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Durham Emergence Project


Onset of Emergence from the Bottom Up


The emergence of turbulent flow, that is to say the way motion of a fluid changes from being simple and well-ordered to being highly complex and in a sense chaotic, remains a very difficult scientific questions with enormous relevance in a wide variety of contexts (for example aircraft design, or distributing working fluids through pipes). Within the context of atomic physics, in particular very low temperature gases, there is the possibility of shedding considerable light on this age-old problem, and how it appears, within a very clean, and in the sense of being easier to understand (if more difficult to realise experimentally) simplified physical system.


  • Charles Adams
  • Thomas Billam
  • Simon Gardiner
  • Kevin Weatherill
  • James Keaveney
  • Peter Vickers
  • Nancy Cartwright

Project Description

Within the formal framework of quantum physics there is the capability of building up complex systems atom by atom or photon by photon, and within the currently rapidly developing field of AMO (Atomic, Molecular & Optical) physics there exists the possibility of putting this into practice experimentally. This is a particular strength of the Joint Quantum Centre (JQC) Durham–Newcastle, which joins together researchers from Durham Atomic and Molecular Physics and Physical Chemistry, and Newcastle Applied Mathematics and Engineering, and of which Charles Adams, Simon Gardiner, and Kevin Weatherill are permanent members. It is an exciting possibility to join up this expertise with the expertise in Philosophy of Science (and particularly of Physics) also available in Durham, in the persons of Peter Vickers and Nancy Cartwright.

We propose a joint theoretical and experimental investigation into the onset of emergence, from the bottom up, as the particle number and complexity increases. By increasing the density or driving to highly excited states, simple atomic systems begin to exhibit behaviour typically associated with condensed matter systems, such as phase transitions. We will consider model systems, building up from a small number of atoms interacting with a light field. We have demonstrated in a recent experiment that even in such a simple system one observes behaviour strongly like a non-equilibrium phase transition [Nonequilibrium Phase Transition in a Dilute Rydberg Ensemble, C. Carr, R. Ritter, C.G. Wade, C.S. Adams, K.J. Weatherill, Phys. Rev. Lett. 111, 113901 (2013)]

The experimental component of the project will focus on further investigation of this and closely related model systems; this will in significant part be supported by recently funded EPSRC research grant EP/L023024/1 Cooperative Quantum Optics in Dense Thermal Vapours. Theoretical and philosophical discussions will focus on what qualifies as an emergent property in a finite system, and how this evolves as the system size increases towards the thermodynamic limit familiar in condensed matter systems. Theoretical investigations will be informed by on-the-ground local experimental realities, and theoretical findings will guide lines of experimental investigation.

Questions to be addressed can be summarised as:

What characterises an emergent property in a quantum system consisting of N subsystems (for example, if the subsystems are atoms), as N is increased?

What is the minimum value of N for such an emergent property to be observable, theoretically and experimentally, in an AMO system? What characterises progression towards the thermodynamic limit familiar in condensed matter systems?

Are there definable distinctions between quantum and classical emergence? For example:

o Are there emergent properties that formally appear to require the existence of a quantum versus a classical theoretical framework?

o Is classicality itself an emergent property?

What evidence do we have for any “strong emergence” (presence of qualities irreducible to the system’s constituent parts) as opposed to “weak emergence” (properties arising as a result of interactions at an elemental level)

o Do the phenomena under study fit into standard definitions of “emergence” at all, or do they suggest new definitions, or new types of emergence?

o What lessons can we draw concerning the relationship between phase transitions and weak/strong emergence?

How might we interrogate these ideas in model systems, theoretically and experimentally?


  • Analysis beyond the Thomas-Fermi approximation of the density profiles of a miscible two-component Bose-Einstein condensate”, Polo, J., Ahufinger, V., Mason, P., Sridhar, S., Billam, T. P., and Gardiner, S. A., Phys. Rev. A 91, 053626 (2015).
  • Stochastic growth dynamics and composite defects in quenched immiscible binary condensates”, Liu, I.-K., Pattinson, R. W., Billam, T. P., Gardiner, S. A., Cornish, S. L., Huang, T.-M., Lin, W.-W., Gou, S.-C., Parker, N. G., and Proukakis, N. P., Phys. Rev. A 93, 023628 (2016).
  • Measuring the disorder of vortex lattices in a Bose-Einstein condensate”, Rakonjac, A., Marchant, A. L., Billam, T. P., Helm, J. L., Yu, M. M. H., Gardiner, S. A., and Cornish, S. L., Phys. Rev. A 93 013607, (2016).
  • Quantum reflection of bright solitary matter waves from a narrow attractive potential”, Marchant, A. L., Billam, T. P., Yu, M. M. H., Rakonjac, A., Helm, J. L., Polo, J., Weiss, C., Gardiner, S. A., and Cornish, S. L., Phys. Rev. A 93, 021604 (2016).


  • Invited seminar “Emergent phenomena in two-dimensional quantum turbulence” (University of East Anglia, February 2015).
  • Interdisciplinary talk “A storm in a (quantum) teacup” at the Durham Emergence Workshop (Durham, June 2015).
  • Invited conference talk: “Emergent phenomena in two-dimensional quantum vortex dynamics” at Non-Equilibrium Quantum Dynamics in Low Dimensions (Durham, July 2015).
  • Contributed conference talk: “Emergent Reynolds number in two-dimensional superfluid turbulence” at CCPQ Non-Equilibrium Quantum Systems Meeting (Windsor, August 2015).
  • Contributed conference talk: “Far-from-equilibrium quantum vortex dynamics” at FInite temperature Non-Equilibrium Superfluid Systems [FINESS] (Sopot, Poland, September 2015).