RT Journal Article T1 Chirality quantum phase transition in the Dirac oscillator A1 Bermúdez, A. A1 Martin-Delgado Alcántara, Miguel Ángel A1 Luis Aina, Alfredo AB We study a relativistic spin-1/2 fermion subjected to a Dirac oscillator coupling and a constant magnetic field. An interplay between opposed chirality interactions culminates in the appearance of a relativistic quantum phase transition, which can be fully characterized. We obtain analytical expressions for the energy gap, order parameter, and canonical quantum fluctuations across the critical point. Moreover, we also discuss the effect of this phase transition on the statistics of the chiral bosonic ensemble, where its super-or sub-Poissonian nature can be controlled by means of external parameters. Finally, we study the entanglement properties between the degrees of freedom in the relativistic ground state, where an interesting transition between a biseparable and a genuinely tripartite entangled state occurs. PB American Physical Society SN 1050-2947 YR 2008 FD 2008-06-11 LK https://hdl.handle.net/20.500.14352/51471 UL https://hdl.handle.net/20.500.14352/51471 LA eng NO [1] S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, England, 2000).[2] N. Lambert, C. Emary, and T. Brandes, Phys. Rev. Lett. 92, 073602 (2004).[3] C. Emary and T. Brandes, Phys. Rev. Lett. 90, 044101 (2003).[4] C. C. Gerry, Phys. Rev. A 37, 3619 (1988).[5] C. C. Gerry and J. Kiefer, Phys. Rev. A 41, 27 (1990).[6] A. P. Hines, C. M. Dawson, R. H. McKenzie, and G. J. Milburn, Phys. Rev. A 70, 022303 (2004).[7] M. Moshinsky and A. Szczepaniak, J. Phys. A 22, L817 (1989).[8] D. Ito, K. Mori, and E. Carrieri, Nuovo Cimento A 51, 1119 (1967).[9] W. Greiner, Relativistic Quantum Mechanics: Wave Equations (Springer, Berlin, 2000).[10] A. Bermúdez, M. A. Martín-Delgado, and E. Solano, Phys. Rev. A 76, 041801(R) (2007).[11] A. Bermúdez, M. A. Martín-Delgado, and E. Solano, Phys. Rev. Lett. 99, 123602 (2007).[12] R. Banerjee and S. Gosh, J. Phys. A 31, L603 (1998).[13] M. M. Horta Barreira and C. Wotzasek, Phys. Rev. D 45, 1410 (1992).[14] G. V. Dunne, R. Jackiw, and C. A. Trugenberger, Phys. Rev. D 41, 661 (1990).[15] E. T. Jaynes and F. W. Cummings, Proc. IEEE 51, 89 (1963).[16] D. Leibfried, R. Blatt, C. Monroe, and D.Wineland, Rev. Mod. Phys. 75, 281 (2003).[17] Note that these creation-annihilation operators do not represent normal modes since they do not commute with each other, but rather fulfill… [18] P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer, Berlin, 2007).[19] S. M. Barnett and P. L. Knight, J. Opt. Soc. Am. B 2, 467 (1985).[20] A. Osterloh, L. Amico, G. Falci, and R. Fazio, Nature (London) 416, 608 (2002).[21] G. Vidal, J. I. Latorre, E. Rico, and A. Kitaev, Phys. Rev. Lett. 90, 227902 (2003).[22] M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).[23] A. Galindo and M. A. Martin-Delgado, Rev. Mod. Phys. 74, 347 (2002).[24] C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).[25] H. Casini, C. D. Fosco, and M. Huerta, J. Stat. Mech.: Theory Exp. (2005), P007.[26] P. Calabrese and J. Cardy, J. Stat. Mech.: Theory Exp. (2004), P06002.[27] L. Amico, R. Fazio, A. Osterloh, and V. Vedral, e-print arXiv:quant-ph/0703044.[28] M. B. Plenio and S. Virmani, Quantum Inf. Comput. 7, 1 (2007).[29] J. Eisert and M. B. Plenio, Int. J. Quantum Inf. 1, 479 (2003).[30] G. S. Agarwal, Phys. Rev. A 3, 828 (1971).[31] A. Serafini, F. Illuminati, and S. De Sienna, J. Phys. B 37, L21 (2004).[32] J. I. Cirac, A. S. Parkins, R. Blatt, and P. Zoller, Phys. Rev. Lett. 70, 556 (1993).[33] J. Janszky and Y. Y. Yushin, Opt. Commun. 59, 151 (1986).[34] D. J. Heinzen and D. J. Wineland, Phys. Rev. A 42, 2977 (1990).[35] R. J. Glauber, Phys. Rev. 130, 2529 (1963_; 131, 2766 (1963).[36] A. M. Perelomov, Commun. Math. Phys. 26, 222 (1972).[37] C. C. Gerry, J. Opt. Soc. Am. B 8, 685 (1991).[38] L. Gilles and P. L. Knight, J. Mod. Opt. 39, 1411 (1992). NO ©2008 The American Physical Society. We acknowledge financial support from Spanish MEC Project No. FIS2006-04885, Project No. CAM-UCM/910758 A.B. and M.A.M.D. and UCM Project No. PR1-A/07-15378 A.L. Additionally, we acknowledge support from a FPU MEC grant A.B., and ESF Science Programme No. INSTANS 2005–2010 M.A.M.D. NO Ministerio de Educación y Ciencia (MEC) NO Universidad Complutense de Madrid (UCM) NO Programa de Formación del Profesorado Universitario (FPU) NO European Science Foundation (ESF) Science Programme DS Docta Complutense RD 1 may 2024