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EPFL Press eBooks

Synchronization of Polariton Condensates

Konstantinos G. Lagoudakis

Published Dec 2, 2013• 0 citations
Publisher

Abstract

Quantum phase transitions realized in inhomogeneous potentials is a topic of major importance in condensed matter physics. It involves non-trivial matter states, as Josephson oscillations for double potential wells [55], Mott insulators for periodic potentials [56], and Bose glasses for disorder potentials [57]. The case of disorder potentials is a crucial matter both for the intrinsic interest of phase transitions and for the unavoidable disorder in real systems. It is worth the effort to address this issue for the case of polariton condensates.

DOI
10.1201/b15531-8

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Quantum phase transitions realized in inhomogeneous potentials is a topic of major importance in condensed matter physics. It involves non-trivial matter states, as Josephson oscillations for double potential wells [55], Mott insulators for periodic potentials [56], and Bose glasses for disorder potentials [57]. The case of disorder potentials is a crucial matter both for the intrinsic interest of phase transitions and for the unavoidable disorder in real systems. It is worth the effort to address this issue for the case of polariton condensates.
One of the most striking manifestations of the quantum collective behavior of matter is the Josephson effect: it allows for a classically forbidden current to flow without dissipation [125]. Traditional Josephson junctions are built by means of superconductors separated by thin non-conducting oxide barriers and they have drawn an intense interest for their striking phenomenology. A bosonic analog is the so-called Bosonic Josephson junction (BJJ) where two macroscopic populations of bosons are trapped in a double well geometry. Bose-Einstein condensation of dilute atomic gases has allowed for the demonstration of BJJs by trapping two condensates in double wells [126],[127].
In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behaviour of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d -wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions is boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.
We review some theories of non-equilibrium Bose-Einstein condensates in potentials, in particular of the Bose-Einstein condensate of polaritons. We discuss such condensates, which are steady-states established through a balance of gain and loss, in the complementary limits of a double-well potential and a random disorder potential. For equilibrium condensates, the former corresponds to a Josephson junction, whereas the latter is the setting for the superfluid/Bose glass transition. We explore the non-equilibrium generalization of these phenomena, and highlight connections with mode selection and synchronization.
The low-temperature states of bosonic condensates exhibit fundamental quantum effects at the macroscopic scale. The combined effects of interaction and disorder in these can have drastic consequences, leading to the Mott insulator and Bose-Anderson glass. The latter is thought to describe helium-4 in porous media, cold atoms in disordered optical potentials, disordered magnetic insulators, and thin superconducting films. The prototypical Bose-Hubbard model without disorder predicts a Beresinskii-Kosterlitz-Thouless quantum phase transition between superfluid and Mott insulator. Experimental implementation using arrays of Josephson junctions has been explored, however, the possibility of the insulating glass has not been considered. The ubiquity of such a phase in Josephson-junction arrays would have important implications for their proposed use as a fundamental current standard. Unlike the Mott insulator, the insulating glass is compressible, therefore AC synchronisation of charge may not be possible. We have measured critical voltages for a large number of simple chains of sub-micron Josephson junctions with significantly varying energy scales. We observe universal scaling of critical voltage with single-junction Bloch bandwidth. Our measurements reveal a localisation length exponent that steepens with Luttinger parameter, arising from precursor fluctuations as one approaches the Bose glass-superfluid quantum phase transition. This contrasts with the fixed exponent found for classical pinning of charge density waves, vortex lattices, and disordered spin systems, and is in excellent agreement with the quantum theory of one-dimensional disordered bosonic insulators. We thereby demonstrate a unique signature of the charged Bose glass in insulating Josephson-junction chains.
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.