Optical continuous-variable quadratic phase gate via Faraday interaction.

The continuous-variable (CV) quadratic phase gate is one of the most fundamental CV quantum gates for universal CV quantum computation, while its experimental realization still remains a challenge. Here we propose a novel and experimentally feasible scheme to realize optical CV quadratic phase gate via Faraday interaction in an atomic ensemble. The gate is performed by simply sending an optical beam three times through an atomic medium prepared in coherent spin state. The fidelity of the gate can ideally run up to one. We show that the scheme also works well as a device to generate optical polarization squeezing. Considering the noise effects due to atomic decoherence and light losses, we find that the observed fidelities of gate operation and the attainable degree of polarization squeezing are still quite high.

Migration-driven aggregate growth on scale-free networks.

We study the kinetics of migration-driven aggregate growth on completely connected scale-free networks. A reversible migration system is considered with the size-dependent rate kernel K(k; l/i;j) approximately k(u)i(v)(lj)(v), at which an i-mer aggregate located on the node with j links gains one monomer from a k-mer aggregate on the node with l links. The results show that the evolution behavior of the aggregate size distribution is drastically different from that for the corresponding same system in normal space. This model can be used to mimic some phenomena such as the distribution of city populations. Moreover, we verify our analytic results in good agreement with the data of the population distributions of all U.S. counties.

Kinetics of migration-driven aggregation processes on scale-free networks.

We propose a solvable model for the migration-driven aggregate growth on completely connected scale-free networks. A reversible migration system is considered with the produce rate kernel K(k;l|i;j) approximately k(u)i(upsilon)(lj)(nu) or the generalized kernel K(k;l|i;j) approximately (k(upsilon)i(omega)+k(omega)i(upsilon)(lj)(nu), at which an i-mer aggregate locating on the node with j links gains one monomer from a k-mer aggregate locating on the node with l links. It is found that the evolution behavior of the system depends crucially on the details of the rate kernel. In some cases, the aggregate size distribution approaches a scaling form and the typical size S(t,l) of the aggregates locating on the nodes with l links grows infinitely with time; while in other cases, a gelation transition may emerge in the system at a finite critical time. We also introduce a simplified model, in which the aggregates independently gain or lose one monomer at the rate I(1)(k;l)=I(2)(k;l) proportional to k(omega)l(nu), and find the similar results. Most intriguingly, these models exhibit that the evolution behavior of the total distribution of the aggregates with the same size is drastically different from that for the corresponding system in normal space. We test our analytical results with the population data of all counties in the U.S. during the past century and find good agreement between the theoretical predictions and the realistic data.