Suppressing Spectral Diffusion of Emitted Photons with Optical Pulses.

In many quantum architectures the solid-state qubits, such as quantum dots or color centers, are interfaced via emitted photons. However, the frequency of photons emitted by solid-state systems exhibits slow uncontrollable fluctuations over time (spectral diffusion), creating a serious problem for implementation of the photon-mediated protocols. Here we show that a sequence of optical pulses applied to the solid-state emitter can stabilize the emission line at the desired frequency. We demonstrate efficiency, robustness, and feasibility of the method analytically and numerically. Taking nitrogen-vacancy center in diamond as an example, we show that only several pulses, with the width of 1 ns, separated by few ns (which is not difficult to achieve) can suppress spectral diffusion. Our method provides a simple and robust way to greatly improve the efficiency of photon-mediated entanglement and/or coupling to photonic cavities for solid-state qubits.

Thermalization of field driven quantum systems.

There is much interest in how quantum systems thermalize after a sudden change, because unitary evolution should preclude thermalization. The eigenstate thermalization hypothesis resolves this because all observables for quantum states in a small energy window have essentially the same value; it is violated for integrable systems due to the infinite number of conserved quantities. Here, we show that when a system is driven by a DC electric field there are five generic behaviors: (i) monotonic or (ii) oscillatory approach to an infinite-temperature steady state; (iii) monotonic or (iv) oscillatory approach to a nonthermal steady state; or (v) evolution to an oscillatory state. Examining the Hubbard model (which thermalizes under a quench) and the Falicov-Kimball model (which does not), we find both exhibit scenarios (i-iv), while only Hubbard shows scenario (v). This shows richer behavior than in interaction quenches and integrability in the absence of a field plays no role.

Solving the parquet equations for the Hubbard model beyond weak coupling.

We find that imposing crossing symmetry in the iteration process considerably extends the range of convergence for solutions of the parquet equations for the Hubbard model. When crossing symmetry is not imposed, the convergence of both simple iteration and more complicated continuous loading (homotopy) methods is limited to high temperatures and weak interactions. We modify the algorithm to impose the crossing symmetry without increasing the computational complexity. We also imposed time reversal and a subset of the point group symmetries, but they did not further improve the convergence. We elaborate the details of the latency hiding scheme which can significantly improve the performance in the computational implementation. With these modifications, stable solutions for the parquet equations can be obtained by iteration more quickly even for values of the interaction that are a significant fraction of the bandwidth and for temperatures that are much smaller than the bandwidth. This may represent a crucial step towards the solution of two-particle field theories for correlated electron models.

Proximity of the superconducting dome and the quantum critical point in the two-dimensional Hubbard model.

We use the dynamical cluster approximation to understand the proximity of the superconducting dome to the quantum critical point in the two-dimensional Hubbard model. In a BCS formalism, T(c) may be enhanced through an increase in the d-wave pairing interaction (V(d)) or the bare pairing susceptibility (χ(0d)). At optimal doping, where V(d) is revealed to be featureless, we find a power-law behavior of χ(0d)(ω=0), replacing the BCS log, and strongly enhanced T(c). We suggest experiments to verify our predictions.

Parquet approximation for the 4x4 Hubbard cluster.

We present a numerical solution of the parquet approximation, a conserving diagrammatic approach which is self-consistent at both the single-particle and the two-particle levels. The fully irreducible vertex is approximated by the bare interaction thus producing the simplest approximation that one can perform with the set of equations involved in the formalism. The method is applied to the Hubbard model on a half-filled 4x4 cluster. Results are compared to those obtained from determinant quantum Monte Carlo (DQMC), FLuctuation EXchange (FLEX), and self-consistent second-order approximation methods. This comparison shows a satisfactory agreement with DQMC and a significant improvement over the FLEX or the self-consistent second-order approximation.