Quantum physics and the beam splitter mystery

Transcription

1 Quantum physics and François Hénault Institut de Planétologie et d Astrophysique de Grenoble Université Joseph Fourier Centre National de la Recherche Scientifique BP 53, 384 Grenoble France Conf. 957 The Nature of Light: What are Photons? VI San Diego, 8--5

2 Plan of presentation Part Beamsplitter theoretical models Quantum physics Classical wave optics Part Beamsplitter experimental setups Hanbury Brown and Twiss experiment Mach-Zehnder interferometer Conf. 957 The Nature of Light: What are Photons? VI San Diego, 8--5

3 Quantum view of the beamsplitter Macroscopic, "black-box" matrix model Energy conservation A A A * * + A A A A * * + A Unitary operator (TBC) Beamsplitter matrix: A Entrance port Exit port A T A R BS A Exit port A T A R A M BS i i A Entrance port Conf. 957 The Nature of Light: What are Photons? VI San Diego,

4 M BS i i Quantum physics and Real world beamsplitters Here are essentially studied "symmetric" beamsplitters A R A R A T A R A T M BS A R A T Cube beamsplitter Pellicle beamsplitter M BS i i A T Asymmetric beamsplitters M BS i i Conf. 957 The Nature of Light: What are Photons? VI San Diego,

5 Wave optics model of the beamsplitter Multi-interference effect as in Fabry-Perot interferometers A tt exp( iϕ ) T r exp( iϕ ) Lossless beamsplitter: A exp( iϕ ) r R r exp( iϕ ) Energy conservation + R A T A ( tt r r ) exp( iϕ ) r exp( iϕ ) A r + r R Achromatic phase-shift * π φ R φt Arg[ AR AT ] Arg[ isinϕ] ± Internal phase ϕ may depend on λ, θ... Conf. 957 The Nature of Light: What are Photons? VI San Diego, O A R O θ e t r r A T t π ϕ k necosθ necosθ λ

6 BS transmitted amplitudes and phase-shift Lossless beamsplitter Achromatic phase-shift of ±π/ Output power (a. u.) Internal phase (Fractions of Pi) Absorbing beamsplitter Transmitted Reflected π Output phase (rad) Conf. 957 The Nature of Light: What are Photons? VI San Diego, Output phase (rad) π/ +π/ π/ +π/ π Internal phase (Fractions of Pi) π Internal phase (Fractions of Pi) Transmitted Reflected Difference [Pi] [π] Transmitted Reflected Difference [Pi] [π]

7 BS correlation experiments Inspired from Hanbury Brown and Twiss experiment on intensity interferometry (956) Used in coincidence counting mode by Grangier, Roger and Aspect (GRA) Anti-correlation at low light levels (986) Demonstrates the particle nature of light (indivisible photon) I R Correlator / Coincidence counter C RT D A BS D Measurement apparatus I T Experimental results Conf. 957 The Nature of Light: What are Photons? VI San Diego,

8 GRA experiment Classical model Uses classical notions of coherence length, generated currents Transmitted amplitude A ( T t, k) exp ( ikct) First integration on spectral domain C δk RT ( t) k + δk δ k k δk Second integration on time domain A T π/ phase shifted A ( R Reflected amplitude t, k) i ( t, k ) AR ( t, k ) dk exp i exp [ k δ k, k + δk ] [ τ, +τ ] ( ikct) ( ikct) sin c( δkct) C RT τ + τ τ τ [ ( )] + τ δk Re al C ( t) dt sin ( kct) sin c ( δkct) RT τ dt Conf. 957 The Nature of Light: What are Photons? VI San Diego,

9 GRA experiment Classical model Final expression C RT ( sin c( kcτ )) 4 Not in excellent agreement due to drastic approximations But accounts for experimental photon anti-correlation.4 Correlation factor C Classical limit Model GRA data Integration time (ns) Conf. 957 The Nature of Light: What are Photons? VI San Diego,

10 The Mach-Zehnder interferometer Originally used as metrology tool in optics, gas dynamics etc. A A M Semireflective coatings Exit port BS Exit port A M Exit port BS Exit port A BS M BS M Non symmetric, one reflexion only configuration Symmetric configuration, double Fabry-Perot effect Conf. 957 The Nature of Light: What are Photons? VI San Diego, 8--5

11 MZ interferometer OPD modulation δ Achromatic phase-shift φ ±π/ when δ Equal to [π] otherwise I ( k ) 4 AT AR + 4 AT AR sin δ δ D M BS D δ +δ I I ( k ) 4 AT AR cos δ Energy conservation OK A BS M OPD modulation In agreement with quantum optics Conf. 957 The Nature of Light: What are Photons? VI San Diego, 8--5

12 MZ interferometer Wave optics model At zero optical path difference. With OPD modulation Arm Arm Output phase (rad) Output power (a. u.) Arm Arm BS internal phase (Fractions of Pi) π As measured in 4 Arm Arm Difference [π] [Pi] π/ 4 +π/ GRA experiment BS internal phase (Fractions of Pi) π OPD (Fractions of Lambda) Arm 8 Arm Difference [Pi] [π] 6 4 +π OPD (Fractions of Lambda) Conf. 957 The Nature of Light: What are Photons? VI San Diego, 8--5

13 Conclusion Quantum and wave optics BS theories are in global agreement. They both describe a ±π/ phase shift between transmitted/reflected electric fields Quantum physics is a macroscopic "black-box" model Classical optics evidences a multi-interference effect 4 th -order interference (HBT) experiments show anticorrelation of BS outputs (GRA) Quantum physics Interpretation confirms photon existence Can also be explained with classical wave optics model including the ±π/ phase shift Future work on other interference experiments Mach-Zehnder, Hong-Ou-Mandel Conf. 957 The Nature of Light: What are Photons? VI San Diego,