臺灣博碩士論文加值系統

Spin decoherence induced by spin baths has become an important subject in the field of quantum information science and quantum computing. In this work, the Heisenberg XXZ spin chain, which has a rich phase diagram, functions as a spin bath. I investigate spin-1/2 qubit decoherence as well as entanglement by mean of time-dependent density matrix renormalization group (t-DMRG). I find that induced decoherence and entanglement crucially depends on the phase
of the spin bath. Moreover, for various interaction types and coupling strengths between the qubit(s) and the spin bath, the induced decoherence and entanglement differs. These show that there is a competition between the induced decoherence and entanglement. Finally, I stimulate two-qubit (dis)entanglement dynamics via a common bath and entanglement sudden death is also observed.

1 Introduction
2 Numerical approach: density matrix renormalization group 2.1 Density matrix renormalization group
2.1.1 DMRG algorithms
2.1.2 Physical quantities in DMRG
2.1.3 Wavefunction transformation
2.2 Time-dependent DMRG
2.2.1 Suzuki-Trotter decomposition
2.2.2 Add qubit(s) in t-DMRG
2.2.3 Add qubit self-Hamiltonian
3 Single-qubit decoherence by 1D Heisenberg XXZ spin baths 3.1 The model
3.2 Single-qubit decoherence and Loschmidt echo
3.3 Single-qubit decoherence dynamics
3.3.1 Ising-type interaction
3.3.2 Heisenberg-type interaction
4 Two-qubit dynamics via common bath
4.1 Measure of entanglement
4.1.1 Wootters concurrence
4.2 Entanglement creation
4.2.1 Ising-type interaction
4.2.2 Heisenberg-type interaction
4.3 Disentanglement dynamics
4.4 Multi-link coupling
5 Conclusion
5.1 Summary
5.2 Future work
Appendices

[1] A. V. Khaetskii and Y. V. Nazarov, Phys. Rev. B, 61, 12639 (2000)
[2] T. D. Ladd, D. Maryenko, and Y. Yamamoto, Phys. Rev. B, 71, 014401 (2005)
[3] K. G. Wilson, Rev. Mod. Phys. 77, 259 (2005)
[4] S. R. White, Phys. Rev. B, 48, 10345 (1993)
[5] S. R. White, Phys. Rev. B, 48, 3844 (1993)
[6] R. M. Noack and S. R. White, P.27, Density-Matrix Renormalization: A New Numerical Method in Physics (Springer, 1999)
[7] R. P. Feynman, Statistical Mechanics: A Set of Lectures, (Benjamin, 1972)
[8] S. R. White and David A. Huse, Phys. Rev. B, 48, 3844 (1993)
[9] S. R. White, Phys. Rev. Lett., 77, 3633 (1996)
[10]M. A. Cazalilla and J. B. Marston, Phyes. Rev. Lett., 88, 256403 (2002)
[11]G. Vidal, Phys. Rev. Lett., 91, 147902 (2003)
[12]G. Vidal, Phys. Rev. Lett., 93, 040502 (2004)
[13]M. Zwolak and G. Vidal, Phys. Rev. Lett., 93, 207205 (2004)
[14]I. P. McCulloch, arXiv:cond-mat/0701428 (2007)
[15]A. J. Daley et al., J. Stat. Mech, P04005 (2004)
[16]S. R. White and Adrian E. Geiguin, Phys. Rev. Lett., 93, 076401 (2004)
[17]D. Gobert et al., Phys. Rev. E, 71, 036102 (2005)
[18]Michael A. Nielsen and Isaac L. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000)
[19]D. Rossini et al., Phys. Rev. A, 75, 032333 (2007).
[20]A. Peres, Phys. Rev. A, 30, 1610 (1984)
[21]C. H. Bennett et al., Phys. Rev. A, 53, 2046 (1996)
[22]H. Scott and W. K. Wooters, Phys. Rev. Lett., 78, 5022 (1997)
[23]W. K. Wootters, Phys. Rev. Lett., 80, 2245 (1998)
[24]D. Braun, Phys. Rev. Lett., 89, 277901 (2002)
[25]D. Solenov et al., Phys. Rev. B, 75, 035134 (2007); V. Privman and D. Solenov, arXiv:cond-mat/0703311
[26]C. Y. Lai et al., Phys. Rev. B, 77, 205419 (2008)
[27]T. Yu, J. H. Elberly, Phys. Rev. Lett., 93, 140404 (2004)
[28]M. P. Almeida et al., Science, 316, 579 (2007)
[29]L. Campos Venuti et al., Phys. Rev. Lett., 96, 247206 (2006)
[30]L. Campos Venuti et al., Phys. Rev. Lett., 99, 060401 (2007)