Quantum-state reconstruction of atoms in optical lattices

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 1, 2000, Pages 114051-114054

  Zucchetti, A ^a   Wallentowitz, S ^a,b   Vogel, W ^a   Bigelow, N P ^b  

^a UNIVERSITY OF ROSTOCK   (Germany)

^b UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4244068595     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. D.T. Smithey, M. Beck, M.G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993); S. Schiller, G. Breitenbach, S.F. Pereira, T. Müller, and J. Mlynek, ibid. 77, 2933 (1996).
2. D.T. Smithey, M. Beck, M.G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993); S. Schiller, G. Breitenbach, S.F. Pereira, T. Müller, and J. Mlynek, ibid. 77, 2933 (1996).
3. T.J. Dunn, I.A. Walmsley, and S. Mukamel, Phys. Rev. Lett. 74, 884 (1995).
4. D. Leibfried, D.M. Meekhof, B.E. King, C. Monroe, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 77, 4281 (1996).
5. Ch. Kurtsiefer, T. Pfau, and J. Mlynek, Nature (London) 386, 150 (1997).
6. K. Vogel and H. Risken, Phys. Rev. A 40, 2847 (1989).
7. S. Wallentowitz and W. Vogel, Phys. Rev. A 53, 4528 (1996); K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 76, 4344 (1996); L.G. Lutterbach and L. Davidovich, ibid. 78, 2547 (1997).
8. S. Wallentowitz and W. Vogel, Phys. Rev. A 53, 4528 (1996); K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 76, 4344 (1996); L.G. Lutterbach and L. Davidovich, ibid. 78, 2547 (1997).
9. S. Wallentowitz and W. Vogel, Phys. Rev. A 53, 4528 (1996); K. Banaszek and K. Wódkiewicz, Phys. Rev. Lett. 76, 4344 (1996); L.G. Lutterbach and L. Davidovich, ibid. 78, 2547 (1997).
10. D.-G. Welsch, W. Vogel, and T. Opatrny, in Progress in Optics, edited by E. Wolf (Elsevier Science, Amsterdam, 1999), Vol. 39, pp. 63-211.
11. A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Lawall, F. Bardou, B. Saubamea, K. Shimizu, M. Leduc, A. Aspect, and C. Cohen-Tannoudji, ibid. 73, 1915 (1994); J. Lawall, S. Kulin, B. Saubamea, N. Bigelow, M. Leduc, and C. Cohen- Tannoudji, ibid. 75, 4194 (1995).
12. A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Lawall, F. Bardou, B. Saubamea, K. Shimizu, M. Leduc, A. Aspect, and C. Cohen-Tannoudji, ibid. 73, 1915 (1994); J. Lawall, S. Kulin, B. Saubamea, N. Bigelow, M. Leduc, and C. Cohen- Tannoudji, ibid. 75, 4194 (1995).
13. A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, Phys. Rev. Lett. 61, 826 (1988); J. Lawall, F. Bardou, B. Saubamea, K. Shimizu, M. Leduc, A. Aspect, and C. Cohen-Tannoudji, ibid. 73, 1915 (1994); J. Lawall, S. Kulin, B. Saubamea, N. Bigelow, M. Leduc, and C. Cohen-Tannoudji, ibid. 75, 4194 (1995).
14. M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992); N. Davidson, H.-J. Lee, M. Kasevich, and S. Chu, ibid. 72, 3158 (1994).
15. M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992); N. Davidson, H.-J. Lee, M. Kasevich, and S. Chu, ibid. 72, 3158 (1994).
16. A. Görlitz, M. Weidenmüller, T.W. Hänsch, and A. Hemmerich, Phys. Rev. Lett. 78, 2096 (1997); G. Raithel, G. Birkl, W.D. Phillips, and S.L. Rolston, ibid. 78, 2928 (1997).
17. A. Görlitz, M. Weidenmüller, T.W. Hänsch, and A. Hemmerich, Phys. Rev. Lett. 78, 2096 (1997); G. Raithel, G. Birkl, W.D. Phillips, and S.L. Rolston, ibid. 78, 2928 (1997).
18. P. Rudy, R. Ejnisman, and N.P. Bigelow, Phys. Rev. Lett. 78, 4906 (1997).
19. A. Kastberg, W.D. Phillips, S.L. Rolston, and R.J.C. Spreeuw, Phys. Rev. Lett. 74, 1542 (1995); T. Esslinger, F. Sander, A. Hemmerich, H. Ritsch, M. Weidemüller, and T.W. Hänsch, Opt. Lett. 21, 991 (1996).
20. A. Kastberg, W.D. Phillips, S.L. Rolston, and R.J.C. Spreeuw, Phys. Rev. Lett. 74, 1542 (1995); T. Esslinger, F. Sander, A. Hemmerich, H. Ritsch, M. Weidemüller, and T.W. Hänsch, Opt. Lett. 21, 991 (1996).
21. H. Stecher, H. Ritsch, P. Zoller, F. Sander, T. Esslinger, and T.W. Hänsch, Phys. Rev. A 55, 545 (1997).
22. R. Taieb, R. Dum, J.I. Cirac, P. Marte, and P. Zoller, Phys. Rev. A 49, 4876 (1994); B.P. Anderson, T.L. Gustavson, and M.A. Kasevich, ibid. 53, R3727 (1996); T. Müller-Seydlitz, M. Hartl, B. Brezger, H. Hansel, C. Keller, A. Schnetz, R.J.C. Spreeuw, T. Pfau, and J. Mlynek, Phys. Rev. Lett. 78, 1038 (1997); D.L. Haycock, S.E. Hamann, G. Klose, and P.S. Jessen, Phys. Rev. A 55, R3991 (1997).
23. R. Taieb, R. Dum, J.I. Cirac, P. Marte, and P. Zoller, Phys. Rev. A 49, 4876 (1994); B.P. Anderson, T.L. Gustavson, and M.A. Kasevich, ibid. 53, R3727 (1996); T. Müller-Seydlitz, M. Hartl, B. Brezger, H. Hansel, C. Keller, A. Schnetz, R.J.C. Spreeuw, T. Pfau, and J. Mlynek, Phys. Rev. Lett. 78, 1038 (1997); D.L. Haycock, S.E. Hamann, G. Klose, and P.S. Jessen, Phys. Rev. A 55, R3991 (1997).
24. R. Taieb, R. Dum, J.I. Cirac, P. Marte, and P. Zoller, Phys. Rev. A 49, 4876 (1994); B.P. Anderson, T.L. Gustavson, and M.A. Kasevich, ibid. 53, R3727 (1996); T. Müller-Seydlitz, M. Hartl, B. Brezger, H. Hansel, C. Keller, A. Schnetz, R.J.C. Spreeuw, T. Pfau, and J. Mlynek, Phys. Rev. Lett. 78, 1038 (1997); D.L. Haycock, S.E. Hamann, G. Klose, and P.S. Jessen, Phys. Rev. A 55, R3991 (1997).
25. R. Taieb, R. Dum, J.I. Cirac, P. Marte, and P. Zoller, Phys. Rev. A 49, 4876 (1994); B.P. Anderson, T.L. Gustavson, and M.A. Kasevich, ibid. 53, R3727 (1996); T. Müller-Seydlitz, M. Hartl, B. Brezger, H. Hansel, C. Keller, A. Schnetz, R.J.C. Spreeuw, T. Pfau, and J. Mlynek, Phys. Rev. Lett. 78, 1038 (1997); D.L. Haycock, S.E. Hamann, G. Klose, and P.S. Jessen, Phys. Rev. A 55, R3991 (1997).
26. n(ξ, τ) remains unchanged during the further free evolution, which is necessary to apply the adiabatic measurement.
27. In the harmonic case for τ=0 only the real part of the density matrix determines the band populations. In order to reconstruct the complete density matrix, an additional measurement with a different time delay has to be performed, where also the imaginary parts of the density matrix elements are contained in the populations.
28. In Ref. [13] the populations of at least 15 bands could be resolved with 200 measurements, so that for the full quantum-state reconstruction approximately 4000 measurements are needed.