Nonlinear optics with cold Rb atoms using tapered optical nanofibres

Optical nanofibres (ONFs) are very thin optical waveguides with sub-wavelength diameters. ONFs have very high evanescent fields and the guided light is confined strongly in the transverse direction. These fibres can be used to achieve strong light-matter interactions. Atoms around the waist of an ONF can be probed by collecting the atomic fluorescence coupling or by measuring the transmission (or the polarisation) of the probe beam sent through it. This thesis presents experiments using ONFs for probing and manipulating laser-cooled 87Rb atoms. As an initial experiment, a single mode ONF was integrated into a magneto-optical trap (MOT) and used for measuring the characteristics of the MOT, such as the loading time and the average temperature of the atom cloud. The effect of a near-resonant probe beam on the local temperature of the cold atoms has been studied. Next, the ONF was used for manipulating the atoms in the evanescent fields region in order to generate nonlinear optical effects. Four-wave mixing, ac Stark effect (Autler-Townes splitting) and electromagnetically induced transparency have been observed at unprecedented ultralow power levels. In another experiment, a few-mode ONF, supporting only the fundamental mode and the first higher order mode group, has been used for studying cold atoms. A higher pumping rate of the atomic fluorescence into the higher order fibreguided modes and more interactions with the surrounding atoms for higher order mode evanescent light, when compared to signals for the fundamental mode, have been identified. The results obtained in the thesis are particularly for a fundamental understanding of light-atom interactions when atoms are near a dielectric surface and also for the development of fibre-based quantum information technologies. Atoms coupled to ONFs could be used for preparing intrinsically fibre-coupled quantum nodes for quantum computing and the studies presented here are significant for a detailed understanding of such a system.

Diagnosing criticality in symmetric and chiral clock models

Quantum clock models are statistical mechanical spin models which may be regarded as a sort of bridge between the one-dimensional quantum Ising model and the one-dimensional quantum XY model. This thesis aims to provide an exhaustive review of these models using both analytical and numerical techniques. We present some important duality transformations which allow us to recast clock models into different forms, involving for example parafermions and lattice gauge theories. Thus, the notion of topological order enters into the game opening new scenarios for possible applications, like topological quantum computing. The second part of this thesis is devoted to the numerical analysis of clock models. We explore their phase diagram under different setups, with and without chirality, starting with a transverse field and then adding a longitudinal field as well. The most important observables we take into account for diagnosing criticality are the energy gap, the magnetisation, the entanglement entropy and the correlation functions.

Kondo screening regimes of a quantum dot with a single Mn ion

We study the Kondo and transport properties of a quantum dot with a single magnetic Mn ion connected to metallic leads. By employing a numerical renormalization group technique we show that depending on the value of ferromagnetic coupling strength between the local electronic spin and the magnetic moment of the Mn, two distinct Kondo regimes exist. In the weak-coupling limit, the system can be found in a completely screened Kondo state describing a local magnetic moment decoupled from the rest of the system. In contrast, in the strong-coupling regime the quantum dot spin and the local magnetic moment form a single large-spin entity partially Kondo screened. A crossover between these two regimes can be suitably tuned by varying the tunnel coupling between the quantum dot and the leads. The model investigated here is also suitable to study magnetic molecules adsorbed on a metallic surface. The rich phenomenology of these systems is reflected in the conductance across the system.

Quantum and classical chaos for a single trapped ion

In this paper we investigate the quantum and classical dynamics of a single trapped ion subject to nonlinear kicks derived from a periodic sequence of Gaussian laser pulses. We show that the classical system exhibits: diffusive growth in the energy, or heating,'' while quantum mechanics suppresses this heating. This system may be realized in current single trapped-ion experiments with the addition of near-field optics to introduce tightly focused laser pulses into the trap.

Quantum signatures of chaos in the dynamics of a trapped ion

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C.A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.

Mode coupling for precise measurements of the electronic g-factor of hydrogen-like ions in Penning traps

The g-factor is a constant which connects the magnetic moment $vec{mu}$ of a charged particle, of charge q and mass m, with its angular momentum $vec{J}$. Thus, the magnetic moment can be writen $ vec{mu}_J=g_Jfrac{q}{2m}vec{J}$. The g-factor for a free particle of spin s=1/2 should take the value g=2. But due to quantum electro-dynamical effects it deviates from this value by a small amount, the so called g-factor anomaly $a_e$, which is of the order of $10^{-3}$ for the free electron. This deviation is even bigger if the electron is exposed to high electric fields. Therefore highly charged ions, where electric field strength gets values on the order of $10^{13}-10^{16}$V/cm at the position of the bound electron, are an interesting field of investigations to test QED-calculations. In previous experiments [H"aff00,Ver04] using a single hydrogen-like ion confined in a Penning trap an accuracy of few parts in $10^{-9}$ was obtained. In the present work a new method for precise measurement of magnetic the electronic g-factor of hydrogen-like ions is discussed. Due to the unavoidable magnetic field inhomogeneity in a Penning trap, a very important contribution to the systematic uncertainty in the previous measurements arose from the elevated energy of the ion required for the measurement of its motional frequencies. Then it was necessary to extrapolate the result to vanishing energies. In the new method the energy in the cyclotron degree of freedom is reduced to the minimum attainable energy. This method consist in measuring the reduced cyclotron frequency $nu_{+}$ indirectly by coupling the axial to the reduced cyclotron motion by irradiation of the radio frequency $nu_{coup}=nu_{+}-nu_{ax}+delta$ where $delta$ is, in principle, an unknown detuning that can be obtained from the knowledge of the coupling process. Then the only unknown parameter is the desired value of $nu_+$. As a test, a measurement with, for simplicity, artificially increased axial energy was performed yielding the result $g_{exp}=2.000~047~020~8(24)(44)$. This is in perfect agreement with both the theoretical result $g_{theo}=2.000~047~020~2(6)$ and the previous experimental result $g_{exp1}=2.000~047~025~4(15)(44).$ In the experimental results the second error-bar is due to the uncertainty in the accepted value for the electron's mass. Thus, with the new method a higher accuracy in the g-factor could lead by comparison to the theoretical value to an improved value of the electron's mass. [H"af00] H. H"affner et al., Phys. Rev. Lett. 85 (2000) 5308 [Ver04] J. Verd'u et al., Phys. Rev. Lett. 92 (2004) 093002-1

Nonlinear quantum optical computing via measurement

We show how the measurement induced model of quantum computation proposed by Raussendorf and Briegel ( 2001, Phys. Rev. Letts., 86, 5188) can be adapted to a nonlinear optical interaction. This optical implementation requires a Kerr nonlinearity, a single photon source, a single photon detector and fast feed forward. Although nondeterministic optical quantum information proposals such as that suggested by KLM ( 2001, Nature, 409, 46) do not require a Kerr nonlinearity they do require complex reconfigurable optical networks. The proposal in this paper has the benefit of a single static optical layout with fixed device parameters, where the algorithm is defined by the final measurement procedure.

Ion trap simulations of quantum fields in an expanding universe

We propose an experiment in which the phonon excitation of ion(s) in a trap, with a trap frequency exponentially modulated at rate kappa, exhibits a thermal spectrum with an Unruh temperature given by k(B)T=h kappa. We discuss the similarities of this experiment to the response of detectors in a de Sitter universe and the usual Unruh effect for uniformly accelerated detectors. We demonstrate a new Unruh effect for detectors that respond to antinormally ordered moments using the ion's first blue sideband transition.

Fast simulation of a quantum phase transition in an ion-trap realizable unitary map

We show that a specific implementation of a unitary map on multiple qubits in an ion trap is physically equivalent to a Hamiltonian evolution that belongs to the same universality class as the transverse Ising Hamiltonian. We suggest experimental signatures, and present numerical simulations for the case of four qubits.

Ion trap transducers for quantum electromechanical oscillators

An enduring challenge for contemporary physics is to experimentally observe and control quantum behavior in macroscopic systems. We show that a single trapped atomic ion could be used to probe the quantum nature of a mesoscopic mechanical oscillator precooled to 4 K, and furthermore, to cool the oscillator with high efficiency to its quantum ground state. The proposed experiment could be performed using currently available technology.

Identifying Multiquark Hadrons from Heavy Ion Collisions

Identifying hadronic molecular states and/or hadrons with multiquark components either with or without exotic quantum numbers is a long-standing challenge in hadronic physics. We suggest that studying the production of these hadrons in relativistic heavy ion collisions offers a promising resolution to this problem as yields of exotic hadrons are expected to be strongly affected by their structures. Using the coalescence model for hadron production, we find that, compared to the case of a nonexotic hadron with normal quark numbers, the yield of an exotic hadron is typically an order of magnitude smaller when it is a compact multiquark state and a factor of 2 or more larger when it is a loosely bound hadronic molecule. We further find that some of the newly proposed heavy exotic states could be produced and realistically measured in these experiments.

Combined Monte Carlo and quantum mechanics study of the solvatochromism of phenol in water. The origin of the blue shift of the lowest pi-pi* transition

A combined and sequential use of Monte Carlo simulations and quantum mechanical calculations is made to analyze the spectral shift of the lowest pi-pi* transition of phenol in water. The solute polarization is included using electrostatic embedded calculations at the MP2/aug-cc-pVDZ level giving a dipole moment of 2.25 D, corresponding to an increase of 76% compared to the calculated gas-phase value. Using statistically uncorrelated configurations sampled from the MC simulation,first-principle size-extensive calculations are performed to obtain the solvatochromic shift. Analysis is then made of the origin of the blue shift. Results both at the optimized geometry and in room-temperature liquid water show that hydrogen bonds of water with phenol promote a red shift when phenol is the proton-donor and a blue shift when phenol is the proton-acceptor. In the case of the optimized clusters the calculated shifts are in very good agreement with results obtained from mass-selected free jet expansion experiments. In the liquid case the contribution of the solute-solvent hydrogen bonds partially cancels and the total shift obtained is dominated by the contribution of the outer solvent water molecules. Our best result, including both inner and outer water molecules, is 570 +/- 35 cm(-1), in very good agreement with the small experimental shift of 460 cm(-1) for the absorption maximum.

Photochemical cleavage of nitrate ion coordinated to a Cr(III) porphyrin#

Photolysis of the nitrato chromium(III) tetraphenylporphyrinato compound Cr(TPP)(NO(3)) (TPP, tetraphenylporphyrin) in toluene solution clearly leads to the formation of the Cr(IV) oxo complex Cr(TPP)(O) with a quantum yield of 0.011. The other product, NO(2), was detected quantitatively by its reaction with the spin trapping agent 2,2,6,6-tetramethyl-piperidine-1-oxyl.

Quantum integrability and exact solution of the supersymmetric U model with boundary terms

Quantum integrability is established for the one-dimensional supersymmetric U model with boundary terms by means of the quantum inverse-scattering method. The boundary supersymmetric U chain is solved by using the coordinate-space Bethe-ansatz technique and Bethe-ansatz equations are derived. This provides us with a basis for computing the finite-size corrections to the low-lying energies in the system. [S0163-1829(98)00425-1].