Calorimetry of & symmetry breaking in a photon Bose-Einstein condensate. Frank Vewinger Universität Bonn

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1 Calorimetry of & symmetry breaking in a photon Bose-Einstein condensate Frank Vewinger Universität Bonn

2 What are we dealing with? System: Photons ultracold : 300K Box: Curved mirror cavity A few µm long

3 ) Photon BEC: HowTo ) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking Work done with Julian Schmitt Tobias Damm Jan Klaers (now@eth Zürich) Martin Weitz 3

4 ) Photon BEC: HowTo ) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking 4

5 dye photon box The box: Dispersion E = ħc n k z + k r ħc n k z + k r k z 7 ᐧλ0/ = πħcq n D 0 + πħcq n R D 0 r + ħc D 0 πqn k r = m 0 c + m 0 Ω r + k r m 0 Photons in the microcavity behave as - Massive particles - Two-dimensional - Harmonically trapped 5 Klaers, Vewinger & Weitz, Nature Physics 6, 5 (00)

6 dye photon box Dye The box: Dispersion E = ħc n k z + k r ħc n k z + k r k z = πħcq n D 0 + πħcq n R D 0 r + ħc D 0 πqn k r = m 0 c + m 0 Ω r + k r m 0 Photons in the microcavity behave as - Massive particles - Two-dimensional - Harmonically trapped ħω ZPL k B T 6 Klaers, Vewinger & Weitz, Nature Physics 6, 5 (00)

7 dye photon box Intensity [a.u.] Dye f(υ) α(υ) TEM 6mn TEM 7mn TEM 8mn ν [THz] Dye reservoir: - Thermalizes gas - Sets chemical potential ħω ZPL k B T e μ γ k BT = w M w M e ħ (ω C Δ) k B T 7 Klaers, Vewinger & Weitz, Nature Physics 6, 5 (00)

8 dye photon box Intensity [a.u.] Dye f(υ) α(υ) TEM 6mn TEM 7mn TEM 8mn ν [THz] Dye reservoir: - Thermalizes gas - Sets chemical potential e μ γ k BT = w M w M e ħ (ω C Δ) k B T 8 Klaers, Vewinger & Weitz, Nature Physics 6, 5 (00)

9 Scales Dye Energy scales Trap frequency Thermal energy Cavity cutoff 50µeV k B T 5meV.eV cutoff Photon mass 0 7 m e Critical particle number N N c k T N B c 300K 3 Critical phase space density n c.3/ µm Klaers, Schmitt, Vewinger & Weitz, Nature 468, 545 (00) See also Marelic & Nyman, PRA 9, (05) 9

10 Scales Dye Energy scales Trap frequency Thermal energy Cavity cutoff 50µeV k B T 5meV.eV cutoff Photon mass 0 7 m e Critical particle number N N c k T N B c 300K 3 Critical phase space density n c.3/ µm Klaers, Schmitt, Vewinger & Weitz, Nature 468, 545 (00) See also Marelic & Nyman, PRA 9, (05) 0

11 Scales Dye Energy scales Trap frequency Thermal energy Cavity cutoff 50µeV k B T 5meV.eV cutoff Photon mass 0 7 m e Critical particle number N N c k T N B c 300K 3 Critical phase space density n c.3/ µm Brute force theory: Appl Phys B 05, 7 33 (0) Klaers, Schmitt, Vewinger & Weitz, Nature 468, 545 (00) See also Marelic & Nyman, PRA 9, (05) Microscopic models: de Leeuw, PRA 88, (03). Kirton/Keeling, PRL,00404 (03) Kopylov et al., PRA 9, (05)

12 Experimental setup

13 Experimental setup 3

14 Experimental setup 4

15 Properties? 5

16 Properties? 6

17 ) Photon BEC: HowTo ) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking 7

18 Condensate Fraction Signal (a.u.) Condensate fraction n 0 /n k B T T T C Wavelength λ (nm) Temperature T/T c Bose-Einstein distribution T T c = N c N Damm, Schmitt, Nature Comm. 7,340 (06)

19 Internal Energy 5 Energy (U-ħω c ) / Nk B T c 4 3 criticality classical limit (Maxwell-Boltzmann) Temperature T/T c 9

20 Internal Energy Phys. Rev. Lett. 77, (996) Phys. Rev. A 90, (04) 5 Atomic systems Energy (U-ħω c ) / Nk B T c Temperature T/T c 0

21 Specific Heat 5 Specific heat C / Nk B 4 3 cusp singularity at criticality k B in D (equipartition theorem) Temperature T/T c Klünder & Pelster, EPJB 68, 457 (009): C=4.38 k B T, TD limit

22 Specific Heat Phys. Rev. B 68, 7458 (003) Science 335, (0) 5 Liquid 4 He Specific heat C / Nk B 4 3 Fermions ( 6 Li) Temperature T/T c Klünder & Pelster, EPJB 68, 457 (009): C=4.38 k B T, TD limit

23 Entropy per Particle Entropy S / N 5 4 S T = 0 T C T T dt 3 S/N 0 (third law of thermodynamics) Temperature T/T c 3

24 Entropy per Particle Entropy S / N 5 4 S T = 0 T C T T dt 3 S/N 0 (third law of thermodynamics) Temperature T/T c 4

25 ) Photon BEC: HowTo ) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking 5

26 Coherence of a Bose-Einstein condensate g () (τ) g () (τ) P. W. Anderson (986): "Do two superfluids which have never 'seen' one another possess a relative phase?" F Spontaneous symmetry breaking Phase selection: long-range order Damping of density fluctuations T >Tc Pn T <Tc Pn Andrews et al., Science 75 (997) τ Öttl et al., PRL 95 (005) n 6 4

27 Coherence of a Bose-Einstein condensate g () (τ) g () (τ) P. W. Anderson (986): "Do two superfluids which have never 'seen' one another possess a relative phase?" F Spontaneous symmetry breaking Closed vs. open system Isolation Reservoir n, E 0 n, E 0 Phase selection: long-range order Damping of density fluctuations T >Tc Pn T <Tc Pn Andrews et al., Science 75 (997) τ n Öttl et al., PRL 95 (005) BEC correlations in open environments? 7 4

28 Heat bath and particle reservoir for light Molecules Heat bath M = Photon condensate ΔE,, Δn n T, μ Grand canonical ensemble, Ω T, V, μ if M n Photon number distribution Master equation Pn Statistics crossover Klaers et al., PRL 08 (0) Sob yanin, PRE 85 (0) 8

29 Limiting cases for BEC number statistics g () (τ) g () (τ) M n Grand-canonical ensemble ( ) Canonical ensemble ( M < n ) Bose-Einstein statistics ("flickering" BEC) Poisson statistics ("quiet" BEC) n=0 3, M=0 7 n=0 3, M=0 4 ɸ(t) ɸ(t) quasi-spin n(t) Time, n(t) Time, τc () Autocorrelation Fluctuation level Delay, τ g 0 = g 0 = τ 9

30 Experiment: intensity correlations of BEC Condensate fraction: 4% Time evolution (PMT) Photon statistics 3 6% 8% 4 Reservoir (fixed size) 58% Probability, Pn BEC photons Time, t (ns) Schmitt et al., Phys. Rev. Lett., (04) see also: Physics 7 (04) 30

31 Experiment: intensity correlations of BEC Autocorrelation, g () (τ) Condensate fraction: 4% Time evolution (PMT) Photon statistics 3 6% 8% 4 Reservoir (fixed size) 58% Probability, Pn BEC photons Time, t (ns) τc ().4 ns Crossover from Bose-Einstein ( ) to Poisson statistics ( ) Schmitt et al., Phys. Rev. Lett., (04) see also: Physics 7 (04) Delay, τ (ns) 3

32 Temporal phase evolution Response of condensate phase to statistical fluctuations? 3

33 Temporal phase evolution I(t) Response of condensate phase to statistical fluctuations? Canonical ensemble (, second-order coherence) regular beating without phase jumps Schmitt et al., Phys. Rev. Lett. 6, (06) 33

34 Temporal phase evolution I(t) Response of condensate phase to statistical fluctuations? Canonical Grand-canonical ensemble ensemble ( (, second-order, intensity coherence) fluctuations) Phase jumps (ΓPJ - = 0ns) regular beating without phase jumps Schmitt et al., Phys. Rev. Lett. 6, (06) 34

35 Temporal phase evolution I(t) # phase jumps Response of condensate phase to statistical fluctuations? Canonical Grand-canonical ensemble ensemble ( (, second-order, intensity coherence) fluctuations) Phase jumps Random distribution: U() symmetry Separation of time scales Schmitt et al., Phys. Rev. Lett. 6, (06) (ΓPJ - = 0ns) regular beating without phase jumps 0 π 0 0 t (ns) 35

36 Separation of correlation times Rates (µs - ) Rate of fluctuations & phase jumps (/τc () & ΓPJ) vs. increasing system size Suppressed fluctuations & phase jumps ΓPJ Schmitt et al., Phys. Rev. Lett. 6, (06) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (996), Imamoḡlu et al., PRL 78 (997), De Leeuw et al., PRA 90 (04), 36

37 Separation of correlation times Rates (µs - ) Rate of fluctuations & phase jumps (/τc () & ΓPJ) vs. increasing system size Suppressed fluctuations & phase jumps ΓPJ Reservoir size 0 0 Schmitt et al., Phys. Rev. Lett. 6, (06) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (996), Imamoḡlu et al., PRL 78 (997), De Leeuw et al., PRA 90 (04), 37

38 Separation of correlation times Rates (µs - ) Rate of fluctuations & phase jumps (/τc () & ΓPJ) vs. increasing system size Suppressed fluctuations & phase jumps ΓPJ Reservoir size 0 0 Schmitt et al., Phys. Rev. Lett. 6, (06) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (996), Imamoḡlu et al., PRL 78 (997), De Leeuw et al., PRA 90 (04), 38

39 Separation of correlation times Rates (µs - ) Rate of fluctuations & phase jumps (/τc () & ΓPJ) vs. increasing system size Suppressed fluctuations & phase jumps ΓPJ Reservoir size 0 0 Schmitt et al., Phys. Rev. Lett. 6, (06) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (996), Imamoḡlu et al., PRL 78 (997), De Leeuw et al., PRA 90 (04), 39

40 Separation of correlation times Rates (µs - ) Rate of fluctuations & phase jumps (/τc () & ΓPJ) vs. increasing system size Suppressed fluctuations & phase jumps ΓPJ (µs - ) ΓPJ Suppression of phase jumps despite bunching! Field Reservoir size 0 0 time giant flickering BEC chaotic light Schmitt et al., Phys. Rev. Lett. 6, (06) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (996), Imamoḡlu et al., PRL 78 (997), De Leeuw et al., PRA 90 (04), 40

41 ) Photon BEC: HowTo ) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking 4) Conclusion 4

42 Photon BEC: Summary Photon BEC versatile platform - grand canonical physics - open & closed system dynamics - reservoir effects - mediated interaction - Calorimetry: Textbook properties of the ideal Bose gas Statistics: Tunable from canonical to grand canonical Effective temperature Phase evolution: Fluctuation-induced phase jumps 4

43 Time What s next? Spatial phase coherence Josephson physics with reservoir Arbitrary potentials J = 44 GHz 8 ps Photon BEC Team Erik Busley Christian Kurtscheid Christian Schilz Tobias Damm David Dung Fahri Öztürk Hadiseh Alaeian Julian Schnmitt Frank Vewinger Jan Klärs Martin Weitz Funding 43

44 Time What s next? Spatial phase coherence Josephson physics with reservoir Arbitrary potentials J = 44 GHz 8 ps Photon BEC Team Erik Busley Christian Kurtscheid Christian Schilz Tobias Damm David Dung Fahri Öztürk Hadiseh Alaeian Julian Schnmitt Frank Vewinger Jan Klärs Martin Weitz Funding Thanks for your attention 44