Stability of Stationary States of Quantum Generators

А. А. Горбачев

Tatiana I. Kuznetsova, Sergey G. Rautian

Mikko Möttönen, Suvi Mirjami Virtanen, Tomoya Isoshima +1 more

We investigate the recently found stationary vortex cluster states in dilute atomic Bose-Einstein condensates confined by a nonrotating trap, and also present a stationary three-vortex cluster. We find the stationary states by minimizing directly an error norm for the stationary Gross-Pitaevskii equation, and study the dynamic and energetic stability of the resulting states by solving the corresponding Bogoliubov equations for the elementary excitations. The results are verified by integrating the time-dependent Gross-Pitaevskii equation. Contrary to previously reported results, the stationary states were observed to be both energetically and dynamically unstable. The dynamical decay rate of the clusters is typically very slow, but it should be experimentally observable. The most promising circumstances to experimentally generate and observe these structures and their dynamics is in weakly dissipative condensate systems, using phase-imprinting techniques.

Matt Coles, Dmitry E. Pelinovsky

We consider stationary Bloch waves in a Bose–Einstein condensate placed in a periodic potential for varying strengths of inter‐atomic interactions. Bifurcations of the stationary states are known to occur in this context. These bifurcations generate loops in the energy bands of the Bloch waves near the ends and the center of the Brillouin zone. Using the method of Lyapunov–Schmidt reductions, we show that these bifurcations are of the supercritical pitchfork type. We also characterize the change in stability of the stationary states across the bifurcation point. Analytical results are illustrated by numerical computations.

Robin Stevenson, J. J. Hope, Andre R. R. Carvalho

We investigate the use of quantum-jump-based feedback to manipulate the stability of multipartite entangled dark states in an open quantum system. Using the model proposed in Phys. Rev. A 76, 010301(R) (2007) for a pair of atoms, we show a general strategy to produce many-body singlet stationary entangled states for larger number of atoms. In the case of four qubits, we propose a simple local feedback control that, although not optimal, is realistic and stabilizes a highly entangled state. We discuss the limitations and analyze alternative strategies within the framework of direct jump feedback schemes.

Vasily E Tarasov