Research Topics

- Foundations of Quantum Physics – Wigner current: In manuscript 32 we
have shown that quantum phase space contains non-classical current patterns with
interesting topological features, including a new conservation law for the vorticity
of the current. This work has been highlighted by the editors and featured on the
cover of the Physical Review Letters. I believe Wigner current will become a widely
used tool for the investigation of quantum phase space features.

In manuscript 34 we have shown that quantum phase space current is well represented in integral form. Furthermore we proved that it cannot be converted into Liouvillian form.

Anharmonic quantum mechanical systems do not feature phase space trajectories 37 shows that the formation of quantum coherences (negativities of Wigner distribution) cannot be viewed from a perspective of classical phase space transport. If one adopts a classical approach and tries to understand quantum phase space evolution from a perspective of classical transport along trajectories paradoxes arise: Liouvillian phase space volumes shrink or expand infinitely quickly, trajectories do not exist globally, computer code breaks down.

- Opto-Mechanics: The paper 30 considers the creation of non-classical states using
optical methods and tiny mirrors. The goal is the generation of non-classical states
of systems with considerable mass such as micro-mirrors.

- Multimode Laser Beam Shaping: This the first publication 24 describing how
‘arbitrary’ potential landscapes can be implemented in the transverse cross section
of a laser beam. This work has been chosen as one of the ‘Highlight in 2005’-articles
in Journal of Optics A. Related work 25 on an intuitive way to understand the
influence of Gouy’s phase on beam shaping has led to cooperation with Miles
Padgett’s group and its experimental verification 26. One of the plots of work
25 appeared on the cover of the American Journal of Physics. Beam shaping to
generate Bright and Dark Helices of Light is useful for the creation of handed
meta-materials.

- Multimode Laser Beams for Atom Lenses: The work 28 shows how to use
laser beams to create ‘perfect’ lenses for atom-beam manipulation. The inability to
create atom-lenses with large numerical apertures has hindered the field of atom
optics, hopefully with this scheme this important obstacle is removed.

- Resolution of the Afshar experiment controversy: The work 27 resolved the
controversy surrounding Afshar’s widely publicised experiment.

- Multiphoton Interference Processes: My scheme 15 was the first
experimentally feasible scheme that allows for a demonstration of quantum
super-resolution with four photons i.e. a reduction of the observed light wavelength
by a factor of four. It was implemented by Nagata et al. Science 316, 726-729 (4
May 2007)

- Multiphoton Interference for Quantum Lithography: In 2003 I investigated
the concentration of photons in arrival time and showed that it severely constrains
the ‘quantum lithography idea’. I tried to get this more widely known in a
comment for Phys. Rev. Lett. in 2003 but a Referee rejected my conclusions.
Then in 2004 I did the spatial analysis showing that the widely celebrated idea of
‘Quantum-Lithography’ also does not work because the photons do not arrive at
the same point, they interestingly scatter apart a bit more than in the classical case:
see ‘On the concentration behaviour of photons’ 22. More recently my somewhat
contentious observations have spawned further investigations by others confirming
my findings: quantum lithography is sadly impractical!

- Fundamentals of Quantum Measurements: this is an underlying topic of much
of my earlier work (see papers 2 - 5, 8, 11, 14). I would like to explore further the
factors that limit quantum measurements, for example, measurements with minimal
intrusion and maximal precision. My more recent work 21 on Heisenberg-limited
interferometry falls into this category.

- Population Dynamics Modelling: In work 29 my colleague Daniel Polani and I
investigate the ef${}^{}$fect
of hibernation on disease eradication. We established the optimal family of medication
strategies to be used in such a case. Our work is the first application of multiobjective
optimisation in the life sciences.

- Traf${}^{}$fic Dynamics Modelling: In work on traf${}^{}$fic flow 17 together with Paul Baalham I showed that traf${}^{}$fic flow on busy multilane highways would benefit greatly from passing restrictions for slow vehicles such as trucks.