Abstract

The magnetization and lifetimes of atoms in gray optical lattices exhibit modulations as functions of an applied B field that are attributed to tunneling resonances between neighboring lattice wells. Expanding on previous observations, we show how these modulations depend on well depth, and we derive spin temperatures for the system. A band-structure-based model and quantum Monte Carlo wave-function simulations are used to explain these results. We predict subrecoil structures in the velocity distributions; these structures undergo systematic variations when the applied magnetic field is varied. Dramatically different behaviors for bosonic and fermionic spin systems are found and explained.

© 2003 Optical Society of America

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  1. P. S. Jessen and I. H. Deutsch, “Optical lattices,” Adv. At. Mol. Opt. Phys. 37, 95–138 (1996).
    [CrossRef]
  2. K. I. Petsas, J.-Y. Courtois, and G. Grynberg, “Temperature and magnetism of gray optical lattices,” Phys. Rev. A 53, 2533–2538 (1996).
    [CrossRef] [PubMed]
  3. D. L. Haycock, P. M. Alsing, I. H. Deutsch, J. Grondalski, and P. S. Jessen, “Mesoscopic quantum coherence in an optical lattice,” Phys. Rev. Lett. 85, 3365–3368 (2000).
    [CrossRef] [PubMed]
  4. W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
    [CrossRef] [PubMed]
  5. D. A. Steck, W. H. Oskay, and M. G. Raizen, “Fluctuations and decoherence in chaos-assisted tunneling,” Phys. Rev. Lett. 88, 120406(1–4) (2002).
    [CrossRef] [PubMed]
  6. B. K. Teo, J. R. Guest, and G. Raithel, “Tunneling resonances and coherence in an optical lattice,” Phys. Rev. Lett. 88, 173001(1-4) (2002).
    [CrossRef] [PubMed]
  7. J. Guo and P. R. Berman, “One-dimensional laser cooling with linearly polarized fields,” Phys. Rev. A 48, 3225–3232 (1993).
    [CrossRef] [PubMed]
  8. A. Hemmerich, M. Weidemüller, T. Esslinger, C. Zimmermann, and T. Hänsch, “Trapping atoms in a dark optical lattice,” Phys. Rev. Lett. 75, 37–40 (1995).
    [CrossRef] [PubMed]
  9. G. Grynberg and J.-Y. Courtois, “Proposal for a magneto-optical lattice for trapping atoms in nearly dark states,” Europhys. Lett. 27, 41–46 (1994).
    [CrossRef]
  10. S. K. Dutta and G. Raithel, “Tunnelling and the Born–Oppenheimer approximation in optical lattices,” J. Opt. B 2, 651–658 (2000).
    [CrossRef]
  11. R. Dum and M. Olshanni, “Gauge structures in atom–laser interaction: Bloch oscillations in a dark lattice,” Phys. Rev. Lett. 76, 1788–1791 (1996).
    [CrossRef] [PubMed]
  12. S. K. Dutta, B. K. Teo, and G. Raithel, “Tunneling dynamics and gauge potentials in optical lattices,” Phys. Rev. Lett. 83, 1934–1937 (1999).
    [CrossRef]
  13. D. R. Meacher, S. Guibal, C. Mennerat, J.-Y. Courtois, K. I. Petsas, and G. Grynberg, “Paramagnetism in a cesium optical lattice,” Phys. Rev. Lett. 74, 1958–1961 (1995).
    [CrossRef] [PubMed]
  14. G. Raithel, W. D. Phillips, and S. L. Rolston, “Magnetization and spin-flip dynamics of atoms in optical lattices,” Phys. Rev. A 58, R2660–R2663 (1998).
    [CrossRef]
  15. A. Hemmerich, C. Zimmerman, and T. W. Hänsch, “Sub-kHz Rayleigh resonance in a cubic atomic crystal,” Europhys. Lett. 22, 89–94 (1993).
    [CrossRef]
  16. J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
    [CrossRef] [PubMed]
  17. K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
    [CrossRef]
  18. R. Kosloff, “Time-dependent quantum-mechanical methods for molecular dynamics,” J. Phys. Chem. 92, 2087–2100 (1988).
    [CrossRef]
  19. Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
    [CrossRef]
  20. I. H. Deutsch, P. M. Alsing, J. Grondalski, S. Ghose, D. L. Haycock, and P. S. Jessen, “Quantum transport in magneto-optical double-potential well,” J. Opt. B 2, 633–644 (2000).
    [CrossRef]
  21. The tunneling frequency actually depends on quasi-momentum q. Experimental observations of the tunneling, as explained in Ref. 12, yield a frequency that corresponds to the maximum band splitting. In Fig. 3(c) we show the maximum band splittings at the centers of the respective tunneling resonances.
  22. A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
    [CrossRef] [PubMed]

2002

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Fluctuations and decoherence in chaos-assisted tunneling,” Phys. Rev. Lett. 88, 120406(1–4) (2002).
[CrossRef] [PubMed]

B. K. Teo, J. R. Guest, and G. Raithel, “Tunneling resonances and coherence in an optical lattice,” Phys. Rev. Lett. 88, 173001(1-4) (2002).
[CrossRef] [PubMed]

2001

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

2000

D. L. Haycock, P. M. Alsing, I. H. Deutsch, J. Grondalski, and P. S. Jessen, “Mesoscopic quantum coherence in an optical lattice,” Phys. Rev. Lett. 85, 3365–3368 (2000).
[CrossRef] [PubMed]

S. K. Dutta and G. Raithel, “Tunnelling and the Born–Oppenheimer approximation in optical lattices,” J. Opt. B 2, 651–658 (2000).
[CrossRef]

I. H. Deutsch, P. M. Alsing, J. Grondalski, S. Ghose, D. L. Haycock, and P. S. Jessen, “Quantum transport in magneto-optical double-potential well,” J. Opt. B 2, 633–644 (2000).
[CrossRef]

1999

S. K. Dutta, B. K. Teo, and G. Raithel, “Tunneling dynamics and gauge potentials in optical lattices,” Phys. Rev. Lett. 83, 1934–1937 (1999).
[CrossRef]

1998

G. Raithel, W. D. Phillips, and S. L. Rolston, “Magnetization and spin-flip dynamics of atoms in optical lattices,” Phys. Rev. A 58, R2660–R2663 (1998).
[CrossRef]

1996

R. Dum and M. Olshanni, “Gauge structures in atom–laser interaction: Bloch oscillations in a dark lattice,” Phys. Rev. Lett. 76, 1788–1791 (1996).
[CrossRef] [PubMed]

P. S. Jessen and I. H. Deutsch, “Optical lattices,” Adv. At. Mol. Opt. Phys. 37, 95–138 (1996).
[CrossRef]

K. I. Petsas, J.-Y. Courtois, and G. Grynberg, “Temperature and magnetism of gray optical lattices,” Phys. Rev. A 53, 2533–2538 (1996).
[CrossRef] [PubMed]

1995

A. Hemmerich, M. Weidemüller, T. Esslinger, C. Zimmermann, and T. Hänsch, “Trapping atoms in a dark optical lattice,” Phys. Rev. Lett. 75, 37–40 (1995).
[CrossRef] [PubMed]

D. R. Meacher, S. Guibal, C. Mennerat, J.-Y. Courtois, K. I. Petsas, and G. Grynberg, “Paramagnetism in a cesium optical lattice,” Phys. Rev. Lett. 74, 1958–1961 (1995).
[CrossRef] [PubMed]

1994

G. Grynberg and J.-Y. Courtois, “Proposal for a magneto-optical lattice for trapping atoms in nearly dark states,” Europhys. Lett. 27, 41–46 (1994).
[CrossRef]

1993

J. Guo and P. R. Berman, “One-dimensional laser cooling with linearly polarized fields,” Phys. Rev. A 48, 3225–3232 (1993).
[CrossRef] [PubMed]

A. Hemmerich, C. Zimmerman, and T. W. Hänsch, “Sub-kHz Rayleigh resonance in a cubic atomic crystal,” Europhys. Lett. 22, 89–94 (1993).
[CrossRef]

K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
[CrossRef]

1992

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

1991

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

1988

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

R. Kosloff, “Time-dependent quantum-mechanical methods for molecular dynamics,” J. Phys. Chem. 92, 2087–2100 (1988).
[CrossRef]

Alsing, P. M.

D. L. Haycock, P. M. Alsing, I. H. Deutsch, J. Grondalski, and P. S. Jessen, “Mesoscopic quantum coherence in an optical lattice,” Phys. Rev. Lett. 85, 3365–3368 (2000).
[CrossRef] [PubMed]

I. H. Deutsch, P. M. Alsing, J. Grondalski, S. Ghose, D. L. Haycock, and P. S. Jessen, “Quantum transport in magneto-optical double-potential well,” J. Opt. B 2, 633–644 (2000).
[CrossRef]

Arimondo, E.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Aspect, A.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Berman, P. R.

J. Guo and P. R. Berman, “One-dimensional laser cooling with linearly polarized fields,” Phys. Rev. A 48, 3225–3232 (1993).
[CrossRef] [PubMed]

Browaeys, A.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

Castin, Y.

K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
[CrossRef]

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

Cohen-Tannoudji, C.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Courtois, J.-Y.

K. I. Petsas, J.-Y. Courtois, and G. Grynberg, “Temperature and magnetism of gray optical lattices,” Phys. Rev. A 53, 2533–2538 (1996).
[CrossRef] [PubMed]

D. R. Meacher, S. Guibal, C. Mennerat, J.-Y. Courtois, K. I. Petsas, and G. Grynberg, “Paramagnetism in a cesium optical lattice,” Phys. Rev. Lett. 74, 1958–1961 (1995).
[CrossRef] [PubMed]

G. Grynberg and J.-Y. Courtois, “Proposal for a magneto-optical lattice for trapping atoms in nearly dark states,” Europhys. Lett. 27, 41–46 (1994).
[CrossRef]

Dalibard, J.

K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
[CrossRef]

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

Deutsch, I. H.

I. H. Deutsch, P. M. Alsing, J. Grondalski, S. Ghose, D. L. Haycock, and P. S. Jessen, “Quantum transport in magneto-optical double-potential well,” J. Opt. B 2, 633–644 (2000).
[CrossRef]

D. L. Haycock, P. M. Alsing, I. H. Deutsch, J. Grondalski, and P. S. Jessen, “Mesoscopic quantum coherence in an optical lattice,” Phys. Rev. Lett. 85, 3365–3368 (2000).
[CrossRef] [PubMed]

P. S. Jessen and I. H. Deutsch, “Optical lattices,” Adv. At. Mol. Opt. Phys. 37, 95–138 (1996).
[CrossRef]

Dum, R.

R. Dum and M. Olshanni, “Gauge structures in atom–laser interaction: Bloch oscillations in a dark lattice,” Phys. Rev. Lett. 76, 1788–1791 (1996).
[CrossRef] [PubMed]

Dutta, S. K.

S. K. Dutta and G. Raithel, “Tunnelling and the Born–Oppenheimer approximation in optical lattices,” J. Opt. B 2, 651–658 (2000).
[CrossRef]

S. K. Dutta, B. K. Teo, and G. Raithel, “Tunneling dynamics and gauge potentials in optical lattices,” Phys. Rev. Lett. 83, 1934–1937 (1999).
[CrossRef]

Esslinger, T.

A. Hemmerich, M. Weidemüller, T. Esslinger, C. Zimmermann, and T. Hänsch, “Trapping atoms in a dark optical lattice,” Phys. Rev. Lett. 75, 37–40 (1995).
[CrossRef] [PubMed]

Ghose, S.

I. H. Deutsch, P. M. Alsing, J. Grondalski, S. Ghose, D. L. Haycock, and P. S. Jessen, “Quantum transport in magneto-optical double-potential well,” J. Opt. B 2, 633–644 (2000).
[CrossRef]

Grondalski, J.

I. H. Deutsch, P. M. Alsing, J. Grondalski, S. Ghose, D. L. Haycock, and P. S. Jessen, “Quantum transport in magneto-optical double-potential well,” J. Opt. B 2, 633–644 (2000).
[CrossRef]

D. L. Haycock, P. M. Alsing, I. H. Deutsch, J. Grondalski, and P. S. Jessen, “Mesoscopic quantum coherence in an optical lattice,” Phys. Rev. Lett. 85, 3365–3368 (2000).
[CrossRef] [PubMed]

Grynberg, G.

K. I. Petsas, J.-Y. Courtois, and G. Grynberg, “Temperature and magnetism of gray optical lattices,” Phys. Rev. A 53, 2533–2538 (1996).
[CrossRef] [PubMed]

D. R. Meacher, S. Guibal, C. Mennerat, J.-Y. Courtois, K. I. Petsas, and G. Grynberg, “Paramagnetism in a cesium optical lattice,” Phys. Rev. Lett. 74, 1958–1961 (1995).
[CrossRef] [PubMed]

G. Grynberg and J.-Y. Courtois, “Proposal for a magneto-optical lattice for trapping atoms in nearly dark states,” Europhys. Lett. 27, 41–46 (1994).
[CrossRef]

Guest, J. R.

B. K. Teo, J. R. Guest, and G. Raithel, “Tunneling resonances and coherence in an optical lattice,” Phys. Rev. Lett. 88, 173001(1-4) (2002).
[CrossRef] [PubMed]

Guibal, S.

D. R. Meacher, S. Guibal, C. Mennerat, J.-Y. Courtois, K. I. Petsas, and G. Grynberg, “Paramagnetism in a cesium optical lattice,” Phys. Rev. Lett. 74, 1958–1961 (1995).
[CrossRef] [PubMed]

Guo, J.

J. Guo and P. R. Berman, “One-dimensional laser cooling with linearly polarized fields,” Phys. Rev. A 48, 3225–3232 (1993).
[CrossRef] [PubMed]

Häffner, H.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

Hänsch, T.

A. Hemmerich, M. Weidemüller, T. Esslinger, C. Zimmermann, and T. Hänsch, “Trapping atoms in a dark optical lattice,” Phys. Rev. Lett. 75, 37–40 (1995).
[CrossRef] [PubMed]

Hänsch, T. W.

A. Hemmerich, C. Zimmerman, and T. W. Hänsch, “Sub-kHz Rayleigh resonance in a cubic atomic crystal,” Europhys. Lett. 22, 89–94 (1993).
[CrossRef]

Haycock, D. L.

I. H. Deutsch, P. M. Alsing, J. Grondalski, S. Ghose, D. L. Haycock, and P. S. Jessen, “Quantum transport in magneto-optical double-potential well,” J. Opt. B 2, 633–644 (2000).
[CrossRef]

D. L. Haycock, P. M. Alsing, I. H. Deutsch, J. Grondalski, and P. S. Jessen, “Mesoscopic quantum coherence in an optical lattice,” Phys. Rev. Lett. 85, 3365–3368 (2000).
[CrossRef] [PubMed]

Heckenberg, N. R.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

Helmerson, K.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

Hemmerich, A.

A. Hemmerich, M. Weidemüller, T. Esslinger, C. Zimmermann, and T. Hänsch, “Trapping atoms in a dark optical lattice,” Phys. Rev. Lett. 75, 37–40 (1995).
[CrossRef] [PubMed]

A. Hemmerich, C. Zimmerman, and T. W. Hänsch, “Sub-kHz Rayleigh resonance in a cubic atomic crystal,” Europhys. Lett. 22, 89–94 (1993).
[CrossRef]

Hensinger, W. K.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

Jessen, P. S.

D. L. Haycock, P. M. Alsing, I. H. Deutsch, J. Grondalski, and P. S. Jessen, “Mesoscopic quantum coherence in an optical lattice,” Phys. Rev. Lett. 85, 3365–3368 (2000).
[CrossRef] [PubMed]

I. H. Deutsch, P. M. Alsing, J. Grondalski, S. Ghose, D. L. Haycock, and P. S. Jessen, “Quantum transport in magneto-optical double-potential well,” J. Opt. B 2, 633–644 (2000).
[CrossRef]

P. S. Jessen and I. H. Deutsch, “Optical lattices,” Adv. At. Mol. Opt. Phys. 37, 95–138 (1996).
[CrossRef]

Kaiser, R.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Kosloff, R.

R. Kosloff, “Time-dependent quantum-mechanical methods for molecular dynamics,” J. Phys. Chem. 92, 2087–2100 (1988).
[CrossRef]

McKenzie, C.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

Meacher, D. R.

D. R. Meacher, S. Guibal, C. Mennerat, J.-Y. Courtois, K. I. Petsas, and G. Grynberg, “Paramagnetism in a cesium optical lattice,” Phys. Rev. Lett. 74, 1958–1961 (1995).
[CrossRef] [PubMed]

Mennerat, C.

D. R. Meacher, S. Guibal, C. Mennerat, J.-Y. Courtois, K. I. Petsas, and G. Grynberg, “Paramagnetism in a cesium optical lattice,” Phys. Rev. Lett. 74, 1958–1961 (1995).
[CrossRef] [PubMed]

Milburn, G. J.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

Mølmer, K.

K. Mølmer, Y. Castin, and J. Dalibard, “Monte Carlo wave-function method in quantum optics,” J. Opt. Soc. Am. B 10, 524–538 (1993).
[CrossRef]

J. Dalibard, Y. Castin, and K. Mølmer, “Wave-function approach to dissipative processes in quantum optics,” Phys. Rev. Lett. 68, 580–583 (1992).
[CrossRef] [PubMed]

Olshanni, M.

R. Dum and M. Olshanni, “Gauge structures in atom–laser interaction: Bloch oscillations in a dark lattice,” Phys. Rev. Lett. 76, 1788–1791 (1996).
[CrossRef] [PubMed]

Oskay, W. H.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Fluctuations and decoherence in chaos-assisted tunneling,” Phys. Rev. Lett. 88, 120406(1–4) (2002).
[CrossRef] [PubMed]

Petsas, K. I.

K. I. Petsas, J.-Y. Courtois, and G. Grynberg, “Temperature and magnetism of gray optical lattices,” Phys. Rev. A 53, 2533–2538 (1996).
[CrossRef] [PubMed]

D. R. Meacher, S. Guibal, C. Mennerat, J.-Y. Courtois, K. I. Petsas, and G. Grynberg, “Paramagnetism in a cesium optical lattice,” Phys. Rev. Lett. 74, 1958–1961 (1995).
[CrossRef] [PubMed]

Phillips, W. D.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

G. Raithel, W. D. Phillips, and S. L. Rolston, “Magnetization and spin-flip dynamics of atoms in optical lattices,” Phys. Rev. A 58, R2660–R2663 (1998).
[CrossRef]

Raithel, G.

B. K. Teo, J. R. Guest, and G. Raithel, “Tunneling resonances and coherence in an optical lattice,” Phys. Rev. Lett. 88, 173001(1-4) (2002).
[CrossRef] [PubMed]

S. K. Dutta and G. Raithel, “Tunnelling and the Born–Oppenheimer approximation in optical lattices,” J. Opt. B 2, 651–658 (2000).
[CrossRef]

S. K. Dutta, B. K. Teo, and G. Raithel, “Tunneling dynamics and gauge potentials in optical lattices,” Phys. Rev. Lett. 83, 1934–1937 (1999).
[CrossRef]

G. Raithel, W. D. Phillips, and S. L. Rolston, “Magnetization and spin-flip dynamics of atoms in optical lattices,” Phys. Rev. A 58, R2660–R2663 (1998).
[CrossRef]

Raizen, M. G.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Fluctuations and decoherence in chaos-assisted tunneling,” Phys. Rev. Lett. 88, 120406(1–4) (2002).
[CrossRef] [PubMed]

Rolston, S. L.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

G. Raithel, W. D. Phillips, and S. L. Rolston, “Magnetization and spin-flip dynamics of atoms in optical lattices,” Phys. Rev. A 58, R2660–R2663 (1998).
[CrossRef]

Rubinsztein-Dunlop, H.

W. K. Hensinger, H. Häffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, “Dynamical tunneling of ultracold atoms,” Nature 412, 52–55 (2001).
[CrossRef] [PubMed]

Steck, D. A.

D. A. Steck, W. H. Oskay, and M. G. Raizen, “Fluctuations and decoherence in chaos-assisted tunneling,” Phys. Rev. Lett. 88, 120406(1–4) (2002).
[CrossRef] [PubMed]

Teo, B. K.

B. K. Teo, J. R. Guest, and G. Raithel, “Tunneling resonances and coherence in an optical lattice,” Phys. Rev. Lett. 88, 173001(1-4) (2002).
[CrossRef] [PubMed]

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Other

The tunneling frequency actually depends on quasi-momentum q. Experimental observations of the tunneling, as explained in Ref. 12, yield a frequency that corresponds to the maximum band splitting. In Fig. 3(c) we show the maximum band splittings at the centers of the respective tunneling resonances.

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Figures (9)

Fig. 1
Fig. 1

B dependence of magnetization mF and area density ntot of 87Rb atoms in a linlin gray optical lattice (I=6.3 mW/cm2) operated on the D1 line. The transverse magnetic field is 0. mF (solid curves) and ntot (dotted curves) are measured (a) in steady state and (b) after development for 600 μs without the repumping beam.

Fig. 2
Fig. 2

(a) Magnetization mF as a function of B for I=4.0, 6.3, 9.4 mW/cm2. (b) dmF/dB shows the modulations in the magnetization more readily; tunneling resonances correspond to the minima of the traces (offset for clarity). The vertical lines mark the second tunneling resonance as counted from B=0. (c) Spin temperature TS as defined in the text versus B. (d) Energy spacing ΔE=2μBΔB between adjacent tunneling resonances in units of the single-photon recoil energy ER obtained from spacings ΔB of the modulations in (b). (e) Spin temperature TSo at B=0 (filled circles), average spin temperature TSa as defined in text (open circles), and theoretical kinetic temperatures (squares) versus lattice intensity for B=0.

Fig. 3
Fig. 3

(a) Adiabatic lattice potentials (top) and band structure (bottom) for a linlin optical lattice operated on the D1 line of a hypothetical alkali atom with parameters as in 85Rb, except that the hyperfine quantum number is F=2 (instead of F=3 in the real atom). The single-beam lattice intensity is 6 mW/cm2; the saturation intensity is 1.6 mW/cm2; linewidth Γ=2π×6 MHz, the lattice detuning with respect to the FF transition is 6Γ, and the upper-state hyperfine splitting is 60Γ. The magnetic field is zero. Energies are in units of the single-photon recoil energy ER. (b) Same as (a), except that we use F=5. (c) Tunneling frequency versus F for the 0–0 (squares) and the 0–1 (triangles) tunneling resonances in units of the recoil frequency (ER/h=3.7 kHz). For the 0–0 tunneling resonance we also show tunneling frequencies versus F obtained under the assumption of adiabatic motion on the LAP (+) and on the sum of the LAP and its gauge potential (×). The average decay rates (circles) are also shown.  

Fig. 4
Fig. 4

Exception values of magnetization mF (top) and lifetime 〈τ〉 (bottom) of atoms in gray optical lattices versus longitudinal magnetic field B for hyperfine quantum numbers F ranging from 1 to 6, obtained from the BSBM. The lattice parameters are the same as in Fig. 3. At the top, dips in mF below the dotted line that marks mF=0 indicate antiparamagnetic behavior.

Fig. 5
Fig. 5

Momentum distributions obtained from the BSBM for longitudinal magnetic fields B ranging from 0 to 40 mG. The darker the color, the higher the probability. The transverse magnetic field is zero. The lattice is a linlin gray lattice operated on the D1 line of a hypothetical alkali atom with parameters as in 85Rb, except the hyperfine quantum number F. The lattice parameters are the same as in Fig. 3.

Fig. 6
Fig. 6

Verification of BSBM calculation by QMCWF simulations for a gray optical lattice on the D1 transition of 87Rb. The single-beam lattice intensity is 6.3 mW/cm2, and the lattice detuning with respect to the F=2F=2 transition is 6Γ. Density plots of momentum distributions for longitudinal magnetic fields B ranging from 0 to 32 mG are shown for the BSBM and for QMCWF results (a) after 1 ms of laser cooling and (b) after an additional 600 μs of repumper-free evolution, during which the less-cold atoms decay into the F=1 ground state (of order 50% of all atoms decay). The momentum distribution of the atoms remaining in the F=2 state is shown.

Fig. 7
Fig. 7

Verification of BSBM calculation by QMCWF simulations for a gray optical lattice on the D1 transition of 85Rb. The single-beam lattice intensity is 6 mW/cm2, and the lattice detuning with respect to the F=3F=3 transition is 6Γ. Density plots of momentum distributions for longitudinal magnetic fields B ranging from 0 to 40 mG are shown for the BSBM and for QMCWF results (a) after 1 ms of laser cooling and (b) after an additional 600 μs of repumper-free evolution. The momentum distribution of the atoms remaining in the F=3 state is shown.  

Fig. 8
Fig. 8

Lowest adiabatic potentials (dashed curves, lower axes) for 87Rb [(a), (b) F=2]; for 85Rb [(c), (d) F=3]; and for a fermionic model atom [(e), (f ) F=2.5] for the indicated values of B. The lowest adiabatic potentials (dashed curves) and the sums of the lowest adiabatic potentials and the gauge potentials (bold solid curves) are plotted versus position (lower axes). The lowest lattice bands (light solid curves) are plotted versus the quasi-momentum (upper axes). In all cases the lattice intensity is 6.3 mW/cm2, the saturation intensity is 1.6 mW/cm2, the lattice detuning with respect to the FF transition is 6Γ, and Γ=2π×6 MHz. The upper-state hyperfine structure splittings are 138 Γ for 87Rb, 60 Γ for 85Rb, and ∞ for the fermionic case.

Fig. 9
Fig. 9

Magnetic behavior of the one-dimensional linlin fermionic gray optical lattice. The lattice is operated on the D1 line of a hypothetical alkali atom with parameters as for 85Rb, except that the hyperfine quantum number is F=3.5. The lattice detuning with respect to the FF transition is 6Γ, and the upper-state hyperfine splitting is 60Γ. The magnetization curve (left) and the corresponding momentum distributions (right) obtained from the BSBM are shown.

Tables (1)

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Table 1 Intensity Dependence of Temperatures and Modulation Spacings a

Equations (8)

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n+=-2IsatλΓhc [ln(t+)-115ln(t-)],
n-=-2IsatλΓhc [ln(t-)-115ln(t+)],
mF=Fn+-n-n++n-=167ln(t+)-ln(t-)ln(t+)+ln(t-),
ntot=n++n-=-14152IsatλΓhc [ln(t+)+ln(t-)].
n+n-=exp-2μBBkBTS.
TS(B)=-2μBBkBmF,
mF=n,q m¯n,qγn,q-1n,q γn,q-1,
τ=n,q γn,q-2n,q γn,q-1.

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