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Synchronization crossover of polariton condensates in weakly disordered lattices

H. Ohadi, Y. del Valle-Inclan Redondo, A. J. Ramsay, Z. Hatzopoulos, T. C. H. Liew, P. R. Eastham, P. G. Savvidis, and J. J. Baumberg
Phys. Rev. B 97, 195109 – Published 8 May 2018
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  • INTRODUCTION
  • FORMATION OF TRAPPED CONDENSATES IN A…
  • NARROWING OF MOMENTUM
  • BUILDUP OF LONG-RANGE COHERENCE AND…
  • THEORETICAL MODEL AND NUMERICAL…
  • CONCLUDING REMARKS
  • ACKNOWLEDGMENTS
  • APPENDICES
    • Supplemental Material
    References

    Abstract

    We demonstrate that the synchronization of a lattice of solid-state condensates when intersite tunneling is switched on depends strongly on the weak local disorder. This finding is vital for implementation of condensate arrays as computation devices. The condensates here are nonlinear bosonic fluids of exciton-polaritons trapped in a weakly disordered Bose-Hubbard potential, where the nearest-neighboring tunneling rate (Josephson coupling) can be dynamically tuned. The system can thus be tuned from a localized to a delocalized fluid as the number density or the Josephson coupling between nearest neighbors increases. The localized fluid is observed as a lattice of unsynchronized condensates emitting at different energies set by the disorder potential. In the delocalized phase, the condensates synchronize and long-range order appears, evidenced by narrowing of momentum and energy distributions, new diffraction peaks in momentum space, and spatial coherence between condensates. Our paper identifies similarities and differences of this nonequilibrium crossover to the traditional Bose-glass to superfluid transition in atomic condensates.

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    • Received 27 February 2018

    DOI:https://doi.org/10.1103/PhysRevB.97.195109

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Exciton polariton
    1. Physical Systems
    Bose-Einstein condensatesSuperfluids
    1. Techniques
    Bose-Hubbard model
    Condensed Matter, Materials & Applied PhysicsNonlinear Dynamics

    Authors & Affiliations

    H. Ohadi1,2,*, Y. del Valle-Inclan Redondo1, A. J. Ramsay3, Z. Hatzopoulos4, T. C. H. Liew5, P. R. Eastham6, P. G. Savvidis4,7,8, and J. J. Baumberg1,†

    • 1Department of Physics, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
    • 2SUPA, School of Physics and Astronomy, University of St Andrews, St Andrews, KY16 9SS, United Kingdom
    • 3Hitachi Cambridge Laboratory, Hitachi Europe Ltd., Cambridge CB3 0HE, United kingdom
    • 4FORTH, Institute of Electronic Structure and Laser, 71110 Heraklion, Crete, Greece
    • 5School of Physical and Mathematical Sciences, Nanyang Technological University 637371, Singapore
    • 6School of Physics and CRANN, Trinity College Dublin, Dublin 2, Ireland
    • 7ITMO University, St. Petersburg 197101, Russia
    • 8Department of Materials Science and Technology, University of Crete, 71003 Heraklion, Crete, Greece

    • *ho35@st-andrews.ac.uk
    • †jjb12@cam.ac.uk

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    Issue

    Vol. 97, Iss. 19 — 15 May 2018

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    Images

    • Figure 1
      Figure 1

      Below threshold, unsynchronized, and synchronized phases. (a) Schematic of condensation in optical lattice potentials (top panel), and synchronization of two energy-detuned condensates in a double-well potential (bottom panel). There is a nonzero energy detuning δE at the UNSYNC phase but this vanishes at the SYNC phase as the Josephson coupling increases. (b)–(d) Real-space and momentum space emission of (b) uncondensed polaritons, (c) unsynchronized (localized), and (d) synchronized (delocalized) condensate lattice. Pump spots are marked by grey circles in (c), (d) and visible by dark spots in (b). The schematic diagrams above the panels show the trapping potential V(x), Josephson coupling J, and energies of the condensates En. Momentum space images are in logarithmic scale.

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    • Figure 2
      Figure 2

      Synchronization phase diagram. Dependence of δk·a versus (a) lattice constant and (b) power. Top panel in (a) shows real-space and momentum-space intensity (log scale) at a=7.8μm (left) and a=11.8μm for P=2.1Pth. (b) Power dependence comparison of δk·a for full lattice (dark blue) and a spatially filtered single condensate (light blue). Real-space scale is 10μm and momentum space scale is 1μm−1.

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    • Figure 3
      Figure 3

      First-order correlation function. (a) Real-space interferograms for the unsynchronized (top) and synchronized (bottom) phases. (b), (c) Power dependence of |g(1)(r,−r)| at various lattice positions r, as a function of total lattice power in (b) experiment and (c) simulations. Lines are exponential fits. In the experiment, an average is taken over six site separations marked A–F and their corresponding mirrors in (a), with separations of (0.5,2,2,4,25,42)a. In simulations, the average is extracted for all site separations in the lattice. Lines are exponential fits. Panels to the right of (c) are the time-averaged momentum space emission for UNSYNC (P=Pth) and SYNC (P=2Pth) phases. The simulated disorder ratio is 10%. (d) Coherence length (Lϕ) versus power in simulations (with and without 10% disorder) and in experiment. Simulation curves are averages of 25 randomly generated disorder potentials.

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    • Figure 4
      Figure 4

      Condensate energies as a function of power. (a) Energy spectra of a column of five condensates crossing the center of the lattice for P=Pth (top panel) and P=2Pth (bottom panel). (b) Standard deviation of condensate energies (σ(E)) as a function of power (light blue) and the corresponding δk·a (dark blue).

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    • Figure 5
      Figure 5

      Time-averaged momentum space, real space, and phase of an unsynchronized lattice (a)–(c) and synchronized lattice (d)–(f). (g) Static potential accounting for sample inhomogeneity. (h) g(1) versus length for UNSYNC (blue) and SYNC phase (red). (i) Power dependence of density (light blue) and momentum width (dark blue) for a synchronized lattice (solid line) and a single site (dotted line) for a=9μm. (j) Power dependence of g(1) for different lattice lengths for a=9μm.

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    • Figure 6
      Figure 6

      Background disorder potential.

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    • Figure 7
      Figure 7

      (a) Intensity in real space. (b) Intensity of the SYNC phase in momentum space. (c) Intensity of the UNSYNC phase in momentum space. The only parameter is L/a=0.22.

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    • Figure 8
      Figure 8

      Fraunhofer diffraction of a single slit (light blue) and five slits (dark blue) with b/a=0.35.

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    • Figure 9
      Figure 9

      Average first-order correlation function g(1)(r/a) versus length r for various lattice constants of a 15×15 condensate lattice.

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