Abstract
We study a one-dimensional system composed of N charged bosons confined in an external harmonic potential. In the limit of a strong interaction between the particles, we apply the harmonic approximation and derive an integral representation for the purity of the one-particle reduced density matrix, enabling an easy determination of the asymptotic entanglement. Results for the dependence of the asymptotic linear entropy on N are provided and discussed in detail for the first time.
Article PDF
Avoid common mistakes on your manuscript.
References
Jacak, L., Hawrylak, P., Wojs, A.: Quantum Dots. Springer-Verlag, Berlin (1977)
Wineland D.J. et al.: Atomic-ion coulomb clusters in an ion trap. Phys. Rev. Lett. 59, 2935 (1987)
Filinov A., Bonitz M., Lozovik Y.E.: Wigner crystallization in mesoscopic 2D electron systems. Phys. Rev. Lett. 86, 3851 (2001)
Coe J.P., Sudbery A., D’Amico I.: Entanglement and density-functional theory: Testing approximations on Hooke’s atom. Phys. Rev. B 77, 205122 (2008)
Nazmitdinov R. et al.: Shape transitions in excited states of two-electron quantum dots in a magnetic field. J. Phys. B At. Mol. Opt. Phys. 45, 205503 (2012)
Nazmitdinov R. et al.: A geometrical crossover in excited states of two-electron quantum dots in a magnetic field. J. Phys. Conf. Ser. 393, 012009 (2012)
Kościk P.: Two-electron entanglement in a two-dimensional isotropic harmonic trap: Radial correlation effects in the low density limit. Phys. Lett. A 375, 458 (2011)
Kościk P.: Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies. Eur. Phys. J. B 85, 173 (2012)
Kościk P., Okopińska A.: Ground-state correlation properties of charged bosons trapped in strongly anisotropic harmonic potentials. Eur. Phys. J. B 85, 93 (2012)
James D.F.V.: Quantum dynamics of cold trapped ions with application to quantum computation. Appl. Phys. B 66, 181 (1998)
Balzer K. et al.: Energy spectrum of strongly correlated particles in quantum dots. J. Phys. Conf. Ser. 35, 209 (2006)
Manfredi G., Feix M.: Entropy and Wigner functions. Phys. Rev. E 62, 4665 (2000)
Grobe R., Rzazewski K., Eberly J.: Measure of electron-electron correlation in atomic physics. J. Phys. B At. Mol. Opt. Phys. 27, L503 (1994)
Borras A., Majtey A.P., Casas M.: Efficient generation of random multipartite entangled states using time-optimal unitary operations. Phys. Rev. A 78, 022328 (2008)
Kościk P., Okopińska A.: Correlation effects in the Moshinsky model. Few-Body Syst. 54, 1637 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
About this article
Cite this article
Kościk, P., Maj, R. Note on the Harmonic Approximation in the Treatment of Entanglement: N Cold Trapped Ions. Few-Body Syst 55, 1253–1257 (2014). https://doi.org/10.1007/s00601-014-0914-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00601-014-0914-3