Non-Abelian off-diagonal geometric phases in nano-engineered four-qubit systems

The concept of off-diagonal geometric phase (GP) has been introduced in order to recover interference information about the geometry of quantal evolution where the standard GPs are not well-defined. In this Letter, we propose a physical setting for realizing non-Abelian off-diagonal GPs. The proposed non-Abelian off-diagonal GPs can be implemented in a cyclic chain of four qubits with controllable nearest-neighbor interactions. Our proposal seems to be within reach in various nano-engineered systems and therefore opens up for first experimental test of the non-Abelian off-diagonal GP.Comment: Some changes, journal reference adde

Non-Abelian quantum holonomy of hydrogen-like atoms

We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogen-like atoms where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian, while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy, and find a relation between the phase of the whole system with corresponding marginal phases. Based on the result for the model system we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [E. Sj\"oqvist {\it et al.} Phys. Rev. Lett. 85, 2845 (2000)] are in general inequivalent.Comment: Shortened version; journal reference adde

Transition-metal dimers and physical limits on magnetic anisotropy

Recent advances in nanoscience have raised interest in the minimum bit size required for classical information storage, i.e. for bistability with suppressed quantum tunnelling and energy barriers that exceed ambient temperatures. In the case of magnetic information storage much attention has centred on molecular magnets[1] with bits consisting of ~ 100 atoms, magnetic uniaxial anisotropy energy barriers ~ 50 K, and very slow relaxation at low temperatures. In this article we draw attention to the remarkable magnetic properties of some transition metal dimers which have energy barriers approaching ~ 500 K with only two atoms. The spin dynamics of these ultra small nanomagnets is strongly affected by a Berry phase which arises from quasi-degeneracies at the electronic Highest Occupied Molecular Orbital (HOMO) energy. In a giant spin-approximation, this Berry phase makes the effective reversal barrier thicker. [1] Gatteschi, D., Sessoli, R. & Villain, J. Molecular Nanomagnets. (Oxford, New York 2006).Comment: 14 pages, 1 figur

Measuring the free fall of antihydrogen

After the first production of cold antihydrogen by the ATHENA and ATRAP experiments ten years ago, new second-generation experiments are aimed at measuring the fundamental properties of this anti-atom. The goal of AEGIS (Antimatter Experiment: Gravity, Interferometry, Spectroscopy) is to test the weak equivalence principle by studying the gravitational interaction between matter and antimatter with a pulsed, cold antihydrogen beam. The experiment is currently being assembled at CERN's Antiproton Decelerator. In AEGIS, antihydrogen will be produced by charge exchange of cold antiprotons with positronium excited to a high Rydberg state (n > 20). An antihydrogen beam will be produced by controlled acceleration in an electric-field gradient (Stark acceleration). The deflection of the horizontal beam due to its free fall in the gravitational field of the earth will be measured with a moire deflectometer. Initially, the gravitational acceleration will be determined to a precision of 1%, requiring the detection of about 105 antihydrogen atoms. In this paper, after a general description, the present status of the experiment will be reviewed

Exploring the WEP with a pulsed cold beam of antihydrogen

The AEGIS experiment, currently being set up at the Antiproton Decelerator at CERN, has the objective of studying the free fall of antimatter in the Earth's gravitational field by means of a pulsed cold atomic beam of antihydrogen atoms. Both duration of free fall and vertical displacement of the horizontally emitted atoms will be measured, allowing a first test of the WEP with antimatter