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Open Craig Price-Dissertation.Pdf The Pennsylvania State University The Graduate School Eberly College of Science COVARIANT FORMULATIONS OF THE LIGHT-ATOM PROBLEM A Dissertation in Physics by Craig Chandler Price © 2018 Craig Chandler Price Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2018 The dissertation of Craig Chandler Price was reviewed and approved∗ by the following: Nathan D. Gemelke Assistant Professor of Physics Dissertation Advisor, Chair of Committee David S. Weiss Professor of Physics Associate Head for Research Marcos Rigol Professor of Physics Zhiwen Liu Professor of Electrical Engineering Nitin Samarth Professor of Physics Department Head ∗Signatures are on file in the Graduate School. ii Abstract We explore the ramifications of the light-matter interaction of ultracold neutral atoms in a covariant, or coordinate free, approach in the quantum limit. To do so we describe the construction and initial characterization of a novel atom-optical system in which there is no obvious preferred coordinate system but is fed back upon itself to amplify coherent quantum excitations of any emergent spontaneous order of the system. We use weakly dissipative, spatially incoherent light that is modulated by amplified fluctuations of the phase profile of a Sagnac interferometer whose symmetry is broken by the action of a generalized Raman sideband cooling process. The cooling process is done in a limit of low probe intensity which effectively produces slow light and forms a platform to explore general relativistic analogues. The disordered potential landscape is populated with k-vector defects where the atomic density contracts with an inward velocity potentially faster than the speed of the slow light at that region. We show preliminary results of characterizing the system that show the effect of atomic participation in the feedback loop that cement the analogy to Kuramoto locked oscillators. In addition, we examine novel formulations of quantum field theory with the aim to capture a simultaneous quantization of covariant light - atom interaction. Instead of using field-theoretic building blocks composed of harmonic excitations, we use nonlinear, complex excitations similar to those used in the Kuramoto model. Generalizing this approach into a continuous, coordinate free version, we consider the effect of electromagnetic induced transparency (EIT) with probe fields that have a vanishingly small amplitude. The associated slow light phenomenon can be exploited as it passes through a dielectric to create a general relativistic analogue whose dynamics may capture limits of dynamical gravity. Further, the topology of such light-atom physics can be used as a new, conceptually simplifying vehicle to understand the propagation of light through more general, and familiar phenomena such as imaging systems and cavities. iii Table of Contents List of Figures viii Acknowledgments x Chapter 1 Introduction 1 Chapter 2 Generalized quantum field theory 4 2.1 QFT as a bath of coupled, classical springs . 4 2.1.1 Complex Lagrangians . 6 2.2 System of oscillators . 7 2.2.1 Clifford algebra with matrices . 9 2.3 Field theory . 10 2.3.1 Adiabatic invariants . 12 2.4 Modified least action principle . 14 2.5 Nonlinear oscillators . 16 2.5.1 Self-injection locked oscillators . 17 2.5.2 Conserved microscopic Hamiltonians . 22 2.5.3 Microscopic relativistic Lagrangian . 24 2.5.4 L as a metric . 25 2.6 Observables behave like response functions . 27 2.6.1 Complex valued observables . 28 Chapter 3 Dielectrics and curved spacetime 32 3.1 Introduction . 32 3.2 Nonlinear media as a covariant tensor . 33 3.2.1 Maxwell’s equations in media . 33 3.2.2 Covariant formulation of Maxwell’s equations . 35 iv 3.2.3 Coordinate transformations of covariant media . 37 3.2.4 χ can include nonlinear dielectrics . 38 3.3 When the linear susceptibility tensor is equivalent to a spacetime metric . 40 3.3.1 Relating the susceptibility to the Riemannian tensor . 40 3.3.2 Topological changes and the susceptibility tensor . 41 3.3.3 Transformations of both the metric and the susceptibility . 42 3.4 Atom-light interaction through EIT . 47 3.4.1 Magnetic couplings and the Zeeman shift . 49 3.4.2 The electric dipole interaction . 50 3.4.2.1 Rotating wave approximation . 56 3.4.3 Scalar and vector light shifts from far-detuned light . 58 3.4.4 Density matrix elements . 59 3.5 Light propagation and topology . 63 3.5.1 At boundaries, rays are ramified . 64 3.5.1.1 Defining cohomology classes . 66 3.5.1.2 Images define Cut Loci . 67 3.5.1.3 Cohomology defines discrete modes in physical optics 68 3.5.1.4 Nonlinear interactions permit ramification and gluing 69 3.5.2 Time delay correlation, oscillation, and lasing . 70 3.5.2.1 Topological classification by laser and parametric oscillation . 70 3.5.2.2 Lasing thresholds tell us when to ramify and glue . 73 3.5.3 Geometric optics and quantum mechanics . 74 3.5.3.1 Geometric pictures of classical optics . 74 3.5.3.2 Polarization of optical variables . 75 3.5.3.3 Geometric quantization . 76 3.5.3.4 EBK quantization . 77 3.5.3.5 Geometric interpretation of the principle quantum number . 78 3.5.3.6 The one-dimensional laser cavity . 79 3.5.3.7 The role of nonlinearities . 80 3.5.3.8 Reconnecting with laser optics . 80 3.5.3.9 Self-consistent lasing and topology . 81 Chapter 4 Feedback to probe excitations of an atom light system 84 4.1 Apparatus to manipulate cold atoms . 85 4.1.1 Vacuum chamber . 85 4.1.2 Atom sources . 89 v 4.1.3 Laser systems . 89 4.1.3.1 Diode lasers . 90 4.1.3.2 Laser frequency locking . 90 4.1.3.2.1 Absorption lock . 91 4.1.3.2.2 Beat note locks . 91 4.1.3.3 Double pass tapered amplifier . 92 4.1.3.4 Optical switchyard . 93 4.1.3.5 High power, 1064 nm light . 94 4.1.4 Water cooling . 95 4.1.5 Magnetic field controllers . 97 4.1.6 Timing system . 98 4.1.7 Trapping and cooling atoms . 98 4.1.8 Imaging and probing the atoms in the UHV cell . 99 4.2 Generalized Raman sideband cooling . 102 4.2.1 Characterization of the optical fiber modes . 103 4.2.2 Expansion of modes in Cartesian coordinates . 108 4.2.3 Effective number of degrees of freedom . 112 4.3 Synthetic thermal body . 113 4.3.1 Preliminary experiments . 116 4.4 Constructing a light-atom oscillator . 119 4.4.1 Feedback loop - 1064 nm section . 121 4.4.2 Feedback loop - 780 nm section . 123 4.4.3 Feedback loop - electronic backend . 123 4.5 Light-atom oscillator characterization . 128 4.5.1 Injection Locking . 130 4.6 Atomic participation in the feedback path . 138 4.6.1 Modeling the propagator . 139 4.6.2 Adding atoms to the closed loop . 143 Appendix A Experimental Apparatus 2.0 148 A.1 Experimental apparatus - Collisional Microscope . 149 A.1.1 Transport and Imaging . 149 Appendix B Novel, UHV compatible Glass Bonding Techniques 153 B.1 Introduction . 153 B.2 Method . 155 B.3 Conclusion . 159 vi Bibliography 161 vii List of Figures 2.1 Mass on a spring QFT . 8 3.1 Folding, or manifold ramification in optics . 65 4.1 Vacuum chamber . 86 4.2 Lock table optics . 92 4.3 Laser switchyard . 94 4.4 1064 nm optical table schematic . 96 4.5 Fiber launches into the UHV cell . 100 4.6 High resolution images of the atom cloud . 101 4.7 The projection of the light that generates the disordered potential . 103 4.8 Roots of the characteristic equation . 107 4.9 Synthetic Thermal Body . 114 4.10 Synthetic bath of photons to maximize entropy and lose energy . 116 4.11 Landau Zener crossings in a disordered potential . 117 4.12 Stretch the optical fiber to make an engineered optical bath . 117 4.13 Disordered magnetic field . 118 4.14 Overview schematic of the experiment . 120 4.15 780 nm optical pumping optics . 124 4.16 Overview of electronics . 125 4.17 Electronic schematic for the closed loop response . 127 4.18 Power spectrum of closed and open loop response . 129 4.19 Power spectrum of closed loop response at increasing gain . 131 4.20 Power spectrum of a clipped beat . 132 4.21 4 ms of the closed loop response . 134 4.22 Relative phase of unlocked oscillators . 135 4.23 Relative phase of locked oscillators . 137 4.24 Unwrapped phase difference at high gain . 138 4.25 Adler wedges . 139 4.26 Frequency of closed loop response . 140 viii 4.27 Phase of the closed loop response during RSC . 144 4.28 Unwrapped phase of multiple shots with and without atoms . 145 4.29 Relative number of phase slips with atoms . 146 A.1 Experiment chamber for collision microscopy . 151 A.2 Experiment chamber with added pumps . 152 B.1 Glass substrates after bonding . 157 B.2 Glass substrate with pocket drilled into center . 157 B.3 Pressure versus time after shutting off the ion pump for the nanopar- ticle hydroxide-catalyzed bonded glass . 158 ix Acknowledgments Graduate school has been an intense, very educational experience and it would be remiss not to single out the key figures who helped me in this story. My fellow travelers, Qi, Jianshi, Rene, and George were great companions and peers. Without their hard work, cold atoms, much less these experiments, would never have happened. George’s cheerfulness and competent precision, Rene’s thoroughness and quiet excellence, Jianshi’s thoughtfulness and sudden stabs of genius, and Qi’s level-headed hard work and tenacity - were instrumental for the work in this thesis.
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