Competing many-body interactions in systems of trapped ions

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 79, Issue 6, 2009, Pages

  Bermudez, A ^a   Porras, D ^a,b   Martin Delgado, M A ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

MANY-BODY INTERACTIONS; QUANTUM PHASE DIAGRAMS; QUANTUM PHASIS; SPIN COUPLINGS; SPIN HAMILTONIAN; SPIN INTERACTION; TRAPPED ION;

ELECTROMAGNETIC FIELD EFFECTS; MAGNETIC COUPLINGS; MAGNETIC FIELDS; PHASE DIAGRAMS; SPIN DYNAMICS;

IONS;

EID: 66749120781     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.79.060303     Document Type: Article

References (18)

1. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, Cambridge, 1999).
2. X. Wen, Quantum Field Theory of Many-body Systems (Oxford University Press, New York, 2004).
3. R. Feynman, Int. J. Theor. Phys. 21, 467 (1982). 10.1007/BF02650179
4. D. Porras and J. I. Cirac, Phys. Rev. Lett. 92, 207901 (2004). 10.1103/PhysRevLett.92.207901
5. A. Friedenauer, Nat. Phys. 4, 757 (2008). 10.1038/nphys1032
6. J. K. Pachos and M. B. Plenio, Phys. Rev. Lett. 93, 056402 (2004). 10.1103/PhysRevLett.93.056402
7. H. P. Büchler, A. Micheli, and P. Zoller, Nat. Phys. 3, 726 (2007). 10.1038/nphys678
8. J. Chiaverini and W. E. Lybarger, Jr., Phys. Rev. A 77, 022324 (2008). 10.1103/PhysRevA.77.022324
9. R. J. Clark, T. Lin, K. R. Brown, and I. L. Chuang, J. Appl. Phys. 105, 013114 (2009). 10.1063/1.3056227
10. D. Liebfried, Nature (London) 422, 412 (2003). 10.1038/nature01492
11. The use of off-resonant walking waves, instead of standing waves, presents the advantage that there is no need to control the position of the ion chain with respect to the applied wave.
12. C. Wunderlich, Laser Physics at the Limit (Springer, Heidelberg, 2001), p. 216.
13. There is also an error term proportional to the transverse magnetic field Herr =2ih jnα ξ jn α a nα † σjy +H.c. However, it gives a negligible contribution for the range of parameters that we are interested in h J2, J3, which leads to insignificant corrections of the order O (Fx6 / δx6).
14. f1 (ωα, δα, βα) = βα2 (ωα + δα) / δα3, f2 (ωα, δα, βα) = βα2 (ωα +3 δα /2) /2 δα3, f3 (ωα, δα, βα) =4 βα ωα (ωα - δα) / δα2 (2 ωα - δα) 2, f4 (ωα, δα, βα) =2 βα ωα4 / δα2 (ωα -2 δα) 2 (3 ωα -2 δα) 2.
15. In order to neglect the error term quadratic in phonon operators, the ion chain should be cooled down to n̄ <0.1, which does not require spectral resolution of the different modes (i.e., kB T βω).
16. X.-L. Deng, D. Porras, and J. I. Cirac, Phys. Rev. A 72, 063407 (2005). 10.1103/PhysRevA.72.063407
17. K. A. Penson, R. Jullien, and P. Pfeuty, Phys. Rev. B 26, 6334 (1982). 10.1103/PhysRevB.26.6334
18. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Rev. Mod. Phys. 75, 281 (2003). 10.1103/RevModPhys.75.281