Nonadiabatic noncyclic geometric phase of a spin-1/2 particle subject to an arbitrary magnetic field

We derive a formula of the nonadiabatic noncyclic Pancharatnam phase for a quantum spin-1/2 particle subject to an arbitrary magnetic field. The formula is applied to three specific kinds of magneic fields. (i) For an orientated magnetic field, the Pancharatnam phase is derived exactly. (ii) For a rotating magnetic field, the evolution equation is solved analytically. The Aharonov-Anandan phase is obtained exactly and the Pancharatnam phase is computed numerically. (iii) We propose a kind of topological transition in one-dimensional mesoscopic ring subject to an in-plane magnetic field, and then address the nonadiabatic noncyclic effect on this phenomenon.Comment: 6 pages and 3 figure

Late-Time Optical Afterglow Observations with LBT and MDM

Using the 2.4m MDM and 8.4m Large Binocular Telescope, we observed nine GRB afterglows to systematically probe the late time behaviors of afterglows including jet breaks, flares, and supernova bumps. In particular, the LBT observations have typical flux limits of 25-26 mag in the Sloan r' band, which allows us to extend the temporal baseline for measuring jet breaks by another decade in time scale. We detected four jet breaks (including a "textbook" jet break in GRB070125) and a fifth candidate, all of which are not detectable without deep, late time optical observations. In the other four cases, we do not detect the jet breaks either because of contamination from the host galaxy light, the presence of a supernova bump, or the intrinsic faintness of the optical afterglow. This suggests that the basic picture that GRBs are collimated is still valid and that the apparent lack of Swift jet breaks is due to poorly sampled afterglow light curves, particularly at late times. Besides the jet breaks, we also detected late time flares, which could attribute to late central engine activities, and two supernova bumps.Comment: 5 pages, 5 figures, 2008 NANJING GAMMA-RAY BURST CONFERENCE. AIP Conference Proceedings, Volume 1065, pp. 93-97 (2008), Eds. Y.F. Huang, Z.G. Dai, B. Zhan

Exploring multipartite quantum correlations with the square of quantum discord

We explore the quantum correlation distribution in multipartite quantum states based on the square of quantum discord (SQD). For tripartite quantum systems, we derive the necessary and sufficient condition for the SQD to satisfy the monogamy relation. Particularly, we prove that the SQD is monogamous for three-qubit pure states, based on which a genuine tripartite quantum correlation measure is introduced. In addition, we also address the quantum correlation distributions in four-qubit pure states. As an example, we investigate multipartite quantum correlations in the dynamical evolution of multipartite cavity-reservoir systems.Comment: 8 pages, 5 figure

Implementing universal nonadiabatic holonomic quantum gates with transmons

Geometric phases are well known to be noise-resilient in quantum evolutions/operations. Holonomic quantum gates provide us with a robust way towards universal quantum computation, as these quantum gates are actually induced by nonabelian geometric phases. Here we propose and elaborate how to efficiently implement universal nonadiabatic holonomic quantum gates on simpler superconducting circuits, with a single transmon serving as a qubit. In our proposal, an arbitrary single-qubit holonomic gate can be realized in a single-loop scenario, by varying the amplitudes and phase difference of two microwave fields resonantly coupled to a transmon, while nontrivial two-qubit holonomic gates may be generated with a transmission-line resonator being simultaneously coupled to the two target transmons in an effective resonant way. Moreover, our scenario may readily be scaled up to a two-dimensional lattice configuration, which is able to support large scalable quantum computation, paving the way for practically implementing universal nonadiabatic holonomic quantum computation with superconducting circuits.Comment: v3 Appendix added, v4 published version, v5 published version with correction