京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第21549号 / 理博第4456号 / 新制||理||1640(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 高橋 義朗, 教授 田中 耕一郎, 教授 前野 悦輝 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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<p>Due to the rapid development of nanophotonics, microring resonators suspended on a membrane holds promises for a scalable optical circuit with strong light-atom interaction. In this dissertation, I introduce a efficiently-coupled microring circuits for on-chip cavity QED with cold atoms and report my experimental efforts to integrate the optical chip into a ultrahigh-vacuum chamber with a magneto-optical trap for Rb atoms. My attempts to load single atoms into optical tweezers are also discussed.</p> <p>  </p> <p>  Although the loading of atom into optical tweezers above the top surface of resonator remains a challenge in experiment, I propose an alternative of cavity cooling based on cavity QED to facilitate the loading of atom into a two-color evanescent field trap around the waveguide. Assuming that the strong interaction between atoms and resonator modes is realized, I theoretically investigate the synthesis via photoassociation and the direct optical detection of a single ground-state cold molecule, whose corresponding excited-state has multiple decay channels. Similarly to the Purcell effect, the decay in a specific decay channel could be enhanced based on cavity QED, and therefore the synthesis efficiency can approach unity when the interaction between the resonator modes and a single cold molecule becomes stronger. In addition, for a single cold molecule without closed optical transition, the electromagnetically induced transparency is possible to be observed on our nanophotonic platform in the case of strong resonator-molecule coupling.</p>

<p dir="ltr">In this work we investigate the existence and experimentally measurable properties of Majorana quasiparticles in a few-body number conserving atomic system.</p>

In this dissertation, we use exact diagonalization to study a few strongly correlated systems, ranging from the Fermi-Hubbard model to the fractional quantum Hall effect (FQHE). The discussion starts with an overview of strongly correlated systems and what is meant by strongly correlated. Then, we extend cluster perturbation theory (CPT), an economic method for computing the momentum and energy resolved Green's function for Hubbard models to higher order correlation functions, specifically the spin susceptibility. We benchmark our results for the one-dimensional Fermi-Hubbard model at half-filling. In addition we study the FQHE at fillings $nu = 5/2$ for fermions and $nu = 1/2$ for bosons. For the $nu = 5/2$ system we investigate a two-body model that effectively captures the three-body model that generates the Moore-Read Pfaffian state. The Moore-Read Pfaffian wave function pairs composite fermions and is believed to cause the FQHE at $nu = 5/2$. For the $nu = 1/2$ system we estimate the entropy needed to observe Laughlin correlations with cold atoms via an ansatz partition function. We find entropies achieved with conventional cooling techniques are adequate. / Doctor of Philosophy / Strongly correlated quantum many-body physics is a rich field that hosts a variety of exotic phenomena. By quantum many-body we mean physics that is concerned with the behavior of interacting particles, such as electrons, where the quantum behavior cannot be ignored. By strongly correlated, we mean when the interactions between particles are sufficiently strong such that they cannot be treated as a small perturbation. In contrast to weakly correlated systems, strongly correlated systems are much more difficult to solve. That is because methods that reduce the many-body problem to a single independent body problem do not work well. In this dissertation we use exact diagonalization, a method to computationally solve quantum many-body systems, to study two strongly correlated systems: the Hubbard model and the fractional quantum Hall effect.The Hubbard model captures the physics of many interesting materials and is the standard toy model. Originally developed with magnetic properties in mind, it has been extended to study superconductivity, topological phases, cold atoms, and much more. The fractional quantum Hall effect is a novel phase of matter that hosts exotic excitations, some of which may have applications to quantum computing.

The establishment of robust laser-cooling techniques for the formation of ultracold atoms has provided a test-bed for low-temperature science, with scattering events changing character from incoherent thermal interactions to coherent quantum mechanical events. A natural extension is the pursuit of ultracold molecules in prescribed low-energy internal states. Atomic cooling techniques, however, do not generalize to the molecular regime due to the complex energy-level structure afforded by its extra degrees of motion. An indirect approach to ultracold molecule formation - photoassociation using ultrafast laser pulses - is the focus of this thesis. A broadband field associates atom pairs into a localized molecular wavepacket that evolves within the attractive excited-state potential. A suitably timed dump pulse may thus be applied to stabilize population into deeply bound ground vibrational states. This strategy may be generalized to any species whose spectroscopy matches the pulse spectrum, and offers a coherent population transfer scheme that does not require precise knowledge of the system. This thesis presents experiments using high-energy photoassociation pulses applied to ultracold rubidium atoms. The pulses quench the background ground-state molecular population but form bound dimers within the excited state. A pump-probe experiment was designed to chart the excited-state dynamics; however, the oscillations predicted by theoretical calculations were not evident in the molecular signal. The nature of the dynamics is expected to be strongly dependent on the initial state of the atom pairs addressed by the ultrafast pulse: a bound molecular population provides an additional candidate to free atoms. A spectroscopic measurement characterizes these bound molecules and identifies their formation mechanism. A subsequent experiment provides evidence that the predominant contributor to the pump-probe signal is the unbound initial population. The consequences with regard to both the observation of excited-state dynamics and the subsequent application of a dump pulse are discussed.

Atoms in optical lattices are promising candidates to implement quantum information processing. Their behaviour is well understood on a microscopic level, they exhibit excellent coherence properties, and they can be easily manipulated using external fields. In very deep optical lattices, each atom is restricted to a single lattice site and can be used as a qubit. If the lattice is shallow enough such that the atoms can move, their properties can be used to simulate certain condensed matter phenomena such as superconductivity. In this thesis, we show how technical problems of optical lattices such as restricted decoherence times, or fundamental shortcomings such as the lack of phonons or strong spin interactions, can be overcome by using current or near-future experimental techniques. We introduce a scheme that makes it possible to simulate model Hamiltonians known from high-temperature superconductivity. For this purpose, previous simulation schemes to realise the spin interaction terms are extended. We especially overcome the condition of a filling factor of exactly one, which otherwise would restrict the phase of the simulated system to a Mott-insulator. This scheme makes a large range of parameters accessible, which is difficult to cover with a condensed matter setup. We also investigate the properties of optical lattices submerged into a Bose-Einstein condensate (BEC). A weak-coupling expansion in the BEC-impurity interaction strength is used to derive a model that describes the lattice atoms in terms of polarons, i.e.~atoms dressed by Bogoliubov phonons. This is analogous to the description of electrons in solids, and we observe similar effects such as a crossover from coherent to incoherent transport for increasing temperatures. Moreover, the condensate mediates an attractive off-site interaction, which leads to macroscopic clusters at experimentally realistic parameters. Since the atoms in the lattice can also be used as a quantum register with the BEC mediating a two-qubit gate, we derive a quantum master equation to examine the coherence properties of the atomic qubits. We show that the system exhibits sub- and superdecoherence and that a fast implementation of the two-qubit gate competes with dephasing. Finally, we show how to realise the encoding of qubits in a decoherence-free subspace (DFS) using optical lattices. We develop methods for implementing robust gate operations on qubits encoded in a DFS exploiting collisional interactions between the atoms. We also give a detailed analysis of the performance and stability of the gate operations and show that a robust implementation of quantum repeaters can be achieved using our setup. We compare the robust repeater scheme to one that makes use of conventional qubits only, and show the conditions under which one outperforms the other.

In recent years there has been much progress in the field of cold and ultracold molecular physics and a variety of experimental techniques for producing cold matter now exist. In particular, the generation of trapped molecular ions at mK temperatures has been achieved by sympathetic-cooling with laser-cooled atomic ions. By implementing schemes to selectively prepare and control the internal quantum state of molecular ions, and developing detection techniques, it will be increasingly possible to study cold state-selected chemical collisions in an ion-trap. Most molecular species produced in a selected rovibrational state have a lifetime of a few seconds, before the population is redistributed across numerous rovibrational states by interaction with the ambient blackbody radiation (BBR). Consequently, the investigation of state-selected reaction dynamics at low temperatures in experiments where long time scales (minutes to hours) are required, is hindered. This thesis looks into developing strategies that maintain state selection in molecular ions, allowing one to observe state-selected reactions in cold environments, in particular the state-selected reaction between C₂H⁺₂ and ND₃. Examining reactive ion molecule collisions under cold conditions provides insight into fundamental reaction dynamics, which are thermally averaged out at higher temperatures. A theoretical model is used to investigate laser-driven, blackbody-mediated, rotational cooling schemes for several ¹&Sigma; and ²Π diatomic species. The rotational cooling is particularly effective for DCl⁺ and HCl⁺, for which 92&percnt; and >99&percnt; (respectively) of the population can be driven into the rovibrational ground state. For the other systems a broadband optical pumping source is found to enhance the population that can be accumulated in the rovibrational ground state by up to 29&percnt; more than that achieved when exciting a single transition. The influence of the rotational constant, dipole moments and electronic state of the diatomics on the achievable rotational cooling is also studied. This approach is extended to consider the BBR interaction and rotational cooling of a linear polyatomic ion, C₂H⁺₂, which has a ²&Pi; electronic ground state. The (1-0) band of the &nu;₅ cis-bending mode is infrared active and strongly overlaps the 300 K blackbody spectrum. Hence the lifetimes of state-selected rotational levels are found to be short compared to the typical timescale of ion trapping experiments. Laser cooling schemes are proposed that could be experimentally viable, which involves simultaneous pumping of a set of closely spaced Q-branch transitions on the ²&Delta;_5/2-²&Pi;_3/2 band together with two ²&Sigma;⁺– ²&Pi;_1/2 lines. It is shown that this should lead to >70&percnt; of total population in the lowest rotational level at 300 K and over 99&percnt; at 77 K. In order to identify states of the acetylene ion that could be trapped sufficiently long enough for state-selected reactions in the ion trap with decelerated ND3, the theoretical work has been complemented by experimental investigations into the production of C₂H⁺₂ in selected states, and ion trapping of the same using sinusoidal and digital trapping voltages. Appropriate (2+1) REMPI (Resonance Enhanced Multiphoton Ionization) schemes are used to produce C₂H⁺₂ in different quantum states, with (1+1) Resonance Enhanced Multiphoton Dissociation (REMPD) employed to detect the ion thus produced. The concept of digital ion trapping for ejection onto MCPs is introduced. A comprehensive comparison between sinusoidal and digital trapping fields has been performed with respect to trap depth and stability regions. Programs have been developed to calculate the stability regions for different ions under varying experimental conditions. The trap depth has been derived for both digital and sinusoidal trapping fields. It is observed that as &tau; increases, the trap depth of a digital trap increases. For &tau; = 0.293, the trap depth and stability diagram for both sinusoidal and digital trapping fields would be equivalent. The trap depth at which the sinusoidal trap operates experimentally in our research group is ~1.36 eV. In contrast, the experimental parameters at which the digital trap operates generates a trap depth of 1.21 eV. Ca⁺ Coulomb crystals have been formed, stably trapped and stored for extended periods of time in both sinusoidally and digitally time-varying trapping fields. The sympathetic cooling of a diverse range of ions into Ca⁺ Coulomb crystals is demonstrated, again using both sinusoidal and digital trapping fields. Mass spectrometric detection of ionic reaction products using a novel ejection scheme has been developed, where ejection is achieved by switching off the trapping voltage and converting the quadrupole trap into an extractor-repeller pair by providing the ion trap electrodes with appropriate ejection pulses. This technique is developed using a digital trapping voltage rather than the sinusoidal trapping voltage, as ejection with sinusoidal trapping voltages is not clean (resonance circuitry used in the electronics induces ringing after switching off the trapping voltage). Coulomb crystals, both pure Ca⁺ and multi-component crystals, are ejected from the ion trap and the TOF trace obtained is recorded on an oscilloscope. When the integrated, base-line subtracted TOF peak is plotted against the number of ions in a Ca+ crystal and sympathetically-cooled Ca⁺ – CaF⁺ crystal, a linear relationship is obtained. This technique is found to be well mass-resolved, with the signal arising from CaOH⁺ (57 amu) and CaOD⁺ (58 amu) resolvable on the TOF trace. This technique would enable one to monitor a reaction in a Coulomb crystal where the reactant and product species are both either lighter or heavier than calcium, such as the reaction between C₂H⁺₂ and ND₃, something which has not been previously possible. It is, also, potentially a very important technique for reactions with many product channels.

Diese Arbeit beschäftigt sich mit der theoretischen Beschreibung eines Hybridsystems eines ultrakalten neutralen Atoms und eines einzelnen Ions. Diese Hybrid-Atom-Ion-Systeme verbinden die wichtigsten Vorteile von ultrakalten neutralen Atomen und Ionen. Neutrale Atome sind leicht skalierbar vor allem und können in großen Stückzahlen vorbereitet werden, wahrend gefangene Ionen über längere Zeiten gelagert werden können und leicht kontrollierbar sind. Einige der vorgeschlagenen Aussichten der hybriden Quantensysteme umfassen die sympathische Kühlung von eingefangenen Ionen, die ultrakalte Chemie, das Quantum Informationsverarbeitung, und Atom-Ionen-Quantensimulatoren. Diese Anwendungen erfordern eine äußerst präzise Steuerung und damit eine sehr genaue theoretische Modellierung. Eine neue Methode, die eine vollständige sechsdimensionale Behandlung von zwei Partikeln ermöglicht In räumlich getrennten dreidimensionalen Fangpotentialen wurde entwickelt. Indem man die raumliche Verschiebung zwischen den Einfangpotentialen erlaubt, ist es möglich, die gesteuerte Bewegung eines einzelnen Ions durch ein optisches Gitterpotential zu beschreiben, das mit neutralen Atomen gefüllt ist. Die Wechselwirkung zwischen dem neutralen Atom und dem geladenen Ion wird durch eine realistische Born-Oppenheimer Potentialkurve beschrieben. Eines der hier diskutierten Hybridsysteme ist 7Li2+ Isotop, das mit der neu entwickelten Methode untersucht wird, dabei wurden vermiedene Kreuzungen im Energiespektrum zwischen molekularen Zuständen und den Schwingungszuständen des Fallenpotentials als Funktion des Abstandes zwischen den beide Fallen beobachtet. Diese vermiedenen Kreuzungen bestatigen die bereits vorhergesagten falleninduzierten Resonanzen, die mithilfe der Quantendefekttheorie bestimmt wurden. Ebenfalls werden die erst kürzlich entdeckten inelastischen falleninduzierten Resonanzen in ultrakalten Atomen auch in den Atom-Ion Systemen beobachtet. / This thesis deals with the theoretical description of a hybrid system of an ultracold neutral atom and a single ion. These hybrid atom-ion systems combine the key advantages of ultracold neutral atoms and ions. In particular, neutral atoms are easily scalable and can be prepared in large numbers, while trapped ions can be stored for much longer times and are easy to control. Some of the proposed prospects of the hybrid quantum systems include sympathetic cooling of trapped ions, ultracold chemistry, quantum information processing, and atom-ion quantum simulators. These applications require extremely precise control and thus very accurate theoretical modeling. A new method that allows for a full 6-dimensional treatment of two particles in spatially separated 3-dimensional trapping potentials was developed. By allowing for the spatial displacement between the trapping potentials, it is possible to describe the controlled motion of a single ion through an optical-lattice potential filled with neutral atoms. The interaction between the neutral atom and the ion is modeled using realistic Born-Oppenheimer potential curves from ab initio quantum chemistry calculations. An application of the developed approach to the hybrid atom-ion system reveals avoided crossings between the molecular bound states and the unbound trap states as a function of the separation between the two traps. These avoided crossings correspond to trap-induced resonances. This finding confirms the trap-induced resonances predicted earlier based on quantum-defect-theory calculations. Also, the recently found inelastic confinement-induced resonances in ultracold neutral atoms are demonstrated to be present in atom-ion systems. These resonances arise due to the coupling between the center-of-mass and relative motions. The inelastic confinement-induced resonances could be used in coherent molecular ion formation and in the determination of atom-ion scattering properties like the scattering lengths.