Interference, Complementarity, Entanglement and all that Jazz

Transcription

1 nterference, Complementarity, Entanglement and all that Jazz Mark Beck Dept. of Physics, Whitman College With lots of help from: Faculty: obert Davies (Seattle U) Students: Ashifi ogo, William Snyder, Jeremy horn (U of O), Matthew eel (OSU), Vinsunt Donato (OSU) Support: SF, Whitman College Quantum Mechanics Quantum information is changing how we think about quantum systems. Convey this to students Many experiments involve photons Doable by undergraduates Project oals 1) Develop a series of advanced undergraduate laboratories exploring modern aspects of quantum mechanics Study the properties of individual photons 2) Develop course materials that take advantage of these labs Use photon polarization as an example 2- dimensional quantum system 1

2 Experiment Proving Photons Exist 1) Should be conceptually simple 2) Should display the "granular" nature of individual photons 3) ecessary to treat the field quantum mechanically ot explainable using classical waves Proving Photons Exist Photoelectric Effect? Satisfies criteria 1) & 2) detector "clicks" are granular Does O satisfy criterion 3) Does not require photons (i.e. a quantum field) for its explanation Can be explained using a semiclassical theory (detector atoms quantized, field is a classical wave) rangier Experiment P. rangier,. oger, and A. Aspect, Europhys. Lett. 1, (1986). Single Photon on a Beamsplitter f a single photon is incident on a beamsplitter, what do we know about "clicks" at output detectors? Only one detector will fire o coincidence detections " a single photon can only be detected once!" - rangier et al. 2

3 Single Photon on a Beamsplitter Quantify: : ˆˆ: (2) g (0) = ˆ ˆ P = PP P = 0 g (2) (0) = 0 (for a single photon input) he degree of second-order coherence Classical Wave on a Beamsplitter g (2) (0) P = = P P = = + = 1 2 (2) g (0) = (Cauchy-Schwartz inequality) g (2) (0) 1 (for a classical wave) Positive Correlations P Fluctuating input wave simply splits equally at a beamsplitter and are most likely to click at the same time Opposite behavior of a single photon 3

4 Distinguishing Classical and Quantum Fields Classical waves: g (2) (0) 1 herefore, any field with g (2) (0) < 1 cannot be described classically, and is inherently quantum mechanical. Single photon state: g (2) (0) = 0 Making a Single Photon State Spontaneous parametric downconversion One photon converted into two ω p ω 1 ω p =ω 1 +ω 2 ominally: ω 1 ~ω 2 ~ω p /2 ω 2 Making a Single Photon State Spontaneous parametric downconversion One photon converted into two Photons always come in pairs ω ω 1 "click" You know you have a photon in the other beam ω 2 n 1986 rangier et al. used a cascade decay in Ca as a photon pair source. 4

5 Our Experiment Look for coincidences between and, conditioned on a detection at. Everything is conditioned on a detection at : P = g P = P P (2) (0) P P = = g = (2) (0) More Details 818 nm 409 nm 20 mw BBO ype 3mm thick 3 o cone angle Detectors have 780 filters > 100,000 cps + > 8,000 cps Experimental Setup 5

6 Experimental Setup Collection Optics esults ntegration time per pt. umber of pts. otal acq. time (2) St. dev. of g (0) g (2) (0) 2.7 s 110 ~ 5 min s 108 ~ 10 min s 103 ~ 20 min s 100 ~ 40 min n 5 minutes of counting we violate the classical inequality g (2) (0) 1 by 146 standard deviations. 6

7 Why not 0? Perfect single photons have g (2) (0) = 0. i.e., we expect no coincidences between and Why do we measure g (2) (0) = ? Accidental coincidences Due to finite coincidence window (2.5 ns) Expected accidental coincidence rate explains difference from 0. Single Photon nterference nsert interference filter (10nm bandpass) here nsert interferometer here Polarization nterferometer φ BDP BDP Easy to align equal pathlengths EXEMELY stable 7

8 esults aw Counts (V=88%) Coincidence Counts, Single Photons (V=89%) Simultaneously displays wave-like (interference) and particle like (g (2) (0)<1) behavior. Wave-Particle Complementarity Wave-Particle Complementarity 8

9 Wave-Particle Complementarity Exits this way Wave-Particle Complementarity Or this way Wave-Particle Complementarity ever both ways ot even if phase of interferometer is adjusted so that on average the photon goes each way half the time. 9

10 Wave-Particle Complementarity oes both ways at first beamsplitter oes one way at second beamsplitter Wave-like behavior inside the interferometer Particle-like behavior outside the interferometer esults aw Counts (V=88%) Coincidence Counts, Single Photons (V=89%) Simultaneously displays wave-like (interference) and particle like (g (2) (0)<1) behavior. esults aw Counts L c =12µm ( λ=57nm) 2 c λ Lc = = ν λ Coincidence Counts, Single Photons L c =70µm ( λ=10nm) nterference filter in gate beam ( λ=10nm) 10

11 Frequency Entanglement nserting interference filter to decrease bandwidth of this beam ncreases the coherence length of coincident photons in this beam Entanglement Frequencies of the two beams are entangled ω p =ω +ω ω ωp frequency of pump (blue) beam, ω frequencies of gate and interferometer beams n coincidence, narrowing the distribution of ω narrows the distribution of ω. Present Source ψ pol =, 11

12 Polarization Entangled Source 2 crystals Axes rotated by 90 o 1 ψ pol = + 2 (,, ) Quantum Eraser ' Horizontal, Vertical ' ψ pol, collapse 12

13 Horizontal, Vertical ' ψ pol, collapse Photon takes one path o interference esults akes one path Have which-path info o interference esults akes one path Have which-path info o interference How do we see interference? Must take both paths Erase which-path info 13

14 Quantum Eraser ' Quantum Eraser rotate ' Entangled in Any Basis 2 crystals Axes rotated by 90 o 1 ψ pol = = + 2 (,, ) (,, ) 14

15 ±45 o rotate ' ±45 o rotate ' ψ pol, collapse Photon takes both paths nterference esults akes both paths Erased which-path info nterference aw counts (not coincidence) o interference Why? 15

16 o Coincidence Detection rotate ' o Coincidence Detection ' Detection at does O yield which-path info. Why no interference? COULD et nfo ' COULD PCPLE know which way the photon went o interference 16

17 ±45 o rotate ' esults Each polarization makes its own interference pattern Out of phase esults Add and coincidences o interference Why? Again, we re not using gate polarization info Could do a different measurement that provides whichpath information 17

18 Quantum Eraser nterference ot having which-path information is not good enough he fact that which-path information is available in principle is enough to destroy interference Only way to erase in principle information is to explicitly perform a measurement that erases it. Conclusions We have performed the following experiments Proof of the existence of photons Single-photon interference Quantum eraser A classical mixed state can mimic certain aspects of the eraser behavior est of Bell inequality S= Violates S<2 by 30 standard deviations All experiments have been performed by undergraduates, and are suitable for an undergraduate laboratory Whole able 18