Bright bichromatic entanglement and quantum dynamics of sum frequency generation

We investigate the quantum properties of the well-known process of sum frequency generation, showing that it is potentially a very useful source of non-classical states of the electromagnetic field, some of which are not possible with the more common techniques. We show that it can produce quadrature squeezed light, bright bichromatic entangled states and symmetric and asymmetric demonstrations of the Einstein-Podolsky-Rosen paradox. We also show that the semiclassical equations totally fail to describe the mean-field dynamics when the cavity is strongly pumped

Quantum ultra-cold atomtronics

It is known that a semi-classical analysis is not always adequate for atomtronics devices, but that a fully quantum analysis is often necessary to make reliable predictions. While small numbers of atoms at a small number of sites are tractable using the density matrix, a fully quantum analysis is often not straightforward as the system becomes larger. We show that the fully quantum positive-P representation is then a viable calculational tool. We postulate an atomtronic phase-gate consisting of four wells in a Bose-Hubbard configuration, for which the semi-classical dynamics are controllable using the phase of the atomic mode in one of the wells. We show that the quantum predictions of the positive-P representation for the performance of this device have little relation to those found semi-classically, and that the performance depends markedly on the actual quantum states of the initially occupied modes. We find that initial coherent states lead to closest to classical dynamics, but that initial Fock states give results that are quite different. A fully quantum analysis also opens the door for deeply quantum atomtronics, in which properties such as entanglement and EPR (Einstein-Podolsky-Rosen) steering become valuable technical properties of a device.Comment: 12 pages, 6 figures, submitted to Phys. Rev

A quantum correlated twin atom laser from a Bose-Hubbard system

We propose and evaluate a method to construct a quantum correlated twin atom laser using a pumped and damped Bose-Hubbard inline trimer which can operate in a stationary regime. With pumping via a source condensate filling the middle well and damping using either an electron beam or optical means at the two end wells, we show that bipartite quantum correlations build up between the ends of the chain, and that these can be measured either in situ or in the outcoupled beams. While nothing similar to our system has yet been achieved experimentally, recent advances mean that it should be practically realisable in the near future.Comment: 15 pages, 8 figures, theory. Typos fixed and material added to introductio

Quantum phase-space analysis of the pendular cavity

We perform a quantum mechanical analysis of the pendular cavity, using the positive-P representation, showing that the quantum state of the moving mirror, a macroscopic object, has noticeable effects on the dynamics. This system has previously been proposed as a candidate for the quantum-limited measurement of small displacements of the mirror due to radiation pressure, for the production of states with entanglement between the mirror and the field, and even for superposition states of the mirror. However, when we treat the oscillating mirror quantum mechanically, we find that it always oscillates, has no stationary steady-state, and exhibits uncertainties in position and momentum which are typically larger than the mean values. This means that previous linearised fluctuation analyses which have been used to predict these highly quantum states are of limited use. We find that the achievable accuracy in measurement is far worse than the standard quantum limit due to thermal noise, which, for typical experimental parameters, is overwhelming even at 2 mK.Comment: 25 pages, 6 figures To be published in Phys. Rev.

Mathematical models for cell-matrix interactions during dermal wound healing

This paper contains a review of our recent work on the mathematical modeling of cell interaction with extracellular matrix components during the process of dermal wound healing. The models are of partial differential equation type and allow us to investigate in detail how various mechanochemical effects may be responsible for certain wound healing disorders such as fibrocontractive and fibroproliferative diseases. We also present a model for wound healing angiogenesis. The latter has several features in common with angiogenesis during cancer tumour growth and spread so a deeper understanding of the phenomenon in the context of wound healing may also help in the treatment of certain cancers

Mesoscopic dynamical differences from quantum state preparation in a Bose-Hubbard trimer

Conventional wisdom is that quantum effects will tend to disappear as the number of quanta in a system increases, and the evolution of a system will become closer to that described by mean field classical equations. In this letter we combine newly developed experimental techniques to propose and analyse an experiment using a Bose-Hubbard trimer where the opposite is the case. We find that differences in the preparation of a centrally evacuated trimer can lead to readily observable differences in the subsequent dynamics which increase with system size. Importantly, these differences can be detected by the simple measurements of atomic number.Comment: 5 pages, 4 figures, theor

Tripartite entanglement from interlinked χ(2)\chi^{(2)} parametric interactions

We examine the tripartite entanglement properties of an optical system using interlinked $\chi^{(2)}$ interactions, recently studied experimentally in terms of its phase-matching properties by Bondani et al [M. Bondani, A. Allevi, E. Gevinti, A. Agliati, and A. Andreoni, arXiv:quant-ph/0604002.]. We show that the system does produce output modes which are genuinely tripartite entangled and that detection of this entanglement depends crucially on the correlation functions which are measured, with a three-mode Einstein-Podolsky-Rosen inequality being the most sensitive.Comment: 15 pages, 5 figure