Calorimetry of & symmetry breaking in a photon Bose-Einstein - - PowerPoint PPT Presentation

Frank Vewinger Universität Bonn

Calorimetry of & symmetry breaking in a photon Bose-Einstein condensate

2

What are we dealing with?

System: 104 – 105 Photons „ultracold“: 300K Box: Curved mirror cavity A few µm long

3

1) Photon BEC: HowTo 2) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking 1) Photon BEC: HowTo 2) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking

Work done with Julian Schmitt Tobias Damm Jan Klaers (now@ETH Zürich) Martin Weitz

4

1) Photon BEC: HowTo 2) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking

5

7 ᐧλ0/2

dye photon box

Klaers, Vewinger & Weitz, Nature Physics 6, 512 (2010)

The box: Dispersion 𝐹 = ℏ𝑑 𝑜 𝑙𝑨

2 + 𝑙𝑠 2 ≈ ℏ𝑑

𝑜 𝑙𝑨 + 𝑙𝑠

2

2 𝑙𝑨

2

= 𝜌ℏ𝑑𝑟 𝑜 𝐸0 + 𝜌ℏ𝑑𝑟 𝑜 𝑆 𝐸0

2 𝑠2 + ℏ𝑑 𝐸0

2𝜌𝑟𝑜 𝑙𝑠

2

= 𝑛0𝑑2 + 1 2 𝑛0 Ω2 𝑠2 + 𝑙𝑠

2

2𝑛0 ⇒ Photons in the microcavity behave as

• Massive particles
• Two-dimensional
• Harmonically trapped

6

dye photon box

Klaers, Vewinger & Weitz, Nature Physics 6, 512 (2010)

The box: Dispersion 𝐹 = ℏ𝑑 𝑜 𝑙𝑨

2 + 𝑙𝑠 2 ≈ ℏ𝑑

𝑜 𝑙𝑨 + 𝑙𝑠

2

2 𝑙𝑨

2

= 𝜌ℏ𝑑𝑟 𝑜 𝐸0 + 𝜌ℏ𝑑𝑟 𝑜 𝑆 𝐸0

2 𝑠2 + ℏ𝑑 𝐸0

2𝜌𝑟𝑜 𝑙𝑠

2

= 𝑛0𝑑2 + 1 2 𝑛0 Ω2 𝑠2 + 𝑙𝑠

2

2𝑛0 ⇒ Photons in the microcavity behave as

• Massive particles
• Two-dimensional
• Harmonically trapped

Dye

ℏ𝜕𝑎𝑄𝑀 ≫ 𝑙𝐶𝑈

7

dye photon box

Klaers, Vewinger & Weitz, Nature Physics 6, 512 (2010)

Dye

ν [THz] Intensity [a.u.]

TEM6𝑛𝑜 TEM7𝑛𝑜 TEM8𝑛𝑜

𝑔(𝜑) 𝛽(𝜑) 400 500 600

Dye reservoir:

• Thermalizes gas
• Sets chemical potential

𝑓

𝜈𝛿 𝑙𝐶𝑈 = 𝑥↓𝑁↑

𝑥↑𝑁↓ 𝑓

ℏ (𝜕𝐷−Δ) 𝑙𝐶𝑈 ℏ𝜕𝑎𝑄𝑀 ≫ 𝑙𝐶𝑈

8

dye photon box

Klaers, Vewinger & Weitz, Nature Physics 6, 512 (2010)

Dye

ν [THz] Intensity [a.u.]

TEM6𝑛𝑜 TEM7𝑛𝑜 TEM8𝑛𝑜

𝑔(𝜑) 𝛽(𝜑) 400 500 600

Dye reservoir:

• Thermalizes gas
• Sets chemical potential

𝑓

𝜈𝛿 𝑙𝐶𝑈 = 𝑥↓𝑁↑

𝑥↑𝑁↓ 𝑓

ℏ (𝜕𝐷−Δ) 𝑙𝐶𝑈

9

Scales

Dye

Critical particle number Critical phase space density Photon mass ≈ 10−7 𝑛𝑓 K T k Nc 300 @ 000 . 80 3

2 B 2

           eV 1 . 2 meV 25 µeV 150

cutoff 

      T kB Energy scales Trap frequency Thermal energy Cavity cutoff

2

/ 3 . 1 µm nc 

c

N N 

Klaers, Schmitt, Vewinger & Weitz, Nature 468, 545 (2010) See also Marelic & Nyman, PRA 91, 033826 (2015)

10

Scales

Dye

Critical particle number Critical phase space density Photon mass ≈ 10−7 𝑛𝑓 K T k Nc 300 @ 000 . 80 3

2 B 2

           eV 1 . 2 meV 25 µeV 150

cutoff 

      T kB Energy scales Trap frequency Thermal energy Cavity cutoff

2

/ 3 . 1 µm nc 

c

N N 

Klaers, Schmitt, Vewinger & Weitz, Nature 468, 545 (2010) See also Marelic & Nyman, PRA 91, 033826 (2015)

11

Scales

Dye

Critical particle number Critical phase space density Photon mass ≈ 10−7 𝑛𝑓 K T k Nc 300 @ 000 . 80 3

2 B 2

           eV 1 . 2 meV 25 µeV 150

cutoff 

      T kB Energy scales Trap frequency Thermal energy Cavity cutoff

2

/ 3 . 1 µm nc 

c

N N 

Klaers, Schmitt, Vewinger & Weitz, Nature 468, 545 (2010) See also Marelic & Nyman, PRA 91, 033826 (2015) Brute force theory: Appl Phys B 105, 17–33 (2011) Microscopic models: de Leeuw, PRA 88, 033829 (2013). Kirton/Keeling, PRL 111,100404 (2013) Kopylov et al., PRA 92, 063832 (2015)

12

Experimental setup

13

Experimental setup

14

Experimental setup

15

Properties?

16

Properties?

17

1) Photon BEC: HowTo 2) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking

18

0.5 1.0 1.5 0.4 0.6 0.8 1.0 0.2

Temperature T/T

c

Condensate fraction n0/n

𝑈 𝑈

𝑑 =

𝑂c 𝑂 ≈ 80.000 1 10 100 1000 0.1

Signal (a.u.) Wavelength λ (nm)

580 570 560 𝑙B𝑈

Bose-Einstein distribution

Condensate Fraction

1 − 𝑈 𝑈𝐷

2

Damm, Schmitt,… Nature Comm. 7,11340 (2016)

19

Temperature T/T

c

0.5 1.0 1.5 2.0 2.5 2 3 4 5 1

Energy (U-ℏωc) / NkBT

c

criticality classical limit (Maxwell-Boltzmann)

Internal Energy

20

Temperature T/T

c

0.5 1.0 1.5 2.0 2.5 2 3 4 5 1

Energy (U-ℏωc) / NkBT

c

• Phys. Rev. Lett. 77, 4984-4987 (1996)
• Phys. Rev. A 90, 043640 (2014)

Atomic systems

Internal Energy

21

Temperature T/T

c

0.5 1.0 1.5 2.0 2.5 2 3 4 5 1

Specific heat C / NkB

cusp singularity at criticality 2kB in 2D (equipartition theorem)

Specific Heat

Klünder & Pelster, EPJB 68, 457 (2009): C=4.38 kBT, TD limit

22

Temperature T/T

c

0.5 1.0 1.5 2.0 2.5 2 3 4 5 1

Specific heat C / NkB

• Phys. Rev. B 68, 174518 (2003)

Science 335, 563-567 (2012)

Liquid 4He Fermions (6Li)

Specific Heat

Klünder & Pelster, EPJB 68, 457 (2009): C=4.38 kBT, TD limit

23

Temperature T/T

c

0.5 1.0 1.5 2.0 2.5 2 3 4 5 1

Entropy S / N

(third law of thermodynamics) 𝑇 𝑈 =

𝑈

𝐷 𝑈′ 𝑈′ 𝑒𝑈′ 𝑇/𝑂 → 0

Entropy per Particle

24

Temperature T/T

c

0.5 1.0 1.5 2.0 2.5 2 3 4 5 1

Entropy S / N

(third law of thermodynamics) 𝑇 𝑈 =

𝑈

𝐷 𝑈′ 𝑈′ 𝑒𝑈′ 𝑇/𝑂 → 0

Entropy per Particle

25

1) Photon BEC: HowTo 2) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking

26

Coherence of a Bose-Einstein condensate

14

• P. W. Anderson (1986): "Do two superfluids which have never 'seen' one another possess a relative phase?"

Andrews et al., Science 275 (1997)

Phase selection: long-range order Damping of density fluctuations

Öttl et al., PRL 95 (2005)

T >Tc T <Tc

𝜐

Pn

n

g(2)(𝜐)

1 2

g(2)(𝜐)

1 2

Pn

Spontaneous symmetry breaking

F

27

Closed vs. open system

∆n,∆E ≃ 0 ∆n,∆E ≠ 0

Isolation Reservoir

Coherence of a Bose-Einstein condensate

14

• P. W. Anderson (1986): "Do two superfluids which have never 'seen' one another possess a relative phase?"

Andrews et al., Science 275 (1997)

Phase selection: long-range order Damping of density fluctuations

Öttl et al., PRL 95 (2005)

T >Tc T <Tc

𝜐

Pn

n

g(2)(𝜐)

1 2

g(2)(𝜐)

1 2

Pn

Spontaneous symmetry breaking

F

→ BEC correlations in open environments?

28

Heat bath and particle reservoir for light

1 5

Heat bath Photon condensate

,

Molecules

Grand canonical ensemble, Ω 𝑈, 𝑊, 𝜈 if 𝑁 ≫ 𝑜

Photon number distribution

Master equation

Pn

Statistics crossover

M = 108–1012

Δ𝐹, Δ𝑜 𝑜 𝑈, 𝜈

Klaers et al., PRL 108 (2012) Sob’yanin, PRE 85 (2012)

29

Limiting cases for BEC number statistics

1 6

Grand-canonical ensemble ( ) Canonical ensemble ( 𝑁 < 𝑜2 ) Poisson statistics ("quiet" BEC)

𝜐

1 2

n(t)

ɸ(t)

Bose-Einstein statistics ("flickering" BEC)

n(t)

ɸ(t) Time, n=103, M=104 n=103, M=107

Delay, 𝜐 𝜐c(2)

1 2

Autocorrelation

≙

Fluctuation level

quasi-spin Time,

𝑁 ≫ 𝑜2

𝑕(2)(𝜐) 𝑕(2)(𝜐) 𝑕 2 0 = 2 𝑕 2 0 = 1

30

Condensate fraction:

Experiment: intensity correlations of BEC

1 7

BEC photons Reservoir (fixed size)

58% 28% 16% 4%

Photon statistics Time evolution (PMT)

Time, t (ns)

Schmitt et al., Phys. Rev. Lett. 112, 030401 (2014) see also: Physics 7 (2014)

1 2 3 4

Probability, Pn

31

Condensate fraction:

Experiment: intensity correlations of BEC

1 7

BEC photons Reservoir (fixed size)

58% 28% 16% 4%

Photon statistics Time evolution (PMT)

Time, t (ns)

Schmitt et al., Phys. Rev. Lett. 112, 030401 (2014) see also: Physics 7 (2014)

1 2 3 4

Probability, Pn

Crossover from Bose-Einstein ( ) to Poisson statistics ( )

Autocorrelation, g(2)(𝜐) Delay, 𝜐 (ns) 0 2 4 6 8

𝜐c(2) ≃ 1.4 ns

32

Temporal phase evolution

1 8

Response of condensate phase to statistical fluctuations?

33

Temporal phase evolution

1 8

Response of condensate phase to statistical fluctuations?

Schmitt et al., Phys. Rev. Lett. 116, 033604 (2016)

Canonical ensemble ( , second-order coherence)

I(t)

regular beating without phase jumps

⤷

34

Temporal phase evolution

1 8

Response of condensate phase to statistical fluctuations?

Schmitt et al., Phys. Rev. Lett. 116, 033604 (2016)

Canonical ensemble ( , second-order coherence)

I(t)

regular beating without phase jumps

⤷

Phase jumps

(𝚫PJ-1 = 20ns)

I(t)

Grand-canonical ensemble ( , intensity fluctuations)

35

Temporal phase evolution

1 8

Response of condensate phase to statistical fluctuations?

Schmitt et al., Phys. Rev. Lett. 116, 033604 (2016)

Canonical ensemble ( , second-order coherence)

I(t)

regular beating without phase jumps

⤷

Phase jumps

(𝚫PJ-1 = 20ns)

I(t)

Grand-canonical ensemble ( , intensity fluctuations)

• Random distribution: U(1) symmetry
• Separation of time scales…

# phase jumps

10 2𝛒

t (ns)

36

Separation of correlation times

1 9

• Rate of fluctuations & phase jumps (1/𝜐c(2) & ΓPJ)
• vs. increasing system size
• Suppressed fluctuations & phase jumps

ΓPJ

Rates (µs-1)

Schmitt et al., Phys. Rev. Lett. 116, 033604 (2016) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (1996), Imamoḡlu et al., PRL 78 (1997), De Leeuw et al., PRA 90 (2014), …

37

Separation of correlation times

1 9

• Rate of fluctuations & phase jumps (1/𝜐c(2) & ΓPJ)
• vs. increasing system size
• Suppressed fluctuations & phase jumps

ΓPJ

Rates (µs-1)

1 10 120 Reservoir size

Schmitt et al., Phys. Rev. Lett. 116, 033604 (2016) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (1996), Imamoḡlu et al., PRL 78 (1997), De Leeuw et al., PRA 90 (2014), …

38

Separation of correlation times

1 9

• Rate of fluctuations & phase jumps (1/𝜐c(2) & ΓPJ)
• vs. increasing system size
• Suppressed fluctuations & phase jumps

ΓPJ

Rates (µs-1)

1 10 120 Reservoir size

Schmitt et al., Phys. Rev. Lett. 116, 033604 (2016) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (1996), Imamoḡlu et al., PRL 78 (1997), De Leeuw et al., PRA 90 (2014), …

39

Separation of correlation times

1 9

• Rate of fluctuations & phase jumps (1/𝜐c(2) & ΓPJ)
• vs. increasing system size
• Suppressed fluctuations & phase jumps

ΓPJ

Rates (µs-1)

1 10 120 Reservoir size

Schmitt et al., Phys. Rev. Lett. 116, 033604 (2016) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (1996), Imamoḡlu et al., PRL 78 (1997), De Leeuw et al., PRA 90 (2014), …

40

Separation of correlation times

1 9

• Rate of fluctuations & phase jumps (1/𝜐c(2) & ΓPJ)
• vs. increasing system size
• Suppressed fluctuations & phase jumps

ΓPJ

Rates (µs-1)

1 10 120 Reservoir size

Schmitt et al., Phys. Rev. Lett. 116, 033604 (2016) Analysis ignores phase diffusion, Lewenstein et al., PRL 77 (1996), Imamoḡlu et al., PRL 78 (1997), De Leeuw et al., PRA 90 (2014), …

ΓPJ (µs-1)

Suppression of phase jumps despite bunching! giant flickering BEC chaotic light Field time

41

1) Photon BEC: HowTo 2) Thermodynamic Properties of Photons 3) Fluctuations & Symmetry Breaking 4) Conclusion

42

Photon BEC: Summary

Photon BEC  versatile platform

• grand canonical physics
• open & closed system dynamics
• reservoir effects
• mediated interaction
• …

Statistics: Tunable from canonical to grand canonical Effective temperature Phase evolution: Fluctuation-induced phase jumps Calorimetry: „Textbook“ properties of the ideal Bose gas

43

What‘s next?

2 2

Funding

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

J = 44 GHz Time 28 ps Spatial phase coherence Arbitrary potentials Josephson physics with reservoir

44

What‘s next?

2 2

Funding

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

J = 44 GHz Time 28 ps Spatial phase coherence Arbitrary potentials Josephson physics with reservoir

Thanks for your attention