Watt Steam Engine

On quantum scales, there are many second laws of thermodynamics

New research from UCL has uncovered additional second laws of thermodynamics which complement the ordinary second law of thermodynamics, one of the most fundamental laws of nature. These new second laws are generally not noticeable except on very small scales, at which point, they become increasingly important. More...

Published: Feb 10, 2015 11:55:53 AM

Spectrum of hot methane

Spectrum of hot methane in astronomical objects using a comprehensive computed line list

A powerful new model to detect life on planets outside of our solar system, more accurately than ever before, has been developed by researchers from UCL Physics & Astronomy and the University of New South Wales. More...

Published: Jun 18, 2014 4:54:56 PM

Quantum Phase Transitions

"Like melting an entire iceberg with a hot poker" – UCL scientists explore the strange world of quantum phase transitions

“What a curious feeling,” says Alice in Lewis Carroll’s tale, as she shrinks to a fraction of her size, and everything around her suddenly looks totally unfamiliar. Scientists too have to get used to these curious feelings when they examine matter on tiny scales and at low temperatures: all the behaviour we are used to seeing around us is turned on its head. More...

Published: May 13, 2014 4:06:57 PM

Dr Thorsten Kohler

Department of Physics and Astronomy

University College London
Gower Street
London WC1E 6BT
Tel +44 (0) 20 7679 0171
Fax +44 (0) 20 7679 2564


Ultracold gases are often realised in dilute vapours of between thousands and millions of alkali-metal atoms held in magnetic or optical traps at temperatures ranging from a thousandth to only a billionth of a degree above the absolute zero. Their spatial extents are typically on the order of several microns.

Due to the low temperatures, the properties of ultra-cold gases are influenced by quantum statistics, depending on whether the atoms are identical bosons or fermions. Bose atoms tend to share the same quantum state in the zero-temperature limit, leading to Bose-Einstein condensation (BEC). Despite the diluteness, the density distributions of Bose-Einstein condensates are sensitive to the inter-atomic interactions. These interactions can be characterised by a single parameter, the s-wave scattering length. Depending on the sign of the scattering length, the colliding atoms in a gas tend to repel (positive sign) or attract (negative sign) each other.

As opposed to Bose gases, the Pauli principle prevents any two atoms to share the same quantum state when the ultra-cold gas consists of identical fermions. The existence of interactions, however, can give rise to pairing of Fermi atoms, a phenomenon known from the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. Such paired atoms have been converted into molecules, without changing their centre-of-mass momentum, by tuning the interactions using time-varying homogeneous magnetic fields. A variety of similar techniques to form ultra-cold diatomic molecules have been demonstrated in both Bose and Fermi gases, even in the absence of initially preformed pairs.

Our aim is to theoretically understand the phenomena of pairing and molecule formation in ultra-cold gases consisting of either Bose or Fermi atoms. This involves microscopic descriptions of diatomic collisions and bound states in the presence of externally applied magnetic fields, and their reduction to effective models that are applicable in a suitable energy range about the threshold between scattering and molecular binding. We use these effective models to study few-body collisions in ultra-cold gases, as well as the genuinely many-body aspects of the dynamics of molecule production.

Ultracold collisions

The possibility of magnetically tuning the inter-atomic interactions relies upon the Zeeman effect in the hyperfine structure of the atoms. Due to the coupling between the nuclear spin and the spin of the single valence electron of an alkali-metal atom, there are two hyperfine levels in the electronic ground state at zero field. By varying an externally applied magnetic field, the splitting between the Zeeman energy levels can be controlled experimentally.

In the narrow range of collision momenta in an ultra-cold gas, the diatomic interactions are sensitive to both the Zeeman states in which the individual atoms are prepared and their coupling to other Zeeman states. New bound states can appear at the zero-energy threshold between scattering and molecular binding, causing the scattering length to diverge. By holding the magnetic field in the vicinity of such a zero-energy resonance, one can thus choose any desired value of the scattering length, generating ultra-cold collision interactions that can vary from strongly attractive to strongly repulsive. By sweeping the magnetic field across a resonance, from negative to positive scattering lengths, a molecular bound state can be created from two initially separated atoms.

The diatomic molecules produced by using this magneto-association technique can decay into energetically lower bound states upon collisions with other molecules or atoms in the gas. These inelastic molecule-molecule and atom-molecule relaxation phenomena set the lifetimes of ultra-cold gases containing diatomic molecules in the highest excited vibrational bound state. Three initially separated atoms can collide and form a diatomic bound state and a third free atom with a relative velocity determined by energy and momentum conservation. This phenomenon, referred to as three-body recombination, limits the lifetimes of ultra-cold gases consisting of Bose or Fermi atoms. Based on the microscopic model of diatomic collision and bound-state properties we determine the rate coefficients for ultra-cold collisions between atoms and weakly bound molecules, as well as for three-body recombination events, and investigate their dependences on an externally applied magnetic field.

Dynamics of molecule formation

Using magnetically tunable interactions, condensed or thermal Bose gases, as well as Fermi gases with or without preformed pairs, can be converted into ultra-cold gases of diatomic molecules with efficiencies depending on their density and temperature. The different molecule-association techniques demonstrated to date involve various sequences of magnetic-field sweeps, resonantly oscillating magnetic fields, and holding the magnetic-field strength at a position of large positive scattering length. These techniques can allow up to about 90% of the atoms to be converted into diatomic molecules.

We perform time dependent many-particle calculations of the molecule production efficiencies obtained from the various techniques of molecule association using magnetically tunable interactions. These theoretical descriptions involve condensed or thermal Bose gases, as well as Fermi gases with or without preformed pairs. Our methods of description rely upon truncations of the infinite hierarchy of dynamical equations for the few-body correlation functions, as obtained from the many-particle Schrodinger equation with ideal-gas or interacting initial states. Depending on the application, we choose different levels of truncation, as well as effective inter-atomic potentials that are designed to systematically recover the microscopic model of diatomic collision and bound-state properties in a suitably wide range of energies about the scattering threshold.

Cold atoms lecture notes