Phase diffusion in a BEC of light - Universiteit Utrechtstoof101/Poster_Phase.pdf · Interference...
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E.C.I. van der Wurff*, A.-W. de Leeuw, R.A. Duine, and H.T.C. Stoof Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands R e f e r e n c e s F l u c t u a t i o n s *erikvanderwurff@gmail.com C o n c l u s i o n s P h a s e d i f f u s i o n i n a B E C o f l i g h t P h a s e D i ff u s i o n [ 2 , 3 ] [1] J. Klaers et al., Nature 468, 545 (2010). [2] E.C.I. van der Wurff et al., Phys. Rev. A 90, 043627 (2014). [3] M. Lewenstein and L. You, Phys. Rev. Lett. 77, 3489 (1996). [4] J. Schmitt et al., arXiv:1512.07148v1 [cond-mat.quant-gas] Thermal fluctuations dominate quantum fluctuations 0 -1 1 0 5 10 15 25 20 t/t μ cos(θ(t)) 0 6 θ 0 - P(θ;t) 3 P h o t o n s i n a d y e - fi l l e d m i c r o c a v i t y [ 1 ] Figures (modified) from Ref. [1] before (L) and after (R) condensation Thermalization photon gas due to coupling to dye Photon gas equivalent to 2D trapped massive Bose gas Conserved number of photons in cavity Experiment at room temperature Pumping increases number of photons condensation R e c e n t e x p e r i m e n t s [ 4 ] Figures (modified) from Ref. [3] Mirror Dye Laser Mirror Camera Pump Beam Mode Filter Proposal for phase diffusion experiment [2] U(1) symmetry: conservation number of particles Formally only in thermodynamic limit Finite number of particles: phase non-trivial dynamics [3] Condensation: spontaneous U(1) symmetry breaking system in well-defined phase Interference experiment condensate photons and external laser: 2) Thermal fluctuations 1) Quantum fluctuations (at T = 0) Interference experiment has been carried out [3] Many measurements should be averaged to verify predicted timescale Solution to Langevin equations. Solid curve: one arbitary noise configuration; dashed: averaged over 500 noise configurations. Schrödinger-like equation for phase wavefunction: Solution displays difussion and collapse and revival Condensate of photons in dye-filled microcavity: new experimental possibilities Measurable timescale proposed to measure phase diffusion Coupling to dye induces damping Langevin field equations with Gaussian noise: Intensity profile Measurable time scale Observation of phase flips possibility to measure phase diffusion frequency (THz) wavenumber (transversal) Energy photon q = 6 q = 7 q = 8
Transcript of Phase diffusion in a BEC of light - Universiteit Utrechtstoof101/Poster_Phase.pdf · Interference...
E.C.I. van der Wurff*, A.-W. de Leeuw, R.A. Duine, and H.T.C. StoofInstitute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands
References
Fluctuations
Conclusions
Phase diffusion in a BEC of light
Phase Diffusion [2,3]
[1] J. Klaers et al., Nature 468, 545 (2010).[2] E.C.I. van der Wurff et al., Phys. Rev. A 90, 043627 (2014).[3] M. Lewenstein and L. You, Phys. Rev. Lett. 77, 3489 (1996). [4] J. Schmitt et al., arXiv:1512.07148v1 [cond-mat.quant-gas]
Thermal fluctuations dominate quantum fluctuations
0
-1
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0 5 10 15 2520t/tμ
cos(θ(
t))
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θ0-
P(θ
;t)
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Photons in a dye-filled microcavity [1]
Figures (modified) from Ref. [1]
before (L) and after (R) condensation
-200 -100 0 100 200
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4
6
8
10
x (µm)
Signa
l (a.u.
)
-200 -100 0 100 200
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x (µm)
Signa
l (a.u.
)
Thermalization photon gas due to coupling to dye
Photon gas equivalent to 2D trapped massive Bose gas
Conserved number of photons in cavity
Experiment at room temperature
Pumping increases number of photons condensation
Recent experiments [4]
Figures (modified) from Ref. [3]
Mirror
Dye
Laser Mirror
Camera
Pump Beam
Mode Filter
Proposal for phase diffusion experiment [2]
U(1) symmetry: conservation number of particles
Formally only in thermodynamic limit
Finite number of particles: phase non-trivial dynamics [3]
Condensation: spontaneous U(1) symmetry breaking
system in well-defined phase
Interference experiment condensate photons and external laser:
2) Thermal fluctuations
1) Quantum fluctuations (at T = 0)
Interference experiment has been carried out [3]
Many measurements should be averaged to verify predicted timescale
Solution to Langevin equations. Solid curve: one arbitary noise configuration; dashed: averaged over 500 noise configurations.
Schrödinger-like equation for phase wavefunction:
Solution displays difussion and collapse and revival
Condensate of photons in dye-filled microcavity: new experimental possibilities
Measurable timescale proposed to measure phase diffusion
Coupling to dye induces damping
Langevin field equations with Gaussian noise:
Intensity profile
Measurable time scale
Observation of phase flips
possibility to measure phase diffusion
frequency (THz)wavenumber (transversal)
Energy photon
q = 6 q = 7q = 8
