1. An Experimental Implementation of Hardy’s Paradox Jeff Lundeen, Kevin Resch Aephraim Steinberg University of Toronto June 2003 Funding by: NSERC, PRO, Sumner. Zeno’s Paradox : Achilles and The Tortoise

2. BS1 BS2 I O D C Bang½Neither Present¼D None¼C ResultProb.Detector Bomb Present: Bomb Absent: Only detector C fires Interaction-Free Measurement A. C. Elitzur, and L. Vaidman, Found. Phys. 23, 987 (1993)

3. IFM On A Quantum Object BS1 BS2 I O D C A click at D collapses the bomb’s superposition

4. BS1 - BS2 - O-O- C-C- BS1 + BS2 + I+I+ e+e+ e-e- I-I- O+O+ D+D+ C+C+ D-D- W OutcomeProb D + and C - 1/16 D - and C + 1/16 C + and C - 9/16 D + and D - 1/16 Explosion4/16 Hardy’s Paradox L. Hardy, Phys. Rev. Lett. 68, 2981 (1992)

5. The Switch  PUMP   Coinc. Counts 22  PUMP - 2 x  LO  LO   +  PUMP 2 x  LO = 2  LO -  PUMP =  K. J. Resch, J. S. Lundeen, and A. M. Steinberg, Phys. Rev. Lett. 87, 123603 (2001).

6. GaN Diode Laser PBS Det. H (D-)Det. V (D+) DC BS 50-50 BS1 50-50 BS2 Switch H V CC PBS Experimental Setup (W)(W)

7. H Pol DC V Pol DC 407 nm Pump

8. What do we need to measure? Ideally If D + clicks  - photon is in I - IFM + If D - clicks  + photon is in I + IFM - There is never a photon in I - and I + Annihilation at W Sometimes both D + and D - click The paradox For a Real Apparatus Vis Hor Int Vis Vert Int Vis Switch Vis Switch + Vis Int 2  7/4

9. Vs + Vmz 2  7/4 Required Interferometer Visibilities To Show Hardy’s Paradox

12. MeasurementPointer Position Uncertainty IdealDirac Delta RealWidth << Change in Position WeakWidth >> Change in Position Weak Measurements  X  P  h/2   small disturbance  little system – pointer entanglement No system disturbance  simultaneous measure of different weak values. Y. Aharonov, A. Botero, S. Popescu, B. Reznik, J. Tollaksen, e-print quant-ph/0104062 (2001). Pointer(X) = exp[-(X - gA W ) 2 /  X]

13. Weak Measurements in Hardy’s Paradox Y. Aharanov, A. Botero, S. Popescu, B. Reznik, J. Tollaksen, e-print quant-ph/0104062 (2001). Det. H (D-)Det. V (D+) /2 N(I - ) N(O  ) N(I + ) N(O + ) Pol. BS2 + BS2 -

14. Conclusions An experimental implementation of Hardy’s Paradox is now possible. A single-photon level switch allows photons to interact with a high efficiency. The first version of the experiment will be a polarization based system. A later extension will look at the results of weak measurements in Hardy’s Paradox.