Supersymmetric analysis for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions

A supersymmetric analysis is presented for the d-dimensional Dirac equation with central potentials under spin-symmetric (S(r) = V(r)) and pseudo-spin-symmetric (S(r) = - V(r)) regimes. We construct the explicit shift operators that are required to factorize the Dirac Hamiltonian with the Kratzer potential. Exact solutions are provided for both the Coulomb and Kratzer potentials.Comment: 12 page

Entanglement genesis by ancilla-based parity measurement in 2D circuit QED

We present an indirect two-qubit parity meter in planar circuit quantum electrodynamics, realized by discrete interaction with an ancilla and a subsequent projective ancilla measurement with a dedicated, dispersively coupled resonator. Quantum process tomography and successful entanglement by measurement demonstrate that the meter is intrinsically quantum non-demolition. Separate interaction and measurement steps allow commencing subsequent data qubit operations in parallel with ancilla measurement, offering time savings over continuous schemes.Comment: 5 pages, 4 figures; supplemental material with 5 figure

Quantum Correction in Exact Quantization Rules

An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the quantum correction is an invariant, independent of the number of nodes in the wave function. In those systems, the energy levels of all the bound states can be easily calculated from the exact quantization rule and the solution for the ground state, which can be obtained by solving the Riccati equation. With this new method, we re-calculate the energy levels for the one-dimensional systems with a finite square well, with the Morse potential, with the symmetric and asymmetric Rosen-Morse potentials, and with the first and the second P\"{o}schl-Teller potentials, for the harmonic oscillators both in one dimension and in three dimensions, and for the hydrogen atom.Comment: 10 pages, no figure, Revte

Reversing quantum trajectories with analog feedback

We demonstrate the active suppression of transmon qubit dephasing induced by dispersive measurement, using parametric amplification and analog feedback. By real-time processing of the homodyne record, the feedback controller reverts the stochastic quantum phase kick imparted by the measurement on the qubit. The feedback operation matches a model of quantum trajectories with measurement efficiency $\tilde{\eta} \approx 0.5$, consistent with the result obtained by postselection. We overcome the bandwidth limitations of the amplification chain by numerically optimizing the signal processing in the feedback loop and provide a theoretical model explaining the optimization result.Comment: 5 pages, 4 figures, and Supplementary Information (7 figures