1D Luttinger liquid QED.pdfVIP

a r X i v : c o n d - m a t / 9 9 0 5 2 5 3 v 1 [ c o n d - m a t .s t r - e l ] 1 8 M a y 1 9 9 9 1D Luttinger liquid QED P. Degiovanni and S. Peysson Laboratoire de Physique (U.M.R. 5672 du CNRS), Ecole Normale Supe?rieure de Lyon 46, alle?e d’Italie, 69364 Lyon Cedex 07, France Using its Conformal Field Theory description, the Luttinger liquid is coupled to the quantum electro- magnetic field. We compute the decoherence properties of a superposition of two states obtained by creating the same elementary excitation at different places in the system. 1 Introduction The Landau-Fermi theory is the simplest theory for interacting electrons in metals. Its basic low energy excitations called quasiparticles are dressed electrons. Despite its success in 3D, the search for more exotic metallic states has been pursued leading to the discovery of the Luttinger liquid. This powerful and simple effective theory plays the role of the Landau-Fermi theory for one dimensional systems and has many applications. As illustrated in the present volume, various systems such as fractional quantum Hall (FQH) edge states, carbon nanotubes, quasi-1D organic conductors and quantum spin chains can be described using this paradigm. Up to now, this is the only known effective theory of a non-Fermi liquid. However, the coupling to an external quantum reservoir such as the quantum electromagnetic field has not attracted much attention. A notable exception is the work by Loss and Martin1 which shows that QED’s fluctuations cannot induce a spontaneous permanent current in a Luttinger ring. A great deal of work has been done within the context of weak localization but mainly in the framework of Landau-Fermi theory. In contrast, questions concerning the real time evolution of a Luttinger liquid coupled to QED have not been addressed. Here, recent results on QED-induced decoherence of Schro?dinger cat states in a Luttinger liquid are reported. Our main questions are: does QED induce a modific