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An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity

SIAM Journal on Numerical Analysis 41:4 (2003) 1406-1426

Authors:

W Bao, D Jaksch

Abstract:

This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrödinger equations (NLSs). The method is explicit, unconditionally stable, and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are presented for cubic focusing NLSs in two dimensions with a linear, cubic, or quintic damping term. Our numerical results show that quintic or cubic damping always arrests blowup, while linear damping can arrest blowup only when the damping parameter δ is larger than a threshold value δth. We note that our method can also be applied to solve the three-dimensional Gross-Pitaevskii equation with a quintic damping term to model the dynamics of a collapsing and exploding Bose-Einstein condensate (BEC).
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Many-particle entanglement in two-component Bose-Einstein condensates

Physical Review A - Atomic, Molecular, and Optical Physics 67:1 (2003)

Authors:

A Micheli, D Jaksch, JI Cirac, P Zoller

Abstract:

The schemes which allow the creation of macroscopically entangled states with a distance 0
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Quantum Information Processing with Quantuim Optics

Annales Henri Poincare 4:SUPPL. 2 (2003)

Authors:

JI Cirac, LM Duan, D Jaksch, P Zoller

Abstract:

We review theoretical proposals for implementation of quantum computing and quantum communication with quantum optical methods.
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Controlling dynamical phases in quantum optics

J OPT B-QUANTUM S O 4:4 (2002) S430-S436

Authors:

T Calarco, D Jaksch, JI Cirac, P Zoller

Abstract:

We review and compare several schemes for inducing precisely controlled quantum phases in quantum optical systems, We focus in particular on conditional dynamical phases, i.e. phases obtained via state- and time-dependent interactions between trapped two-level atoms and ions, We describe different possibilities for the kind of interaction to be exploited, including cold controlled collisions, electrostatic forces, and dipole-dipole interactions.
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Creation of a molecular condensate by dynamically melting a Mott-insulator

Physical Review Letters 89 (2002) 040402, 4pp

Authors:

DH Jaksch, V. Venturi, J.I. Cirac, P. Zoller
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