump larger slope in t t tighter locking 0 (b) Pump intensity Absorption 40 90 70 60 20 Slope (a.u.) – Probe detuning spin T2* peak-to-dip ratio -0.5 0 1.5 0.5 1.0 Pump Rabi (GHz) Suppression of Nuclear Field Inhomogeneous Broadening Thermal value – Spin decoherence rate extracted from dip-to-peak ratio – T2* extended well above thermal value Deficiency: locking position changes with probe scan – ehe |T-> Ωpump |X+> e Ωprobe e |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., Nature 59, 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