To understand the relation between nonequilibrium quantum condensates,
equilibrium quantum condensates, and lasers. In particular, to
understand superfluidity, metastability of vortices, coherence
properties, and dynamics of nonequilibrium quantum condensates.
To discover the ways in which phase transitions and metastability in
systems with a flux of particles differ from thermal equilibrium.
To find further examples of many body quantum systems in which their
dynamical behaviour is profoundly non-classical. To understand the
crossovers in these dynamic systems, which may arise due to system
size, explicit decoherence, number of channels for excitations to be
created in.
To see whether quantum fluctuations that result from driving through a
phase transition at zero temperature can be made to show coherent
quantum effects -- i.e. interference and cancellation of processes due
to accumulated phases.
To determine the ways in which novel quantum condensed systems --- in
particular solid state quantum condensates such as excitons,
polaritons and magnons --- differ from previous examples (cold atoms,
Helium, superconductors), and the practical implications of these
differences (in terms of phase diagrams, transport properties,
correlations, robustness under various perturbations).
My research studies systems in which quantum mechanical effects can be
observed in macroscopic systems. With thousands or millions of
particles at relatively high temperatures (such as room temperature)
most effects of quantum mechanics are washed out. Hence, most things
in day to day life are entirely classical. There are however large
systems in which quantum mechanical effects can be seen at medium
temperatures, these can arise when a phase transition to a quantum
condensate occurs. Examples of such condensates include
superconductivity (where there is flow of current without electrical
resistance) and superfluidity of liquid Helium (where there is fluid
flow without mechanical resistance). These are striking examples of
how ``more is different'': In systems of many interacting particles,
collective phenomena can arise, where no such effect would be apparent
with only a few particles.
Superconductivity and superfluid Helium are however somewhat
exceptional as quantum condensates: they are the true equilibrium
states of the given material. The last decade has seen an increasing
range of other quantum condensates in systems which are not in perfect
equilibrium. These include cold dilute gases of alkali atoms and very
recently condensates of quasi-particle excitations in semiconductors,
microcavity polaritons. Microcavity polaritons are mixtures of
photons (quantised particles of light) and excitons (quantised
polarisation of the semiconductor); this mixing is achieved using
mirrors to build a cavity that confines light, and placing a quantum
well that confines excitons between these mirrors. Microcavity
polaritons can form quantum condensates at much higher temperatures
than the cold atomic gases, but are further from equilibrium due to
the finite lifetime of the polaritons. While the equilibrium
condensate, and the highly non-equilibrium laser have been extensively
studied, exploration of systems between these two limits have has only
begun recently. This will be a major area of my research.
In addition to allowing the investigation of coherence out of
equilibrium, the new quantum condensates have other differences from
previous condensates; these include the effect of confining a
condensate to two dimensions and the consideration of particles whose
internal structure is relevant. Combining the effects of reduction to
two dimensions, internal structure, and nonequilibrium behaviour, the
description of coherence in these systems can differ significantly
from previous examples of condensates. An understanding of how and
when these differences inhibit the formation of quantum condensates is
important both in terms of producing quantum condensates under easily
attainable conditions (i.e. room temperature), and in extending the
variety of properties that these condensates may have.
Another area in which non-equilibrium many-body quantum mechanical
problems arise is when parameters of the system (e.g. applied
electric and magnetic fields, applied laser beams) are deliberately
varied in time. In many cases it is sufficient to describe such
systems classically, since systems with many particles often wash out
quantum mechanical effects; however there are examples, such as
varying parameters near the transition to a quantum condensate when
quantum effects should be seen. Building on recent examples of
strongly coupled light-matter systems in which semiclassical
treatments are inadequate, I will study whether there are cases where
there can be dramatic signatures of quantum mechanics in such driven
systems.
In summary, my work aims to study the conditions under which
macroscopic physical systems show quantum behaviour, to consider what
uses this behaviour may have, and to understand what is required to
extend the range of conditions where such behaviour can be seen.
The unifying theme of my fellowship has been non-equilibrium quantum systems, including both the dynamics of many body quantum systems and non-equilibrium (non-thermal) steady state condensation. These ideas relate to a range of different experimental systems, from microcavity polaritons (superpositions of photons and bound electron-hole pairs), to superconducing qubits in microwave resonators, to cold atoms. Cold atoms and superconducting qubits play a role as particularly well controlled systems in which one may explore the consequences of non-equilibrium quantum dynamics in straightforward settings. In contrast, polariton condensates show more complex behaviours, due to effects of disorder, decoherence and energy relaxation induced by the solid state environment – they thus require a clear understanding of the influence that these unavoidable effects have on non-equilibrium condensation. During the course of my fellowship, experimental progress in all of these fields has prompted new questions, in addition to those originally anticipated. The Key findings relate to these, but are classified below under the categories identified in the original proposal.
Driven quantum condensates:
I have calculated the superfluid density of a non-equilibrium polariton condensate, and the results of this have been published in [5]. I showed that superfluidity can survive despite finite particle lifetime, and proposed how to measure polariton superfluid density; this achieves a major aim of this strand. Building on a microscopic model of non-equilibrium polariton condensation, I have shown the important role of temperature in distinguishing lasing and condensation[6]. I have collaborated with the experimental group of Y. Yamamoto (Stanford) to interpret their measurements of coherence in a polariton condensate; we have shown that power law decay of coherence (as expected in a 2D system) survives finite particle lifetime, but the power law seen differs significantly from equilibrium[13]. I have also written an invited review on polariton condensation[3].
During the course of this fellowship, I was awarded an additional "Developing Leaders" grant to work on problems of "Photon Condensation" in dye-filled microcavities[4].
This lead to the development of a quantum model, which takes account of the thermalisation as well as the losses in the cavity, published in [14]. Based on this model, we are continuing to explore the conditions under which photon condensation differs from lasing.
Other properties of exotic condensates:
I have studied how the polarisation degree of freedom affects non-equilibrium pattern formation in a polariton condensate[7,8]. This work has shown that the polarisation state adopted in a non-equilibrium context can be significantly more complicated than in equilibrium, since pumping may prevent the lowest polarisation states from being achieved. I have also worked on polarisation phenomena in cold exciton gases[1]. I have also shown that the polarisation dependent interaction between polaritons suggests the existence of an entirely new phase of the polariton system [15]
Dynamical many body systems:
As originally proposed, I have explored how large quantum corrections exist in the dynamics if starting near unstable classical equilibrium, and how this may be described using the WKB approach[9,10]. This work lead to productive collaboration with groups in ETH leading to a number of other projects, based on experimental developments occurring during the fellowship. In particular, experiments on collective dynamics showed the first realisation of the superradiance transition of the Dicke model[2]. In these experiments, atoms were placed in an optical cavity and pumped from the side. Above a critical pump strength a transition to a non-equilibrium self-organised steady state occured. We have shown[11,12] how the collective dynamics in this system shows surprisingly long timescales, and how persistent oscillating phases can also be achieved. Recently, we have extended this to see how fermionic atoms lead to a range of exotic critical behaviour [16]. I have also begun to explore how non-equilibrium behaviour affects quantum simulation in coupled qubit-resonator systems[17], involving collaborative work with the world-leading Wallraff group[18].
[1] N. Sinclair et al. Phys. Rev. B 83, 245304 (2011).
[2] K. Baumann, C. Guerlin, F. Brennecke, and T. Esslinger, Nature 464, 1301-1306 (2010).
[3] J. Keeling and N. G. Berloff, Contemporary Physics 52, 131-151 (2011).
[4] J. Klaers, J. Schmitt, F. Vewinger, and M. Weitz, Nature 468, 545-548 (2010).
[5] J. Keeling, Phys. Rev. Lett. 107, 080402 (2011).
[6] J. Keeling, M. H. Szymanska, and P. B Littlewood, in Optical Generation and Control of Quantum Coherence in Semiconductor Nanostructures, edited by G. Slavcheva and P. Roussignol (2010), p. 293.
[7] J. Keeling and N. G Berloff, arXiv:1102.5302v2 (2011).
[8] M. O. Borgh, J. Keeling, and N. G. Berloff, Phys. Rev. B 81, 235302 (2010).
[9] J. Keeling, Phys. Rev. A 79, 053825 (2009).
[10] F. Nissen and J. Keeling, Phys. Rev. A 81, 063628 (2010).
[11] J. Keeling, M. J. Bhaseen, and B. D. Simons, Phys. Rev. Lett. 105, 043001 (2010).
[12] M. J. Bhaseen, J Mayoh, B. D. Simons, and J Keeling, Phys. Rev. A 85, 013817 (2012).
[13] G. Roumpos, et al., J. Keeling, et al. Submitted to Proc. Natl. Acad. Sci (2012).
[14] P. Kirton and J. Keeling, Phys. Rev. Lett. 111 100404 (2013).
[15] F. Marchetti and J. Keeling arXiv:1308.1032
[16] J. Keeling, M. J. Bhaseen and B. D. Simons arXiv:1309.2464, Phys. Rev. Lett. In press.
[17] F. Nissen, S. Schmidt, M. Biondi, G. Blatter, H. E. Türeci, and J. Keeling, Phys. Rev. Lett. 108 233603 (2012)
[18] F. Nissen, J. M. Fink, J. A. Mlynek, A. Wallraff, and J. Keeling, Phys. Rev. Lett. 110 203602 (2013)