Scattering into one-dimensional waveguides from a coherently-driven quantum-optical system

We develop a new computational tool and framework for characterizing the scattering of photons by energy-nonconserving Hamiltonians into unidirectional (chiral) waveguides, for example, with coherent pulsed excitation. The temporal waveguide modes are a natural basis for characterizing scattering in quantum optics, and afford a powerful technique based on a coarse discretization of time. This overcomes limitations imposed by singularities in the waveguide-system coupling. Moreover, the integrated discretized equations can be faithfully converted to a continuous-time result by taking the appropriate limit. This approach provides a complete solution to the scattered photon field in the waveguide, and can also be used to track system-waveguide entanglement during evolution. We further develop a direct connection between quantum measurement theory and evolution of the scattered field, demonstrating the correspondence between quantum trajectories and the scattered photon state. Our method is most applicable when the number of photons scattered is known to be small, i.e. for a single-photon or photon-pair source. We illustrate two examples: analytical solutions for short laser pulses scattering off a two-level system and numerically exact solutions for short laser pulses scattering off a spontaneous parametric downconversion (SPDC) or spontaneous four-wave mixing (SFWM) source. Finally, we note that our technique can easily be extended to systems with multiple ground states and generalized scattering problems with both finite photon number input and coherent state drive, potentially enhancing the understanding of, e.g., light-matter entanglement and photon phase gates.Comment: Numerical package in collaboration with Ben Bartlett (Stanford University), implemented in QuTiP: The Quantum Toolbox in Python, Quantum 201

Clinical evaluation of subepithelial connective tissue graft and guided tissue regeneration for treatment of Miller's class 1 gingival recession: comparative, split mouth, six months study

Objectives: The present study aims to clinically compare and evaluate subepithelial connective tissue graft and the GTR based root coverage in treatment of Miller's Class I gingival recession. Study Design: 30 patients with at least one pair of Miller's Class I gingival recession were treated either with Sube - pithelial connective tissue graft (Group A) or Guided tissue regeneration (Group B). Clinical parameters monitored included recession RD, width of keratinized gingiva (KG), probing depth (PD), clinical attachment level (CAL), attached gingiva (AG), residual probing depth (RPD) and % of Root coverage(%RC). Measurements were taken at baseline, three months and six months. A standard surgical procedure was used for both Group A and Group B. Data were recorded and statistical analysis was done for both intergroup and intragroup. Results: At end of six months % RC obtained were 84.47% (Group A) and 81.67% (Group B). Both treatments resulted in statistically significant improvement in clinical parameters. When compared, no statistically significant difference was found between both groups except in RPD, where it was significantly greater in Group A. Conclusions: GTR technique has advantages over subepithelial connective tissue graft for shallow Miller's Class I defects and this procedure can be used to avoid patient discomfort and reduce treatment time

Classically computing performance bounds on depolarized quantum circuits

Quantum computers and simulators can potentially outperform classical computers in finding ground states of classical and quantum Hamiltonians. However, if this advantage can persist in the presence of noise without error correction remains unclear. In this paper, by exploiting the principle of Lagrangian duality, we develop a numerical method to classically compute a certifiable lower bound on the minimum energy attainable by the output state of a quantum circuit in the presence of depolarizing noise. We provide theoretical and numerical evidence that this approach can provide circuit-architecture dependent bounds on the performance of noisy quantum circuits.Comment: 17 pages, 7 figure