Session P10: Invited Session: Quantum Simulations

Quantum simulations and artificial gauge fields with ultracold atoms

Here I present our experimental work synthesizing gauge fields for Bose-Einstein condensates (BECs). I will first summarize our earlier work creating a scalar (abelian) gauge field (akin to the electromagnetic vector potential) and then focus in detail our current work creating a matrix valued (although still abelian) gauge field. I will discuss this gauge field in the language of spin-orbit coupling where it consists of an equal sum of Rashba and Dresselhaus couplings. Specifically, we couple two internal states of rubidium 87 with a pair of ``Raman'' lasers and load our BEC into the resulting adiabatic eigenstates. In agreement with theory, we observe that below a critical coupling strength our BEC has well defined spin degrees of freedom and acts like a spin-orbit-coupled spin-1/2 Bose gas. As a function of the Raman laser strength, a new exchange-driven interaction between the two dressed spins develops, which drives a (quantum) phase transition from a state where the two dressed spin states spatially mix, to one where they phase separate. Our 3D mean field theory accurately locates the critical laser strength for this transition.   

Circuit QED Simulation of Interacting Bosons with Microwave Polaritons

A polariton is a coherent superposition of a photon and an electronic excitation such as an exciton. Polaritons can have very low mass (associated with the photon component) and repulsive interactions (associated with the exciton component). Recent experimental progress has observed Bose-Einstein condensation and superfluidity in polaritons in semiconductor quantum wells. In this talk I will discuss the possibility that many-body physics and quantum phase transitions of interacting polaritons [1-3] can be observed in arrays of microwave resonators containing superconducting qubits [4-6]. If the qubits are not far-detuned from the cavities, the natural excitations are coherent superpositions of cavity and qubit excitations and they have interactions acquired from the anharmonicity of the qubits. These interactions can lead to quantum phase transitions in the limit of weak dissipation. It may even be possible to simulate the fractional quantum Hall effect for bosons by coupling the polaritons between sites using superconducting structures which act as `circulators' that break time-reversal and charge-conjugation symmetry. In light of recent progress in achieving very long-coherence times for superconducting qubits and strong qubit coupling to microwave photons, experimental prospects for observing quantum phase transitions in microwave resonator lattices will be described. \\[4pt] [1] A. D. Greentree, et al., {\sl Nat. Phys.} {\bf 2}, 856 (2006).\\[0pt] [2] M. J. Hartmann et al., {\sl Nat. Phys.} {\bf 2}, 849 (2006).\\[0pt] [3] D. G. Angelakis, M. F. Santos, and S. Bose, {\sl Phys. Rev. A} {\bf 76}, 031805 (2007).\\[0pt] [4] J. Koch and K. Le Hur, {\sl Phys. Rev. A} {\sl 80}, 023811 (2009).\\[0pt] [5] `Time-reversal symmetry breaking in circuit-QED based photon lattices,'Jens Koch, Andrew A. Houck, Karyn Le Hur, and S. M. Girvin, {\sl Phys. Rev. A} {\bf 82}, 043811 (2010).\\[0pt] [6] `Synthetic gauge fields and homodyne transmission in Jaynes-Cummings lattices,' A. Nunnenkamp, Jens Koch, and S. M. Girvin, {\sl New J. Phys.} {\bf 13} 095008 (2011).   

Quantum Hall physics with photons and its application

Phenomena associated with the topological properties of physical systems can be naturally robust against perturbations. This robustness is exemplified by quantized conductance and edge state transport in the quantum Hall and quantum spin Hall effects. Here we demonstrate how quantum spin Hall Hamiltonians can be simulated with linear optical elements using a network of coupled resonator optical waveguides (CROW) in two dimensions. Key features of quantum Hall systems, including the characteristic Hofstadter butterfly and robust edge state transport, can be obtained in such systems. As a specific application, we show that topological protection can be used to improve the performance of optical delay lines and to overcome some limitations related to disorder in photonic technologies. Furthermore, the addition of an optical non-linearity to our proposed system leads to the possibility of implementing a fractional quantum Hall state of photons, where phenomenon such as fractional statistics may be observable.   

Mixed Bose-Fermi Mott Phases and Phase Transitions

A recent experiment with an ultra-cold mixture of $^174$Yb and $^173$Yb atoms in an optical lattice [S. Sugawa e. al. Nature Physics 7, 642 (2011)] found a remarkable quantum phase that can be described as a mixed Mott insulator. Such a an incompressible state established at integer combined filling of the two species, must have residual low energy Fermionic degrees of freedom associated with relative motion of the two species. I will discuss the novel quantum states formed by the composite Fermions in the mixed Mott insulator as well as the unconventional phase transitions separating these states from the compressible Bose-Fermi mixture established at weak interactions. Finally I will propose to utilize the mixed Mott insulator as a quantum simulator for models of the doped Mott insulator relevant to high Tc superconductivity. The new approach, where the bosonic atoms play the role of doped holes offers significant advantages over direct simulation of the Hubbard model. In particular the mixed Mott plateau naturally provides a flat trap potential to the doped holes, while the hole doping is easily tuned by varying the relative fraction of the bosons.