Bottle microresonators for applications in quantum optics and all-optical signal processing

This thesis reports on the experimental realization, characterization and application of a novel microresonator design. The so-called “bottle microresonator” sustains whispering-gallery modes in which light fields are confined near the surface of the micron-sized silica structure by continuous total internal reflection. While whispering-gallery mode resonators in general exhibit outstanding properties in terms of both temporal and spatial confinement of light fields, their monolithic design makes tuning of their resonance frequency difficult. This impedes their use, e.g., in cavity quantum electrodynamics (CQED) experiments, which investigate the interaction of single quantum mechanical emitters of predetermined resonance frequency with a cavity mode. In contrast, the highly prolate shape of the bottle microresonators gives rise to a customizable mode structure, enabling full tunability. The thesis is organized as follows: In chapter I, I give a brief overview of different types of optical microresonators. Important quantities, such as the quality factor Q and the mode volume V, which characterize the temporal and spatial confinement of the light field are introduced. In chapter II, a wave equation calculation of the modes of a bottle microresonator is presented. The intensity distribution of different bottle modes is derived and their mode volume is calculated. A brief description of light propagation in ultra-thin optical fibers, which are used to couple light into and out of bottle modes, is given as well. The chapter concludes with a presentation of the fabrication techniques of both structures. Chapter III presents experimental results on highly efficient, nearly lossless coupling of light into bottle modes as well as their spatial and spectral characterization. Ultra-high intrinsic quality factors exceeding 360 million as well as full tunability are demonstrated. In chapter IV, the bottle microresonator in add-drop configuration, i.e., with two ultra-thin fibers coupled to one bottle mode, is discussed. The highly efficient, nearly lossless coupling characteristics of each fiber combined with the resonator's high intrinsic quality factor, enable resonant power transfers between both fibers with efficiencies exceeding 90%. Moreover, the favorable ratio of absorption and the nonlinear refractive index of silica yields optical Kerr bistability at record low powers on the order of 50 µW. Combined with the add-drop configuration, this allows one to route optical signals between the outputs of both ultra-thin fibers, simply by varying the input power, thereby enabling applications in all-optical signal processing. Finally, in chapter V, I discuss the potential of the bottle microresonator for CQED experiments with single atoms. Its Q/V-ratio, which determines the ratio of the atom-cavity coupling rate to the dissipative rates of the subsystems, aligns with the values obtained for state-of-the-art CQED microresonators. In combination with its full tunability and the possibility of highly efficient light transfer to and from the bottle mode, this makes the bottle microresonator a unique tool for quantum optics applications.

Optics and lasers : a compilation /

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Macroscopic quantum Schrdinger and Einstein-Podolsky-Rosen paradoxes

We propose macroscopic generalizations of the Einstein-Podolsky-Rosen paradox in which the completeness of quantum mechanics is contrasted with forms of macroscopic reality and macroscopic local reality defined in relation to Schrodinger's original 'cat' paradox.

Modelling photo-detectors in quantum optics

Photo-detection plays a fundamental role in experimental quantum optics and is of particular importance in the emerging field of linear optics quantum computing. Present theoretical treatment of photo-detectors is highly idealized and fails to consider many important physical effects. We present a physically motivated model for photo-detectors which accommodates for the effects of finite resolution, bandwidth and efficiency, as well as dark counts and dead-time. We apply our model to two simple well-known applications, which illustrates the significance of these characteristics.

Experimental tests of quantum nonlinear dynamics in atom optics

Cold atoms in optical potentials provide an ideal test bed to explore quantum nonlinear dynamics. Atoms are prepared in a magneto-optic trap or as a dilute Bose-Einstein condensate and subjected to a far detuned optical standing wave that is modulated. They exhibit a wide range of dynamics, some of which can be explained by classical theory while other aspects show the underlying quantum nature of the system. The atoms have a mixed phase space containing regions of regular motion which appear as distinct peaks in the atomic momentum distribution embedded in a sea of chaos. The action of the atoms is of the order of Planck's constant, making quantum effects significant. This tutorial presents a detailed description of experiments measuring the evolution of atoms in time-dependent optical potentials. Experimental methods are developed providing means for the observation and selective loading of regions of regular motion. The dependence of the atomic dynamics on the system parameters is explored and distinct changes in the atomic momentum distribution are observed which are explained by the applicable quantum and classical theory. The observation of a bifurcation sequence is reported and explained using classical perturbation theory. Experimental methods for the accurate control of the momentum of an ensemble of atoms are developed. They use phase space resonances and chaotic transients providing novel ensemble atomic beamsplitters. The divergence between quantum and classical nonlinear dynamics is manifest in the experimental observation of dynamical tunnelling. It involves no potential barrier. However a constant of motion other than energy still forbids classically this quantum allowed motion. Atoms coherently tunnel back and forth between their initial state of oscillatory motion and the state 180 out of phase with the initial state.

Schrodinger cats and their power for quantum information processing

We outline a toolbox comprised of passive optical elements, single photon detection and superpositions of coherent states (Schrodinger cat states). Such a toolbox is a powerful collection of primitives for quantum information processing tasks. We illustrate its use by outlining a proposal for universal quantum computation. We utilize this toolbox for quantum metrology applications, for instance weak force measurements and precise phase estimation. We show in both these cases that a sensitivity at the Heisenberg limit is achievable.

Measuring entangled qutrits and their use for quantum bit commitment

We produce and holographically measure entangled qudits encoded in transverse spatial modes of single photons. With the novel use of a quantum state tomography method that only requires two-state superpositions, we achieve the most complete characterization of entangled qutrits to date. Ideally, entangled qutrits provide better security than qubits in quantum bit commitment: we model the sensitivity of this to mixture and show experimentally and theoretically that qutrits with even a small amount of decoherence cannot offer increased security over qubits.

Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling

By using a complex field with a symmetric combination of electric and magnetic fields, a first-order covariant Lagrangian for Maxwell's equations is obtained, similar to the Lagrangian for the Dirac equation. This leads to a dual-symmetric quantum electrodynamic theory with an infinite set of local conservation laws. The dual symmetry is shown to correspond to a helical phase, conjugate to the conserved helicity. There is also a scaling symmetry, conjugate to the conserved entanglement. The results include a novel form of the photonic wavefunction, with a well-defined helicity number operator conjugate to the chiral phase, related to the fundamental dual symmetry. Interactions with charged particles can also be included. Transformations from minimal coupling to multi-polar or more general forms of coupling are particularly straightforward using this technique. The dual-symmetric version of quantum electrodynamics derived here has potential applications to nonlinear quantum optics and cavity quantum electrodynamics.

Quantum atom optics with fermions from molecular dissociation

We study a fermionic atom optics counterpart of parametric down-conversion with photons. This can be realized through dissociation of a Bose-Einstein condensate of molecular dimers consisting of fermionic atoms. We present a theoretical model describing the quantum dynamics of dissociation and find analytic solutions for mode occupancies and atomic pair correlations, valid in the short time limit. The solutions are used to identify upper bounds for the correlation functions, which are applicable to any fermionic system and correspond to ideal particle number-difference squeezing.

Quantum memory scheme based on optical fibers and cavities

An optical quantum memory scheme using two narrow-linewidth cavities and some optical fibers is proposed. The cavities are connected via an optical fiber, and the gap of each cavity can be adjusted to allow photons with a certain bandwidth to transmit through or reflect back. Hence, each cavity acts as a shutter and the photons can be stored in the optical fiber between the cavities at will. We investigate the feasibility of using this device in storing a single photon. We estimate that with current technology storage of a photon qubit for up to 50 clock cycles (round trips) could be achieved with a probability of success of 85%. We discuss how this figure could be improved.

Error models for mode mismatch in linear optics quantum computing

One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for the effects of mode mismatch on its operation, and relate these error models to current fault-tolerant-threshold estimates.

Studies of nonlinear absorption and aggregation in aqueous solutions of rhodamine 6G using a transient thermal lens technique

Dual-beam transient thermal lens studies were carried out in aqueous solutions of rhodamine 6G using 532 nm pulses from a frequency-doubled Nd:YAG laser. The analysis of the observed data showed that the thermal lens method can effectively be utilized to study the nonlinear absorption and aggregation which are taking place in a dye medium.

Ancilla-assisted quantum process tomography

Complete and precise characterization of a quantum dynamical process can be achieved via the method of quantum process tomography. Using a source of correlated photons, we have implemented several methods, each investigating a wide range of processes, e.g., unitary, decohering, and polarizing. One of these methods, ancilla-assisted process tomography (AAPT), makes use of an additional ancilla system, and we have theoretically determined the conditions when AAPT is possible. Surprisingly, entanglement is not required. We present data obtained using both separable and entangled input states. The use of entanglement yields superior results, however.