Direct Measurement of the Photon Wavefunction Single Photon Workshop: Boulder Nov 3, 2009

Transcription

1 Direct Measurement of the Photon Wavefunction Single Photon Workshop: Boulder Nov 3, 2009 Charles Bamber, Jeff Lundeen, Joanne Zwinkels, Rick Gerson, Aabid Patel, Corey Stewart, Brandon Sutherland

2 Presentation Outline Direct Measurement of the wavefunction What does that mean? How can that be achieved? Setting up the wavefunction /identical photons Projection of the wavefunction Results with a classical source Single photon experiment Conclusion

3 How can the wavefunction of a photon be measured directly? We normally measure intensity, *

4 The wavefunction is generated by collimating the output of a single mode fiber Sequential measurements on a source of identical photons = Simultaneous measurements of single photon

5 A2 nd lens converts to momentum space for post-selectionselection x f f p Photon Pos sition (x) Mom mentum (p) Lens, focal length=f

6 Position x f The electric field as sampled by the halfwaveplate sliver interferes with the undisturbed field at the pinhole f Moment um p LHC (LHC-RHC) Im (x) RHC (x) H=gtS y x x half-waveplate sliver (p) /4 waveplate PBS H BS V (H-V) Re (x) Lens, focal length=f Pinhole

7 Weak measurement of position, while postselecting on momentum Weak Value = < A > A W = < > A W = x x =π, Initial state = ψ, Final State = p π w = p x x ψ / p ψ If p=0, π w = ψ(x)[1/ (0)] Where (p) is the Fourier Transform of x

8 E probed sinθ is projected onto the s & p axes in opposite directions -45 θ probed field unprobed field +45 Rotation of polarizer wrt halfwave sliver sets θ Width of sliver sets magnitude of probed field vector

9 Initial data has been taken with a CW source Direct Measurement of Transverse Wavefunction real imaginary lens edge < A > A W = < > A < A > W = < > lens edge transverse position (mm) -0.03

10 Parametric downconversion In the next phase a single photon source will be measured

11 Conclusions Direct measurements of single photons are possible Initial study with CW beam is underway Single photon source measurements will begin in the near future

12 INMS Research Team Right to left: Dr. Jeff Lundeen (RA) Corey Stewart (student) Dr. Charles Bamber Rick Gerson Aabid Patel (student) Brandon Sutherland (small student) New INMS Quantum Metrology Research Facility

13 Thank you for your attention

14 Measurement dependence on coupling strength has been confirmed relative effect normalized (A-B)/(A+B) coupling strength i.e pol ang 5 deg 10 deg 15 deg 20 deg 0 deg - 5 deg -10 deg -15 deg -20 deg position halfwave plate in analyser

15 Usually the act of measurement changes the wavefunction

16 Measurements can still be made with reduced coupling strength Initial Pointer Position Uncertainty Pointer shift due to interaction Ideal E ¼ ½ ¾ F gt H int =gpâ E ¼ ½ ¾ F gt Real E ¼ ½ ¾ F H int =gpâ E ¼ ½ ¾ F gt gt Weak E ¼ ½ ¾ F gt X >> gt H int =gpâ < A > Weak <ψ Â ψ> Value = A W = < > E ¼ ½ ¾ F gt Aharonov, Albert,&Vaidman, PRL 60, 1351 ('88)

17 Weak Measurement of a photon s polarization using it s transverse momentum as a pointer H int =g H H P pointer Final Polarization State (post-selection) 45º gt -45º + Gaussian spatial profile Initial Polarization state Weak Measurement with a Calcite Crystal weak value Readout of Weak Measurement