Variable potentials for thermalized light and coupled condensates

Abstract

For over a decade, cold atoms in lattice potentials have been an attractive platform to simulate phenomena known from solid state theory, as the Mott-insulator transition 1 . In contrast, the field of photonics usually deals with non-equilibrium physics 2-5 . Recent advances towards photonic simulators of solid state equilibrium effects include polariton double-site and lattice experiments 6-10 , as well as the demonstration of a photon condensate in a dye-filled microcavity 11,12 . Here we demonstrate a technique to create variable micropotentials for light using thermo-optic imprinting within an ultrahighreflectivity mirror microcavity filled with a dye-polymer solution that is compatible with photon gas thermalization. By repeated absorption-emission cycles photons thermalize to the temperature of the dye solution, and in a single microsite we observe a photon Bose-Einstein microcondensate. Effective interactions between the otherwise nearly noninteracting photons are observed due to thermo-optic effects, and in a double-well system tunnel coupling between sites is demonstrated, as well as the hybridization of eigenstates. Prospects of the new experimental platform include photonic structures in which photons thermalize into entangled manybody states 5 .Periodic potentials for light are at the core of proposals for Mott insulator physics for light, topological effects, as well as driven-dissipative phase transitions 13-18 . Exciton-polariton experiments, involving mixed states of matter and light under conditions of strong coupling, have used permanent semiconductor micro-structuring, as molecular beam epitaxy, metal depositing techniques, and mirror patterning 19,20 , to demonstrate double-well and periodic potentials 6-9 . In the regime of weak light-matter coupling, thermalization and Bose-Einstein condensation of a photon gas has been achieved in a high finesse microcavity containing dye molecules in liquid solution 11,12 .Here we demonstrate a microstructuring technique that allows to generate variable potentials for light within an optical high-finesse microcavity. The long photon lifetime enables the thermalization of photons and the demonstration of a microscopic photon condensate in a single localized site. We observe effective photon interactions as well as tunnel coupling between two microsites. The associated hybridization of eigenstates of the double well system is monitored spectroscopically.The scheme for thermo-optic imprinting of potentials is shown in Fig.1a. Within a microcavity of finesse near 35000, variations of the refractive index are induced through irradiation with a laser beam inducing heat from absorption in a 30nm thick silicon layer below one of the mirror surfaces. A thermosensitive polymer (PNIPAM) 21 , which undergoes

Cooperative phases and phase transitions of Bose condensed light in dye filled cavities

“…Phase separation effect leads to forming regions of higher TLS density which invokes the necessity to consider the near field direct interaction between TLSs as initiated in [22]. In view of the emerging very promising experimental possibilities [17] going beyond BEC, these questions acquire much greater significance.…”

“…The most recent exciting development in this field includes realization of the lattice consisting of micro photonic condensates with the Josephson interaction between them [17]. It clearly opens up a pathway toward realization of strongly interacting phases of light-by means of independent tuning of the Josephson tunneling amplitude and onsite interaction.…”

“…An option to include photon-photon interaction has been suggested in [12]-by taking into account the Kerr effect. Another option is the thermal lensing effect in the dye subsystem [10,17].…”

“…As will be discussed below, to achieve algebraic condensation of photons in 2D at finite temperature T it is important to have polarizational anisotropy of the photon-photon interaction. In this respect, the thermooptical effect, which is insensitive to the polarization [10,17], cannot provide such an anisotropy. Here we will address this aspect by including the anisotropic photon-photon interaction induced by the dye molecules each represented as a two level system (TLS) with randomly oriented vector d  of the dipolar transition between the ground and excited states.…”

Toward Arbitrary Control of Lattice Interactions in Nonequilibrium Condensates

“…We are particularly interested in the new subclass of simulators based on networks of lasers or nonequilibrium condensates such as polariton or photon condensates. These are gain driven systems with dissipation: when gain exceeds the threshold and overcomes the losses a phase transition to a coherent state characterized by a wavefunction occurs.…”