Quantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions

Gough, John, (2004) 'Quantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions', Communications in Mathematical Physics 254 pp.498-512 RAE2008

Correlations in low dimensional quantum systems

In this thesis I present the work done during my PhD in the area of low dimensional quantum gases. The chapters of this thesis are self contained and represent individual projects which have been peer reviewed and accepted for publication in respected international journals. Various systems are considered, the first of which is a two particle model which possesses an exact analytical solution. I investigate the non-classical correlations that exist between the particles as a function of the tunable properties of the system. In the second work I consider the coherences and out of equilibrium dynamics of a one-dimensional Tonks-Girardeau gas. I show how the coherence of the gas can be inferred from various properties of the reduced state and how this may be observed in experiments. I then present a model which can be used to probe a one-dimensional Fermi gas by performing a measurement on an impurity which interacts with the gas. I show how this system can be used to observe the so-called orthogonality catastrophe using modern interferometry techniques. In the next chapter I present a simple scheme to create superposition states of particles with special emphasis on the NOON state. I explore the effect of inter-particle interactions in the process and then characterise the usefulness of these states for interferometry. Finally I present my contribution to a project on long distance entanglement generation in ion chains. I show how carefully tuning the environment can create decoherence-free subspaces which allows one to create and preserve entanglement.

Techniques for engineering quantum states

In this thesis I theoretically study quantum states of ultracold atoms. The majority of the Chapters focus on engineering specific quantum states of single atoms with high fidelity in experimentally realistic systems. In the sixth Chapter, I investigate the stability and dynamics of new multidimensional solitonic states that can be created in inhomogeneous atomic Bose-Einstein condensates. In Chapter three I present two papers in which I demonstrate how the coherent tunnelling by adiabatic passage (CTAP) process can be implemented in an experimentally realistic atom chip system, to coherently transfer the centre-of-mass of a single atom between two spatially distinct magnetic waveguides. In these works I also utilise GPU (Graphics Processing Unit) computing which offers a significant performance increase in the numerical simulation of the Schrödinger equation. In Chapter four I investigate the CTAP process for a linear arrangement of radio frequency traps where the centre-of-mass of both, single atoms and clouds of interacting atoms, can be coherently controlled. In Chapter five I present a theoretical study of adiabatic radio frequency potentials where I use Floquet theory to more accurately model situations where frequencies are close and/or field amplitudes are large. I also show how one can create highly versatile 2D adiabatic radio frequency potentials using multiple radio frequency fields with arbitrary field orientation and demonstrate their utility by simulating the creation of ring vortex solitons. In the sixth Chapter I discuss the stability and dynamics of a family of multidimensional solitonic states created in harmonically confined Bose-Einstein condensates. I demonstrate that these solitonic states have interesting dynamical instabilities, where a continuous collapse and revival of the initial state occurs. Through Bogoliubov analysis, I determine the modes responsible for the observed instabilities of each solitonic state and also extract information related to the time at which instability can be observed.

On the disentangling process for two-mode squeezed state

A pure state decoheres into a mixed state as the system entangles with an environment which is initially in a pure state. However, it is not definite that the system becomes entangled with a confined environment with which it only ever interacts. We investigate the disentangling mechanism by considering the quantum correlation between a two-mode squeezed state and a thermal environment.

Dynamical entanglement transfer for quantum-information networks

A key element in the architecture of a quantum-information processing network is a reliable physical interface between fields and qubits. We study a process of entanglement transfer engineering, where two remote qubits respectively interact with an entangled two-mode continuous-variable (CV) field. We quantify the entanglement induced in the qubit state at the expenses of the loss of entanglement in the CV system. We discuss the range of mixed entangled states which can be obtained with this setup. Furthermore, we suggest a protocol to determine the residual entangling power of the light fields inferring, thus, the entanglement left in the field modes which, after the interaction, are no longer in a Gaussian state. Two different setups are proposed: a cavity-QED system and an interface between superconducting qubits and field modes. We address in detail the practical difficulties inherent in these two proposals, showing that the latter is promising in many aspects.

Ultrafast coherent control and quantum encoding of molecular vibrations in D2+ using intense laser pulses

Intense, few-femtosecond pulse technology has enabled studies of the fastest vibrational relaxation processes. The hydrogen group vibrations can be imaged and manipulated using intense infrared pulses. Through numerical simulation, we demonstrate an example of ultrafast coherent control that could be effected with current experimental facilities, and observed using high-resolution time-of-flight spectroscopy. The proposal is a pump-probe-type technique to manipulate the D2+ ion with ultrashort pulse sequences. The simulations presented show that vibrational selection can be achieved through pulse delay. We find that the vibrational system can be purified to a two-level system thus realizing a vibrational qubit. A novel scheme for the selective transfer of population between these two levels, based on a Raman process and conditioned upon the delay time of a second control-pulse is outlined, and may enable quantum encoding with this system.

Quantum revivals in ultrashort intense field dissociation of molecular ions

Ultrashort (<15 fs) high intensity (1014-1016 W cm-2) laser pulses have provided novel methods for investigation of the dynamics of simple molecular ions such as H2+ and D2+. In this paper we report on simulations carried out for the D2+ molecular ion, within the Born- Oppenheimer and two-state approximations. These simulations allow one to investigate the dissociation dynamics of the D2+ molecular ion when subjected to such ultrashort, intense laser pulses. In particular, these simulations are compared to the results from recent pump-probe experiments, in which, the nuclear vibrational motion of D2+ has been imaged. Simulations suggest that the nature of the dissociation process, be it 1- or 2-photon, may be influenced by the tuning of the pump-probe delay time.

Passing quantum correlations to qubits using any two-mode state

We draw an explicit connection between the statistical properties of an entangled two-mode continuous variable (CV) resource and the amount of entanglement that can be dynamically transferred to a pair of noninteracting two-level systems. More specifically, we rigorously reformulate entanglement-transfer process by making use of covariance matrix formalism. When the resource state is Gaussian, our method makes the approach to the transfer of quantum correlations much more flexible than in previously considered schemes and allows the straightforward inclusion of the effects of noise affecting the CV system. Moreover, the proposed method reveals that the use of de-Gaussified two-mode states is almost never advantageous for transferring entanglement with respect to the full Gaussian picture, despite the entanglement in the non-Gaussian resource can be much larger than in its Gaussian counterpart. We can thus conclude that the entanglement-transfer map overthrows the

Physical model for the generation of ideal resources in multipartite quantum networking

We propose a physical model for generating multipartite entangled states of spin-s particles that have important applications in distributed quantum information processing. Our protocol is based on a process where mobile spins induce the interaction among remote scattering centers. As such, a major advantage lies in the management of stationary and well-separated spins. Among the generable states, there is a class of N-qubit singlets allowing for optimal quantum telecloning in a scalable and controllable way. We also show how to prepare Aharonov, W, and Greenberger-Horne-Zeilinger states.

Quantum chemistry and in situ FTir spectroscopy studies on potential-dependent properties of CO adsorbed on Pt electrodes

The electronic and vibrational properties of CO adsorbed on Pt electrodes at different potentials have been studied, by using methods of self-consistent-charge discrete variational Xa (SCC-DV-Xa) cluster calculations and in situ FTir spectroscopy. Two new models have been developed and verified to be successful: (1) using a "metallic state cluster" to imitate a metal (electrode) surface; and (2) charging the cluster and shifting its Fermi level (e{lunate}) to simulate, according to the relation of -d e{lunate}e dE, quantitatively the variation of the electrode potential (E). It is shown that the binding of PtCO is dominated by the electric charge transfer of dp ? 2p, while that of s ? Pt is less important in this binding. The electron occupancy of the 2p orbital of CO weakens the CO bond and decreases the v. Variation of E mainly influences the charge transfer process of dp ? 2p, but hardly influences that of s ? Pt. A linear potential-dependence of v has been shown and the calculated dv/dE = 35.0 cm V. All results of calculations coincide with the ir experimental data. © 1993.

Quantum chemistry studies on electronic properties of CN adsorbed on silver electrodes

The electronic properties of CN adsorbed on Ag electrodes at different potentials have been studied by using the method of self-consistent-charge discrete variational Xa (SCC-DV-Xa) cluster calculations. It is shown that the binding of NCAg is dominated by both electrostatic and polarization effects derived from the charge of CN, and that the transfer of s charge from CN to silver is the largest donation contribution. The electrode potential influences this charge transfer process and the interaction between CN adsorbate and silver electrode. The results of quantum chemistry calculations fit well with the experimental data of in situ spectroscopic studies on the CN/Ag electrode systems. © 1991.

Linear Optics Simulation of Quantum Non-Markovian Dynamics

The simulation of open quantum dynamics has recently allowed the direct investigation of the features of system-environment interaction and of their consequences on the evolution of a quantum system. Such interaction threatens the quantum properties of the system, spoiling them and causing the phenomenon of decoherence. Sometimes however a coherent exchange of information takes place between system and environment, memory effects arise and the dynamics of the system becomes non-Markovian. Here we report the experimental realisation of a non-Markovian process where system and environment are coupled through a simulated transverse Ising model. By engineering the evolution in a photonic quantum simulator, we demonstrate the role played by system-environment correlations in the emergence of memory effects.

Quantum and classical properties of the fields generated by two interlinked second-order non-linear interactions

We consider two interlinked non-linear interactions occurring simultaneously in a single chi((2)) crystal. Classical and quantum working regimes are considered and their peculiar properties analysed. In particular, we describe an experiment, realized in the classical regime, that verifies the holographic nature of the process, and predict, for the quantum regime, the generation of a fully inseparable tripartite Gaussian state of light that can be used to support a general 1--> 2 continuous variable telecloning protocol.

Kinetics of levoglucosan and formaldehyde formation during cellulose pyrolysis process

The mechanisms and kinetics studies of the formation of levoglucosan and formaldehyde from anhydroglucose radical have been carried out theoretically in this paper. The geometries and frequencies of all the stationary points are calculated at the B3LYP/6-31+G(D,P) level based on quantum mechanics, Six elementary reactions are found, and three global reactions are involved. The variational transition-state rate constants for the elementary reactions are calculated within 450-1500 K. The global rate constants for every pathway are evaluated from the sum of the individual elementary reaction rate constants. The first-order Arrhenius expressions for these six elementary reactions and the three pathways are suggested. By comparing with the experimental data, computational methods without tunneling correction give good description for Path1 (the formation of levoglucosan); while methods with tunneling correction (zero-curvature tunneling and small-curvature tunneling correction) give good results for Path2 (the first possibility for the formation of formaldehyde), all the test methods give similar results for Path3 (the second possibility for the formation of formaldehyde), all the modeling results for Path3 are in good agreement with the experimental data, verifying that it is the most possible way for the formation of formaldehyde during cellulose pyrolysis. © 2012 Elsevier Ltd. All rights reserved.

Out-of-equilibrium thermodynamics of quantum optomechanical systems

We address the out-of-equilibrium thermodynamics of an isolated quantum system consisting of a cavity optomechanical device. We explore the dynamical response of the system when driven out of equilibrium by a sudden quench of the coupling parameter and compute analytically the full distribution of the work generated by the process. We consider linear and quadratic optomechanical coupling, where the cavity field is parametrically coupled to either the position or the square of the position of a mechanical oscillator, respectively. In the former case we find that the average work generated by the quench is zero, whilst the latter leads to a non-zero average value. Through fluctuations theorems we access the most relevant thermodynamical figures of merit, such as the free energy difference and the amount of irreversible work generated. We thus provide a full charac- terization of the out-of-equilibrium thermodynamics in the quantum regime for nonlinearly coupled bosonic modes. Our study is the first due step towards the construction and full quantum analysis of an optomechanical machine working fully out of equilibrium.