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Hui Deng Stephan Gotzinger David Press Yoshihisa Yamamoto

Quantum Phase Transition. in Exciton Polariton Systems. Robin Huang Hui Cao Francesco Tassone Gregor Weihs Stanley Pau (Former members). Hui Deng Stephan Gotzinger David Press Yoshihisa Yamamoto. Quantum Entanglement Project, SORST, JST E.L. Ginzton Laboratory, Stanford University

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Hui Deng Stephan Gotzinger David Press Yoshihisa Yamamoto

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  1. Quantum Phase Transition in Exciton Polariton Systems Robin Huang Hui Cao Francesco Tassone Gregor Weihs Stanley Pau (Former members) Hui Deng Stephan Gotzinger David Press Yoshihisa Yamamoto Quantum Entanglement Project, SORST, JST E.L. Ginzton Laboratory, Stanford University and National Institute of Informatics BaCa Tec-Summer School, Würzburg, June 26 – July 01, 2005

  2. Outline • Microcavity exciton polaritons • Polariton BEC vs. exciton BEC • Non-equilibrium, quasi-equilibrium and thermal equilibrium BEC • Final state stimulation in exciton-exciton scattering processes • Amplification of exciton polaritons • Dynamic condensation (lasing) of exciton polaritons in CdTe and GaAs MQW-microcavities • Polariton population per state N(k//) • Effective mass • Relaxation time tpolariton vs. lifetime t0 • Momentum and real space distributions • Chemical potential and polariton temperature • Second order coherence function • Transverse confinement of exciton polaritons

  3. Microcavity Exciton Polaritons

  4. Wannier-Mott Excitons in Quantum Wells Momentum eigenstate – A valence electron with and is excited to a conduction electron with and Exciton state electron mode index envelope function in k-space plane wave hole momentum eigenstate

  5. QW Excitons and Microcavity Polaritons Exciton creation operator Composite boson in the 1st order approximation Exciton Hamiltonian Hamiltonian of Coupled Cavity Photon-QW Exciton Diagonalize with polariton operator: Rabi-splitting: when cavity photon on resonance with bare exciton

  6. r’B 1 or 2? r’A rB 1 or 2? rA e1 r’A h1 rA e2 r’B h2 rB e2 r’A h1rA e1r’B h2rB y ~ e1 r’A h2rA e2 r’B h1 rB e2 r’A h2 rA e1 r’B h1 rB + 1  = + ex1 rA ex2rB ex2 rA ex1rB 2 Exciton as a Composite Boson Two-Exciton State: Spatial Correlation induced by Coulomb Interaction. A composite particle (exciton) behaves as a “massive boson”.

  7. E Microcavity photon (mph ~ 10-5 me) Upper plariton QW exciton (mexc ~ 10-1 me) Rabi splitting k // Lower polariton wexc0 = wph0 (meff ~ 2 mph) Exciton Polariton Dispersion, Normal Mode Splitting and Oscillation Polariton dispersion curves osc~ 1 THz ～ UP LP C. Weisbuch, et al. Phys. Rev. Lett. 69, 3314 (1992) S. Jiang et al., Appl. Phys. Lett. 73, 3031 (1998)

  8. Atom Cavity QED vs. Semiconductor Cavity QED single-atom cavity QED many-atom cavity QED exciton cavity QED QWs ensemble of atoms single atom eigenstate of collective angular momentum effective # of atomic oscillators: d: atomic dipole moment V: optical mode volume S: cavity mode area, ~2mm f : Bohr radius, ~100A (J =N/2, N: # of atoms)

  9. Non-equilibrium Polariton Laser vs. Equilibrium Polariton BEC

  10. exciton-phonon scattering exciton-exciton scattering polariton decay leakage photon k// k// k// equilibrium is established with a lattice at tlattice equilibrium is established within polaritons at tpolariton polariton decay by leakage of photonic component at t0 Dynamic vs. Equilibrium Condensation Polariton decay vs. Two relaxation processes

  11. higher critical temperature lower particle density Polariton BEC vs. Exciton BEC Enemies of exciton BEC: • Dissociation of excitons (screening, phase space filling) • Disorder, localization and inhomogeneous broadening Advantage of Polariton BEC • Extended phase coherence reinforced by a cavity field suppressed localization, disorder and inhomogeneous broadening • Light effective mass by dressing a cavity field mpolariton ~ 10-4mexciton ~10-7mH-atom • Enhanced binding energy/decreased Bohr radius in the very-strong-coupling regime [J. B. Khurgin et. al., Solid State Commun.117, 307 (2002)] suppressed dissociation of excitons • Photonic component out-coupling from the cavity with k conservation in contrast to spontaneous decay of an un-dressed exciton direct experimental access to internal polariton population

  12. Bosonic Final State Stimulation

  13. T1/2 T1/2 smaller spitting Blue shift U1 Exciton LP UP Exciton-polariton Nonlinear Interaction same spins opposite spins • M. Kuwata-Gonokami et al., Phys. Rev. Lett. 79, 1341 (1997) • S. Schmitt-Rink, et al., Phys. Rev. B 32, 6601 (1985) • J. Fernandez-Rossier et al., Phys. Rev. B 54, 11582 (1996) • J. Inoue, et al., Phys. Rev. B 61, 2863 (2000)

  14. Probe Energy (theory) (experiment) (Fermionic exchange + phase space filling) (theory) (experiment) (Fermionic exchange) Measurement of Exciton Interaction – Pump-probe experiments with optical heterodyne detection Experimental results Experimental setup Excitons with same spins

  15. Idea:UP=background free measurement window leakage from cavity phonon scattering exciton-exciton scattering Spontaneous scattering Stimulated scattering exc. beam exc. beam

  16. nexc = 1.5109 cm-2 1.2 0.54 Observation of Bosonic Final State Stimulationin exciton-exciton scattering in a GaAs SQW-Microcavity • Upper-polariton emission decay time ~ 95 ps • bottle-neck polariton decay time ~ 190 ps • R. Huang et al., Phys. Rev. B 61, R7854 (2000)

  17. Amplification of Exciton Polaritons—Probing Quantum Degeneracy

  18. cavity photon polariton Strong Coupling to Weak Coupling Transition Normal mode splitting at resonance (wc=wexc) (weak coupling) Exciton densities:A: 1.1108 cm-2 , B: 1.1109 cm-2 , C: 5.5109 cm-2 , D: 1.11010 cm-2 , E: 2.01010 cm-2 , F: 2.71010 cm-2 G: 4.41010 cm-2 , H: 6.61010 cm-2 , I: 1.11010 cm-2 • S. Jiang et al., Appl. Phys. Lett. 73, 3031 (1998)

  19. extended phase coherence Obstacles and Tricks for Polariton Lasing 1. Exciton localization and inhomogeneous broadening QW excitons are easily trapped by a local minimum of a QW potential fluctuation. Dressing QW excitons with a microcavity vacuum field 2. Exciton saturation Strong coupling to weak coupling transition when an exciton decoherence rate exceeds a normal mode splitting. Use of multiple QWs Comparison of Exciton Properties CdTe GaAs Use of excitons with small Bohr radius Bohr Radius in QW(A) 90 28 Binding Energy (meV) 10 25 Saturation Density (1010 cm-2) 4 50

  20. Bottleneck Exciton decay rate = 120 ps Bottleneck effect Gain =15 Gain decay rate = 60 ps Bare Exciton k// = 0:LP Observation of Stimulated Scattering Gainin a CdTe DQW-Microcavity • A gain is provided by two-body exciton-exciton scattering. • A CdTe QW exciton survives at higher densities due to small Bohr radius. • R. Huang et al., Phys. Rev. B 65, 165314 (2002)

  21. High Gain Regime exciton-phonon scattering exciton-exciton scattering A. Imamoglu et al. Phys. Rev. A 53, 4250 (1996) Rate equation solutions F. Tassone et al., Phys. Rev. B 59, 10830 (1999) Nexc=3.4x106 Gain =23 Nexc=1.6x106 Gain =5.4 Probe (mW/cm2) Circles: 2104 Squares: 900 Nexc = 0.41x106 Gain = 0.34 Low Gain Regime Amplification of Polaritonsin a CdTe DQW-Microcavity • R. Huang et al., Phys. Rev. B 65, 165314 (2002)

  22. Dynamic Condensation (Lasing) of Exciton Polaritons Experimental evidence: Spontaneous build-up of ground state population Polariton effective mass Spontaneous spin polarization Second order coherence Real space distribution (spontaneous localization) Momentum space distribution (BE) (chemical potential and temperature)

  23. Polariton Lasing vs. Photon Lasing • standard photon • laser • polariton laser lasing threshold observed without electronic population inversion • H. Deng et al., Proc. Natl. Acad. Sci., 100, 15318 (2003)

  24. Polariton Laser 1.62 P/P =0.5 Photon Laser th 1.618 photon Energy (eV) 1.616 polariton 1.614 1.612 -2 0 2 k (10 4 cm -1 ) || 1.62 1.654 P/P =7.6 photon laser th P/P' =3 1.618 1.652 th Energy (eV) 1.616 1.65 Energy (eV) 1.614 1.648 polariton mass measured to be ~ twice the photon mass strong-coupling preserved above threshold 1.612 1.646 -2 0 2 -2 0 2 k (10 4 cm -1 ) k (10 4 cm -1 ) || || Effective Mass Measurement: Polariton and Photon Dispersions • H. Deng et al., Proc. Natl. Acad. Sci., 100, 15318 (2003)

  25. Spontaneous Spin Polarization

  26. Second Order Coherence (Hanbury Brown-Twiss experiment) single-mode thermal state Poissonian light single-mode coherent state • The on-set of bosonic final state stimulation manifests itself by increased g(2)(0). • A gradual decrease in g(2)(0) suggests non-standard macroscopic coherence. • H. Deng et al., Science 298, 199 (2002)

  27. P/Pth = 1.5 polariton photon photon laser fitted spot size: 26 mm polariton laser suppressed ‘expansion’ Real Space Distribution below threshold broad Gaussian above threshold steep central peak

  28. Momentum Space Distribution P/Pth =1.5 P/Pth =0.6 resolution Exp. Data BE Fit MB Fit • The k-distribution is in agreement with BE distribution, except for the population at k11=0. • H. Deng et al., Proc. Natl. Acad. Sci., 100, 15318 (2003) • J．Keeling et al., Phys. Rev. Lett. 93, 226403 (2004)

  29. BEC threshold Tpolariton >> Tlattice Chemical Potential and Effective Temperature fitted (normalized) chemical potential fitted polariton temperature • chemical potential m ~ -kBT at threshold • chemical potential m zero above threshold • H. Deng et al., Proc. Natl. Acad. Sci., 100, 15318 (2003)

  30. From Non-equilibrium Polariton Laser To Equilibrium Polariton BEC

  31. Non- • equilibrium • Equilibrium Relaxation Rate vs. Decay Rate of Polaritons

  32. Future Prospects Practical issues: Room temperature polariton laser (GaN（ＮＴＴ）, ZnSe（Ｐａｄｅｒｂｏｒｎ）, ·····) Transverse confinement by a cavity trap (V~10meV for 12 GaAs MQW) Very low-threshold and very fast (~psec) coherent light source Transverse confinement and long polariton lifetime by a 2D photonic crystal or microdisk cavity Theoretical issues: Bogoliubov theory predicting a squeezed ground state • F. Tassone et al., Phys.Rev.B59,10830(1999) • F.P. Laussy et al., Phys. Rev. Lett. 93, 016402 (2004) phase-locked • BEC  BCS phase transition • Impurity bound exciton in homogeneous bulk • (F. M. Marchetti, et al., arXiv:cond-mat/0405295) • Acknowledgement • Atac Imamoglu, David Snoke, Jacqueline Bloch, Regis Andres, Hiromi Ezaki

  33. A. Forchel (Würzburg) Optical Trapping of Microcavity Polaritons

  34. BEC-BCS Phase Transition UP gap 4g|l| normal state m condensate m Coherent light LP • thick lines: quasi-particle excitations in the condensed phase • upper line: creating a quasi-particle • lower line: absorbing a quasi-particle • M.H. Szymanska et al., Solid State Comm. 124, 103 (2002)

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