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Classic Experiments in Quantum Optics Experimental Quantum Optics and Quantum Information Part II, Photonic Quantum Optics Morgan W. Mitchell Spring 2007 ICFO – Institut de Ciencies Fotoniques Quantum Optics and Quantum Information Light source Interesting physics State of light Detection Continuous Variables ← Approach → Lasers ← Light Source → Field operators, e.g. E(t) ← Description of light → Field distributions ← mixed states → Linear and NL optics, atoms ← Physics → Homodyne detection ← Detection → Discrete variables Lasers Particles, state vectors | > Density matrices Linear and NL optics, atoms Photon counting “Squeezing” Low-noise measurements (grav-wave detection) “Hong-Ou-Mandel” Foundations of physics (non-locality, Q. meas.) ← Favourite word → ← Classic → Applications Quantum Optics and Quantum Information Continuous Variables ← Approach → Lasers ← Light Source → Field operators, e.g. E(t) ← Description of light → Field distributions ← mixed states → Linear and NL optics, atoms ← Physics → Homodyne detection ← Detection → Discrete variables Lasers Particles, state vectors | > Density matrices Linear and NL optics, atoms Photon counting “Squeezing” Low-noise measurements (grav-wave detection) “Hong-Ou-Mandel” Foundations of physics (non-locality, Q. meas.) ← Favourite word → ← Classic → Applications Continuous Var. QI Discrete Var. QI Q. Entanglement Q. Teleportation Q. Gates Q. Memory Q. Entanglement Q. Teleportation Q. Gates Q. Memory Schrodinger Kittens / Cats Loophole free Bell I. tests Quantum Teleportation Quantum info output: 3 has state of 1 Joint measurement Of 1 & 2 Manipulation of half of entangled state, 3 Quantum info input: Unknown state of 1 Quantum resources input: Entangled state of 2 & 3 Better than measure 1, prepare 3, because of uncertainty principle. DV Teleportation Quantum info output: Unknown state Joint measurement: Project onto singlet state 12 1 unknown 12 1 unknown 1 cH H 1 cV V unknown 3 Manipulation of half of entangled state Quantum info input: Unknown state 3 23 23 1 H V V H 2 1 Quantum resources input: Entangled state Bouwmeester, et al. "Experimental Quantum Teleportation," Nature 390, 575, 11 Dec 1997 CV Teleportation Quantum info output: Unknown state Xˆ 3 , Pˆ3 Xˆ 1 , Pˆ1 Joint measurement: Combined variables Xˆ 1 Xˆ 2 Pˆ Pˆ 1 Manipulation of half of entangled state 2 Quantum info input: Unknown state Xˆ 1 , Pˆ1 Xˆ 3 Xˆ 3 Xˆ 1 Xˆ 2 Pˆ Pˆ Pˆ Pˆ 3 Xˆ 3 Xˆ 2 0 Pˆ Pˆ 0 3 2 3 1 2 Quantum resources input: Einstein-Podolsky-Rosen Entangled state Furusawa et al. "Unconditional Quantum Teleportation," Science, 282, 706, 23 October 1998 Quantum Optics and Quantum Information Course Topics What is quantum light? • Quantization of the EM Field • Quantum states of light How to measure quantum light • Direct detection • Homodyne detection • Correlation functions • Distribution functions How to manipulate quantum light • Linear optics • Nonlinear optics How to produce quantum light • Single photons • Squeezing Light – matter interactions • Single atoms (see JE) • Atomic ensembles • Collective variables • Collective excitations Theory Experiment Taylor 1909 Dirac, 1920s Glauber, 1960s Glauber, 1960s Glauber, 1960s Glauber, 1960s Hanbury-Brown 1956 Many: 1980s And 1990s Hong, Ou, Mandel 1987 Many: 1980s to present Kimble, Mandel 1977 Slusher, 1985 Many: 2000s Kuzmich, Mandel 2000 Many, 2005 Optical Quantum Information Optical Quantum Information Taylor’s experiment (1909) film slit needle diffraction pattern f(y) Proceedings of the Cambridge philosophical society. 15 114-115 (1909) Taylor’s experiment (1909) Interpretation: Classical: f(y) <E2(y)> film Early Quantum (J. J. Thompson): if photons are localized concentrations of E-M field, at low photon density there should be too few to interfere. Modern Quantum: f(y) = <n(y)> = <a+(y)a(y)> <E-(y)E+(y)> f(y) same as in classical. Dirac: “Each photon interferes only with itself. Interference between two different photons never occurs.” (not entirely correct, but close). slit needle diffraction pattern f(y) Perkin-Elmer Avalanche Photodiode V negative thin p region (electrode) absorption region intrinsic silicon e- h+ multiplication region V positive “Geiger mode”: operating point slightly above breakdown voltage Avalanche Photodiode Mechanism Many valence electrons, each with a slightly different absorption frequency wi. Broadband detection. E conduction band (empty) valence band (filled) possible transitions wi = DE/hbar k “Classic” Photomultiplier Tube E Many valence electrons, each can be driven into the continuum wi. Broadband detection. Photocathode Response Broad wavelength range: 120 nm – 900 nm Lower efficiency: QE < 30% Microchannel Plate Photomultiplier Tube For light, use same photocathode materials, same Q. Eff. and same wavelength ranges. Much faster response: down to 25 ps jitter (TTS = Transit time spread) Proposal for squeezing (C. Caves, 1981) C. Caves, “Quantum Mechanical Noise In an Interferometer” Phys. Rev. D 23 1693 1981 Proposal for squeezing (C. Caves, 1981) C. Caves, “Quantum Mechanical Noise In an Interferometer” Phys. Rev. D 23 1693 1981 Proposal for squeezing (C. Caves, 1981) C. Caves, “Quantum Mechanical Noise In an Interferometer” Phys. Rev. D 23 1693 1981 Proposal for squeezing (C. Caves, 1981) EIN ELO (ELO+EIN)/√2 (ELO+EIN) ei /√2 (ELO-EIN)/√2 (ELO-EIN)/√2 2 E1 = ELO (1+ei) - EIN (1-ei) 2 E2 = ELO (1-ei ) - EIN (1+ei) 2 E1 = ELO (1+i) - EIN (1-i) Like homodyne, with LO phase 90° One quadrature of EIN contributes noise Squeeze this and make better interferometers. 2 E2 = ELO (1-i ) - EIN (1+i) E1 (1+i) / √2 = (iELO - EIN )/ √2 E2 (i-1) / √2 = (iELO + EIN )/ √2 C. Caves, “Quantum Mechanical Noise In an Interferometer” Phys. Rev. D 23 1693 1981 First Squeezed Light Experiment (Slusher, et. al. 1985) SLUSHER RE, HOLLBERG LW, YURKE B, et al. OBSERVATION OF SQUEEZED STATES GENERATED BY 4WAVE MIXING IN AN OPTICAL CAVITY Phys. Rev. Lett. 55 (22): 2409-2412 1985 Second Squeezed Light Expt. (Wu, Xiao, Kimble 1985) Wu L-A., Xiao M., Kimble H.J. SQUEEZED STATES OF LIGHT FROM AN OPTICAL PARAMETRIC OSCILLATOR JOSA B 4 (10): 1465-1475 OCT 1987 Theorist’s Spectrum Analyzer band-pass filter. V In V Out Frequency Power meter Sweep frequency → Power Spectrum |V()|2 Fixed frequency → Power in one freq. component |V()|2(t) Quadrature Detection Electronics environmental noise P measurement frequency P freq Spectrum analyzer Slusher, et. al. 1985 time Wu, et. al. 1987 Quadrature Detection of Squeezed Vacuum LO input is squeezed vacuum q in D1 Di(t) input is vacuum 63% VRMS (40% power) D2 LO phase X2 vacuum Pn X2 q q X1 X1 squeezed vacuum Correlation Functions CT C(t )T (t ) C T 0 C (t )T (t ) [C (t ) C ][T (t ) T ] C (t )T (t ) C T Correlation Functions C(t )T (t ) , years Ppm °C Stellar Interferometry Robert Hanbury-Brown Stellar Interferometry Robert Hanbury-Brown Hanbury-Brown and Twiss (1956) Nature, v.117 p.27 Correlation g(2) Tube position I Detectors see same field t I Detectors see different fields Signal is: g(2) = <I1(t)I2(t)> / <I1(t)><I2(t)> t Hanbury-Brown and Twiss (1956) Signal is: g(2) = <I1I2 / <I1><I2> = < (<I1>+I1) (<I2>+ I2) > / <I1><I2> Note: Correlation g(2) <I1> + I1 ≥ 0<I2> + I2 ≥ 0 <I1> = <I2> = 0 g(2) = (<I1><I2>+<I1><I2>+<I2><I1>+<I1I2>)/<I1><I2> I = 1 + <I1I2>)/<I1><I2> = 1 for uncorrelated <I1I2> = 0 > 1 for positive correlation <I1I2 > 0 e.g. I1I2 < 1 for anti-correlation <I1I2 < 0 Classical optics: viewing the same point, the intensities must be positively correlated. I0 Tube position Detectors see same field t I Detectors see different fields I1= I0/2 t I2= I0/2 Hanbury-Brown and Twiss (1956) The publication of these results led to much dispute in the scientific community (see for example 119, p.120). In particular, two independent groups attempted to repeat the experiment and concluded that Hanbury and Twiss had misinterpreted their data and that if such a correlation existed, a major revision of fundamental concepts in quantum mechanics would be required (Ádám, Jánossy & Varga, 1955; Brannen & Ferguson, 1956). In their response (25) Hanbury and Twiss pointed out that although the experimental procedure in both cases was beyond reproach, their critics had missed the essential point that correlation could not be observed in a coincidence counter unless one had an extremely intense source of light of narrow bandwidth. Hanbury and Twiss had used a linear multiplier that was counting a million times more photons than the coincidence system used in their critics' experiments. In fact, they calculated that Brannen and Ferguson would need to count for 1,000 years before observing the effect and Ádám et al. for 1011 years. They also responded (27) to a criticism of their theoretical treatment by Fellgett (1957) and subsequently, in order to settle all remaining arguments, the laboratory experiment was repeated using the coincidence counting system of Brannen and Ferguson but with an intense narrow-band isotope light source with which they observed the expected correlation in a series of twenty-minute runs. With the isotope light source replaced by a tungsten filament lamp, no correlation could be found (29). Not just for photons! Not just for photons! g(1) g(2) Smithey, Beck, Raymer and Faridani 1993 Smithey, Beck, Raymer and Faridani 1993 Neergaard-Nielsen, Nielsen, Hettich, Molmer and Polzik 2006 (arxiv) Neergaard-Nielsen, Nielsen, Hettich, Molmer and Polzik 2006 Neergaard-Nielsen, Nielsen, Hettich, Molmer and Polzik 2006 Kimble, Dagenais + Mandel 1977 PRL, v.39 p691 Correlation g(2) I0 I1= I0/2 Classical: correlated I2= I0/2 Correlation g(2) n0=1 t1 - t 2 n1=0 or 1 Quantum: can be n2= 1 - n1 anti-correlated t1 - t 2 Kimble, Dagenais + Mandel 1977 PRL, v.39 p691 Kimble, Dagenais + Mandel 1977 PRL, v.39 p691 Interpretation: g(2)() < a+(t)a+(t+)a(t+)a(t)> < E-(t) E-(t+) E+(t+)E+(t)> HI(t) -Ed E+(t) |e><g| + E-(t) |g><e| HI(t) HI(t+) E-(t) E-(t+) |g><e| |g><e| + h.c. Pe t time Kuhn, Hennrich and Rempe 2002 Kuhn, Hennrich and Rempe 2002 Pelton, et al. 2002 Pelton, et al. 2002 InAs QD relax fs pulse emit Pelton, et al. 2002 Goal: make the pure state |> = a+|0> = |1> Accomplished: make the mixed state r 0.38 |1><1| + 0.62 |0><0| Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982 J=0 J=1 J=0 Total angular momentum is zero. For counter-propagating photons implies a singlet polarization state: |> =(|L>|R> - |R>|L>)/2 Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982 Total angular momentum is zero. For counter-propagating photons, implies a singlet polarization state: |> =(|L>|R> - |R>|L>)/2 |> = 1/2(aL+aR+ - aR+aL+)|0> = 1/2(aH+aV+ - aV+aH+)|0> = 1/2(aD+aA+ - aA+aD+)|0> Detect photon 1 in any polarization basis (pA,pB), detect pA, photon 2 collapses to pB, or vice versa. If you have classical correlations, you arrive at the Bell inequality -2 ≤ S ≤ 2. Holt + Pipkin / Clauser + Freedman / Aspect, Grangier + Roger 1973-1982 a 22.5° b a' b' |SQM| ≤ 22 = 2.828... Coincidence Detection with Parametric Downconversion Using MCP PMTs for best time-resolution. CF Disc. = Constant-fraction discriminator: identifies “true” detection pulses, rejects background, maintains timing. TDC = “Time to digital converter”:Measures delay from A detection to B detection. PDP11: Very old (1979) computer from DEC. FRIBERG S, HONG CK, MANDEL L MEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): 2011-2013 1985 Physical Picture of Parametric Downconversion phase matching conduction collinear non-collinear or valence k-vector conservation ks + ki = kp Material (KDP) is transparent to both pump (UV) and downconverted photons (NIR). Process is “parametric” = no change in state of KDP. This requires energy and momentum conservation: ws + wi = wp ks + ki = kp Even so, can be large uncertainty in ws wi Intermediate states (virtual states) don’t even approximately conserve energy. Thus must be very short-lived. Result: signal and idler produced at same time. Coincidence Detection with Parametric Downconversion TDC = time-to-digital converter. Measures delay from A detection to B detection. transit time through KDP ~400 ps Dt < 100 ps FRIBERG S, HONG CK, MANDEL L MEASUREMENT OF TIME DELAYS IN THE PARAMETRIC PRODUCTION OF PHOTON PAIRS Phys. Rev. Lett. 54 (18): 2011-2013 1985 Cauchy Schwarz Inequality Violation Cauchy Schwarz Inequality Violation 202Hg 9P 567.6 nm 7S e- impact 435.8 nm 7P Cauchy Schwarz Inequality Violation First observation of optical frequency conversion ruby laser (694 nm) quartz crystal chi-2 medium prism film Position-momentum entanglement Howell, Bennink, Bentley and Boyd, Phys. Rev. Lett. 92 210403 (2004) Position-momentum entanglement Howell, Bennink, Bentley and Boyd, Phys. Rev. Lett. 92 210403 (2004) Two-photon diffraction Two IR photons (pairs) One IR photon 2,0 Pump high,low 0,2 high,low D’Angelo, Chekhova and Shih, Phys. Rev. Lett. 87 013602 (2001) Two-photon diffraction Two paths to coincidence detection: e Two IR photons (pairs) i 2k r r ' One IR photon 2,0 Pump high,low 0,2 high,low D’Angelo, Chekhova and Shih, Phys. Rev. Lett. 87 013602 (2001) Hong-Ou-Mandel effect 2,0 Hong, Ou and Mandel, Phys. Rev. Lett. 59 2044 (1987) high,low 0,2 high,low Hong-Ou-Mandel effect 2,0 Hong, Ou and Mandel, Phys. Rev. Lett. 59 2044 (1987) high,low 0,2 high,low Hong-Ou-Mandel effect with polarization Sergienko, Shih, and Rubin, JOSA B, 12, 859 (1995) Single-pass squeezing Wenger,Tualle-Brouri, and Grangier, Opt. Lett. 29, 1267 (2004) Single-pass squeezing Wenger,Tualle-Brouri, and Grangier, Opt. Lett. 29, 1267 (2004) Correlation Function of Castelldefels Correlation Function of Pedralbes N Z P R Spectrum Analyzer Log amp Mixer Out In Band-pass. “Resolution Bandwidth” Local Oscillator Peak detector Low-pass. “Video Bandwidth”