#### Research interests

My research concerns ultracold atomic gases and I am mostly interested in condensed matter and many-body problems which arise in those systems.

If we cool a very hot gas of say, sodium or potassium to room temperature, the atoms usually come together to form a solid - a metal. However, if we do it carefully enough, in very high vacuum, then it will remain a gas even if we continue cooling it down to ultralow temperatures (around 1 microKelvin). Under these conditions the quantum mechanical properties of the gas as a whole become very important since the thermal de Broglie wavelength of the atoms becomes comparable with the average distance between them. In particular, we say that the gas becomes statistically degenerate. So, for example, if the atom is a boson (like sodium 27) then it can

undergo Bose-Einstein condensation. If it is a fermion (e.g. lithium 6), it can form a Fermi surface.

When these things happen, there can be spectacular consequences. For example, the gas can become superfluid, and we can observe vortices forming a triangular lattice when the gas is stirred. Or we can see interference phenomena between clouds of atoms - something that we

usually associate with light or waves in liquids.

I have been particularly interested in what happens in Fermi gases. If two spin species are present then they can form Cooper pairs and these can condense as a Fermi superfluid. It is in essence the same phenomenon that occurs in superconductors but with atoms instead of electrons. I have been looking at exotic kinds of pairing that have long been predicted in superconductors but never observed there. In atomic gases by contrast, you might be able to see them - making the hunt for them all the more exciting.

Another project I'm interested in that of mediated interactions: if you put two impurities in an atomic gas (for example, two atoms of a different kind), these atoms can interact with each other using the surrounding gas as a go-between! For example, one of the atoms can create a sound wave which propagates until it hits the other one. There is in fact a long history to this problem, going back to liquid helium mixtures in the 1960's. Now we have a chance to study this problem in a new context when we don't even know some of the basic physics. Typically what we do to model this problem is solve perturbation theory - using for example Feynman diagrams to calculate the scattering of one impurity off the other.

I've also worked in understanding time-dependent problems in quantum gases. There we are interested in driving the system out of equilibrium and seeing what happens. For example, if you send one cloud of atoms violently against another, sometimes they bounce off each other as if they were elastic! Together with some colleagues we were able to give an explanation of this using a simulation of the Boltzmann equation and our results match closely the experimental ones obtained at MIT. Other times we are only interested in perturbing the gas very slightly. By studying the resulting wobbles we can tell a lot about its equilibrium properties such as its equation of state.

#### Research group

Applied Mathematics

#### Affiliate research group

Computational Applied Mathematics

#### Research project(s)

**Dr Carlos Lobo**Building 54 Mathematical Sciences University of Southampton Highfield Southampton SO17 1BJ

For all Erasmus and study abroad queries: studyabroad.maths@soton.ac.uk

**Room Number:**54/6027

**Telephone:**(023) 8059 3681

**Email:**C.Lobo@soton.ac.uk