Topology and phase: two ways to control the coherent dynamics of electrons >

Gloria Platero Topology and phase: two ways to control the coherent dynamics of electrons The excellent coherence properties of low dimensional semiconductor nanostructures, together with the degree of control over their geometry and specifications, make them ideal candidates for studying coherent transport, where quantum interference is used to regulate the movement of particles. Such control is particularly vital for quantum information, in which the coherence and entanglement of the initial state must be preserved during the evolution of the system. A powerful method of manipulating the coherent dynamics of quantum particles is to control the phase of their tunnelling. In this work we show how such phases can be produced in two distinct and complementary ways. If we consider a particle hopping on a lattice, interference will occur if the hopping acquires a phase factor. A direct way of doing this is to apply a magnetic field, which produces the well-known Aharonov-Bohm (AB) phase. In Ref. [1] it was shown that such phases could produce a localization effect termed AB caging, in which destructive interference bounds the set of sites that can be visited by an initially localized wave packet. This caging effect has been observed in superconducting wire networks, mesoscopic semiconductor lattices, and arrays of Josephson junctions. AB caging is resistant to small quantities of disorder but is swiftly destroyed by interactions due to the formation of spatially extended states. A different form of localization, also arising from quantum interference, is termed ‘‘Coherent Destruction of Tunneling’’ (CDT). This arises in systems subjected to a time-periodic driving field. Tunneling processes acquire phase factors from the interaction of the system with the driving, producing an effective renormalization of the tunneling. In this talk we consider the dynamics of two interacting electrons hopping on a quasi one-dimensional lattice with a non-trivial topology threaded by a uniform magnetic flux, and study the effect of adding a time- periodic driving field. We will show that the dynamical phases produced by the driving field can combine with the familiar Aharonov-Bohm phases arising from the magnetic flux to restore AB caging [2]. This occurs when CDT causes the (repulsive) electrons to bind together into a composite object of charge 2e termed a ‘‘doublon,’’ which can then be caged by the magnetic flux. We then go on to consider the effect of a low-frequency driving field and show that this gives rise to an unusual form of propagation in which the doublon moves in steps of two lattice sites, via the virtual occupation of the intermediate sites. This permits the creation and control of spatially separated entangled states of two electrons via the beam-splitter effect, with many potential applications to quantum information. In summary, we show that the dynamical phases produced by the driving can combine with the Aharonov-Bohm phases to give precise control of the localization and dynamics of the particles, even in the presence of strong particle interactions. [1] J. Vidal, R. Mosseri, and B. Douc¸ot, Phys. Rev. Lett. 81, 5888 (1998). [2]C.E. Creffield and G. Platero, Phys. Rev. Lett. 105, 086804 (2010).

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