The seminal theoretical works of Berezinskii, Kosterlitz, and Thouless presented a new paradigm for phase transitions in condensed matter that are driven by topological excitations.These transitions have been extensively studied in the context of two-dimensional XY models — coupled compasses — and have generated interest in the context of quantum simulation. Here, we use a circuit quantum-electrodynamics architecture to study the critical behavior of engineered XY models through their dynamical response. In particular, we examine not only the unfrustrated case but also the fully-frustrated case which leads to enhanced degeneracy associated with the spin rotational [U(1)] and discrete chiral (Z2) symmetries. The nature of the transition in the frustrated case has posed a challenge for theoretical studies while direct experimental probes remain elusive. Here we identify the transition temperatures for both the unfrustrated and fully-frustrated XY models by probing a Josephson junction array close to equilibrium using weak microwave excitations and measuring the temperature dependence of the effective damping obtained from the complex reflection coefficient. We argue that our probing technique is primarily sensitive to the dynamics of the U(1) part.
We investigate a hybrid quantum system consisting of spatially separated resonant exchange qubits, defined in three-electron semiconductor triple quantum dots, that are coupled viaa superconducting transmission line resonator. Drawing on methods from circuit quantum electrodynamics and Hartmann-Hahn double resonance techniques, we analyze three specific approaches for implementing resonator-mediated two-qubit entangling gates in both dispersive and resonant regimes of interaction. We calculate entangling gate fidelities as well as the rate of relaxation via phonons for resonant exchange qubits in silicon triple dots and show that such an implementation is particularly well-suited to achieving the strong coupling regime. Our approach combines the favorable coherence properties of encoded spin qubits in silicon with the rapid and robust long-range entanglement provided by circuit QED systems.
Photons are not conserved in interactions with other matter. Consequently, when understanding the equation of state and thermodynamics of photons, while we have a concept of temperaturefor energy conservation, there is no equivalent chemical potential for particle number conservation. However, the notion of a chemical potential is crucial in understanding a wide variety of single- and many-body effects, from transport in conductors and semi-conductors to phase transitions in electronic and atomic systems. Here we show how a direct modification of the system-bath coupling via parametric oscillation creates an effective chemical potential for photons even in the thermodynamic limit. Specific implementations, using circuit-QED or optomechanics, are feasible using current technologies, and we show a detailed example demonstrating the emergence of Mott Insulator-superfluid transition in a lattice of nonlinear oscillators. Our approach paves the way for quantum simulation, quantum sources and even electron-like circuits with light.
One approach to quantum information processing is to use photons as quantum
bits and rely on linear optical elements for most operations. However, some
optical nonlinearity is necessaryto enable universal quantum computing. Here,
we suggest a circuit-QED approach to nonlinear optics quantum computing in the
microwave regime, including a deterministic two-photon phase gate. Our specific
example uses a hybrid quantum system comprising a LC resonator coupled to a
superconducting flux qubit to implement a nonlinear coupling. Compared to the
self-Kerr nonlinearity, we find that our approach has improved tolerance to
noise in the qubit while maintaining fast operation.