Condensate Wavefunction: Superposition, Entanglement, Nonlinearity, and Quantum Computation
Yu Shi · arXiv (Cornell University) · 1999
A Bose-Einstein condensate can be well described by an order parameter called condensate wavefunction. If Bose-Einstein condensation occurs in a superposed single particle state, the condensate wavefunction is correspondingly superposed. Likewise, if two coupled distinguishable or non-overlapping Bose systems condense in an entangled single particle pair state, the condensate wavefunction is correspondingly entangled. With superposition and entanglement, condensate wavefunction can thus be used to implement quantum bit in quantum computation. Because many identical particles occupy a same state, a Bose condensate has intrinsic robustness. Furthermore, the nonlinearity of the condensate wavefunction due to particle-particle interaction can be utilized to realize nonlinear quantum computation, which may deal with NP-complete problems. Therefore, indistinguishability of identical particles is a resource of fault tolerance and computational power. These ideas are illustrated in terms of Bose-Einstein condensation of trapped atoms.