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Optics and Quantum Optics with Semiconductor Nanostructures

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Optics and Quantum Optics with Semiconductor Nanostructures Optics and Quantum Optics with Semiconductor Nanostructures Stephan W. Koch Department of Physics, Philipps University, Marburg/Germany and Optical Sciences Center, University of Arizona, Tucson/AZ Overview • background: optics with atoms • semiclassical semiconductor optics • semiconductor quantum optics: “which way” experiments and light – matter entanglement Collaborators theory: Kira, Hoyer et al., Marburg Hader, Moloney et al., Tucson experiments: Gibbs/Khitrova et al., Tucson, Stolz et al., Rostock Marburg Marburg You do not really understand something unless you can explain it to your grandmother (Albert Einstein) From Atoms to Solids … atom 4 3 2 optical absorption/emission = transitions between atomic levels n=1 From Atoms to Solids … (2 - 5) * 10-8cm atom solid unit cell energy states 4 3 2 bands n=1 Bandstructure E possible energy values of electrons in crystal Eg k intrinsic semiconductor: full valence band(s), empty conduction band Realistic Bandstructure GaAs 6 4 effective mass approximation 2 0 ) V -2 e ( y -4 g r -6 e n -8 E -10 -12 L Γ X often: photon momentum typical carrier momentum perpendicular transitions, Energy Gap in Semiconductors conduction band > > ω2 ω1 valence band gap energy determines frequency and therefore color (wavelength) of absorbed and/or emitted light LEDs based on group-III nitride materials (Fraunhofer-Institut Freiburg) Bandgaps of III-V Alloys (300 K) 2.5 GaP 0.517 AlAs 2.0 0.620 ) ) n V AlSb o r e ( 0.775 c i 1.5 p m ( a GaAs g InP h y 1.00 t g g r n e 1.0 e l n e E v GaSb 1.55 a 2.0 w 0.5 InAs 5.0 InSb 10.0 0.0 5.4 5.6 5.8 6.0 6.2 6.4 6.6 lattice constant (Angstrom) Quasi-Two Dimensional Structure TEM picture: quantum well structure band gap at Γ-point (direct semiconductor) discrete states (z direction) and continuous bands (x-y plane) Semiconductors as Designer Materials ° quantum well = two-dimensional electronic mobility ° quantum wire = one-dimensional electronic mobility ° quantum dot = no (zero-dimensional) electronic mobility self organized quantum dots Interband Light-Matter Interaction: Semiclassical Theory classical Maxwell’s wave equation macroscopic optical polarization semiconductor: Bloch basis Coulomb interaction of charge carriers → quantum mechanical many-body problem of interacting Fermions Semiconductor Bloch Equations (SBE) field renormalization energy renormalization • nonlinearities: phase space fillinging, gap renormalization, Coulomb attraction • correlation effects: scattering, dephasing, screening, … Wannier Excitons c • 2 parabolic bands electron-hole pair interband Coulomb v attraction • wavefunction • relative motion (Wannier equation) Coulomb potential • hydrogen atom like solutions, Wannier excitons = quasi atoms (finite lifetime < nanoseconds) Wannier Excitons • linear absorption Elliott formula • linear optics: excitonic resonances • INTERACTION induced resonances, not just transitions between bands Exciton Saturation F. Jahnke, M. Kira, and S.W. Koch, Z. Physik B 104, 559 (1997) Born-Markov approximation Detuning saturation via excitation induced dephasing (EID) = Coulomb induced destructive interference between different Exciton Saturation F. Jahnke, M. Kira, and S.W. Koch, Z. Physik B 104, 559 (1997) Detuning n o i t p r o s b A • experiment: InGaAs/GaAs QW • Khitrova, Gibbs, Jahnke, Kira, Koch, Rev. Mod. Phys. 71, 1591 (1999) • EID first observed in 4-wave mixing, Wang et al. PRL 71, 1261 (1993) Lineshape Problem 0.2 ] m c 0.0 / 3 0 dephasing rate approximation 1 [ n -0.2 o i t p r full calculation o s -0.4 b A -0.6 -20 -10 0 10 Detuning • • gain of two-band bulk material • nondiagonal scattering contributions → lineshape modification, no absorption below the gap Optical Gain in Semiconductors: Theory and Experiment 10nm (9.2nm) InGaAs/AlGaAs ] m ) c / m 1 c [ / 3 n i 0 a 1 g x / ( n n o i o t i t p r p r o o s s b b a a Detuning N=1.6, 2.2, 2.5, 3.0*1012/cm2 exp: D. Bossert et al., theory: A. Girndt et al., Marburg 8nm InGaAs/AlGaAs 6.8 nm In0.4Ga0.5P/(Al0.5Ga0.5)In0.51P0.49 n i a g / n o i t p r o s b a Detuning Photon Energy (eV) Current 0-20mA… Density 0.6-3.0x1012cm-2 Courtesy of W.W. Chow, P.M. Smowton, P. Blood, exp: C. Ellmers et al., theory: A. Girndt et al. Marburg A. Grindt, F. Jahnke, and S.W. Koch Summary of Semiclassical Phenomena • quantitative understanding of interaction phenomena • strong experiment – theory interactions • predictive capability of theory CHALLENGES: • modified photonic environment (nano optics with nano structures) • optimized design for specific applications • nonequilibrium phenomena …. Selected References: • Haug/Koch, “Quantum Theory of the Optical and Electronic Properties of Semiconductors” 4th ed., World Scientific Publ. (2004) • Khitrova et al., Rev. Mod. Phys. 71, 1591 (1999) Quantized Light-Matter Interaction where is proportional to dipole matrix element and mode strength at the QW position Kira et al., Prog. Quantum. Electron. 23, 189 (1999) Spontaneous Emission from Quantum Wells + -|qz| - +|qz| recombination in electron-hole system no translational invariance perpendicular to QW no momentum conservation emission occurs simultaneously to left and right, i.e. with and Non Resonantly Excited Photoluminescence Experiments non resonant excitation of QW ? (weak excitation) incoherent (random) emission at exciton resonance BS different emission directions collected in interferometer setup Path 1 Path 2 measurement combines emission QW t to the left and right directions (less than one photon in interferometer) AP AP control of phase via delay Experiments (I) QW perpendicular BS Path 1 Path 2 QW t AP AP Experiments (II) QW tilted ? BS Path 1 Path 2 QW t AP AP Experiments (II) QW tilted BS Path 1 Path 2 QW t AP AP Experiments (III) Oct. 2003 no tilt 0.4 | clear interferences visible 0.2 Contrast if QW NOT tilted with tilt 0.0 -2 0 2 t (ps) intensity (a.u.) PL interferences vanish single beam if QW tilted intensities 0 20 40 60 80 100 CCD pixels Hoyer et al. PRL 93, 067401 (2004) Summary of Experimental Observations interferences seen in incoherent (single photon) emission , but intensity shows interferences interference shows strong directional sensitivity Summary of Experimental Observations interferences seen in incoherent (single photon) emission , but intensity shows interferences interference shows strong directional sensitivity effects predicted in Prog. Quantum. El. 23, 189 (1999) origin of effects: light-matter entanglement & which-way interferences Spontaneous Emission from Quantum Wells q|| + -|qz| - +|qz| electron-hole recombination simultaneous emission in and directions photon emission with same recoil momentum transferred to carrier system Explanation of Interferences (I) CASE A: Emission with same q|| q|| photon emission to the left many-body wavefunction with recoil emission to the right paths not distinguishable with respect to carrier system (i.e. no entanglement) Explanation of Interferences (II) q|| q|| variable phase BL BR interferometry: emission intensity IL to the left IR to the right interference INTERFERENCE can be seen Explanation of Entanglement (I) CASE B: Emission with different photons q|| q'|| many-body wavefunction with recoil emission to the left emission to the right paths identified by entanglement Explanation of Entanglement (II) q|| q'|| emission to the left (BL) und to the right (BR) is combined in detector D = BL +BR emissions intensity IL to the left IR to the right interference NO interference pattern due to entanglement Theory of Entanglement-Interferences semiconductor luminescence equations PRL 97, 5170 (1997) photon-assisted correlations photon correlations in the presence of Coulomb interaction QUESTION: WHAT HAPPENS IF WE TAKE MANY QUANTUM WELLS ? Theory of Entanglement-Interferences Predictions for n quantum wells with spacing d perfect interferences for Bragg no interferences for anti-Bragg (n-even) Prog. Quantum. El. 23, 189 (1999) /2 /4 1.0 I d 0.5 0.0 0 1 2 3 4 5 6 7 8 9 Number of QWs Entanglement-Interference Experiment (IV) interferences seen in multiple QW system with λ/2 spacing interferences vanish in multiple QW system with λ/4 spacing λ/4 spacing leads to complete randomizing of emission to the left and to the right confirmation of theoretical predictions Summary of Entanglement-Interferences incoherent emission to the left and to the right are entangled with the many-body carrier system emission to the left and to the right with same q|| is not entangled emission to the left and to the right with same q|| is entangled description of entanglement via photon- carrier and photon-photon correlations of the type: more in: Hoyer et al. PRL 93, 067401 (2004) Summary • variety of novel quantum optical effects in semiconductors • strong experiment – theory interactions MANY CHALLENGES: • optimization and application of non-classical properties (quantum information science, …) • modified photonic environment (phot. x-tals, …) • role of incoherent excitons, biexcitons, …. Selected References: • Haug/Koch, “Quantum Theory of the Optical and Electronic Properties of Semiconductors” 4th ed., World Scientific Publ. (2004) • Khitrova et al., Rev. Mod. Phys. 71, 1591 (1999) • Kira et al., Prog. Quantum. Electron. 23, 189 (1999).
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