Measurement and state preparation via ion trap quantum computing

We investigate in detail the effects of a QND vibrational number measurement made on single ions in a recently proposed measurement scheme for the vibrational state of a register of ions in a linear rf trap [C. D'HELON and G. J. MILBURN, Phys Rev. A 54, 5141 (1996)]. The performance of a measurement shows some interesting patterns which are closely related to searching.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics I. Theory

The quasi mode theory of macroscopic quantization in quantum optics and cavity QED developed by Dalton, Barnett and Knight is generalized. This generalization allows for cases in which two or more quasi permittivities, along with their associated mode functions, are needed to describe the classical optics device. It brings problems such as reflection and refraction at a dielectric boundary, the linear coupler, and the coupling of two optical cavities within the scope of the theory. For the most part, the results that are obtained here are simple generalizations of those obtained in previous work. However the coupling constants, which are of great importance in applications of the theory, are shown to contain significant additional terms which cannot be 'guessed' from the simpler forms. The expressions for the coupling constants suggest that the critical factor in determining the strength of coupling between a pair of quasi modes is their degree of spatial overlap. In an accompanying paper a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary is given as an illustration of the generalized theory. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics II. Application to reflection and refraction at a dielectric interface

The generalization of the quasi mode theory of macroscopic quantization in quantum optics and cavity QED presented in the previous paper, is applied to provide a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes. The derivation of the laws of reflection and refraction is achieved through the dual application of the quasi mode theory and a quantum scattering theory based on the Heisenberg picture. Formal expressions from scattering theory are given for the reflection and transmission coefficients. The behaviour of the intensity for a localized one photon wave packet coming in at time minus infinity from the incident direction is examined and it is shown that at time plus infinity, the light intensity is only significant where the classical laws of reflection and refraction predict. The occurrence of both refraction and reflection is dependent upon the quasi mode theory coupling constants between incident and transmitted region quasi modes being nonzero, and it is seen that the contributions to such coupling constants come from the overlap of the mode functions in the boundary layer region, as might be expected from a microscopic theory.

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

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.

Mesoscopic one-way channels for quantum state transfer via the quantum hall effect

We show that the one-way channel formalism of quantum optics has a physical realization in electronic systems. In particular, we show that magnetic edge states form unidirectional quantum channels capable of coherently transporting electronic quantum information. Using the equivalence between one-way photonic channels and magnetic edge states, we adapt a proposal for quantum state transfer to mesoscopic systems using edge states as a quantum channel, and show that it is feasible with reasonable experimental parameters. We discuss how this protocol may be used to transfer information encoded in number, charge, or spin states of quantum dots, so it may prove useful for transferring quantum information between parts of a solid-state quantum computer

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.

Three-dimensional imaging with optical tweezers

We demonstrate a three-dimensional scanning probe microscope in which the extremely soft spring of an optical tweezers trap is used. Feedback control of the instrument based on backscattered light levels allows three-dimensional imaging of microscopic samples in an aqueous environment. Preliminary results with a 2-mu m-diameter spherical probe indicate that features of approximately 200 nm can be resolved, with a sensitivity of 5 nm in the height measurement. The theoretical resolution is limited by the probe dimensions. (C) 1999 Optical Society of America.

Signatures of the pair-coherent state

We explore in detail the possibility of generating a pair-coherent state in the nondegenerate parametric oscillator when decoherence is included. Such states are predicted in the transient regime in parametric oscillation where the pump mode is adiabatically eliminated. Two specific signatures are examined to indicate whether the state of interest has been generated, the Schrodinger cat state-like signatures, and the fidelity. Solutions in a transient regime reveal interference fringes which are indicative of the formation of a Schrodinger cat state. The fidelity indicates the purity of our prepared state compared with the ideal pair-coherent state.

Single-electron measurements with a micromechanical resonator

A mechanical electroscope based on a change in the resonant frequency of a cantilever one micron in size in the presence of charge has recently been fabricated. We derive the decoherence rate of a charge superposition during measurement with such a device using a master equation theory adapted from quantum optics. We also investigate the information produced by such a measurement, using a quantum trajectory approach. Such instruments could be used in mesoscopic electronic systems, and future solid-state quantum computers, so it is useful to know how they behave when used to measure quantum superpositions of charge.