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Acta Physica Sinica

Spin squeezing of two-component Bose-Einstein condensate

Dong Yan, Song Li-Jun, Chen Dian-Wei, (1)长春大学理学院，长春 130022; (2)吉林化工学院理学院，吉林 132022

Published Jan 1, 2009• 11 citations
Publisher

Abstract

Spin squeezing of two-component Bose-Einstein condensate, which is impacted by the periodic impulses, is investigated. The results show that spin squeezing can reveal the underlying chaotic and regular structures of phase space, namely, spin squeezing vanishes after a very short time for an initial coherent state centred in a chaotic region, but spin squeezing exists for a long time for an initial coherent state centred in a regular region. In particular, with time evolution, distribution and swing of the mean spin direction is closely related to the structure of the space where the initial coherent state centred in. Finally, spin squeezing dynamics of initial states centred in the whole phase space is investigated and a better quantum-classical correspondence is obtained.

DOI
10.7498/aps.58.3679

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Spin squeezing of two-component Bose-Einstein condensate, which is impacted by the periodic impulses, is investigated. The results show that spin squeezing can reveal the underlying chaotic and regular structures of phase space, namely, spin squeezing vanishes after a very short time for an initial coherent state centred in a chaotic region, but spin squeezing exists for a long time for an initial coherent state centred in a regular region. In particular, with time evolution, distribution and swing of the mean spin direction is closely related to the structure of the space where the initial coherent state centred in. Finally, spin squeezing dynamics of initial states centred in the whole phase space is investigated and a better quantum-classical correspondence is obtained.
We study spin squeezing, an intrinsically quantum property, in the quantum kicked top model exhibiting chaotic behaviours in the classical limit. We show that spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a sphere with a unit radius, namely, spin squeezing vanishes after a very short time for an initial spin coherent state centred in a chaotic region of the phase space, whereas spin squeezing occurs over a long period of time for the coherent state centred in an elliptic fixed point. We also study the distribution of the mean spin directions when quantum dynamics take places and give a comparison between the dynamics of spin squeezing and quantum entanglement.
We study spin squeezing, an intrinsic quantum property, in the Dicke model without the rotating-wave approximation. We show that the spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a Poincaré section, namely, it acts as an indicator of quantum chaos. Spin squeezing vanishes after a very short time for an initial coherent state centered in a chaotic region, whereas it persists over a longer time for the coherent state centered in a regular region of the phase space. We also study the distribution of the mean spin directions when quantum dynamics takes place. Finally, we discuss relations among spin squeezing, bosonic quadrature squeezing, and two-qubit entanglement in the dynamical processes.
The quantum information is a new interdisciplinary science in the 21st century, and it has become a research field which attracts strongly much attention in the world. Recently, the study of the quantum computer is in the ascendant. In the process of finding a scheme for quantum computation, quantum chaos aroused much attention. It has been shown that it is possible to induce quantum chaos when running quantum computer and consequently it may destroy the operational condition of the quantum computer. The relationship between quantum entanglement and quantum chaos has already been investigated, and the spin squeezing is regarded as another classical quantum property indeed, then is there a natural relationship between quantum chaos and spin squeezing? In this paper a very typical QKT model in the quantum chaos has been discussed,and the properties of spin squeezing in the quantum chaotic system has been studied. The relation between spin squeezing parameters and chaotic parameter in the two different definitions is worked out by numerical calculation. The stronger that the regular regions are than chaotic ones, which are chosen firstly, in the classical phase space, the stronger the spin system which the initial states locate at the centre of elliptical regions as a result. If the initial states are chosen another condition, the contrary result is obtained naturally. It indicates the spin squeezing is very sensitive to the classical chaos and the classical chaos suppresses the spin squeezing. It is interesting that the definition by Wineland is more sensitive than the one by Kitagawa and Ueda, consequently a conclusion, which the quantum chaos can be described by spin squeezing, is acquired.
Quantum Fisher information,derived from the classical Fisher information, is closely related to the quantum entanglement in quantum information. The entanglement and the quantum information which are both associated with the classical phase space are investigated in a two-component Bose-Einstein condensate impacted by the impulses. The results reveal that the states regardless of disorder of the phase space after the first impulse are entangled. However, the quantum information is very sensitive to the state centred in the classical phase space, concretely, the value of the quantum information centred in the chaotic region is greater than in the regular region. By employing the good quantum-classical correspondence, we conclude that the quantum information can serve as a signature of the quantum chaos.