Quantum and random effects on cooperative phenomena in spin systems

Hidetsugu Kitatani, 北谷 英嗣

Yoshihiko Nonomura, Hidetoshi Nishimori, 野々村 喜彦 +1 more

D A Rodrigues, Balazs L. Gyorffy, Timothy P. Spiller

We consider an array of Cooper Pair Boxes, each of which is coupled to a superconducting reservoir by a capacitive tunnel junction. We discuss two effects that probe not just the quantum nature of the islands, but also of the superconducting reservoir coupled to them. These are analogues to the well-known quantum optical effects `superradiance,' and `revival.' When revival is extended to multiple systems, we find that `entanglement revival' can also be observed. In order to study the above effects, we utilise a highly simplified model for these systems in which all the single-electron energy eigenvalues are set to be the same (the strong coupling limit), as are the charging energies of the Cooper Pair Boxes, allowing the whole system to be represented by two large coupled quantum spins. Although this simplification is drastic, the model retains the main features necessary to capture the phenomena of interest. Given the progress in superconducting box experiments over recent years, it is possible that experiments to investigate both of these interesting quantum coherent phenomena could be performed in the forseeable future.

A. Oubelkacem, K. Htoutou, A. Ainane +1 more

The random field Ising model (RFIM) has been investigated extensively both theoretically and experimentally in recent years [1–4]. Some questions, such as the lower critical dimension and the existence of a static phase transition, have already been solved from the theoretical point of view, but other questions, such as the existence of the tricritical point, are still open. However, it is now understood that the RFIM describes the essential physics of a rich class of experimentally accessible disordered systems. These include structural phase transitions in random alloys, commensurate charge-density-wave systems with impurity pinning, binary fluid mixtures in random porous media, and the melting of intercalates in layered compounds such as TiS2. The behavior of the RFIM is governed by the competing tendencies of the spins to align ferromagnetically under impetus of the exchange or to follow the local fields and thus be uncorrelated. The RFIM has been studied using different methods. One of the authors [5] of the present paper has developed a new version of effective field theory, which extends the approximation methods [6, 7] to random Ising systems, in which randomness can be described by discrete random variables and the geometry of the lattice can be easily taken into account. This method is based on the determination of the probability distribution of the discrete variables, which takes into account exactly the self-site correlations. This approach has been used to study cooperative phenomena and phase transitions in various systems, and gives useful qualitative and quantitative insights for the critical behavior of a wide variety of classical and quantum lattice spin systems [8–10]. In recent decades, the renormalization group theory of phase transitions and critical phenomena represents one of the most powerful tools of theoretical physics. Therefore, employing this theory (which can be applied for weak fields), the proof

V. P. Karassiov

1. Cooperative phenomena and processes in various many-body physical systems (atoms, molecules, nuclei etc.) are now the topic of great interest (see e.g. [ 1-6 ] and references therein). A natural and efficient tool for studying cooperative phenomena in quantum systems is the second quantization method [ 7 ], which is closely connected with the representation theory of Lie groups and supergroups [ 8 – 12 ]. Therefore, group-theoretical methods are very adequate to an analysis of different cooperative effects within the general approach of dynamic symmetries [ 13 ].

Abel Klein