Physics 2108-S1 (Special Topics in QO)
Classic experiments in multi-photon interference: an approach to quantum foundations & quantum information

• General remarks from lecture 1 concerning "background" reading (before I start assigning specific research papers):
  • Review your favorite quantum optics textbook, regarding second quantization, creation & annihilation operators, classical & nonclassical states of light, and the beam splitter. [Gerry-Knight / Loudon / Walls-Milburn / Sargent-Scully-Lamb / Scully-Zubairy / Garrison-Chiao / Grynberg-Aspect-Fabre / ... Fox's book also appears very good on this score.]
    • {Mandl+Shaw / Heitler / Sakurai / CCT–Dupont-Roc–Grynberg can be excellent if you want a deeper discussion of the meat of the field theory, which we'll be using at a very cursory level only.}
  • But I strongly recommend the horse's mouth, which is to say Glauber, e.g. the articles collected in "Quantum Theory of Optical Coherence"
  • I'll share some excerpts of these things by Piazza, along with an ancient review article I & Paul Kwiat wrote with our PhD supervisor, but which I still think serves as a "table of contents" trying to draw a thread among these different phenomena and experiments. Also Ivan Deutsch's lecture notes on QO.




• From lecture 2 (for 12-19 January):
  • As needed, review:
    • Field quantization [e.g., chapter 2 of Gerry + Knight]
    • Coherent states [e.g., 3.1-2 of G&K; more of ch 3 may be of interest]
  • The QM of beam splitters [e.g., 6.1-2 of G&K]
  • Horse's mouth: Glauber, e.g., sections 2.1-2.4 of Quantum Theory of Optical Coherence (Wiley, 2007) [or via http://quantum.phys.unm.edu/400-18/Glauber1965a.pdf]
  • As threatened, I recommend the short review "Quantum Optical Tests of the Foundations of Physics" by myself, Paul Kwiat, & Ray Chiao: https://www.physics.utoronto.ca/~steinber/Quantum_Optical.pdf for an overview of how some of these topics fit together.
  
  
  • Bibliography of relevant research papers (I recommend glancing at all but reading the GRA paper)
    • R. Hanbury Brown & R.Q. Twiss, "A new type of interferometer for use in radio astronomy," Philosophical Magazine. 45, 663 (1954) : doi:10.1080/14786440708520475
    • Grangier, Roger, & Aspect, "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on Single-Photon Interferences," Europhys. Lett. 1, 173 (1986)
    • Magyar & Mandel, "Interference Fringes Produced by Superposition of Two Independent Maser Light Beams," Nature 4877, 255 (1963)
  
  

• For 21-28 January:
  • Another "overview" option, complementary to Glauber suggestion: Mandel + Wolf Rev. Mod. Phys. 37, 231 (1965)
  • Required reading for this week:
    • "Interaction-Free Measurement," Kwiat, Weinfurter, Herzog, Zeilinger, and Kasevich, PRL 74, 4763 (1995)
      • See also: "Quantum Mechanical Interaction-Free Measurements," Elitzur & Vaidman, Found. Phys. 23, 987 (1993)
    • "Quantum optical tests of complementarity," Scully, Englert, & Walther, Nature 351, 111 (1991)
      • See also "Delayed `Choice' Quantum Eraser," Kim, Yu, Kulik, Shih, & Scully, PRL 84, 1 (2000); "Three proposed `quantum erasers'," Kwiat, Steinberg, & Chiao, PRA 49, 61 (1994)
    • "Induced Coherence and Indistinguishability in Optical Interference," Zou, Wang, & Mandel, PRL 67, 318 (1991)
    • "Fringe Visibility and Which-Way Information: An Inequality," Berthold-Georg Englert, PRL 77, 2154 (1996)
  • Looking ahead to next week:
    • "Measurement of Subpicosecond Time Intervals between Two Photons by Interference," Hong, Ou, & Mandel, PRL 59, 2044 (1987)>
      • See also: "Observation of Nonclassical Effects in the Interference of Two Photons," Ghosh & Mandel, PRL 59, 1903 (1987); "Observation of Spatial Quantum Beating with Separated Photodetectors," Ou & Mandel, PRL 61, 54 (1988)
  
  
• For 1-8 February:
  • Required reading:
    • "Measurement of Subpicosecond Time Intervals between Two Photons by Interference," Hong, Ou, & Mandel, PRL 59, 2044 (1987)
    • "Bell Inequality for Position and Time," J.D. Franson, PRL 62, 2205 (1989)
    • "High-visibility interference in a Bell-inequality experiment for energy and time," P.G. Kwiat, A.M. Steinberg, and R.Y. Chiao, PRA 47, R2472 (1993)
  • Complementary recommendations:
    • Again, "Observation of Nonclassical Effects in the Interference of Two Photons," Ghosh & Mandel, PRL 59, 1903 (1987); "Observation of Spatial Quantum Beating with Separated Photodetectors," Ou & Mandel, PRL 61, 54 (1988) may be of interest
    • "Dispersion cancellation and high-resolution time measurements in a fourth-order optical interferometer," A.M. Steinberg, P.G. Kwiat, and R.Y. Chiao, PRA 45, 6659 (1992)
    • "Frustrated two-photon creation via interference," T.J. Herzog, J.G. Rarity, H. Weinfurter, and A. Zeilinger, PRL 72, 629 (1994)
    • "Electromagnetically induced opacity for photon pairs," K.J. Resch, J.S. Lundeen, & A.M. Steinberg, J. Mod. Opt. 49, 487 (2002)


• Supplementary bibliography on enhanced & inhibited spontaneous emission (Purcell effect):
  Although it's not precisely the subject of this class, during the discussion of the "railcross" experiment it was revealed that most of you were unaware of the Purcell effect – not only a classic (and fundamentally provocative) quantum optics effect, but also important in modern lasers, single-photon sources, et cetera. While originally discussed in terms of modification of the density of states, and/or the vacuum itself, one can think of it in terms of a quantum interference effect. To reach a certain point inside a cavity, a photon could have been emitted by an atom at that point just this instant, or emitted any multiple of 2L/c ago and made the appropriate number of round trips. Do these possibilities interfere constructively or destructively? A beautiful semiclassical picture of the inhibition of spontaneous emission for an atom sitting very close to a metallic mirror is that the mirror creates "image charges" equal and opposite to those of the atom: these radiate out of phase with the atom's radiation pattern, and if the distance approaches zero, destructive interference becomes perfect. [Considering the "other output port" of the "interferometer," one might say that while the atom can emit, the field reflected by the mirror has just the right phase to be perfectly reabsorbed by the atom.]
  • "Inhibited spontaneous emission," Dan Kleppner, PRL 47, 233 (1981)
  • "Inhibited Spontaneous Emission by a Rydberg Atom," Hulet, Hilfer, & Kleppner, PRL 55, 2137 (1985)
  • "Enhanced Spontaneous Emission by Quantum Boxes in a Monolithic Optical Microcavity," Gérard et al., PRL 81, 1110 (1998)
  • To see the relevance to emerging technologies today: "Ultrabright source of entangled photon pairs," Dousse et al., Nature 466, 217 (2010)
  • For a maagazine-level review: "Cavity Quantum Electrodynamics," Haroche & Kleppner, Physics Today 42, 24 (1989) [see http://ursula.chem.yale.edu/~batista/classes/CHEM584/Physics_Today-042-1989-January-044-Haroche.pdf if you have trouble accessing it directly]
  • For a pedagogical & semiclassical approach: "Dipole radiators in a cavity: A radio frequency analog for the modification of atomic spontaneous emission rates between mirrors," Seeley et al., Am. J. Phys. 61, 545 (1993); and "Spontaneous Emission in Cavities: How Much More Classical Can You Get?", Jon Dowling, Found. Phys. 23, 895 (1993).
  • For those who want to dig more deeply: "The Quantum Vacuum: an introduction to quantum electrodynamics," Peter Milonni (Academic Press, 2013), which I hope we still have in the library, because someone ran off with my copy, and https://www.amazon.ca/Quantum-Vacuum-Introduction-Electrodynamics-ebook/dp/B01H5GQI3O claims that at $107.09, the hardcover is slightly cheaper than the (!) Kindle edition.
  • For additional subtleties (polarization- and field-dependence, and the "anisotropy of the vacuum"(?): Jhe et al., PRL 58, 666 (1987)
  • For a dramatic, personal, historical account, perhaps the most interesting source would be Serge Haroche's Nobel Lecture: Controlling Photons in a Box and Exploring the Quantum to Classical Boundary (2012); and/or videos at https://www.nobelprize.org/prizes/physics/2012/haroche/lecture/
  
  
• For 8-13 February:
  • Required reading:
    • "Probabilistic quantum logic operations using polarizing beam splitters," Pittman, Jacobs, and Franson, Phys. Rev. A 64, 062311 (2001)
      • For further info, see: experiment = "Demonstration of Nondeterministic Quantum Logic Operations Using Linear Optical Elements," Pittman, Jacobs, and Franson, Phys. Rev. Lett. 88, 257902 (2002)
    • "Nondeterministic Noiseless Linear Amplification of Quantum Systems," Ralph and Lund, arXiv: 0809.0326 (2008)
      For further information, see:
      • "Heralded noiseless amplification of a photon polarization qubit," Kocsis, Xiang, Ralph, and Pryde, Nat. Phys. 9, 23 (2013)
      • "Nondeterministic noiseless amplification of optical signals: a review of recent experiments," Barbieri, Ferreyrol, Blandino, Tualle-Brouri, and Grangier, Laser Phys. Lett. 8, 411 (2011)
      • Earlier inspiration = "Optical State Truncation by Projection Synthesis," Pegg, Phillips, and Barnett, Phys. Rev. Lett. 81, 1604 (1998)
    • Entanglement Test on a Microscopic-Macroscopic System, De Martini, Sciarrino, and Vitelli, Phys. Rev. Lett. 100, 253601 (2008)
    If interested, see more:
    • "Proposal for exploring macroscopic entanglement with a single photon and coherent states," Sekatski, Sangouard, Stobinska, Bussieres, Afzelius, and Gisin, Phys. Rev. A 86, 060301 (2012)
    • "Entanglement of macroscopically distinct states of light," Sychev, Novikov, Pirov, Simon, and Lvovsky, Optica 6, 1425 (2019)
  • Supplementary recommendations:
    • "Quantum-mechanical noise in an interferometer," Carlton M. Caves, Phys. Rev. D 23, 1693 (1981)
    • "A scheme for efficient quantum computation with linear optics," Knill, Laflamme, and Milburn, Nature 409, 46 (2001)
    • Demonstration of an all-optical quantum controlled-NOT gate, O'Brien, Pryde, White, Ralph, and Branning, Nature 426, 264 (2003)
    • For a review, "Linear optical quantum computing with photonic qubits," Kok, Munro, Nemoto, Ralph, Dowling, and Milburn, Rev Mod Phys 79, 135 (2007)
    • Preparation of pure and mixed polarization qubits and the direct measurement of figures of merit, Adamson, Shalm, and Steinberg, Phys Rev A 75, 012104 (2007); see also "Measuring entanglement entropy in a quantum many-body system," Islam, Ma, Preiss, Tai, Lukin, Rispoli, and Greiner, Nature 528, 77 (2015)
  
  
• Final assignment (14-17 February):
  • Required:
    • Quantum State Reconstruction of the Single-Photon Fock State, Lvovsky, Hansen, Aichele, Benson, Mlynek, and Schiller, PRL 87, 050402 (2001); you may also wish to look at "Quantum process tomography with coherent states," Rahimi-Keshari, Scherer, Mann, Rezakhani, Lvovsky, and Sanders, New J. Phys. 13, 013006 (2011)
    • Photonic Boson Sampling in a Tunable Circuit, Broome, Fedrizzi, Rahimi-Keshari, Dove, Aaronson, Ralph, and White, Science 339, 794 (2013); you may also wish to look at "Quantum computational advantage with a programmable photonic processor," Madsen et al., Nature 606, 75 (2022)
  • Supplementary:
    • Weak nonlinearities: a new route to optical quantum computation, Munro, Nemoto, and Spiller, New J. Phys. 7, 137 (2005)

• Problem set 1 assigned Sun 21.1.23, due Thu 2.2.23
• Problem set 2 assigned 3.2.23, due 13.2.23