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Integrated Optics for Coupled-Cavity Quantum Electrodynamics

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Integrated Optics for Coupled-Cavity Quantum Electrodynamics Integrated optics for coupled-cavity quantum electrodynamics Guillaume Lepert A thesis submitted for the degree of Doctor of Philosophy of Imperial College London Physics Department Quantum Optics and Laser Science/Centre for Cold Matter January 2013 Abstract This thesis reports on the development of an array of plane-concave Fabry-P´erot mi- crocavities containing atoms (or other quantum emitters), interconnected by UV-written waveguides on a silica-on-silicon chip. The microcavities are formed by a mirror coated on the end facet of the chip and an array of spherical micromirrors etched on silicon. This is to our knowledge the first attempt at implementing the emerging coupled-cavities QED paradigm. The device we propose possesses a degree of control, flexibility and tuning un- matched in other suggested implementations: The atoms can be manipulated inside the cavity by auxiliary lasers and the cavity-cavity coupling rate as well as the atom-cavity coupling can be tuned. It is highly scalable. Calculation of the complete (classical) optical spectrum of the device is presented. The quantum dynamics that may eventually be observed has also been studied. Waveguide chips containing couplers and phase shifter have been fabricated. We have successfully demonstrated the operation of the elementary sub-systems: the strong optical coupling between a microcavity and a waveguide resonator, and the tunable strong coupling be- tween two evanescently coupled waveguide resonators. No experiments with atoms or other quantum emitters were attempted, because the waveguide propagation loss is so large that no quantum physics can be observed. There is hope that this can be overcome in the future by using other waveguide technologies. 1 Statement Of Originality I hereby declare that this thesis and the work presented herein are my own, except where otherwise credited. Referees Professor Vahid Sandoghdar Professor Mark Neil Max Planck Institute for the Science of Light Physics Department, Photonics Group Erlangen Imperial College London 2 Contents 1 A new dawn for cavity QED 7 1.1 The problem with atomic physics . .7 1.2 Strong light-matter interactions I: Shrinking the photons . .8 1.2.1 Solid immersion lenses . .8 1.2.2 High-index nanowaveguides . .9 1.3 Strong light-matter interactions II: Recycling the photons with cavities . 10 1.3.1 Fundamentals of cavity QED . 11 1.3.2 Historical overview . 16 1.4 Coupled-cavity QED . 20 1.4.1 The Bose-Hubbard model . 20 1.4.2 Theoretical proposals . 21 1.5 Practical implementation . 22 1.5.1 CCM's efforts toward integration . 22 1.5.2 Possible implementations of coupled-cavity QED . 24 1.5.3 Array of waveguide-coupled Fabry-P´erotmicrocavties . 26 1.5.4 Thesis outline . 29 2 Waveguide chips: theory, fabrication and characterisation 30 2.1 Guided optics: An introduction . 30 2.2 Waveguide fabrication . 34 2.2.1 Deposition and etching: CIP chip . 34 2.2.2 UV-written waveguides: ORC chips . 35 2.2.3 Femtosecond laser writing: Jena chip . 37 2.3 Waveguide characterisation . 38 2.3.1 Methods . 38 2.3.2 ORC chips . 40 2.3.3 Jena chip . 40 2.4 Couplers . 42 2.4.1 Theory . 43 3 2.4.2 ORC's X-couplers . 45 2.4.3 Evanescent couplers . 48 2.4.4 Our devices: coupling ratios measurements . 48 2.5 Thermo-optic phase shifters . 51 2.5.1 Introduction: electro- vs thermo-optics phase shifters . 51 2.5.2 Fabrication of thermo-optic phase shifters . 51 3 Single cavities 56 3.1 Theory of lossless Fabry-P´erot cavities . 56 3.2 Theory of lossy Fabry-P´erot cavities . 59 3.2.1 Propagation loss . 60 3.2.2 Mode mismatch . 61 3.2.3 Mirror transmission loss . 62 3.2.4 Experimental measurement of loss and reflectivity . 62 3.2.5 Cooperativity . 63 3.3 Dielectric mirrors . 63 3.4 Waveguide cavities . 64 3.4.1 Optimising the mirror reflectivities . 64 3.4.2 Tuning the cavity length with phase shifters . 67 3.5 Waveguide- and fibre-coupled microcavities . 69 3.5.1 Plane-concave microcavities . 69 3.5.2 Microcavity length scan . 72 4 Coupled cavities 75 4.1 Microcavity coupled to a waveguide cavity . 75 4.1.1 Derivation of the coupled-cavities spectrum . 75 4.1.2 Analytical expression of the coupling rate gcw ............ 80 4.1.3 Experiments . 82 4.2 Coupled waveguide cavities . 83 4.2.1 Analytical derivation of the coupling rate gww ............ 83 4.2.2 Derivation of the coupled cavity spectrum . 84 4.2.3 Tuning the coupling rate with phase shifters . 87 4.2.4 Experiments . 87 5 Bragg grating cavities 95 5.1 Introduction . 95 5.2 Direct UV-writing of Bragg gratings . 96 5.3 Modelling Bragg gratings . 100 5.3.1 Couple-mode theory for Bragg gratings . 101 5.3.2 Applications . 103 4 5.4 Bragg grating cavities: experiments . 105 5.4.1 Apparatus . 106 5.4.2 Measurement method . 107 5.4.3 Experimental results I . 112 5.4.4 Experimental results II: group delay spectroscopy . 115 5.4.5 Conclusion . 117 6 Conclusion and prospects 119 Appendix A Optics of Gaussian beams 123 A.1 Fundamentals . 123 A.2 Mode matching efficiency . 124 A.3 Propagation of Gaussian beam in optical systems . 125 Appendix B Coupling of a dipole to a nanofibre 128 B.1 Derivation of coupling rates from Fermi's golden rule . 128 B.1.1 Dipole in free space . 129 B.1.2 Dipole on waveguide/nanofibre . 130 B.1.3 Guided to free space ratios . 131 B.2 Modes of the nanofibre . 131 B.3 Discussion . 133 Appendix C Conversion between different loss parameters 135 Bibliography 136 5 Acknowledgements I am forever in debt to Ed, Michael and Jaesuk for the chance of working and learning alongside them. I have had many enlightening discussions with and received invaluable help from the bright people at CCM; Rob, Adrian, Joe and Stefan deserve special thanks. Kudos to Steve, Jon and Val in the workshop: nothing is impossible for them. Special mention goes to Helen and James in Southampton, with whom it has been a real pleasure to collaborate. It's been (mostly) fun. 6 Chapter 1 A new dawn for cavity QED The interaction of a single dipole with a monochromatic radiation field presents an important theoretical problem in electrodynamics. It is an unrealistic problem in the sense that experiments are not done with single atoms and single-mode fields. | L Allen and JH Eberly, Optical resonance and two-level atoms, 1975 (p. 157) The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland \for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems". | The Royal Swedish Academy of Sciences, 9 October 2012 1.1 The problem with atomic physics The two quotes above illustrate in a rather dramatic way the huge progress that has been made in the field of light-matter interactions in the last decades. For Allen and Eberly, and for all atomic physicists at the time, the semiclassical approximation was sufficient for all practical purpose; quantum electrodynamics was merely an intellectual curiosity. Yet shortly before the Nobel prize announcement Haroche demonstrated full quantum feedback control, using single atoms to inject or remove { on demand { single photons from the electromagnetic field inside a cavity (1). The traditional difficulty with atomic physics is two-fold: the light-matter interaction is weak, and the probability of detecting photons is very low. As a result, experiments demanded that many photons scatter off many atoms, and the realm of interactions between single quanta remained elusive. It is not hard to see why this had to be. The collection efficiency of a standard optical system, as a function of its numerical aperture NA and assuming isotropic emission, is 1 p η = 1 − 1 − NA2 : (1.1) coll 2 7 The NA is defined as NA=n sin θ, where θ is the optics' collection angle and n the refractive index at the source. Thus a low-NA optics observing an atomic ensemble from outside the vacuum chamber would only collect NA2=4 of all emitted photons | typically as low as 10−4. Even a large NA system, say an NA=0.5 diffraction-limited asphere lens, placed inside the vacuum, only boosts ηcoll to a 5%. On the other hand, the absorption cross-section of a simple two-level atom 3λ2 σ = (1.2) abs 2π is typically an order of magnitude or two smaller than the focussed spot size achievable with such an optical system, and so the interaction probability is very small. For the sake of concreteness, let's consider a single rubidium atom and calculate, in a very crude semiclassical way, the probability that a single 780 nm photon may excite it to the upper state of the D2 transition. We assume that the photon wavepacket has a duration τ = 3 ns (which is much shorther than the D2 spontaneous lifetime γ ∼MHz) with a top hat profile g and a 50 µm waist. The Rabi frequency is then 2π ∼ 0:2 MHz and the probability of exciting the atom is only sin2(gτ=2) ∼ 3 × 10−6. The road to seeing single quanta interact is not necessarily closed however, for there are two obvious ways of solving these problems of weak collection and interaction probability. The first one is to match the optical and atomic cross-section, which is in principle possible since the latter is of the same order as the diffraction limited spot size wdiff : λ p w ' ∼ σ ; (1.3) diff 2 sin θ abs λ being the wavelength in the medium.
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