In this thesis we relate the formal description of various cold atomic systems in the\nenergy eigenbasis, to the observable spatial mode dynamics. Herein the `spatial mode\ndynamics' refers to the direction of photon emission following the spontaneous emission\nof an excited fermion in the presence of a same species and spin ideal anisotropic Fermi\nsea in its internal ground state. Due to the Pauli principle, the presence of the ground\nstate Fermi sea renders the phase space, anisotropic and only partially accessible, thereby\na ecting the direction of photon emission following spontaneous emission.\nThe spatial and energetic mode dynamics also refers to the quantum `tunneling' interaction\nbetween localised spatial modes, synonymous with double well type potentials.\nHere we relate the dynamics of the wavefunction in both the energetic and spatial representations.\nUsing this approach we approximate the relationship between the spatial\nand energetic representations of a wavefunction spanning three spatial and energetic\nmodes. This is extended to a process known as Spatial Adiabatic Passage, which is a\ntechnique to transport matter waves between localised spatial modes. This approach\nallows us to interpret the transport of matter waves as a signature of a geometric phase\nacquired by the one of the internal energy eigenstates of the system during the cyclical\nevolution. We further show that this geometric phase may be used to create spatial\nmode qubit and qutrit states.
In this thesis we relate the formal description of various cold atomic systems in the\nenergy eigenbasis, to the observable spatial mode dynamics. Herein the spatial mode\ndynamics' refers to the direction of photon emission following the spontaneous emission\nof an excited fermion in the presence of a same species and spin ideal anisotropic Fermi\nsea in its internal ground state. Due to the Pauli principle, the presence of the ground\nstate Fermi sea renders the phase space, anisotropic and only partially accessible, thereby\na ecting the direction of photon emission following spontaneous emission.\nThe spatial and energetic mode dynamics also refers to the quantum tunneling' interaction\nbetween localised spatial modes, synonymous with double well type potentials.\nHere we relate the dynamics of the wavefunction in both the energetic and spatial representations.\nUsing this approach we approximate the relationship between the spatial\nand energetic representations of a wavefunction spanning three spatial and energetic\nmodes. This is extended to a process known as Spatial Adiabatic Passage, which is a\ntechnique to transport matter waves between localised spatial modes. This approach\nallows us to interpret the transport of matter waves as a signature of a geometric phase\nacquired by the one of the internal energy eigenstates of the system during the cyclical\nevolution. We further show that this geometric phase may be used to create spatial\nmode qubit and qutrit states.
In this Thesis the interaction of an electromagnetic field and matter is studied from various aspects in the general framework of cold atoms. Our subjects cover a wide spectrum of phenomena ranging from semiclassical few-level models to fully quantum mechanical interaction with structured reservoirs leading to non-Markovian open quantum system dynamics. Within closed quantum systems, we propose a selective method to manipulate the motional state of atoms in a time-dependent double-well potential and interpret the method in terms of adiabatic processes. Also, we derive a simple wave-packet model, based on distributions of generalized eigenstates, explaining the finite visibility of interference in overlapping continuous-wave atom lasers. In the context of open quantum systems, we develop an unraveling of non-Markovian dynamics in terms of piecewise deterministic quantum jump processes confined in the Hilbert space of the reduced system - the non-Markovian quantum jump method. As examples, we apply it for simple 2- and 3-level systems interacting with a structured reservoir. Also, in the context of ion-cavity QED we study the entanglement generation based on collective Dicke modes in experimentally realistic conditions including photonic losses and an atomic spontaneous decay.
Recent efforts in the field of ultracold atoms have goneinto creating wave guides of sub-micron sizes. In this thesis,the quantum dynamics of matter waves in such confiningpotential structures with minima extended in space isinvestigated. A general framework based upon the separation ofthe wave function for the quantum particle using a discrete setof mode functions is introduced to reduce the dimensionality ofthe problem. Conditions for propagation in the form ofindependent modes, i.e. adiabatic propagation, are determinedfor the case of matter waves with spatially varying width andfound to be connected to the diffraction of matter wavesthrough a dimensionless parameter, the Fresnel parameter. Further, the analysis is extended to include situationswhere a transition to completely non-adiabatic dynamics takesplace. Here it is found that focusing of matter waves due toenergy redistribution at the end of adiabatic guiding isdetermined by the Fresnel parameter found earlier. In theadiabatic regime, the essential dynamics in the directiontransverse to the minimal valley of the guiding potentialstructure occurs at a time-scale much shorter than that ofchanges in the propagating direction. As a result of this,reection of matter waves is likely to occur unless the changesare made over very long distances. The formalism of adiabatic propagation is also applied thesituation of splitting of matter waves in potential structures.It is found that the adiabaticity criteria are identical tothose for a single guide of spatially varying width. Aformulation of adiabatic splitting in terms of states localizedclose to either of the two minima is developed. The inuence oflongitudinal localization on the splitting of coherentsuperposition states is examined and found to be described by asimple analytical expression.
This thesis is concerned with the theory of spontaneous emission in the context of cavity QED and the guiding of atoms by laser light in confined geometries. We focus on three different geometrical shapes of waveguide, namely the parallel plate guide and two kinds of cylindrical waveguide: one with a rectangular cross section and another with a circular cross section. These waveguides are assumed to be characterised by two distinct properties. Firstly, all three types of guide have perfect conductor boundary conditions, which means that the guide walls are infinitely conducting and, consequently, lossless. Secondly, the guides are assumed to have subwavelength dimensions (less than the atom electric dipole transition wavelength #lambda#). The first consequence of this is that the spontaneous emission process is possible only via a few cavity modes. For each type of structure, we examine the confinement of electromagnetic fields within it and proceed to quantise these fields by following the standard procedure, incorporating the boundary conditions at the guide walls. This allows the position-dependent spontaneous emission rate to be evaluated for an electric dipole located at an arbitrary point within the guide. Asymptotic limits of the spontaneous emission rate are then derived which serve as useful checks of the calculations. For the rectangular guide, we are able to recover the results appropriate for the parallel-plate case when side a of the rectangular cross section becomes large, while side b is kept fixed. For the circular guide, we are able to recover the results appropriate for the free space case when the radius of the guide becomes large. The second part of the thesis deals with the theory of the motion of atoms in the spatially varying light fields inside the three different shapes of waveguide. In each structure we examine the forces that act on the atom and solve the equation of motion leading to the atom dynamics when an electric dipole within the guide is subject to an excited p-polarised cavity mode. The characteristics of the atomic motion in the guide in the presence of a cavity mode are then explored. We show that under these conditions the atom becomes subject to a transverse dipole potential and a dissipative force, both of which vary across the guide and are also functions of the atom velocity along the mode propagation direction. The dipole potential is responsible for the transverse trapping (and hence the channelling) of atoms at specific regions of the cross section, while the dissipative force controls the longitudinal motion of the channelled atoms. The conditions facilitating atom guiding are explored using typical parameters for sodium atoms in guides of subwavelength dimensions. The roles of the van der Waals and Casimir-Polder potentials on the atomic motion in waveguides is clarified theoretically in the context of the parallel-plate guide and we show that such potentials are effective only at relatively short distances from the guide walls. Finally, we show that atomic motion in a hollow circular guide is subject to a quantised torque arising from the orbital angular momentum effects associated with any excited waveguide mode of order l > 0. We find that an appropriately detuned atom immersed in such a mode may be trapped radially in a vibrational state and be made to exhibit novel rotational effects associated with the light torque, including a rotational frequency shift. (author)
This thesis is concerned with modelling the dynamics of open quantum systems in several different contexts. Of principal interest is the manner in which the environment can modify, or even dominate, a system’s quantum behaviour in order to facilitate the transport of energetic excitations. In the first research chapter, a time-local, non-Markovian quantum master equation is derived in a variationally defined reference frame, for networks of two-level systems coupled to bosonic environments. The predictions of this master equation are then compared with those derived using both weak-coupling and polaron approximations. The variational master equation is found to agree with these standard approaches in their regimes of validity, whilst interpolating between them in intermediate parameter regimes. The second research chapter focusses on the dynamics of a superconducting double quantum dot embedded in a resonant circuit. The device is considered in a regime where the ground state consists of a coherent spatial superposition of a single Cooper pair, which can be excited by a variety of interactions with the environment. The relevant transition rates are calculated and the processes responsible are identified. A numerical simulation of the system is then used to explain experimental data, and show that for certain parameters a significant fraction of excitations occur via absorption of photons from the environment. The final chapter considers a model for an olfactory receptor, in which odorant molecules are recognised by their vibrational modes. Electron transfer occurs in the receptor, dependent on the presence of a vibrational mode of the right frequency. A quantum master equation for the system is derived, and the resulting dynamics is compared to earlier semi-classical treatments. The behaviour of the receptor is found to be sensitive not only to the frequency of the vibrational mode, but also to the character of the surrounding environment. Increased dissipation on the odorant mode, as well as the presence of higher frequencies in the environment is found to improve the frequency resolution of the receptor.
Adiabatic techniques are known to allow for engineering quantum states with high fidelity. This requirement is currently of large interest, as applications in quantum information require the preparation and manipulation of quantum states with minimal errors. Here we review recent progress on developing techniques for the preparation of spatial states through adiabatic passage, particularly focusing on three state systems. These techniques can be applied to matter waves in external potentials, such as cold atoms or electrons, and to classical waves in waveguides, such as light or sound.
Starting from the postulate that the electromagnetic field appearing in the transverse set of microscopic Maxwell-Lorentz equations governing field-matter interactions, properly normalized, can be looked upon as describing one-photon-emission and -absorption processes in space and time, a first-quantized initiation of photon emission by a single atom is presented. The wave function for the emerging photon is introduced as a six-vector object constructed from the complex analytical signals of the Riemann-Silberstein vectors belonging to opposite photon helicities. When the atom is no longer electrodynamically active, the emitted photon is described in first quantization by the so-called energy wave function well known for photons in free space. From the momentum representation of the emerging photon wave function a condition on the analytical part of the transverse atomic current density is established which ensures that precisely one photon is emitted. A propagator description of the emerged photon dynamics in the coordinate representation is established. The photon propagator is introduced as a two-component spinor, where upper and lower tensor components are constructed, respectively, from positive and negative helicity combinations of the propagators describing the time-space evolution of the transverse electric and magnetic fields. It is shown that the emission region for the photon coincides with the region in space where the transverse atomic current density is nonvanishing. For a photon emitted in an electric dipole transition the emission region essentially is the near-field zone of the atom, and this zone therefore determines the initial (and best) spatial confinement of the photon. The photon emerging from an atom active for a finite time necessarily is of the polychromatic sort and the associated wave packet essentially is confined between spherical shells moving outwards with the vacuum speed of light. To illustrate the main principles of the fundamental theory in a heuristic fashion we apply it to a study of the emission of a one-photon sinusoidal wavetrain from a pointlike atom. It is found that the atomic current density needed to create just one photon is independent of the oscillation period in the train and thus depends only on the number of periods in the wave train. An explicit expression for the one-photon energy is derived, and it is shown that only for extremely short pulse trains pronounced deviations from the textbook result, $E=\ensuremath{\Elzxh}{\ensuremath{\omega}}_{0},$ occur. The radial energy flow in the coupled atom-photon system in the near-field zone of the atom is investigated, and the cycle-averaged outwards energy transport carried by the emerging photon in a given distance from the atom is determined.