TEACHING EXPERIMENTS ON PHOTON QUANTUM MECHANICS

1. TEACHING EXPERIMENTS ON PHOTON QUANTUM MECHANICS Svetlana Lukishova, Carlos Stroud, Jr, Luke Bissell, Wayne Knox The Institute of Optics, University of Rochester, Rochester NY OSA Annual Meeting Special Symposium “Quantum Optics and Quantum Engineering for Undergraduates , 23 October 2008, Rochester NY

2. Generation and detection of single and entangled photons using modern photon counting instrumentation Areas of applications of photon counting instrumentation [prepared by organizers of second international workshop “Single Photon: Sources, Detectors, Applications and Measurements Methods” (Teddington, UK, 24-26 October 2005)].

3. Students Anand C. Jha, Laura Elgin, Sean White contributed to the development of these experiments and to the alignment of setups In this talk the results of the following students (Fall 2008) are used: Kristin Beck, Jacob Mainzer, Mayukh Lahiri, Roger Smith, Carlin Gettliffe

4. Teaching course “Quantum Optics and Quantum Information Laboratory” consists of four experiments: Lab. 1: Entanglement and Bell inequalities; Lab. 2: Single-photon interference: Young’s double slit experiment and Mach-Zehnder interferometer; Lab. 3: Confocal microscope imaging of single-emitter fluorescence; Lab. 4: Hanbury Brown and Twiss setup. Fluorescence antibunching and fluorescence lifetime measurement. Lab 1 is also part of the Advanced Physics Laboratory course of the Department of Physics and Astronomy

5. Lab. 1. Entanglement and Bell inequalities In quantum mechanics, particles are called entangled if their state cannot be factored into single-particle states. Any measurements performed on first particle would change the state of second particle, no matter how far apart they may be. This is the standard Copenhagen interpretation of quantum measurements which suggests nonlocality of the measuring process . The idea of entanglement was introduced into physics by Einstein-Podolsky-Rosen GEDANKENEXPERIMENT (Phys. Rev., 47, 777 (1935)).

6. In the mid-sixties it was realized that the nonlocality of nature was a testable hypothesis (J. Bell (Physics, 1, 195 (1964)), and subsequent experiments confirmed the quantum predictions. 1966: Bell Inequalities – John Bell proposed a mathematical theorem containing certain inequalities. An experimental violation of his inequalities would suggest the quantum theory is correct.

7. Lab. 1. Entanglement and Bell inequalities Creation of Polarization Entangled Photons: Spontaneous Parametric Down Conversion Type I BBO crystals

8. Downconverted light cone with λ = 2 λinc from 2mm thick type I BBO crystal

9. Lab. 1. Entanglement and Bell inequalities Initial experiment of P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, P.H. Eberhand, ”Ultrabright source of polarization-entangled photons”, Phys. Rev. A. 60, R773 (1999). • D. Dehlinger and M.W.Mitchell, “Entangled Photon Apparatus for the Undergraduate Laboratory,”Am. J. Phys,70, 898 (2002). • D. Dehlinger and M.W.Mitchell, “ Entangled Photons, Nonlocality, and Bell Inequalities in the Undergraduate Laboratory”,Am. J. Phys, 70, 903 (2002).

10. Laser Quartz Plate Mirror BBO Crystals Experimental Setup

11. Filters and Lenses APD Beam Stop APD Polarizers Experimental Setup

12. Dependence of Coincidence Counts on Polarization Angle The probability P of coincidence detection for the case of 45o incident polarization and phase compensated by a quartz plate, depends only on the relative angleβ-α: P(α, β) ~ cos2 (β-α).

13. Dependence of Coincidence Counts on Polarization Angle

14. , where: Calculation of Bell’s Inequality We used Bell’s inequality in the form of Clauser, Horne, Shimony and Holt, Phys. Rev. Lett., 23, 880 (1969) Bell’s inequalities define the sum S. A violation of Bell’s inequalities means that |S|>2. The above calculation of S requires a total of sixteen coincidence measurements (N), at polarization angles α and β:

15. Entanglement and Bell’s inequalities QUEST = QUantumEntanglement in Space ExperimenTs (ESA) A. Zeilinger. Oct. 20, 2008. “Photonic Entanglement and Quantum Information” Plenary Talk at OSA FiO/DLS XXIV 2008, Rochester, NY.

16. Lab. 2. Single-photon interference Concepts addressed: • Interference by single photons • “Which-path” measurements • Wave-particle duality M.B. Schneider and I.A. LaPuma, Am. J. Phys., 70, 266 (2002).

17. Polarizer D NPBS mirror |V> screen Polarizer C Path 2 Polarizer A Path 1 |H> mirror laser PBS Spatial filter Polarizer B Polarizer D at 45 Fringes Polarizer D, absent No Fringes Lab. 2. Single-photon interference Mach-Zehnder interferometer

18. Photograph of Mach-Zehnder Interferometer Setup

19. Single-photon Interference Fringes

20. Young’s Double Slit Experiment with Electron Multiplying CCD iXon Camera of Andor Technologies 0.5 s 1 s 2 s 3 s 4 s 5 s 10 s 20 s

21. Labs 3-4: Single-photon Source Lab. 3. Confocal fluorescence microscopy of single-emitter Lab. 4. Hanbury Brown and Twiss setup. Fluorescence antibunching

22. Single-photon Source (Labs 3-4) • Efficiently produces photons with antibunching characteristics; • Key hardware element in quantum communication technology

23. To produce single photons, a laser beam is tightly focused into a sample area containing a very low concentration of emitters, so that only one emitter becomes excited. It emits only one photon at a time. To enhance single photon efficiency a cavity should be used

24. Confocal fluorescence microscope and Hanbury Brown and Twiss setup 76 MHz repetition rate, ~6 ps pulsed-laser excitation at 532 nm

25. We are using cholesteric liquid crystal 1-D photonic bandgap microcavity o= navPo,  = on/nav , where pitch Po = 2a (a is a period of the structure); nav= (ne + no)/2; n = ne - no .

26. Selective reflection curves of 1-D photonic bandgap planar-aligned dye-doped cholesteric layers(mixtures of E7 and CB15)

27. Blinking of single colloidal quantum dots in photonic bandgap liquid crystal host (video)

28. Confocal microscope raster scan images of single colloidal quantum dot fluorescence in a 1-D photonic bandgap liquid crystal host Histogram showing fluorescence antibunching (dip in the histogram) Antibunching is a proof of a single-photon nature of a light source.

29. Values of a second order correlation function g(2)(0) g(2)(0) = 0.18 ±0.03 g(2)(0) = 0.11 ±0.06

30. Future plans for new teaching experiments • Using a new UV argon ion laser we are planning to make some new experiments on entangled photon generation in a spontaneous parametric down conversion process • Development of the experiments on spectroscopy and fluorescence lifetime measurements of colloidal quantum dots in microcavities for single-photon source applications. • Development of a simple single-photon source setup Acknowledgements By courtesy of S. Trpkovski (QCV) The authors acknowledge the support by the National Science Foundation Awards DUE-0633621,ECS-0420888,the University of Rochester Kauffman Foundation Initiative, and the Spectra-Physics division of Newport Corporation. The authors thank L. Novotny, A. Lieb, J. Howell, T. Brown, R. Boyd, P. Adamson for advice and help, and students A. Jha, L. Elgin and S. White for assistance.