Experiments with correlated photons: From advanced-lab projects to dedicated laboratories. Advanced-Lab Conference 2009

Transcription

1 Experiments with correlated photons: From advanced-lab projects to dedicated laboratories Advanced-Lab Conference 009

2 Contributors Charles Holbrow Lauren Heilig 0 Naomi Courtemanche 0 James Martin 03 Matt Pysher 04, Justin Spencer 05 Mehul Malik 06 Brad Melius 06 Kyle Wilson 06 Bryce Gadway 07 Ben Reschovski 07 Erik Johnson 08 Ushnish Ray 08 Laura Coyle 09 Claire Watts 0 Ashish Shah 0 Colgate University, Hamilton, New York Liberal-arts college in Central New York 800 students Thanks to: Mark Beck, Joe Eberly, Paul Kwiat, Vic Mansfield, Beth Parks, Anton Zeilinger, Bill Wooters. Funded by CCLI grants DUE DUE-04488

3 Quantum Agenda at Colgate st semester course on modern physics (0+ years old) Text: Modern Introductory Physics, Holbrow et al Covers main features of modern physics: wave-particle duality, relativity, quantization, plus baby quantum mechanics (5 years old). Includes a lab on the quantum eraser. Rationale: teach the topics that excite physicists first. Junior-Senior quantum mechanics with lab (since 005) Dirac notation (text: Townsend) Emphasize fundamentals (Superposition etc.-include Bell) Lab has five experiments using single photons. See Holbrow et al AJP 70, 60 (00) ; Galvez et al AJP 73, 7 (005). See also (Friday workshop Rm 447). Capstone projects as advanced-lab requirement (poster 7) Independent, table-top Ulterior goal is to develop new labs for QM course Very productive side-shows: Phys Rev A s, J. Phys B, more to come.

4 Agenda: new labs, but also new views Main Apparatus Quantum labs Quantum superposition: one photon at a time The Eraser and distinguishability: quantum interference without Heisenberg Wavepackets and measurement Biphotons: nonclassical path interference Entanglement and reality

5 The photon source: photon pairs produced by spontaneous parametric down conversion Parametric down conversion (DC) requires that the photon energy and momentum must be conserved: E p = E DC-signal + E DC-idler energy correlation k p = k DC cos θ s + k DC cos θ i spatial correlation Leonard Mandel k p BBO crystal k DC-signal k DC-idler θ s θ i Crystal: Beta-bariumborate 5x5x3 mm $0.5- k Downconverted photons are produced simultaneously

6 Pump laser SPDC produce photon pairs at half the energy, twice the wavelength. Visible lasers would produce DC in near-ir, where PMT are inefficient. Best option are avalanche photodiodes APD. Peak efficiency at 700 nm. Best affordable source are blue diode lasers at 40 nm--40 nm. GaN laser: 375nm (few mw), 405 nm (up to 00 mw) ($7k module) ($.5k no temp control) If other gas lasers are at hand they also work: Ar ion lasers 350 nm, 458 nm HeCd 44 nm

7 Optical layout x5 optical breadboard Standard optics for Near-IR Low-height mounting hardware (pedestals are best). HeNe or fiber laser needed for alignment.

8 Avalanche Photodiode Detectors detectors Bare or fiber-coupled (best): $4k each or $0k for four lenses Bare (need to be boxed in) Multimode fibers

9 Key to insure single-photon events: coincidence detection Options: - NIM Electronics - black box does it all + PC (Mark Beck Whitman College Branning et al AJP 77, 667 (009))

10 Quantum superposition Light going through an interferometer moves in two directions (qubit). If the arms have the same length and no distinguishable features, the path taken by the light from A to B is undefined. The state of the light is in a superposition of going through both paths: x BS x BS i x + + M i i y y ( iδ ) ( ) iδ iδ iδ e + e x + e + e y interference P A B = y x A δ = i πli λ ( + cos( δ δ )) l l C B

11 Feynman s approach Outcomes of measurements are described in terms of probabilities P. The probability amplitude has both magnitude p and phase δ, and the probability of an outcome is the square of the probability amplitude for that outcome: P = p When an event can occur in several alternative ways, with probability amplitudes (p,δ ) and (p,δ ) then the total probability amplitude is the (vector) sum of the individual probability amplitudes, and the probability is the square of the magnitude of the combination P = p + p + p p cos δ δ For the interferometer p = p = So, if the paths are indistinguishable then P = + cosδ if we make δ = δ δ M If the alternate paths are distinguishable + = P = p p there is no interference ( ) ( ) BS Richard Feynman M BS

12 An experiment: single photons through an interferometer Ingredients: Heralded photon source Interferometer Single-photon detectors Electronics/computer The probability is P = ½ ( + cos δ ) We change δ by changing the length of one of the arms (πδl/λ). the photon then only interferes with itself P.A.M. Dirac coincidences δ/π data fit

13 Classical vs. non-classical source Why not an attenuated source? The single photon must not split at a beam splitter: source must pass the Hanbury-Brown-Twiss test of the degree of second order coherence C () PBC g (0) quant = = 0 () I BIC g (0) class = P P I I B Experiment: measure triple coincidences at A, B and C B () C g (0) = C B exp N N AB ABC N AC coincidences B C datab fit datac triples g*000 A δ/π

14 The Eraser M HWP (θ) BS ( ) APD John Wheeler: it is bit APD HWP=0 : polarization is not disturbed: indistinguishable paths. The probability is: P = ½ ( + cos δ) there is interference HWP=45 : Rotates the polarization to horizontal. The probability is: P = ½ no interference (possibilities are distinguishable) BS coincidences M Polarizer at 45 = ( ) = ( + ) Voltage on piezo x5 (V) HWP=0 HWP=0 HWP=45 HWP=0 HWP=45 Pol in A polarizer (at 45 ) is added after the interferometer. The probability becomes: P = ¼ ( + cos δ) interference reappears (the distinguishing information is erased) Note: photon is not disturbed: we do not need to appeal to Heisenberg to destroy the interference.

15 Photon Wavepackets and post selection The photons are in a coherent superposition of energy eigenstates. They form a wavepacket. Δλ Δt = λ /(cδλ) The length of the photon wavepacket λ t l c = c Δt is the coherence length

16 Which way? skip When the paths are indistinguishable there is interference. If the difference in length of the two arms is Δ l M BS Δl > l c BS M Δl < l c Photons arrive at similar times: paths are indistinguishable. Photons arrive at distinguishable times: in principle we can determine the whichway information by timing the photon pulses.

17 M BS APD F APD F BS M The experiment:. We put 0-nm filters in front of the detectors: the length of the photon wave packet is l c = 80 μm.. We align the laser to see fringes (as in previous experiment). 3. We quantify the degree of coherence with the visibility of the fringes V: P = ½ ( + V cos δ ) coincidences in 0 s phase / pi V = (N max N min ) / (N max + M min ) V = 0.8 ± 0.05

18 00 Increase the length of one of the arms by 36 μm coincidences in 0 s V = 0.3 ± phase / pi 00 by 7 μm V = 0.0 coincidences in 0 s phase / pi

19 Increase the path length difference by 80 μm V = 0.0 ± 0.0 coincidences in 0 s phase / pi Note: a timing measurement of photon arrival times is not made. Interference disappears as soon as the path information is available, regardless of whether we measure it or not.

20 Post-selection M BS APD F Put a 0.-nm filter (in front of the idler). APD F F=0. nm BS M This forces the detected photon wave packet to be ten times larger: l c = 8 mm > Δl, making the which-way information unavailable, and thus the paths indistinguishable. V = 0.59 ± 0.04 coincidences in 0 s phase / pi State of the light is determined by post-selection: a collapse of the two-photon wave function.

21 Two Photons or biphotons? An example of nonclassical path interference Two collinear photons enter an interferometer. C Displaced for sake of clarity B A Counts in 5 s δ/π Possibilities for one-photon: + P = (/) ( + cos δ ) Possibilities for photons leaving through the same port: P AB = (/4) ( + cos δ ) Possibilities for two-photons leaving through separate ports : P xx = (/4) ( + cos δ ) Glauber: it is amplitudes that interfere + + +

22 Apparatus C piezo+stage B BBO crystal A optical fiber polarizers MZ iris filter The two photons are in a correlated state. They act as a single quantum: the biphoton The result can be shown analytically to be due to the symmetry of the bosonic wave function. Galvez & Beck, Proceedings of ETOP, 007

23 Entanglement and Reality H W H P D st crystal produces nd crystal produces b b P D If the source crystal is indistinguishable then the light is in a superposition: Φ ± = ( ± bb ) Erwin Schrödinger Entangled state cannot be decomposed into a product of single-particle states; measurement on one photon determines the state of the other. Two qubits Einstein: spukhafte fernwirkung or spooky action at a distance.

24 Polarization Correlations Φ + = ( + ) ( + ) Photon pairs are correlated (parallel) regardless of the orientation: P = ½ cos (θ θ ). If θ = π/4 P = ¼ ( + sin θ ) 50 θ Polarizers Experiment: P fixed ( ), P turned θ If photons are in a mixed state (i.e., half the time in and the other half in ), then the results are different: when θ = π/4, P = ¼ coincidences in 0 s P=45 Ent P=45 ent P=45 mix This can best be treated analytically with the density matrix Polarizer (degrees)

25 Bell Inequalities From lab write-up John Bell Realistic view: a reality exists independent of the observation Quantum view: observables do not have preexisting values Other quantum tenets: indeterminism, nonlocality, contextuality The Clauser-Horne-Shimony Holt tests against reality and locality Correlation parameter: E( α, β ) = P( α, β ) + P( α, β ) P( α, β ) P( α, β ) α, β angles, α = α + π/, β = β + π/. For an entangled state E = ±, and for a mixed state If we define E = 0 S = E( α, β ) E( α, β ) + E( α, β ) + E( α, β ) Realistic view predicts: S In the lab students get S =.39 ± 0.09: violation! (see also Dehlinger & Mitchell AJP 70, 903 (00))

26 The quantum labs Advanced lab

27 To conclude Experiments with single photons directly probe quantum mechanics they are explained by the quantum mechanics of a single quantum ( on your face quantum mechanics ). Experiments are table-top, feasible, and reproducible. Student feedback is very positive. Experiments provoke discussion and debate about fundamental questions, plus they are fun and spooky Webpage: see also

28 Density Matrix Crash course: states are represented by matrices ψ ψ ρ ψ = ˆ If = + = a a a a φ φ ψ = ˆ a a a a a a a a ρ ψ then Thus ˆ) ( = ρ Tr (conservation of probability) The probability of state Ψ> being in state ϕ> is ) ˆ ˆ ( ˆ ψ ϕ ψ ρ ρ ϕ ρ ϕ Tr P = = An incoherent mixture of basis states φ > and φ > can be represented by = + = 0 0 P P P P m φ φ φ φ ρ ϕ φ Mixed state does not have off-diagonal elements.

29 Measuring correlations Basis H = 0 V 0 = Photon pol at angle θ Photon pol at 45º θ D = θ D θ Two-photon state: cosθ = cosθ H + sinθ V = sinθ = H + V = cosθ cosθ D = 50 sinθ 00 sinθ θ D θ D ˆ ρ + Φ θ D = ( + sin θ ) θ D Entangled state projected onto : Entangled state projected onto θ D ˆ ρ D = m θ coincidences in 0 s ret θ Polarizers Polarizer (degrees) π/4 P=45 Phi+ P=45 mix