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Single-photon NV sources Pauli Kehayias March 16, 2011 March 16, 2011 Pauli Kehayias 1 Outline ● Quantum nature of light ● Photon correlation functions ● Single-photon sources ● NV diamond single-photon sources March 16, 2011 Pauli Kehayias 2 Wave/particle duality ● Light exhibits wave and particle properties ● Wave: oscillating E & B fields ● Double slit experiment, dipole radiation ● Particle: quantized energy (E = hν) ● Photoelectric effect March 16, 2011 Pauli Kehayias 3 Quantum light 1 1 2 3 2 E ∫ 0 0 B d r 2 ● H EM = ● After a lot of math, H EM =∑ ℏ k a k , s a k , s ● This is like a SHO: [a k , s a†k ' , s ' ]= k , k ' s , s ' , a†k ,s a k , s =n k , s ● nk , s ● a †k , s ● k ,s † 1 1 = ∑ ℏ k nk , s 2 2 k ,s is the photon number & a are photon creation & destruction operators k ,s Eigenstates are March 16, 2011 | nk , s > for each mode/polarization Pauli Kehayias 4 Coherence of light ● ● ● Given a phase at time t, how well can we predict the phase at t + τ ? Light sources emit pulse trains, with phase discontinuities between them A typical time between discontinuities can be thought of as the coherence time March 16, 2011 Pauli Kehayias 5 An example ● ● ● ● Young's double slit experiment Consider Imax – Imin Screen Slits Source Largest when perfectly coherent Smallest when incoherent March 16, 2011 Pauli Kehayias 6 A classical coherence function ● ● A classical coherence function 〈 E * t E t〉 = 〈∣E t ∣2 〉 〈∣E t∣2 〉 1 Is proportional to fringe visibility and interference term ● Magnitude ranges from 0 to 1 ● For coherence time τ0, ● We can also define a quantum version g(1)(τ) March 16, 2011 1 =1− Pauli Kehayias 0 7 Second order coherence ● ● ● ● Hanbury-Brown and Twiss experiment Beam splitter Coincident count rate ~ 〈 I t I t 〉 2 = Detector 〈 I t I t 〉 〈 I t 〉 〈 I t 〉 For number states, for n = 0,1 g 0=0 1 g 0=1− otherwise n 2 τ Coinc. Time delay 2 March 16, 2011 Pauli Kehayias 8 Uses for single-photon states ● Quantum optics experiments (Hanbury-Brown and Twiss, Mach-Zehnder, Pfleegor-Mandel) ● Quantum key distribution [2,3] ● Quantum computing March 16, 2011 Pauli Kehayias 9 Single-photon sources ● Attenuated lasers ● Atoms and molecules ● Quantum dots ● NV diamond centers [4] March 16, 2011 Pauli Kehayias 10 Single-photon NV diamond realizations ● Things to consider: excitation efficiency, collection efficiency, manufacturing difficulty ● Extract photons without any help [4] ● Attach a separate waveguide or cavity ● Make diamond nanostructures with embedded NV centers March 16, 2011 Pauli Kehayias 11 Bulk diamond + waveguide ● Attach a GaP layer on top of a bulk diamond as the waveguide (2.26 eV bandgap, n = 3.3) ● Achieved for many NV centers ● Easy to make, but is lossy [5] March 16, 2011 Pauli Kehayias 12 Diamond nanoparticle + cavity ● ● High-Q microsphere resonators Hard to position microsphere and diamond pillar close together [6] March 16, 2011 Pauli Kehayias 13 Diamond nanowires (1) ● Etch diamond pillars onto bulk diamond (ebeam lithography & reactive-ion etching) [7] March 16, 2011 Pauli Kehayias 14 Diamond nanowires (2) ● ● Advantage: better excitation and collection efficiency Disadvantages: hard to manufacture [8] March 16, 2011 Pauli Kehayias 15 Commercial realization ● Diamond grown on an optical fiber ● Runs at room temperature [9] March 16, 2011 Pauli Kehayias 16 References 1. C. Gerry, P. Knight, “Introductory Quantum Optics”, Cambridge University Press (2004). 2. G. Greenstein, A. G. Zajonc, “The Quantum Challenge: Modern Research on the Foundations of Quantum Mechanics” 2nd ed., Jones and Bartlett (2006). 3. A. Beveratos et al., “Single photon quantum cryptography”, PRL 89, 187901 (2002). 4. R. Brouri et al., “Photon antibunching in the fluorescence of individual color centers in diamond”, Optics Letters, Vol. 25, Issue 17 (2000). 5. K.-M. C. Fu et al., “Coupling of nitrogen-vacancy centers in diamond to a GaP waveguide”, Appl. Phys. Lett. 93, 234107 (2008). 6. M. Larsson et al., “Composite Optical Microcavity of Diamond Nanopillar and Silica Microsphere”, Nano Lett. 9 4 (2009). 7. T. Babinec et al., “A diamond nanowire single-photon source”, Nature Nanotechnology 5 (2010) . 8. B. J. M. Hausmann et al., “Fabrication of Diamond Nanowires for Quantum Information Processing Applications”, Diamond and Related Materials 19 (2010). 9. Quantum Communications Victoria (QCV), <http://qcvictoria.com/> March 16, 2011 Pauli Kehayias 17