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Internal tunneling effect in an entangled cold atom condensate Jinlong Wang and Yu Shi

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Internal tunneling effect in an entangled cold atom condensate Jinlong Wang and Yu Shi

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  1. Conclusion. Tunneling effect in the internal species of an entangled BEC system can cause the time evolutions of the spin components and spin fluctuations. This may be used to find the squeezed spin state in such a system and this conclusion may also be regarded as the realization of interesting spin dynamics. References [1] Yu Shi, Phys. Rev. Lett. 96, 140401 (2006). [2]M. Kitagawa, M. Ueda, Phys. Rev. A 47, 5318 (1993) . Internal tunneling effect in an entangled cold atom condensate Jinlong Wang and Yu Shi Department of Physics, Fudan University Tunneling effect is a usual phenomenon in the two component Bose-Einstein condensation (BEC). We an entangled cold atom condensate, which is of two types of atoms, each of which has two hyperfine states [1]. Spin-exchange scattering causes interspecies entanglement in this system. This system has no tunneling effect in absence of an external field, with the total pseudospin and the energy are conserved. If there is tunneling effect within each type of atom, the total pseudospin of the system evolves with time starting with an appropriate initial state. We try to find the way to realize squeezed spin states [2] in this system. The system introduction The total Hamiltonian is The Hamiltonian consists of two parts. The first part is of the atoms only, and can be simplified as The evolution operator is in the isotropic parameter point. a, b repesents the type of atom, Jz is related to the scattering length of atoms. Other pseudo-spin components have similar expressions. The second part is the tunneling term due to the coupling with the external field: which can be rewritten as We can obtain: We can derive the following results If the initial state is a maximal entangled state with the same atom number N of two type If the initial state has non-zero spin z-component, for example, in the state |Gsz>, which is the degenerate ground state of H0 , which is the ground state of H0, we can calculate the expectation values of Sx (t), Sy (t), Sz(t) in the initial state This means that if the initial state has no spin in each component these expectation values of Sx (t), Sy (t), Sz(t) are not envolved with time. But the fluctuations of these spin operators in |G0> vary with time

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