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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum entanglement at dynamical bifurcations (Invited Paper)

Gerard J Milburn, Andrew P. Hines

Published May 23, 2005• 0 citations
Publisher

Abstract

We show how quantum entanglement in the ground state of interacting quantum systems can arise from dynamical instabilities in the phase space of the corresponding classical system. Using the example of coupled giant spins we show that, when the fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state - the ground state - achieves its maximum amount of entanglement near the critical parameter.

DOI
10.1117/12.609027

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We show how quantum entanglement in the ground state of interacting quantum systems can arise from dynamical instabilities in the phase space of the corresponding classical system. Using the example of coupled giant spins we show that, when the fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state - the ground state - achieves its maximum amount of entanglement near the critical parameter.
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We consider the effective spin Hamiltonian describing a mixture of two species of pseudo-spin-12\frac{1}{2}21​ Bose gases with interspecies spin exchange. First we analyze the stability of the fixed points of the corresponding classical dynamics, of which the signature is found in quantum dynamics with a disentangled initial state. Focusing on the case without an external potential, we find all the ground states by taking into account quantum fluctuations around the classical ground state in each parameter regime. The nature of entanglement and its relation with classical bifurcation is investigated. When the total spins of the two species are unequal, the maximal entanglement at the parameter point of classical bifurcation is possessed by the excited state corresponding to the classical fixed point which bifurcates, rather than by the ground state.