Single-photon NV sources 1
Outline Quantum nature of light Photon correlation functions Single-photon sources NV diamond single-photon sources 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 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 nk, s > for each mode/polarization 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 5
An example Young's double slit experiment Consider Imax Imin Screen Slits Source Largest when perfectly coherent Smallest when incoherent 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) 1 =1 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 8
Uses for single-photon states Quantum optics experiments (Hanbury-Brown and Twiss, Mach-Zehnder, Pfleegor-Mandel) Quantum key distribution [2,3] Quantum computing 9
Single-photon sources Attenuated lasers Atoms and molecules Quantum dots NV diamond centers [4] 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 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] 12
Diamond nanoparticle + cavity High-Q microsphere resonators Hard to position microsphere and diamond pillar close together [6] 13
Diamond nanowires (1) Etch diamond pillars onto bulk diamond (ebeam lithography & reactive-ion etching) [7] 14
Diamond nanowires (2) Advantage: better excitation and collection efficiency Disadvantages: hard to manufacture [8] 15
Commercial realization Diamond grown on an optical fiber Runs at room temperature [9] 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/> 17