Microcavity exciton-polaritons are half-light, half-matter quantum quasi-particles, resulting from the strong light-matter coupling in a combined structure of quantum wells and cavity photon cavity [1]. Figure 1 illustrates the schematic of microcavity structure, where a quantum well is embedded at the anti-node of the cavity photon field. The strong light-matter coupling in the microcavity system exhibits anti-crossing behavior as a split to two polariton branches: upper polaritons (UPs) and lower polaritons (LPs) shown in Fig. 2. The energy difference between two branches is named as vacuum-Rabi splitting (Ω), adopting from atom-cavity terminologies. The quantity Ω represents a collective dipole coupling strength depending on the exciton oscillator strength and the penetration depth of the Bragg mirror.

As Boson particles composed of quantum well excitons and optical cavity photons, microcavity exciton-polaritons possess unique intrinsic features: reminiscent excitonic nature leads to important interaction dynamics among exciton-polaritons. Polariton-polariton repulsive interactions are indeed crucial to stimulated scattering processes in order to relax into the ground state Bose-Einstein condensates (BECs). In fact, these interactions enrich the system dynamics arising from the intrinsic long-ranged Coulomb interaction, screening at high densities, and exchange interactions. With much lighter effective mass inherited from photonic component, exciton-polariton condensates occur at elevated temperatures via unequivocal evidence in terms of spontaneous spatial coherence, temporal coherence, and thermal equilibrium to the lattice temperatures [2-6].

We explore fundamental aspects of the boson nature with exciton-polaritons in terms of dynamic condensation and superfluidity. We also investigate the rich quantum phases and their phase crossover phenomena, including phase fluctuations and the Berezinskii-Kosterlitz-Thouless (BKT) transition, and BEC to Bardeen-Cooper-Schrieffer (BCS) crossover. Lastly, we aim to build solid-state quantum simulator for implementing quantum Ising model and quantum Hubbard model.

**Figure 1.** **(Left)** A schematic of a microcavity quantum well structure. **(Right)** Energy dispersion of upper polariton (UP, blue) and lower polariton (LP, red) resulting from the strong coupling between a cavity photon (black) and a quantum well exciton (gray).

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[2] H. Deng et al. *Science* **298**, 199 (2002).

[3] J. Kasprzak et al. *Nature* **410**, 409 (2006).

[4] R. Balili, V. Hartwell, D. Snoke, L. Pfeiffer, and K. West, *Science* **316**, 1007 (2007).

[5] C. W. Lai et al. *Nature* **450**, 529 (2007).

[6] H. Deng et al. *Phys. Rev. Lett.* **97**, 146402 (2006).

Dynamical Condensation and Superfluidity of Exciton-Polaritons

Quantum Phase Transition of Exciton-Polariton Condensates

Quantum Simulation of Condensed Matter Systems

Dr. Na Young Kim

Dr. Tomoyuki Horikiri

Georgios Roumpos

Kai Wen

Wolfgang H. Nitsche

Crystal C. Bray

Prof. Yoshihisa Yamamoto

Prof. Alfred Forchel (University of Würzburg, Germany)

Prof. Congjun Wu (University of California at San Diego)