Polariton and photon condensates with organic molecules

Transcription

1 Polariton and photon condensates with organic molecules Jonathan Keeling University of St Andrews 6 YEARS Telluride, July 213 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

2 Polariton and photon condensates with organic molecules: The Dicke-Holstein model Jonathan Keeling University of St Andrews 6 YEARS Telluride, July 213 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

3 Coherent states of matter and light Atomic BEC T 1 7 K Polariton Condensate T 2K Cavity Quantum Wells [Kasprzak et al. Nature, 6] [Anderson et al. Science 95] Photon Condensate T 3K Laser T?, <, Superradiance transition T κ κ z x [Klaers et al. Nature, 1] Jonathan Keeling Pump [Baumann et al. Nature, 1] Polariton and photon condensates Telluride, July / 37

4 Textbook BEC Non-interacting viewpoint BE distribution: µ < ω ( ) 2/d T c = 2π 2 n m Temperature Normal ξ d Density BEC Interacting approach (WIDBG) H = k ω k ψ k ψ k + g 2V Occupation k,k,q Density of states Energy ψ k+q ψ k q ψ k+qψ k Decreasing T Mean field: ψ 2 = (µ ω )/V Fluctuations deplete condensate, vanishes at T > Tc Jonathan Keeling Polariton and photon condensates Telluride, July / 37

5 Textbook BEC Non-interacting viewpoint BE distribution: µ < ω ( ) 2/d T c = 2π 2 n m Temperature Normal ξ d Density BEC Interacting approach (WIDBG) H = k ω k ψ k ψ k + g 2V Occupation k,k,q Density of states Energy ψ k+q ψ k q ψ k+qψ k Decreasing T Mean field: ψ 2 = (µ ω )/V Fluctuations deplete condensate, vanishes at T > Tc Jonathan Keeling Polariton and photon condensates Telluride, July / 37

6 Textbook BEC Non-interacting viewpoint BE distribution: µ < ω ( ) 2/d T c = 2π 2 n m Temperature Normal ξ d Density BEC Interacting approach (WIDBG) H = k ω k ψ k ψ k + g 2V Occupation k,k,q Density of states Energy ψ k+q ψ k q ψ k+qψ k Decreasing T Mean field: ψ 2 = (µ ω )/V Fluctuations deplete condensate, vanishes at T > Tc Jonathan Keeling Polariton and photon condensates Telluride, July / 37

7 Textbook Laser: Maxwell Bloch equations H = ω ψ ψ + ɛ α Sα z + g α,k (ψs α + + ψ Sα α γn Maxwell-Bloch eqns: P = i S, N = 2 S z g t ψ = iω ψ κψ + α g αp α ) γn κ t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) Jonathan Keeling Polariton and photon condensates Telluride, July / 37

8 Textbook Laser: Maxwell Bloch equations H = ω ψ ψ + ɛ α Sα z + g α,k (ψs α + + ψ Sα α γn Maxwell-Bloch eqns: P = i S, N = 2 S z g t ψ = iω ψ κψ + α g αp α ) γn κ t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) 2γκ/g 2 N α bg.dat N α ψ 2 ψ 2 ψ 2 > if N g 2 > 2γκ N 2γκ/g 2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

9 Textbook Dicke-Hepp-Lieb superradiance H = ωψ ψ + α ( ) ɛsα z + g ψ Sα + ψs α + Coherent state: Ψ e λψ +ηs + Ω Small g, min at λ, η = [Hepp, Lieb, Ann. Phys. 73] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

10 Textbook Dicke-Hepp-Lieb superradiance H = ωψ ψ + α ( ) ɛsα z + g ψ Sα + ψs α + Coherent state: Ψ e λψ +ηs + Ω Small g, min at λ, η = [Hepp, Lieb, Ann. Phys. 73] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

11 Textbook Dicke-Hepp-Lieb superradiance H = ωψ ψ + α ( ) ɛsα z + g ψ Sα + ψs α + Coherent state: Ψ e λψ +ηs + Ω Small g, min at λ, η = Spontaneous polarisation if: Ng 2 > ωɛ [Hepp, Lieb, Ann. Phys. 73] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

12 Textbook Dicke-Hepp-Lieb superradiance H = ωψ ψ + α ( ) ɛsα z + g ψ Sα + ψs α + ω SR Coherent state: Ψ e λψ +ηs + Ω Small g, min at λ, η = Spontaneous polarisation if: Ng 2 > ωɛ ḡ N [Hepp, Lieb, Ann. Phys. 73] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

13 Outline 1 Introduction Polariton condensation Condensation, superradiance, lasing Condensation vs superradiance transition Non-equilibrium condensation vs lasing 2 Room temperature condensates: Organic polaritons Dicke phase diagram with phonons Condensation of phonon replicas? Ultra-strong phonon coupling? 3 Room temperature condensates: Photons Lasing model and thermalisation Critical properties Jonathan Keeling Polariton and photon condensates Telluride, July / 37

14 Acknowledgements GROUP: COLLABORATORS: Szymanska (Warwick), Reja (Cam.), Littlewood (ANL) FUNDING: Jonathan Keeling Polariton and photon condensates Telluride, July / 37

15 Microcavity polaritons Cavity Quantum Wells Jonathan Keeling Polariton and photon condensates Telluride, July / 37

16 Microcavity polaritons Cavity Quantum Wells Cavity photons: ω k = ω 2 + c2 k 2 ω + k 2 /2m m 1 4 m e Energy n=4 n=3 n=2 n=1 Bulk Momentum Jonathan Keeling Polariton and photon condensates Telluride, July / 37

17 Microcavity polaritons Cavity Quantum Wells Cavity photons: ω k = ω 2 + c2 k 2 ω + k 2 /2m m 1 4 m e Energy Photon Exciton In plane momentum Jonathan Keeling Polariton and photon condensates Telluride, July / 37

18 Microcavity polaritons Cavity Quantum Wells Cavity photons: ω k = ω 2 + c2 k 2 ω + k 2 /2m m 1 4 m e Energy Photon Exciton In plane momentum Jonathan Keeling Polariton and photon condensates Telluride, July / 37

19 Microcavity polaritons θ Cavity Quantum Wells Cavity Cavity photons: ω k = ω 2 + c2 k 2 ω + k 2 /2m m 1 4 m e Energy Photon Exciton In plane momentum Jonathan Keeling Polariton and photon condensates Telluride, July / 37

20 Polariton experiments: occupation and coherence [Kasprzak, et al. Nature, 6] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

21 Polariton experiments: occupation and coherence Sample Coherence map: CCD Beam Splitter Tunable Delay + = Retroreflector [Kasprzak, et al. Nature, 6] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

22 (Some) other polariton condensation experiments Quantised vortices [Lagoudakis et al. Nat. Phys. 8. Science 9, PRL 1; Sanvitto et al. Nat. Phys. 1; Roumpos et al. Nat. Phys. 1 ] Josephson oscillations [Lagoudakis et al. PRL 1] = + Pattern formation/hydrodynamics [Amo et al. Science 11, Nature 9; Wertz et al. Nat. Phys 1] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

23 Non-equilibrium condensation vs lasing 1 Introduction Polariton condensation Condensation, superradiance, lasing Condensation vs superradiance transition Non-equilibrium condensation vs lasing 2 Room temperature condensates: Organic polaritons Dicke phase diagram with phonons Condensation of phonon replicas? Ultra-strong phonon coupling? 3 Room temperature condensates: Photons Lasing model and thermalisation Critical properties Jonathan Keeling Polariton and photon condensates Telluride, July / 37

24 Lasing-condensation crossover model Use model that can show lasing and condensation: γn g γn κ Energy Photon Exciton In plane momentum Jonathan Keeling Polariton and photon condensates Telluride, July / 37

25 Lasing-condensation crossover model Use model that can show lasing and condensation: γn g γn κ Energy Photon Exciton In plane momentum Dicke model: [ ɛs z α + g α,k ψ k S + α + H.c. ] H sys = k ω k ψ k ψ k + α Jonathan Keeling Polariton and photon condensates Telluride, July / 37

26 Dicke-Hepp-Lieb superradiance and modes H = ωψ ψ + ɛs z + g (ψ S + ψs +) Spontaneous polarisation if: Ng 2 > ωɛ ω SR Normal state, S z = N/2 + B B H = ωψ ψ + ɛb B + g N (ψ B + ψb ) Excitation cost E: (E ω)(e ɛ) = g 2 N ḡ N [Hepp, Lieb, Ann. Phys. 73] Transition when E = Jonathan Keeling Polariton and photon condensates Telluride, July / 37

27 Dicke-Hepp-Lieb superradiance and modes H = ωψ ψ + ɛs z + g (ψ S + ψs +) Spontaneous polarisation if: Ng 2 > ωɛ ω SR Normal state, S z = N/2 + B B H = ωψ ψ + ɛb B + g N (ψ B + ψb ) Excitation cost E: (E ω)(e ɛ) = g 2 N ḡ N [Hepp, Lieb, Ann. Phys. 73] Transition when E = Jonathan Keeling Polariton and photon condensates Telluride, July / 37

28 Dicke-Hepp-Lieb superradiance and modes H = ωψ ψ + ɛs z + g (ψ S + ψs +) Spontaneous polarisation if: Ng 2 > ωɛ ω SR Normal state, S z = N/2 + B B H = ωψ ψ + ɛb B + g N (ψ B + ψb ) Excitation cost E: (E ω)(e ɛ) = g 2 N ḡ N [Hepp, Lieb, Ann. Phys. 73] Transition when E = Jonathan Keeling Polariton and photon condensates Telluride, July / 37

29 Dicke-Hepp-Lieb superradiance and modes H = ωψ ψ + ɛs z + g (ψ S + ψs +) Spontaneous polarisation if: Ng 2 > ωɛ ω SR Normal state, S z = N/2 + B B H = ωψ ψ + ɛb B + g N (ψ B + ψb ) Excitation cost E: (E ω)(e ɛ) = g 2 N ḡ N [Hepp, Lieb, Ann. Phys. 73] Transition when E = Jonathan Keeling Polariton and photon condensates Telluride, July / 37

30 Grand canonical ensemble Grand canonical ensemble: If H H µ(s z + ψ ψ), need only: g 2 N > (ω µ) ɛ µ Fix density / fix µ > pumping Transition at: g 2 N > (ω µ)(ɛ µ) µ hits lowest mode [Eastham and Littlewood, PRB 1] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

31 Grand canonical ensemble Grand canonical ensemble: If H H µ(s z + ψ ψ), need only: g 2 N > (ω µ) ɛ µ Fix density / fix µ > pumping Transition at: g 2 N > (ω µ)(ɛ µ) µ hits lowest mode [Eastham and Littlewood, PRB 1] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

32 Grand canonical ensemble Grand canonical ensemble: If H H µ(s z + ψ ψ), need only: g 2 N > (ω µ) ɛ µ Fix density / fix µ > pumping (µ-ω)/g 2 1 unstable -1 SR (ε - ω)/g [Eastham and Littlewood, PRB 1] Transition at: g 2 N > (ω µ)(ɛ µ) µ hits lowest mode Jonathan Keeling Polariton and photon condensates Telluride, July / 37

33 Grand canonical Dicke, finite temperature Finite temperature: Ng 2 tanh(βɛ) > ωɛ ω SR = T SR ḡ N ḡ N [Hepp, Lieb, Ann. Phys. 73] With chemical potential Ng 2 tanh(β(ɛ µ)) > (ω µ)(ɛ µ) Jonathan Keeling Polariton and photon condensates Telluride, July / 37

34 Grand canonical Dicke, finite temperature Finite temperature: Ng 2 tanh(βɛ) > ωɛ ω SR = T SR ḡ N ḡ N [Hepp, Lieb, Ann. Phys. 73] With chemical potential Ng 2 tanh(β(ɛ µ)) > (ω µ)(ɛ µ) (µ-ω)/g unstable T c /g 1-1 SR -1-2 = (µ-ω)/g (ε - ω)/g Jonathan Keeling (ε - ω)/g Polariton and photon condensates Telluride, July / 37

35 Polariton model and equilibrium results Localised excitons, propagating photons H µn = (ω k µ)ψ k ψ k + (ɛ α µ)sα z + g α,k ψ k S α + + H.c. k α Self-consistent polarisation and field (ω µ) ψ = α g 2 αψ 2E α tanh (βe α ), E α 2 = ( ɛα µ 2 ) 2 + g 2 α ψ 2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

36 Polariton model and equilibrium results Localised excitons, propagating photons H µn = (ω k µ)ψ k ψ k + (ɛ α µ)sα z + g α,k ψ k S α + + H.c. k α Self-consistent polarisation and field (ω µ) ψ = α g 2 αψ 2E α tanh (βe α ), E α 2 = ( ɛα µ 2 ) 2 + g 2 α ψ 2 Phase diagram: 4 non-condensed 3 condensed T (K) n (cm) -2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

37 Polariton model and equilibrium results Localised excitons, propagating photons H µn = (ω k µ)ψ k ψ k + (ɛ α µ)sα z + g α,k ψ k S α + + H.c. k α Self-consistent polarisation and field (ω µ) ψ = α g 2 αψ 2E α tanh (βe α ), E α 2 = ( ɛα µ 2 ) 2 + g 2 α ψ 2 Phase diagram: 4 non-condensed 3 condensed T (K) n (cm) -2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

38 Polariton model and equilibrium results Localised excitons, propagating photons H µn = (ω k µ)ψ k ψ k + (ɛ α µ)sα z + g α,k ψ k S α + + H.c. k α Self-consistent polarisation and field (ω µ) ψ = α g 2 αψ 2E α tanh (βe α ), E α 2 = ( ɛα µ 2 ) 2 + g 2 α ψ 2 Phase diagram: 4 non-condensed 3 condensed T (K) n (cm) -2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

39 Simple Laser: Maxwell Bloch equations H = ωψ ψ + ) ɛ α Sα z + g α,k (ψs α + + ψ Sα α γn g γn κ Maxwell-Bloch eqns: P = i S, N = 2 S z t ψ = iωψ κψ + α g αp α 2γκ/g 2 N α bg.dat N α ψ 2 ψ 2 t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) N 2γκ/g 2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

40 Simple Laser: Maxwell Bloch equations H = ωψ ψ + ) ɛ α Sα z + g α,k (ψs α + + ψ Sα α γn g γn κ Maxwell-Bloch eqns: P = i S, N = 2 S z 2γκ/g 2 bg.dat N α ψ 2 t ψ = iωψ κψ + α g αp α N α ψ 2 t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) N 2γκ/g Absorption N Strong coupling. κ, γ < g n Inversion causes collapse before g 2 N = 2γκ -1 1 Energy/g Jonathan Keeling Polariton and photon condensates Telluride, July / 37

41 Simple Laser: Maxwell Bloch equations H = ωψ ψ + ) ɛ α Sα z + g α,k (ψs α + + ψ Sα α γn g γn κ Maxwell-Bloch eqns: P = i S, N = 2 S z 2γκ/g 2 bg.dat N α ψ 2 t ψ = iωψ κψ + α g αp α N α ψ 2 t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) N 2γκ/g Absorption N Strong coupling. κ, γ < g n Inversion causes collapse before g 2 N = 2γκ -1 1 Energy/g Jonathan Keeling Polariton and photon condensates Telluride, July / 37

42 Simple Laser: Maxwell Bloch equations H = ωψ ψ + ) ɛ α Sα z + g α,k (ψs α + + ψ Sα α γn g γn κ Maxwell-Bloch eqns: P = i S, N = 2 S z 2γκ/g 2 bg.dat N α ψ 2 t ψ = iωψ κψ + α g αp α N α ψ 2 t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) N 2γκ/g Absorption N Strong coupling. κ, γ < g n Inversion causes collapse before g 2 N = 2γκ -1 1 Energy/g Jonathan Keeling Polariton and photon condensates Telluride, July / 37

43 Poles of Retarded Green s function and gain [ 1 D (ν)] R g 2 N = ν ωk + iκ + ν 2ɛ + i2γ Jonathan Keeling Polariton and photon condensates Telluride, July / 37

44 Poles of Retarded Green s function and gain [ 1 D (ν)] R g 2 N = ν ωk + iκ + ν 2ɛ + i2γ = A(ν) + ib(ν) 1-1 (a) A(ν) B(ν) Absorption N Energy/g -1 1 Energy/g Jonathan Keeling Polariton and photon condensates Telluride, July / 37

45 Poles of Retarded Green s function and gain [ 1 D (ν)] R g 2 N = ν ωk + iκ + ν 2ɛ + i2γ = A(ν) + ib(ν) 1-1 (a) A(ν) B(ν) Absorption N (b) A(ν) B(ν) -1 1 Energy/g -1 1 Energy/g -1 1 Energy/g Jonathan Keeling Polariton and photon condensates Telluride, July / 37

46 Poles of Retarded Green s function and gain [ 1 D (ν)] R g 2 N = ν ωk + iκ + ν 2ɛ + i2γ = A(ν) + ib(ν) 1-1 Laser: 2 (a) -1 1 (a) Energy/g A(ν) B(ν) (b) Absorption Energy/g N (b) -1 1 Energy/g A(ν) B(ν) 1 ω/g -1-2 Zero of Re Zero of Im -(2γ/g) 2 2γκ/g 2 Inversion, N Jonathan Keeling Polariton and photon condensates Telluride, July / 37

47 Poles of Retarded Green s function and gain [ 1 D (ν)] R g 2 N = ν ωk + iκ + ν 2ɛ + i2γ = A(ν) + ib(ν) 1-1 Laser: 2 1 (a) -1 1 (a) Energy/g A(ν) B(ν) (b) Absorption Energy/g N 1-1 Equilibrium: 2 UP (b) -1 1 Energy/g A(ν) B(ν) ω/g -1-2 Zero of Re Zero of Im -(2γ/g) 2 2γκ/g 2 Inversion, N Energies/g -2-4 LP µ non-condensed µ/g condensed Jonathan Keeling Polariton and photon condensates Telluride, July / 37

48 Non-equilibrium description: baths Pumping Bath γ Excitons System Cavity mode κ Bulk photon modes Pump bath Photon Energy Exciton H = H sys + H sys,bath + H bath Decay bath: Empty (µ ) System In plane momentum Decay bath Pump bath: Thermal µ B, T B Jonathan Keeling Polariton and photon condensates Telluride, July / 37

49 Non-equilibrium description: baths Pumping Bath γ Excitons System Cavity mode κ Bulk photon modes Pump bath Photon Energy Exciton H = H sys + H sys,bath + H bath Decay bath: Empty (µ ) System In plane momentum Decay bath Pump bath: Thermal µ B, T B Jonathan Keeling Polariton and photon condensates Telluride, July / 37

50 Strong coupling and lasing low temperature phenomenon Energy/g Eqbm. polariton ξ µ eff condensed -2-1 µ/g Inversionless allows strong coupling Non-eqbm. polariton condensed -2-1 µ B /g requires low T condensation Related weak-coupling inversionless lasing Laser noncondensed noncondensed noncondensed [Szymanska et al. PRL 6; Keeling et al. book chapter ] condensed -1 1 Inversion, N Jonathan Keeling Polariton and photon condensates Telluride, July / 37

51 Strong coupling and lasing low temperature phenomenon Energy/g Eqbm. polariton ξ µ eff condensed -2-1 µ/g Inversionless allows strong coupling Non-eqbm. polariton condensed -2-1 µ B /g requires low T condensation Related weak-coupling inversionless lasing Laser noncondensed noncondensed noncondensed [Szymanska et al. PRL 6; Keeling et al. book chapter ] condensed -1 1 Inversion, N Jonathan Keeling Polariton and photon condensates Telluride, July / 37

52 Strong coupling and lasing low temperature phenomenon Energy/g Eqbm. polariton ξ µ eff condensed -2-1 µ/g Inversionless allows strong coupling Non-eqbm. polariton condensed -2-1 µ B /g requires low T condensation Related weak-coupling inversionless lasing Laser noncondensed noncondensed noncondensed [Szymanska et al. PRL 6; Keeling et al. book chapter ] condensed -1 1 Inversion, N Jonathan Keeling Polariton and photon condensates Telluride, July / 37

53 Organic polaritons: photon-exciton-phonon coupling 1 Introduction Polariton condensation Condensation, superradiance, lasing Condensation vs superradiance transition Non-equilibrium condensation vs lasing 2 Room temperature condensates: Organic polaritons Dicke phase diagram with phonons Condensation of phonon replicas? Ultra-strong phonon coupling? 3 Room temperature condensates: Photons Lasing model and thermalisation Critical properties Jonathan Keeling Polariton and photon condensates Telluride, July / 37

54 Dicke Holstein Model Energy H = ωψ ψ+ α [ ( ) ɛsα z + g ψs α + + ψ Sα { +Ω b αb α + ) }] S (b α + b α Sα z Photon l S l nuclear coordinate Phonon frequency Ω Huang-Rhys parameter S phonon coupling Phase diagram with S 2LS energy ɛ nω Polariton spectrum, phonon replicas Ultra-strong phonon coupling? Jonathan Keeling Polariton and photon condensates Telluride, July / 37

55 Dicke Holstein Model Energy H = ωψ ψ+ α [ ( ) ɛsα z + g ψs α + + ψ Sα { +Ω b αb α + ) }] S (b α + b α Sα z Photon l S l nuclear coordinate Phonon frequency Ω Huang-Rhys parameter S phonon coupling Phase diagram with S 2LS energy ɛ nω Polariton spectrum, phonon replicas Ultra-strong phonon coupling? Jonathan Keeling Polariton and photon condensates Telluride, July / 37

56 Dicke Holstein Model Energy H = ωψ ψ+ α [ ( ) ɛsα z + g ψs α + + ψ Sα { +Ω b αb α + ) }] S (b α + b α Sα z Photon l S l nuclear coordinate Questions? Phase diagram with S 2LS energy ɛ nω Polariton spectrum, phonon replicas Ultra-strong phonon coupling? Phonon frequency Ω Huang-Rhys parameter S phonon coupling Jonathan Keeling Polariton and photon condensates Telluride, July / 37

57 Dicke Holstein Model Energy H = ωψ ψ+ α [ ( ) ɛsα z + g ψs α + + ψ Sα { +Ω b αb α + ) }] S (b α + b α Sα z Photon l S l nuclear coordinate Questions? Phase diagram with S 2LS energy ɛ nω Polariton spectrum, phonon replicas Ultra-strong phonon coupling? Phonon frequency Ω Huang-Rhys parameter S phonon coupling Jonathan Keeling Polariton and photon condensates Telluride, July / 37

58 Dicke Holstein Model Energy H = ωψ ψ+ α [ ( ) ɛsα z + g ψs α + + ψ Sα { +Ω b αb α + ) }] S (b α + b α Sα z Photon l S l nuclear coordinate Questions? Phase diagram with S 2LS energy ɛ nω Polariton spectrum, phonon replicas Ultra-strong phonon coupling? Phonon frequency Ω Huang-Rhys parameter S phonon coupling Jonathan Keeling Polariton and photon condensates Telluride, July / 37

59 Phase diagram H = ωψ ψ+ α [ ( ) { ɛsα z + g ψs α + + ψ Sα +Ω b αb α + ) }] S (b α + b α Sα z S suppresses condensation reduces overlap Reentrant behaviour Min µ at T.2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

60 Phase diagram H = ωψ ψ+ α [ ( ) { ɛsα z + g ψs α + + ψ Sα +Ω b αb α + ) }] S (b α + b α Sα z T g=2. S=2, =4, Ω=.1 S= -x*y Coherent field ψ µ-ω c S suppresses condensation reduces overlap Reentrant behaviour Min µ at T.2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

61 Polariton spectrum: photon weight Energy -4.4 T=.4, S=2, =4, Ω=.1, g= µ.1.2 Density ρ Photon spectral weight Saturating 2LS: g 2 eff g2 (1 2ρ) What is nature of polariton mode? D(t) = i ψ (t)ψ(), D(ω) = n Z n ω ω n [Cwik et al. arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

62 Polariton spectrum: photon weight Energy -4.4 T=.4, S=2, =4, Ω=.1, g= µ.1.2 Density ρ Photon spectral weight Saturating 2LS: g 2 eff g2 (1 2ρ) What is nature of polariton mode? D(t) = i ψ (t)ψ(), D(ω) = n Z n ω ω n [Cwik et al. arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

63 Polariton spectrum: photon weight Energy -4.4 T=.4, S=2, =4, Ω=.1, g= µ.1.2 Density ρ Photon spectral weight Saturating 2LS: g 2 eff g2 (1 2ρ) What is nature of polariton mode? D(t) = i ψ (t)ψ(), D(ω) = n Z n ω ω n [Cwik et al. arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

64 Polariton spectrum: what condensed Repeat weight for n-phonon channel Eigenvector that is macroscopically occupied Optimal T 2Ω [Cwik et al. arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

65 Polariton spectrum: what condensed Repeat weight for n-phonon channel Eigenvector that is macroscopically occupied Sideband spectral weight S=2, =4, Ω=.1, g=2 T=. Optimal T 2Ω Absorbed phonons: q-p [Cwik et al. arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

66 Polariton spectrum: what condensed Repeat weight for n-phonon channel Eigenvector that is macroscopically occupied Sideband spectral weight S=2, =4, Ω=.1, g=2 T=. T=.5 T=.15 Optimal T 2Ω Absorbed phonons: q-p [Cwik et al. arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

67 Polariton spectrum: what condensed Repeat weight for n-phonon channel Eigenvector that is macroscopically occupied Sideband spectral weight S=2, =4, Ω=.1, g=2 T=. T=.5 T=.15 T=.2 T=.3 T=.4 T=.45 Optimal T 2Ω Absorbed phonons: q-p [Cwik et al. arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

68 Polariton spectrum: what condensed Repeat weight for n-phonon channel Eigenvector that is macroscopically occupied Sideband spectral weight S=2, =4, Ω=.1, g=2 T=. T=.5 T=.15 T=.2 T=.3 T=.4 T= Absorbed phonons: q-p T Optimal T 2Ω g=2. S=2, =4, Ω=.1 -x*y µ-ω c Coherent field ψ [Cwik et al. arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

69 Organic polaritons 1 Introduction Polariton condensation Condensation, superradiance, lasing Condensation vs superradiance transition Non-equilibrium condensation vs lasing 2 Room temperature condensates: Organic polaritons Dicke phase diagram with phonons Condensation of phonon replicas? Ultra-strong phonon coupling? 3 Room temperature condensates: Photons Lasing model and thermalisation Critical properties Jonathan Keeling Polariton and photon condensates Telluride, July / 37

70 Critical coupling with increasing S 4 ε - ω=-4 3 Re-orient phase diagram g vs µ, T Colors Jump of ψ 2 g c Ν µ-ω T Jonathan Keeling Polariton and photon condensates Telluride, July / 37

71 Critical coupling with increasing S 4 ε - ω=-4 3 Re-orient phase diagram g vs µ, T Colors Jump of ψ 2 g c Ν µ-ω T g c Ν µ-ω -3 S= =4, Ω=1-2 T.1 7 S= µ-ω -3 g c Ν -2 T.1 7 S= µ-ω -3 g c Ν -2 T Jump in ψ Jonathan Keeling Polariton and photon condensates Telluride, July / 37

72 Explanation: Polaron formation Unitary transform H α H α = e Kα H α e Kα K = SS z α(b α b α ) Coupling moves to S ± [ ] H α = const. + ɛsα z + Ωb αb α + g ψs α + S(b e α b α ) + H.c. Optimal phonon displacements, S Reduced g eff g exp( S/2) For ψ, competition Variational MFT ψ α exp( ηk α ζb α), S α Jonathan Keeling Polariton and photon condensates Telluride, July / 37

73 Explanation: Polaron formation Unitary transform H α H α = e Kα H α e Kα K = SS z α(b α b α ) Coupling moves to S ± [ ] H α = const. + ɛsα z + Ωb αb α + g ψs α + S(b e α b α ) + H.c. Optimal phonon displacements, S Reduced g eff g exp( S/2) For ψ, competition Variational MFT ψ α exp( ηk α ζb α), S α Jonathan Keeling Polariton and photon condensates Telluride, July / 37

74 Explanation: Polaron formation Unitary transform H α H α = e Kα H α e Kα K = SS z α(b α b α ) Coupling moves to S ± [ ] H α = const. + ɛsα z + Ωb αb α + g ψs α + S(b e α b α ) + H.c. Optimal phonon displacements, S Reduced g eff g exp( S/2) For ψ, competition Variational MFT ψ α exp( ηk α ζb α), S α Jonathan Keeling Polariton and photon condensates Telluride, July / 37

75 Explanation: Polaron formation Unitary transform H α H α = e Kα H α e Kα K = SS z α(b α b α ) Coupling moves to S ± [ ] H α = const. + ɛsα z + Ωb αb α + g ψs α + S(b e α b α ) + H.c. Optimal phonon displacements, S Reduced g eff g exp( S/2) For ψ, competition Variational MFT ψ α exp( ηk α ζb α), S α Jonathan Keeling Polariton and photon condensates Telluride, July / 37

76 Explanation: Polaron formation Unitary transform H α H α = e Kα H α e Kα K = SS z α(b α b α ) Coupling moves to S ± [ ] H α = const. + ɛsα z + Ωb αb α + g ψs α + S(b e α b α ) + H.c. Optimal phonon displacements, S Reduced g eff g exp( S/2) For ψ, competition Variational MFT ψ α exp( ηk α ζb α), S α Jonathan Keeling Polariton and photon condensates Telluride, July / 37

77 Collective polaron formation Compares well at S 1 Coherent bosonic state g Ν 3 Feedback: Large/small g eff λ = ψ Variational free energy F = (ω c µ)λ 2 + N { Ω Effective 2LS energy in field: ( ɛ µ ξ 2 = 2 [Cwik et al. arxiv: ] [ ζ 2 S 2 (a) Exact diagonalization 4 g Ν µ-ω -2 T T c µ-ω c (b) Ansatz S=6, =4, Ω= ] [ ( )]} η(2 η) ξ T ln 2 cosh 4 T + Ω ) 2 S(1 η)ζ + g 2 λ 2 e Sη2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37 λ

78 Collective polaron formation Compares well at S 1 Coherent bosonic state g Ν 3 Feedback: Large/small g eff λ = ψ Variational free energy F = (ω c µ)λ 2 + N { Ω Effective 2LS energy in field: ( ɛ µ ξ 2 = 2 [Cwik et al. arxiv: ] [ ζ 2 S 2 (a) Exact diagonalization 4 g Ν µ-ω -2 T T c µ-ω c (b) Ansatz S=6, =4, Ω= ] [ ( )]} η(2 η) ξ T ln 2 cosh 4 T + Ω ) 2 S(1 η)ζ + g 2 λ 2 e Sη2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37 λ

79 Collective polaron formation Compares well at S 1 Coherent bosonic state g Ν 3 Feedback: Large/small g eff λ = ψ Variational free energy F = (ω c µ)λ 2 + N { Ω Effective 2LS energy in field: ( ɛ µ ξ 2 = 2 [Cwik et al. arxiv: ] [ ζ 2 S 2 (a) Exact diagonalization 4 g Ν µ-ω -2 T T c µ-ω c (b) Ansatz S=6, =4, Ω= ] [ ( )]} η(2 η) ξ T ln 2 cosh 4 T + Ω ) 2 S(1 η)ζ + g 2 λ 2 e Sη2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37 λ

80 Polariton and photon Condensation 1 Introduction Polariton condensation Condensation, superradiance, lasing Condensation vs superradiance transition Non-equilibrium condensation vs lasing 2 Room temperature condensates: Organic polaritons Dicke phase diagram with phonons Condensation of phonon replicas? Ultra-strong phonon coupling? 3 Room temperature condensates: Photons Lasing model and thermalisation Critical properties Jonathan Keeling Polariton and photon condensates Telluride, July / 37

81 Photon BEC experiments Dye filled microcavity No strong coupling [Klaers et al, Nature, 21] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

82 Photon BEC experiments Dye filled microcavity No strong coupling [Klaers et al, Nature, 21] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

83 Photon BEC experiments Dye filled microcavity No strong coupling [Klaers et al, Nature, 21] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

84 Relation to dye laser No electronic inversion No strong coupling No single cavity mode Condensate mode is not maximum gain Gain/Absorption in balance Thermalised many-mode system Jonathan Keeling Polariton and photon condensates Telluride, July / 37

85 Relation to dye laser No electronic inversion No strong coupling 4 Level Dye Laser Energy Cavity nuclear coordinate No single cavity mode Condensate mode is not maximum gain Gain/Absorption in balance Thermalised many-mode system Jonathan Keeling Polariton and photon condensates Telluride, July / 37

86 Relation to dye laser No electronic inversion No strong coupling 4 Level Dye Laser Energy Cavity nuclear coordinate But: No single cavity mode Condensate mode is not maximum gain Gain/Absorption in balance Thermalised many-mode system Jonathan Keeling Polariton and photon condensates Telluride, July / 37

87 Relation to dye laser No electronic inversion No strong coupling 4 Level Dye Laser Energy Cavity nuclear coordinate But: No single cavity mode Condensate mode is not maximum gain Gain/Absorption in balance Thermalised many-mode system Jonathan Keeling Polariton and photon condensates Telluride, July / 37

88 Modelling H sys = m ω m ψ mψ m + α ] [ ɛs z α + g ( ψ m S + α + H.c. ) 2D harmonic cavity ω m = ω cutoff + mω H.O. Degeneracies g m = m + 1 Local vibrational mode Jonathan Keeling Polariton and photon condensates Telluride, July / 37

89 Modelling H sys = m ω m ψ mψ m + α [ ɛs z α + g ( ψ m S + α + H.c. ) { +Ω b αb α + 2 })] SSα (b z α + b α 2D harmonic cavity ω m = ω cutoff + mω H.O. Degeneracies g m = m + 1 Local vibrational mode Jonathan Keeling Polariton and photon condensates Telluride, July / 37

90 Modelling Rate equation ρ = i[h, ρ] 2 L[ψ m] m α [ Γ(δm = ω m ɛ) 2 m,α κ [ Γ 2 L[S+ α ] + Γ ] 2 L[S α ] L[S α + ψ m ] + Γ( δ m = ɛ ω m ) L[Sα ψ 2 m] ] Γ( δ) Γ(δ) Γ(+δ) Γ( δ)e βδ Γ at large δ δ [Marthaler et al PRL 11, Kirton & JK arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

91 Modelling Rate equation ρ = i[h, ρ] 2 L[ψ m] m α [ Γ(δm = ω m ɛ) 2 m,α κ [ Γ 2 L[S+ α ] + Γ ] 2 L[S α ] L[S α + ψ m ] + Γ( δ m = ɛ ω m ) L[Sα ψ 2 m] ] Γ( δ) Γ(δ) Γ(+δ) Γ( δ)e βδ Γ at large δ δ [Marthaler et al PRL 11, Kirton & JK arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

92 Distribution g m n m Rate equation include spontaneous emission Bose-Einstein distribution without losses [Kirton & JK arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

93 Distribution g m n m Rate equation include spontaneous emission Bose-Einstein distribution without losses Low loss: Thermal [Kirton & JK arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

94 Distribution g m n m Rate equation include spontaneous emission Bose-Einstein distribution without losses Low loss: Thermal [Kirton & JK arxiv: ] High loss Laser Jonathan Keeling Polariton and photon condensates Telluride, July / 37

95 Threshold condition 6 κ κ κ κ =1 MHz κ =.5 GHz κ =5 GHz Increasing loss Compare threshold: Pump rate (Laser) Critical density (condensate) Thermal at low κ/high temperature High loss, κ competes with Γ(±δ ) Low temperature, Γ(±δ ) shrinks [Kirton & JK arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

96 Threshold condition 6 κ κ κ κ =1 MHz κ =.5 GHz κ =5 GHz Increasing loss Compare threshold: Pump rate (Laser) Critical density (condensate) Thermal at low κ/high temperature High loss, κ competes with Γ(±δ ) Low temperature, Γ(±δ ) shrinks [Kirton & JK arxiv: ] Jonathan Keeling Polariton and photon condensates Telluride, July / 37

97 Threshold condition 6 κ κ κ κ =1 MHz κ =.5 GHz κ =5 GHz Increasing loss Compare threshold: Pump rate (Laser) Critical density (condensate) Thermal at low κ/high temperature High loss, κ competes with Γ(±δ ) Low temperature, Γ(±δ ) shrinks [Kirton & JK arxiv: ].8.6 Γ( δ) Γ(δ) δ 1 2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

98 Threshold condition 6 κ κ κ κ =1 MHz κ =.5 GHz κ =5 GHz Increasing loss Compare threshold: Pump rate (Laser) Critical density (condensate) Thermal at low κ/high temperature High loss, κ competes with Γ(±δ ) Low temperature, Γ(±δ ) shrinks [Kirton & JK arxiv: ].8.6 Γ( δ) Γ(δ) δ 1 2 Jonathan Keeling Polariton and photon condensates Telluride, July / 37

99 Summary Reentrance, phonon assisted transition, 1st order at S µ.1 Density ρ S=2, =4, Ω=.1, g=2 1 -x*y.4 Coherent field ψ -4.7 g=2. S=2, =4, Ω=.1.5 Sideband spectral weight T Energy 1 Photon spectral weight (a) Exact diagonalization T=. T=.5 T=.15 T=.2 T=.3 T=.4 T= µ-ωc g Ν 3 g Ν (b) Ansatz Absorbed phonons: q-p S=6, =4, Ω=1 2-4 µ-ωc T µ-ωc λ.4 T=.4, S=2, =4, Ω=.1, g= T Photon condensation and thermalisation Jonathan Keeling Polariton and photon condensates Telluride, July / 37

100 Many body quantum optics and correlated states of light 9: am on Monday 28 October 213 5: pm on Tuesday 29 October 213 at:the Royal Society at Chicheley Hall, home of the Kavli Royal Society International Centre, Buckinghamshire Theo Murphy international scientific meeting organised by Dr Jonathan Keeling, Professor Steven Girvin, Dr Michael Hartmann and Professor Peter Littlewood FRS. List of speakers and chairs Professor Iacoppo Carusotto, Professor Andrew Cleland, Professor Hui Deng, Professor Tilman Esslinger, Professor Rosario Fazio, Professor Ed Hinds, Professor Andrew Houck, Professor Ataç İmamoğlu, Professor Jens Koch, Professor Misha Lukin, Professor Martin Plenio, Professor Arno Rauschenbeutel, Professor Timothy Spiller, Professor Jacob Taylor, Professor Hakan Tureci, Professor Andreas Wallraff Attending this event This is a residential conference which allows for increased discussion and networking. It is free to attend, however participants need to cover their accommodation and catering costs if required. Places are limited and therefore preregistration is essential.

101 Jonathan Keeling Polariton and photon condensates Telluride, July / 44

102 Extra slides 4 No go theorem 5 Retarded Green s function for laser 6 Organic properties 7 Anticrossing vs ρ Jonathan Keeling Polariton and photon condensates Telluride, July / 44

103 No go theorem and transition Spontaneous polarisation if: Ng 2 > ωɛ [Rzazewski et al PRL 75] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

104 No go theorem and transition Spontaneous polarisation if: Ng 2 > ωɛ No go theorem:. Minimal coupling (p ea) 2 /2m i e m A p i g(ψ S + ψs + ), i A 2 2m Nζ(ψ + ψ ) 2 [Rzazewski et al PRL 75] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

105 No go theorem and transition Spontaneous polarisation if: Ng 2 > ωɛ No go theorem:. Minimal coupling (p ea) 2 /2m i e m A p i g(ψ S + ψs + ), For large N, ω ω + 2Nζ. (RWA) i A 2 2m Nζ(ψ + ψ ) 2 [Rzazewski et al PRL 75] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

106 No go theorem and transition Spontaneous polarisation if: Ng 2 > ωɛ No go theorem:. Minimal coupling (p ea) 2 /2m i e m A p i g(ψ S + ψs + ), For large N, ω ω + 2Nζ. (RWA) Need Ng 2 > ɛ(ω + 2Nζ). i A 2 2m Nζ(ψ + ψ ) 2 [Rzazewski et al PRL 75] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

107 No go theorem and transition Spontaneous polarisation if: Ng 2 > ωɛ No go theorem:. Minimal coupling (p ea) 2 /2m i e m A p i g(ψ S + ψs + ), i A 2 2m Nζ(ψ + ψ ) 2 For large N, ω ω + 2Nζ. (RWA) Need Ng 2 > ɛ(ω + 2Nζ). But Thomas-Reiche-Kuhn sum rule states: g 2 /ɛ < 2ζ. No transition [Rzazewski et al PRL 75] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

108 Dicke phase transition: ways out Problem: g 2 /ω < 2ζ for intrinsic parameters. Solutions: Interpretation Ferroelectric transition in D r gauge. [JK JPCM 7, Vukics & Domokos PRA 212 ] Circuit QED [Nataf and Ciuti, Nat. Comm. 1; Viehmann et al. PRL 11] Grand canonical ensemble: If H H µ(s z + ψ ψ), need only: g 2 N > (ω µ)(ω µ) Incoherent pumping polariton condensation. Dissociate g, ω, e.g. Raman scheme: ω ω. [Dimer et al. PRA 7; Baumann et al. Nature 1. Also, Black et al. PRL 3 ] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

109 Dicke phase transition: ways out Problem: g 2 /ω < 2ζ for intrinsic parameters. Solutions: Interpretation Ferroelectric transition in D r gauge. [JK JPCM 7, Vukics & Domokos PRA 212 ] Circuit QED [Nataf and Ciuti, Nat. Comm. 1; Viehmann et al. PRL 11] Grand canonical ensemble: If H H µ(s z + ψ ψ), need only: g 2 N > (ω µ)(ω µ) Incoherent pumping polariton condensation. Dissociate g, ω, e.g. Raman scheme: ω ω. [Dimer et al. PRA 7; Baumann et al. Nature 1. Also, Black et al. PRL 3 ] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

110 Dicke phase transition: ways out Problem: g 2 /ω < 2ζ for intrinsic parameters. Solutions: Interpretation Ferroelectric transition in D r gauge. [JK JPCM 7, Vukics & Domokos PRA 212 ] Circuit QED [Nataf and Ciuti, Nat. Comm. 1; Viehmann et al. PRL 11] Grand canonical ensemble: If H H µ(s z + ψ ψ), need only: g 2 N > (ω µ)(ω µ) Incoherent pumping polariton condensation. Dissociate g, ω, e.g. Raman scheme: ω ω. [Dimer et al. PRA 7; Baumann et al. Nature 1. Also, Black et al. PRL 3 ] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

111 Dicke phase transition: ways out Problem: g 2 /ω < 2ζ for intrinsic parameters. Solutions: Interpretation Ferroelectric transition in D r gauge. [JK JPCM 7, Vukics & Domokos PRA 212 ] Circuit QED [Nataf and Ciuti, Nat. Comm. 1; Viehmann et al. PRL 11] Grand canonical ensemble: If H H µ(s z + ψ ψ), need only: g 2 N > (ω µ)(ω µ) Incoherent pumping polariton condensation. Dissociate g, ω, e.g. Raman scheme: ω ω. [Dimer et al. PRA 7; Baumann et al. Nature 1. Also, Black et al. PRL 3 ] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

112 Dicke phase transition: ways out Problem: g 2 /ω < 2ζ for intrinsic parameters. Solutions: Interpretation Ferroelectric transition in D r gauge. [JK JPCM 7, Vukics & Domokos PRA 212 ] Circuit QED [Nataf and Ciuti, Nat. Comm. 1; Viehmann et al. PRL 11] Grand canonical ensemble: If H H µ(s z + ψ ψ), need only: g 2 N > (ω µ)(ω µ) Incoherent pumping polariton condensation. Dissociate g, ω, e.g. Raman scheme: ω ω. [Dimer et al. PRA 7; Baumann et al. Nature 1. Also, Black et al. PRL 3 ] κ Pump κ Cavity Pump Jonathan Keeling Polariton and photon condensates Telluride, July / 44

113 Maxwell-Bloch Equations: Retarded Green s function Absorption N Energy/g Introduce D R (ω): Response to perturbation Absorption = 2I[D R (ω)] Jonathan Keeling Polariton and photon condensates Telluride, July / 44

114 Maxwell-Bloch Equations: Retarded Green s function Absorption N Energy/g Introduce D R (ω): Response to perturbation t ψ = iω ψ κψ + α g αp α t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) Absorption = 2I[D R (ω)] [ 1 D (ω)] R g 2 N = ω ωk + iκ + ω 2ɛ + i2γ Jonathan Keeling Polariton and photon condensates Telluride, July / 44

115 Maxwell-Bloch Equations: Retarded Green s function Absorption N Energy/g Introduce D R (ω): Response to perturbation t ψ = iω ψ κψ + α g αp α t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) Absorption = 2I[D R (ω)] = 2B(ω) A(ω) 2 + B(ω) 2 [ 1 D (ω)] R g 2 N = ω ωk + iκ + ω 2ɛ + i2γ = A(ω) + ib(ω) Jonathan Keeling Polariton and photon condensates Telluride, July / 44

116 Maxwell-Bloch Equations: Retarded Green s function (a) Absorption N -1 A(ν) Energy/g Energy/g Introduce D R (ω): Response to perturbation t ψ = iω ψ κψ + α g αp α t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) Absorption = 2I[D R (ω)] = 2B(ω) A(ω) 2 + B(ω) 2 [ 1 D (ω)] R g 2 N = ω ωk + iκ + ω 2ɛ + i2γ = A(ω) + ib(ω) Jonathan Keeling Polariton and photon condensates Telluride, July / 44

117 Maxwell-Bloch Equations: Retarded Green s function (a) Absorption N -1 A(ν) B(ν) Energy/g Energy/g Introduce D R (ω): Response to perturbation t ψ = iω ψ κψ + α g αp α t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) Absorption = 2I[D R (ω)] = 2B(ω) A(ω) 2 + B(ω) 2 [ 1 D (ω)] R g 2 N = ω ωk + iκ + ω 2ɛ + i2γ = A(ω) + ib(ω) Jonathan Keeling Polariton and photon condensates Telluride, July / 44

118 Maxwell-Bloch Equations: Retarded Green s function (a) (b) 1 Absorption N -1 A(ν) B(ν) A(ν) B(ν) Energy/g Energy/g Energy/g Introduce D R (ω): Response to perturbation t ψ = iω ψ κψ + α g αp α t P α = 2iɛ α P α 2γP + g α ψn α t N α = 2γ(N N α ) 2g α (ψ P α + P αψ) Absorption = 2I[D R (ω)] = 2B(ω) A(ω) 2 + B(ω) 2 [ 1 D (ω)] R g 2 N = ω ωk + iκ + ω 2ɛ + i2γ = A(ω) + ib(ω) Jonathan Keeling Polariton and photon condensates Telluride, July / 44

119 Organic materials in microcavities State of art: Strong coupling: J aggregates [Bulovic et al. ] Crystaline anthracene [Forrest et al. ] Thresold: Anthracene [Kena Cohen and Forrest, Nat. Photon 21] Differences Stronger coupling Singlet-Triplet conversion dark states Vibrational sidebands Jonathan Keeling Polariton and photon condensates Telluride, July / 44

120 Organic materials in microcavities State of art: Strong coupling: J aggregates [Bulovic et al. ] Crystaline anthracene [Forrest et al. ] Thresold: Anthracene [Kena Cohen and Forrest, Nat. Photon 21] Differences Stronger coupling Singlet-Triplet conversion dark states Vibrational sidebands Jonathan Keeling Polariton and photon condensates Telluride, July / 44

121 Organic materials in microcavities State of art: Strong coupling: J aggregates [Bulovic et al. ] Crystaline anthracene [Forrest et al. ] Thresold: Anthracene [Kena Cohen and Forrest, Nat. Photon 21] Differences Stronger coupling Singlet-Triplet conversion dark states Vibrational sidebands Jonathan Keeling Polariton and photon condensates Telluride, July / 44

122 Organic materials in microcavities State of art: Strong coupling: J aggregates [Bulovic et al. ] Crystaline anthracene [Forrest et al. ] Thresold: Anthracene [Kena Cohen and Forrest, Nat. Photon 21] Differences Stronger coupling Singlet-Triplet conversion dark states Vibrational sidebands Jonathan Keeling Polariton and photon condensates Telluride, July / 44

123 Organic materials in microcavities State of art: Strong coupling: J aggregates [Bulovic et al. ] Crystaline anthracene [Forrest et al. ] Thresold: Anthracene [Kena Cohen and Forrest, Nat. Photon 21] Differences Stronger coupling Energy Singlet-Triplet conversion dark states Vibrational sidebands Photon nuclear coordinate l S l Jonathan Keeling Polariton and photon condensates Telluride, July / 44

124 Polariton spectrum coupled oscillators Jonathan Keeling Polariton and photon condensates Telluride, July / 44

125 Polariton spectrum coupled oscillators 1 Photon Exciton UP Energy -1-2 LP Coupling, g Jonathan Keeling Polariton and photon condensates Telluride, July / 44

126 Polariton spectrum coupled oscillators 1 Photon Exciton Exciton-Ω UP Energy -1-2 LP Coupling, g Jonathan Keeling Polariton and photon condensates Telluride, July / 44

127 Polariton spectrum coupled oscillators 1 Photon Exciton-nΩ UP Energy Coupling, g Jonathan Keeling Polariton and photon condensates Telluride, July / 44

128 Polariton spectrum coupled oscillators 1 Photon Exciton-nΩ UP Energy Coupling, g Jonathan Keeling Polariton and photon condensates Telluride, July / 44