Bose-Einstein condensate soliton qubit states for metrological applications.

We propose a novel platform for quantum metrology based on qubit states of two Bose-Einstein condensate solitons, optically manipulated, trapped in a double-well potential, and coupled through nonlinear Josephson effect. We describe steady-state solutions in different scenarios and perform a phase space analysis in the terms of population imbalance-phase difference variables to demonstrate macroscopic quantum self-trapping regimes. Schrödinger-cat states, maximally path-entangled (N00N) states, and macroscopic soliton qubits are predicted and exploited to distinguish the obtained macroscopic states in the framework of binary (non-orthogonal) state discrimination problem. For an arbitrary frequency estimation we have revealed these macroscopic soliton states have a scaling up to the Heisenberg and super-Heisenberg (SH) limits within linear and nonlinear metrology procedures, respectively. The examples and numerical evaluations illustrate experimental feasibility of estimation with SH accuracy of angular frequency between the ground and first excited macroscopic states of the condensate in the presence of moderate losses, which opens new perspectives for current frequency standard technologies.

Mean-field theory of superradiant phase transition in complex networks.

In this work we consider a superradiant phase transition problem for the Dicke-Ising model, which generalizes the Dicke and Ising models for annealed complex networks presuming spin-spin interaction. The model accounts for the interaction between a spin-1/2 (two-level) system and external classical (magnetic) and quantized (transverse) fields. We examine regular, random, and scale-free network structures characterized by the δ function, random (Poisson), and power-law exponent [p(k)∝k^{-γ}] degree distributions, respectively. To describe paramagnetic (PM)-ferromagrenic (FM) and superradiant (SR) phase transitions we introduce two order parameters: the total weighted spin z component and the normalized transverse field amplitude, which correspond to the spontaneous magnetization in z and x directions, respectively. For the regular networks and vanishing external field we demonstrate that these phase transitions generally represent prerequisites for the crossover from a disordered spin state to the ordered one inherent to the FM and/or SR phase. Due to the interplay between the spin interaction and the finite-size effects in networks we elucidate novel features of the SR state in the presence of the PM-FM phase transition. In particular, we show that the critical temperature may be high enough and essentially depends on parameters which characterize statistical properties of the network structure. For the scale-free networks we demonstrate that the network architecture, characterized by the particular value of γ, plays a key role in the SR phase transition problem. Within the anomalous regime scale-free networks possess a strong effective spin-spin interaction supporting fully ordered FM state, which is practically nonsensitive to variations of the quantum transverse field or moderate classical magnetic field. In a scale-free regime the networks exhibit vanishing of the collective spin component in z direction with increasing γ accompanied by establishing spontaneous magnetization in the transverse field. The SR phase transition occurs in the presence of some FM state. We establish the conditions for the network parameters, classical and quantum field features to obtain a quantum phase transition in the spin system when the critical temperature approaches zero.