Abstract
We investigate the Berry phase of a spin system in a q-deformed magnetic field. The Berry phase depends on parameter q and which causes the deformation of the Berry phase. When q ≠ 1, the parameter space for the spin-half particles in magnetic field is deformed and immovable at the point of φ = 0, π/2, π. The same Hamiltonian can also be constructed by q-deformed Lie-algebra and magnetic field.
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References
Aharonov Y., Anandan J.: Phase change during a cyclic quantum evolution. Phys. Rev. Lett. 58, 1593–1596 (1987)
Sjoqvist E., Pati A.K., Ekert A., Anandan J.S., Ericsson M., Oi D.K.L., Vedral V.: Geometric Phases for Mixed States in Interferometry. Phys. Rev. Lett. 85, 2845–2849 (2000)
Samuel J., Bhandari R.: General setting for Berry’s phase. Phys. Rev. Lett. 60, 2339–2342 (1988)
Tong D.M., Sjoqvist E., Kwek L.C., Oh C.H.: Kinematic approach to the mixed state geometric phase in nonunitary evolution. Phys. Rev. Lett. 93, 080405 (2004)
Wilczek F., Zee A.: Appearance of gauge structure in simple dynamical systems. Phys. Rev. Lett. 52, 2111–2114 (1984)
Berry M.V.: Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. Ser. A. 392, 45–57 (1984)
Simon B.: Holonomy, the quantum adiabatic theorem, and Berry’s phase. Phys. Rev. Lett. 51, 2167–2170 (1983)
Rohrlich, D.: Berry’s phase. arxiv. 0708.3749v1
Born M., Oppenheimer J.R.: Zur quantentheorie der molekeln. Annalen der Physik 84, 457–484 (1927)
Mead C.A., Truhlar D.G.: On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei. J. Chem. Phys. 70, 2284–2296 (1979)
Delacretaz G. et al.: Fractional quantization of molecular pseudorotation in Na3. Phys. Rev. Lett. 56, 2598–2601 (1986)
Harn F.S.: Berrys geometrical phase and the sequence of states in the Jahn–Teller effect. Phys. Rev. Lett. 58, 725–728 (1987)
Bohm A., Mostafazadeh A., Koizumi H., Niu Q., Appelt J., Wakerle G., Mehring M.: Deviation from Berrys adiabatic geometric phase in a 131Xe nuclear gyroscope. Phys. Rev. Lett. 73, 3921–3924 (1994)
Duan L.M., Cirac J.I., Zoller P.: Geometric manipulation of trapped ions for quantum computation. Science 292, 1695–1697 (2001)
Sorensen A., Molmer K.: Entanglement and quantum computation with ions in thermal motion. Phys. Rev. A. 62, 022311 (2000)
Leibfried D., DeMarco B., Meyer V., Lucas D., Barrett M., Britton J., Itano W.M., Jelenkovic B., Langer C., Rosenband T., Wineland D.J.: Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature (London) 422, 412–415 (2003)
Garcia-Ripoll J.J., Zoller P., Cirac J.I.: Speed optimized two-qubit gates with laser coherent control techniques for ion trap quantum computing. Phys. Rev. Lett. 91, 157901 (2003)
Staanum P., Drewsen M., Molmer K.: Geometric quantum gate for trapped ions based on optical dipole forces induced by Gaussian laser beams. Phys. Rev. A. 70, 052327 (2004)
Recati A., Calarco T., Zanardi P., Cirac J.I., Zoller P.: Holonomic quantum computation with neutral atoms. Phys. Rev. A. 66, 032309 (2002)
Unanyan R.G., Shore B.W., Bergmann K.: Laser-driven population transfer in four-level atoms: consequences of non- Abelian geometrical adiabatic phase factors. Phys. Rev. A. 59, 2910–2919 (1999)
Sun C.P., Li Y., Liu X.F.: Quasi-spin-wave quantum memories with a dynamical symmetry. Phys. Rev. Lett. 91, 147903 (2003)
Solinas P., Zanardi P., Zanghi N., Rossi F.: Semiconductor-based geometrical quantum gates. Phys. Rev. B. 67, 121307(R) (2003)
Carvalho A.R.R., Hope J.J.: Stabilizing entanglement by quantum-jump-based feedback. Phys. Rev. A. 76, 010301(R) (2007)
Jimbo M.: Aq-difference analogue of U(g) and the Yang–Baxter equation. Lett. Math. Phys. 10, 63–69 (1985)
Jimbo M.: A q-analogue of U(g(N+1)), Hecke algebra, and the Yang–Baxter equation. Lett. Math. Phys. 11, 247–252 (1985)
Jimbo M.: Quantum R matrix for the generalized Toda system. Commun. Math. Phys. 102, 537–547 (1986)
Drinfeld, V.G.: Quantum groups. In: Proc. ICM, Berkeley, CA, MSRI, pp. 798–820 (1986)
Macfarlane A.J.: Quantum groups, proceedings for the ICM, Berkeley. J. Phys. A. Math. Gen. 22, 4581–4588 (1989)
Zurong Yu: Some realization of the quantum algebra Uq(su(2)). J. Phys. A. Math. Gen. 24, L1321–L1325 (1991)
Sun C.-P., Fu H.-C.: The q-deformed boson realisation of the quantum group SU(n)q and its representations. J. Phys. A. Math. Gen. 22, L983–L986 (1989)
Fu L.-B., Liu J.: Adiabatic Berry phase in an atom-molecule conversion system. Ann. Phys. 325, 2425–2434 (2010)
Kulish P.P., Reshetikhin N.Yu.: Quantum linear problem for the sine-Gordon equation and higher representations. J. Sov. Math. 23, 2435–2441 (1983)
Drinfeld V.: Hopf algebras and the quantum Yang–Baxter equation. Sov. Math. Dokl. 32, 254–258 (1985)
Batchelor M.T., Yung C.M.: Q-deformations of quantum spin chains with exact valence-bond ground states. Int. J. Mod. Phys. B. 8, 3645–3654 (1994)
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Du, G., Xue, K., Wang, G. et al. The Berry phase subject to q-deformed magnetic field. Quantum Inf Process 12, 815–824 (2013). https://doi.org/10.1007/s11128-012-0420-9
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DOI: https://doi.org/10.1007/s11128-012-0420-9