Gradient Symplectic Algorithms for Solving the Radial Schrodinger Equation

The radial Schrodinger equation for a spherically symmetric potential can be regarded as a one dimensional classical harmonic oscillator with a time-dependent spring constant. For solving classical dynamics problems, symplectic integrators are well known for their excellent conservation properties. The class of {\it gradient} symplectic algorithms is particularly suited for solving harmonic oscillator dynamics. By use of Suzuki's rule for decomposing time-ordered operators, these algorithms can be easily applied to the Schrodinger equation. We demonstrate the power of this class of gradient algorithms by solving the spectrum of highly singular radial potentials using Killingbeck's method of backward Newton-Ralphson iterations.Comment: 19 pages, 10 figure

An Invisible Quantum Tripwire

We present here a quantum tripwire, which is a quantum optical interrogation technique capable of detecting an intrusion with very low probability of the tripwire being revealed to the intruder. Our scheme combines interaction-free measurement with the quantum Zeno effect in order to interrogate the presence of the intruder without interaction. The tripwire exploits a curious nonlinear behaviour of the quantum Zeno effect we discovered, which occurs in a lossy system. We also employ a statistical hypothesis testing protocol, allowing us to calculate a confidence level of interaction-free measurement after a given number of trials. As a result, our quantum intruder alert system is robust against photon loss and dephasing under realistic atmospheric conditions and its design minimizes the probabilities of false positives and false negatives as well as the probability of becoming visible to the intruder.Comment: Improved based on reviewers comments; 5 figure

Quantum coherence phenomena in x-ray optics

The effects of quantum coherence in X-ray optics at nuclear transitions are investigated from a theoretical point of view. First, we introduce the general concept of the decaying dressed states and present a classification of the quantum coherence effects in a three-level coherently driven system. Second, we show that the interference effects may appear in X-ray radiation at the nuclear transitions under the condition of the nuclear level anti-crossing. This effects are similar to electromagnetically induced transparency, which has been widely studied earlier at the electronic transitions in optics. We also suggest a new technique for inhomogeneous line narrowing at nuclear transitions. This technique is based on the combined action of RF and DC fields and adopted to be applied in the M¨ossbauer spectroscopy. Numerical simulation of a simple model with the dipole-dipole interaction is presented in order to demonstrate the efficiency of the technique. Finally, we study the possibility to suppress the nuclear elastic forward scattering in the synchrotron experiments using trains of pulses. A numerical model is developed to confirm this possibility and the main issue of relative phases of consecutive pulses is discussed

Coherent and Squeezed Vacuum Light Interferometry: Parity detection hits the Heisenberg limit

The interference between coherent and squeezed vacuum light can produce path entangled states with very high fidelities. We show that the phase sensitivity of the above interferometric scheme with parity detection saturates the quantum Cramer-Rao bound, which reaches the Heisenberg-limit when the coherent and squeezed vacuum light are mixed in roughly equal proportions. For the same interferometric scheme, we draw a detailed comparison between parity detection and a symmetric-logarithmic-derivative-based detection scheme suggested by Ono and Hofmann.Comment: Change in the format from aps to iop since we decided to submit it to NJP; Minor changes in tex

Dynamical Decoupling in Optical Fibers: Preserving Polarization Qubits from Birefringent Dephasing

One of the major challenges in quantum computation has been to preserve the coherence of a quantum system against dephasing effects of the environment. The information stored in photon polarization, for example, is quickly lost due to such dephasing, and it is crucial to preserve the input states when one tries to transmit quantum information encoded in the photons through a communication channel. We propose a dynamical decoupling sequence to protect photonic qubits from dephasing by integrating wave plates into optical fiber at prescribed locations. We simulate random birefringent noise along realistic lengths of optical fiber and study preservation of polarization qubits through such fibers enhanced with Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling. This technique can maintain photonic qubit coherence at high fidelity, making a step towards achieving scalable and useful quantum communication with photonic qubits.Comment: 8 pages, 5 figure