The role of proton tunnelling in biological catalysis is investigated here within the frameworks of quantum information theory and thermodynamics. We consider the quantum correlations generated through two hydrogen bonds between a substrate and a prototypical enzyme that first catalyses the tautomerization of the substrate to move on to a subsequent catalysis, and discuss how the enzyme can derive its catalytic potency from these correlations. In particular, we show that classical changes induced in the binding site of the enzyme spreads the quantum correlations among all of the four hydrogen-bonded atoms thanks to the directionality of hydrogen bonds. If the enzyme rapidly returns to its initial state after the binding stage, the substrate ends in a new transition state corresponding to a quantum superposition. Open quantum system dynamics can then naturally drive the reaction in the forward direction from the major tautomeric form to the minor tautomeric form without needing any additional catalytic activity. We find that in this scenario the enzyme lowers the activation energy so much that there is no energy barrier left in the tautomerization, even if the quantum correlations quickly decay.

We discuss Danny Segal's key roles in the development of the spectroscopy of collision complexes at Imperial College and Oxford. We explain how his work lead to a number of new insights into collision dynamics in external fields.

We give a brief historical overview of the physical realisations of quantum degeneracy and Bose-Einstein condensation observed to date, with the aim of showing why quantum gases is a key rapidly evolving interdisciplinary field of physics. We motivate the need for developing more advanced theories to understand all the features observed in ultracold gases, and present some of the unresolved issues where the theories discussed in this book can play an important role.

Scattering probe particles from a quantum system can provide experimental access to information about the system's state. However, measurement backaction and momentum transfer during scattering changes the state of the system, potentially destroying the state we wish to probe. Here we investigate how to probe the system's initial state even in the presence of backaction and momentum transfer. We show that summing the scattering distributions of an ensemble of measurements reveals the initial state scattering pattern even when each of the individual measurements completely destroys the initial state. This procedure is effective provided the scattering takes place on a timescale that is short compared with the free evolution of the system.

We describe how quasiclassical relative positions of particles emerge in an initially delocalized quantum system as scattering of a probe beam is observed. We show that in the multiparticle case this localization in position space occurs via intermediate states that are quantum superpositions of spatial configurations. These superpositions are robust to consecutive scattering events, and scattering alone does not lead to their decoherence. Instead the free evolution of the system combines with scattering to destroy these superpositions, leading the particles to adopt classical-like positions relative to one another.

We study the emergence of localization and entanglement in many-body systems as a result of scattering measurements. We show that consecutive scattering measurements on a many-body system can produce superposition states in position space. The resulting states are signaled in the scattering distribution and these states are robust under continued scattering. We also show that the average scattering distribution for an ensemble of experiments gives the initial state scattering distribution even when the initial state is completely destroyed by the scattering process.

We study light scattering from atoms in optical lattices at finite temperature. We examine the light scattered by fermions in the noninteracting regime and by bosons in the superfluid and Mott insulating regimes. We extend previous theoretical studies to include the full band structure of the optical lattice. We find that light scattering that excites atoms out of the lowest band leads to an increase in light scattering away from the classical diffraction peaks and is largely temperature independent. This additional light scattering leads to lower efficiency of temperature measurements based on photon counting.

We examine off-resonant light scattering from ultracold atoms in the quantum Hall regime. When the light scattering is spin dependent, we show that images formed in the far field can be used to distinguish states of the system. The spatial dependence of the far-field images is determined by the two-particle spin-correlation functions, which the images are related to by a transformation. Quasiholes in the system appear in images of the density formed by collecting the scattered light with a microscope, where the quasihole statistics are revealed by the reduction in density at the quasihole position.

In a recent paper [Phys. Rev. A 82, 063623 (2010)] Hallwood et al. argued that it is feasible to create large superposition states with strongly interacting bosons in rotating rings. Here we investigate in detail how the superposition states in rotating-ring lattices depend on interaction strength and barrier height. With respect to the latter we find a trade-off between energy gap and quality of the superposition state. Most importantly, we go beyond the delta-function approximation for the barrier potential and show that the energy gap decreases exponentially with the number of particles for weak barrier potentials of finite width. These are crucial issues in the design of experiments to realize superposition states.

We review some recent developments in the theory of rotating atomic gases. These studies have thrown light on the process of nucleation of vortices in regimes where mean-field methods are inadequate. In our review, we shall describe and compare quantum vortex nucleation of a dilute ultracold bosonic gas trapped in three different configurations: a one-dimensional ring lattice, a one-dimensional ring superlattice and a two-dimensional asymmetric harmonic trap. In all of them, there is a critical rotation frequency, at which the particles in the ground state exhibit strong quantum correlations. However, the entanglement properties vary significantly from case to case. We explain these differences by characterizing the intermediate states that participate in the vortex nucleation process. Finally, we show that noise correlations are sensitive to these differences. These new studies have, therefore, shown how novel quantum states may be produced and probed in future experiments with rotating neutral atom systems.

We investigate imaging of the spatial spin distribution of atoms in optical lattices using nonresonant light scattering. We demonstrate how scattering spatially correlated light from the atoms can result in spin state images with enhanced spatial resolution. Furthermore, we show how using spatially correlated light can lead to direct measurement of the spatial correlations of the atomic spin distribution.

We study the dynamics of a pair of molecular ensembles trapped inside a superconducting resonator through which they are strongly coupled via a microwave field mode. We find that entanglement can be generated via 'vacuum fluctuations' even when the molecules and cavity field are initially prepared in their ground state. This entanglement is created in a relatively short time and without the need for further manipulation of the system. It therefore provides a convenient scheme to entangle two mesoscopic systems, and may well be useful for quantum information processing.

Ultracold bosons in rotating ring lattices have previously been shown to form macroscopic superpositions of different quasimomentum states. We demonstrate that the generation of this kind of state using slightly nonuniform ring lattices has several advantages: the energy gap decreases less severely with increasing number of particles, the sensitivity to detunings from the critical rotation frequency is reduced, and the scheme is not limited to commensurate filling. We show that different quasimomentum states can be distinguished in time-of-flight absorption imaging and propose to probe correlations via the many-body oscillations induced by a sudden change in the rotation frequency.

Ultracold bosons in rotating ring lattices have previously been shown to form macroscopic superpositions of different quasi-momentum states. We demonstrate that the generation of such kind of states using slightly non-uniform ring lattices has several advantages: the energy gap decreases less severely with the number of particles, the sensitivity to detunings from the critical rotation frequency is reduced, and the scheme is not limited to commensurate filling. We show that different quasi-momentum states can be distinguished in time-of-flight absorption imaging and propose to probe correlations via the many-body oscillations induced by a sudden change in the rotation frequency.

We use second- and fourth-order correlation functions accessible in time-of-flight images to investigate the effects of rotation on one-dimensional ultracold bosons confined to a ring lattice. There exists a critical rotation frequency at which the ground state of a weakly interacting and integer-filled atomic gas is fragmented into a macroscopic superposition of two states with different circulation. The formation of such a quantum superposition (``cat'') state is accompanied by the opening of a gap in the spectrum, and by a sudden rearrangement of the momentum distribution which lowers the threshold of the Mott insulator transition. We show that both the entangled character of the ground state and the enhancement of quantum correlations can be detected in the density-density correlations of the expanding cloud. Our studies demonstrate the usefulness of these correlations for identifying physics in cold atomic systems.

We study the area-dependent entropy and two-site entanglement for two-state Bose-Einstein condensates in a two-dimensional optical lattice. We consider the case where the array of two-component condensates behaves like an ensemble of spin-half particles with the interaction to its nearest neighbors and next-nearest neighbors. We show how the Hamiltonian of their Bose-Einstein condensate lattice with nearest-neighbor and next-nearest-neighbor interactions can be mapped onto a harmonic lattice. We use this to determine the entropy and entanglement content of the lattice.

We present a theoretical study of a type of Josephson device, the so-called ``optical Josephson junction'' [Y. Shin et al. Phys. Rev. Lett. 95, 170402 (2005).]. In this device, two condensates are optically coupled through a waveguide by a pair of Bragg beams. This optical Josephson junction differs from the usual Josephson junction where condensates are weakly coupled by tunneling through a barrier. We discuss the use of this optical Josephson junction, for making precision measurements.

We study why it is quite so hard to make a superposition of super fluid flows in a Bose-Einstein condensate. To do this we initially investigate the quantum states of N atoms trapped in a 1D ring with a barrier at one position and a phase applied around it. We show how macroscopic superpositions can in principle be produced and investigate factors which affect the superposition. We then use the Bose-Hubbard model to study an array of Bose-Einstein condensates trapped in optical potentials and coupled to one another to form a ring. We derive analytic expressions for the quality of the superposition for this system, which agrees well with direct diagonalization of the Hamiltonian for relatively small numbers of atoms. We show that for macroscopic superpositions to be realized there are essentially three straightforward requirements, other than an absence of decoherence, which become harder to achieve as the system size increases. Firstly, the energies of the two distinct superfluid states must be sufficiently close. Secondly, coupling between the two states must be sufficiently strong, and thirdly, other states must be well separated from those participating in the superposition.