Josephson Junctions and SQUIDsNo Access

NON-LINEAR DYNAMICS, ENTANGLEMENT AND THE QUANTUM-CLASSICAL CROSSOVER OF TWO COUPLED SQUID RINGS

M. J. EVERITT

Centre for Theoretical Physics, The British University in Egypt, El Sherouk City, Postal No. 11837, P.O. Box 43, Egypt

Department of Physics, Loughborough University, Loughborough, Leics LE11 3TU, United Kingdom

https://doi.org/10.1142/S0217979209063468Cited by:0 (Source: Crossref)

Abstract

We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. We note that the motivation for this work is based on a study of a similar system comprising two coupled Duffing oscillators. In that work we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy model. Motivated by a wish to explore more experimentally realisable systems we now extend our work to an analysis of two coupled SQUID rings. We observe some differences in behaviour between the system that is based on SQUID rings rather than on Duffing oscillators. However, we show that the two systems share a common feature. That is, even when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists.

Keywords:

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

T. Bhattacharya, S. Habib and K. Jacobs, Phys. Rev. Lett. 85, 4852 (2000), DOI: 10.1103/PhysRevLett.85.4852. Crossref, Web of Science, ADS, Google Scholar
T. Bhattacharya, S. Habib and K. Jacobs, Phys. Rev. A 67, 042103 (2003), DOI: 10.1103/PhysRevA.67.042103. Crossref, Web of Science, Google Scholar
S. Ghoseet al., Phys. Rev. A 69, 052116 (2004), DOI: 10.1103/PhysRevA.69.052116. Crossref, Web of Science, Google Scholar
R. Schack, T. A. Brun and I. C. Percival, J. Phys. A 28, 5401 (1995), DOI: 10.1088/0305-4470/28/18/028. Crossref, ADS, Google Scholar
I. C. Percival , Quantum State Diffusion ( Cambridge University Press , 1998 ) . Google Scholar
S. Habib, K. Shizume and W. H. Zurek, Phys. Rev. Lett. 80, 4361 (1998), DOI: 10.1103/PhysRevLett.80.4361. Crossref, Web of Science, ADS, Google Scholar
T. P. Spilleret al., J. Low Temp. Phys. 101, 279 (1995), DOI: 10.1007/BF00754523. Web of Science, Google Scholar
B. D. Greenbaumet al., Phys. Rev. E 76, 046215 (2007), DOI: 10.1103/PhysRevE.76.046215. Crossref, Web of Science, Google Scholar
T. A. Brunet al., Phys. Lett. A 229, 267 (1997), DOI: 10.1016/S0375-9601(97)00217-X. Crossref, Web of Science, ADS, Google Scholar
T. A. Brun, I. C. Percival and R. Schack, J. Phys. A-Math. Gen. 29, 2077 (1996), DOI: 10.1088/0305-4470/29/9/020. Crossref, Google Scholar
T. P. Spiller and J. F. Ralph, Phys. Lett. A 194, 235 (1994), DOI: 10.1016/0375-9601(94)91244-0. Crossref, Web of Science, ADS, Google Scholar
N. Gisin and I. C. Percival, J. Phys. A-Math. Gen. 26, 2233 (1993), DOI: 10.1088/0305-4470/26/9/018. Crossref, ADS, Google Scholar
N. Gisin and I. C. Percival, J. Phys. A-Math. Gen. 26, 2245 (1993), DOI: 10.1088/0305-4470/26/9/019. Crossref, ADS, Google Scholar
M. J. Everittet al., N. J. Phys. 7, (2005), DOI: 10.1088/1367-2630/7/1/064. Google Scholar
M. J. Everittet al., Phys. Rev. E 7, 066209 (2005). Google Scholar
M. Everitt, Phys. Rev. E 75, 036217 (2007), DOI: 10.1103/PhysRevE.75.036217. Crossref, Web of Science, Google Scholar
M. J. Everitt. On the correspondence principle: implications from a study of the chaotic dynamics of a macroscopic quantum device. 2007 , arXiv:0712.3043 . Google Scholar
E. Merzbacher , Quantum Mechanics , 3rd edn. ( John Wiley & Sons, Inc. , New York , 1998 ) . Google Scholar
C. H. Bennettet al., Phys. Rev. A 53, 2046 (1996), DOI: 10.1103/PhysRevA.53.2046. Crossref, Web of Science, Google Scholar
M. A. Nielsen and I. L. Cheung , Quantum Computation and Information ( Cambridge University Press , 2000 ) . Google Scholar
K. Likharev , Dynamics of Josephson Junctions and Circuits ( Taylor & Francis , London , 1986 ) . Google Scholar
A. Barone and G. Paterno , Physics and Applications of the Josephson Effect ( John Wiley & Sons Inc. , 1982 ) . Crossref, Google Scholar
S. Ghose, P. M. Alsing, B. C. Sanders, and I. H. Deutsch. Entanglement vs. the quantum-to-classical transition. 2004 , quant-ph/0409133 . Google Scholar