Abstract

We propose a new method to create an asymmetric two-dimensional magnetic lattice which exhibits magnetic band gap structure similar to semiconductor devices. The quantum device is assumed to host bound states of collective excitations formed in a magnetically trapped quantum degenerate gas of ultracold atoms such as a Bose-Einstein condensate (BEC) or a degenerate Fermi gas. A theoretical framework is established to describe possible realization of the exciton-Mott to discharging Josephson states oscillations in which the adiabatically controlled oscillations induce ac and dc Josephson atomic currents where this effect can be used to transfer n Josephson qubits across the asymmetric two-dimensional magnetic lattice. We consider second-quantized Hamiltonians to describe the Mott insulator state and the coherence of multiple tunneling between adjacent magnetic lattice sites where we derive the self consistent non-linear Schrödinger equation with a proper field operator to describe the exciton Mott quantum phase transition via the induced Josephson atomic current across the n magnetic bands.

© 2009 Optical Society of America

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  9. Y. Shin, G.-B. Jo, M. Saba, T. A. Pasquini, W. Ketterle, and D. E. Pritchard, "Optical weak link between two spatially Separated Bose-Einstein Condensates," Phys. Rev. Lett. 95, 170402 (2005).
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  10. M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, "Direct observation of tunneling and nonlinear self-trapping in a single Bosonic Josephson junction," Phys. Rev. Lett. 95, 010402 (2005).
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  21. J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, "Spin domains in ground state spinor Bose-Einstein condensates," Nature 396, 345 (1998).
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  27. S. Ghanbari, P. B. Blakie, P. Hannaford, and T. D. Kien, "Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice," Eur. Phys. J. B 70305 (2009).
    [CrossRef]
  28. J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, "Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate," Phys. Rev. A 59, R31 (1999).
    [CrossRef]
  29. S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose- Einstein condensates: Josephson effects, p oscillations, and macroscopic quantum self-trapping," Phys. Rev. A 59, 620 (1999).
    [CrossRef]
  30. G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060 (1999).
    [CrossRef]
  31. B. D. Josephson, "Tunneling Into Superconductors," Phys. Lett. 1, 251 (1962).
    [CrossRef]
  32. S. Shapiro, "Josephson Currents in Superconducting Tunneling: The Effect of Microwaves and Other Observations," Phys. Rev. Lett. 11, 80 (1963).
    [CrossRef]
  33. S. Giovanazzi, A. Smerzi, and S. Fantoni, "Josephson effects in dilute Bose-Einstein condensates," Phys. Rev. Lett. 84, 4521 (2000).
    [CrossRef] [PubMed]
  34. S. Ashhab and Carlos Lobo, "External Josephson effect in Bose-Einstein condensates with a spin degree of freedom," Phys. Rev. A 66, 013609 (2002).
    [CrossRef]
  35. F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
    [CrossRef] [PubMed]
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    [CrossRef]
  37. R. Gati, M. Albiez, J. Folling, B. Hemmerling, and M. K. Oberthaler, "Realization of a single Josephson junction for Bose-Einstein condensates," Appl. Phys. B 82, 207 (2006).
    [CrossRef]
  38. B. P. Anderson and M. A. Kasevich, "Macroscopic quantum interference from atomic tunnel arrays," Science 282, 1686 (1998).
    [CrossRef] [PubMed]

2009 (3)

S. Ghanbari, P. B. Blakie, P. Hannaford, and T. D. Kien, "Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice," Eur. Phys. J. B 70305 (2009).
[CrossRef]

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. C. Spreeuw, "Two-dimensional array of microtraps with atomic shift register on a chip," New J. Phys. 11, 023021 (2009).
[CrossRef]

B. Julia-Diaz, M. Guilleumas, M. Lewenstein, A. Polls, and A. Sanpera, "Josephson oscillations in binary mixtures of F=1 spinor Bose-Einstein condensates," Phys. Rev. A 80, 023616 (2009).
[CrossRef]

2008 (2)

H. Zoubi and H. Ritsch, "Bright and dark excitons in an atom-pairfilled optical lattice within a cavity," EPL 82, 14001 (2008).
[CrossRef]

M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, "One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip," J. Phys. B: At. Mol. Opt. Phys. 41, 065301 (2008).
[CrossRef]

2007 (5)

S. Ghanbari, T. D. Kieu, and P. Hannaford, "A class of permanent magnetic lattices for ultracold atoms," J. Phys. B: At. Mol. Opt. Phys. 40, 1283 (2007).
[CrossRef]

V. S. Shchesnovich and V. V. Konotop, "Nonlinear tunneling of Bose-Einstein condensates in an optical lattice: Signatures of quantum collapse and revival," Phys. Rev. A 75, 063628 (2007).
[CrossRef]

B. J. Dalton, "Two-mode theory of BEC interferometry," J. Mod. Opt. 54, 615 (2007).
[CrossRef]

S. Folling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera1, T.Muller, and I. Bloch, "Direct observation of second-order atom tunnelling," Nature 448, 1029 (2007).
[CrossRef] [PubMed]

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, William D. Phillips, and J. V. Porto, "Controlled exchange interaction between pairs of neutral atoms in an optical lattice," Nature 448, 452 (2007).
[CrossRef] [PubMed]

2006 (3)

S. Ghanbari, T. D Kieu, A. Sidorov, and P. Hannaford, "Permanent magnetic lattices for ultracold atoms and quantum degenerate gases," J. Phys. B 39, 847 (2006).
[CrossRef]

B.V. Hall, S. Whitlock, F. Scharnberg, P. Hannaford, and A. Sidorov, "A permanent magnetic film atom chip for Bose-Einstein condensation," J. Phys. B: At. Mol. Opt. Phys. 39, 27 (2006).
[CrossRef]

R. Gati, M. Albiez, J. Folling, B. Hemmerling, and M. K. Oberthaler, "Realization of a single Josephson junction for Bose-Einstein condensates," Appl. Phys. B 82, 207 (2006).
[CrossRef]

2005 (3)

Y. Shin, G.-B. Jo, M. Saba, T. A. Pasquini, W. Ketterle, and D. E. Pritchard, "Optical weak link between two spatially Separated Bose-Einstein Condensates," Phys. Rev. Lett. 95, 170402 (2005).
[CrossRef] [PubMed]

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, "Direct observation of tunneling and nonlinear self-trapping in a single Bosonic Josephson junction," Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective Oscillations of Strongly Correlated One- Dimensional Bosons on a Lattice," Phys. Rev. Lett. 95, 110402 (2005).
[CrossRef] [PubMed]

2004 (1)

W. Zhang, S. Yi, and L. You, "Bose-Einstein condensation of trapped interacting spin-1 atoms," Phys. Rev. A 70, 043611 (2004).
[CrossRef]

2003 (1)

A. Smerzi, A. Trombettoni, T. Lopez-Arias, C. Fort, P. Maddaloni, F. Minardi, and M. Inguscio, "Macroscopic oscillations between two weakly coupled Bose-Einstein condensates," Eur. Phys. J. B 31, 457 (2003).
[CrossRef]

2002 (3)

L. Perakis, "Condensed-matter physics: Exciton developments," Nature 33, 417 (2002).

L. V. Butov, A. C. Gossard, and D. S. Chemla, "Towards Bose-Einstein condensation of excitons in potential traps," Nature 47, 417 (2002).

S. Ashhab and Carlos Lobo, "External Josephson effect in Bose-Einstein condensates with a spin degree of freedom," Phys. Rev. A 66, 013609 (2002).
[CrossRef]

2001 (2)

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

M. Holthaus and S. Stenholm, "Coherent control of the self-trapping transition," Eur. Phys. J. B 20, 451 (2001).
[CrossRef]

2000 (1)

S. Giovanazzi, A. Smerzi, and S. Fantoni, "Josephson effects in dilute Bose-Einstein condensates," Phys. Rev. Lett. 84, 4521 (2000).
[CrossRef] [PubMed]

1999 (3)

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, "Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate," Phys. Rev. A 59, R31 (1999).
[CrossRef]

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose- Einstein condensates: Josephson effects, p oscillations, and macroscopic quantum self-trapping," Phys. Rev. A 59, 620 (1999).
[CrossRef]

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060 (1999).
[CrossRef]

1998 (2)

B. P. Anderson and M. A. Kasevich, "Macroscopic quantum interference from atomic tunnel arrays," Science 282, 1686 (1998).
[CrossRef] [PubMed]

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, "Spin domains in ground state spinor Bose-Einstein condensates," Nature 396, 345 (1998).
[CrossRef]

1997 (2)

G. J. Milburn and J. Corney, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. Lett. 55, 4318 (1997).

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, "Quantum coherent atomic tunneling between two Trapped Bose-Einstein condensates," Phys. Rev. Lett. 79, 4950 (1997).
[CrossRef]

1986 (1)

J. Javanainen, "Oscillatory exchange of atoms between traps containing Bose condensates," Phys. Rev. Lett. 57, 3164 (1986).
[CrossRef] [PubMed]

1963 (1)

S. Shapiro, "Josephson Currents in Superconducting Tunneling: The Effect of Microwaves and Other Observations," Phys. Rev. Lett. 11, 80 (1963).
[CrossRef]

1962 (1)

B. D. Josephson, "Tunneling Into Superconductors," Phys. Lett. 1, 251 (1962).
[CrossRef]

Akulshin, A.

M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, "One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip," J. Phys. B: At. Mol. Opt. Phys. 41, 065301 (2008).
[CrossRef]

Albiez, M.

R. Gati, M. Albiez, J. Folling, B. Hemmerling, and M. K. Oberthaler, "Realization of a single Josephson junction for Bose-Einstein condensates," Appl. Phys. B 82, 207 (2006).
[CrossRef]

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, "Direct observation of tunneling and nonlinear self-trapping in a single Bosonic Josephson junction," Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

Anderlini, M.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, William D. Phillips, and J. V. Porto, "Controlled exchange interaction between pairs of neutral atoms in an optical lattice," Nature 448, 452 (2007).
[CrossRef] [PubMed]

Anderson, B. P.

B. P. Anderson and M. A. Kasevich, "Macroscopic quantum interference from atomic tunnel arrays," Science 282, 1686 (1998).
[CrossRef] [PubMed]

Ashhab, S.

S. Ashhab and Carlos Lobo, "External Josephson effect in Bose-Einstein condensates with a spin degree of freedom," Phys. Rev. A 66, 013609 (2002).
[CrossRef]

Blakie, P. B.

S. Ghanbari, P. B. Blakie, P. Hannaford, and T. D. Kien, "Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice," Eur. Phys. J. B 70305 (2009).
[CrossRef]

Brennen, G. K.

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060 (1999).
[CrossRef]

Brown, B. L.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, William D. Phillips, and J. V. Porto, "Controlled exchange interaction between pairs of neutral atoms in an optical lattice," Nature 448, 452 (2007).
[CrossRef] [PubMed]

Burger, S.

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

Butov, L. V.

L. V. Butov, A. C. Gossard, and D. S. Chemla, "Towards Bose-Einstein condensation of excitons in potential traps," Nature 47, 417 (2002).

Cataliotti, F. S.

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

Caves, C. M.

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060 (1999).
[CrossRef]

Chemla, D. S.

L. V. Butov, A. C. Gossard, and D. S. Chemla, "Towards Bose-Einstein condensation of excitons in potential traps," Nature 47, 417 (2002).

Chikkatur, A. P.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, "Spin domains in ground state spinor Bose-Einstein condensates," Nature 396, 345 (1998).
[CrossRef]

Cooper, J.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, "Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate," Phys. Rev. A 59, R31 (1999).
[CrossRef]

Cornell, E.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, "Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate," Phys. Rev. A 59, R31 (1999).
[CrossRef]

Corney, J.

G. J. Milburn and J. Corney, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. Lett. 55, 4318 (1997).

Dalton, B. J.

B. J. Dalton, "Two-mode theory of BEC interferometry," J. Mod. Opt. 54, 615 (2007).
[CrossRef]

Deutsch, I. H.

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060 (1999).
[CrossRef]

Fantoni, S.

S. Giovanazzi, A. Smerzi, and S. Fantoni, "Josephson effects in dilute Bose-Einstein condensates," Phys. Rev. Lett. 84, 4521 (2000).
[CrossRef] [PubMed]

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose- Einstein condensates: Josephson effects, p oscillations, and macroscopic quantum self-trapping," Phys. Rev. A 59, 620 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, "Quantum coherent atomic tunneling between two Trapped Bose-Einstein condensates," Phys. Rev. Lett. 79, 4950 (1997).
[CrossRef]

Fernholz, T.

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. C. Spreeuw, "Two-dimensional array of microtraps with atomic shift register on a chip," New J. Phys. 11, 023021 (2009).
[CrossRef]

Fort, C.

A. Smerzi, A. Trombettoni, T. Lopez-Arias, C. Fort, P. Maddaloni, F. Minardi, and M. Inguscio, "Macroscopic oscillations between two weakly coupled Bose-Einstein condensates," Eur. Phys. J. B 31, 457 (2003).
[CrossRef]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

Gati, R.

R. Gati, M. Albiez, J. Folling, B. Hemmerling, and M. K. Oberthaler, "Realization of a single Josephson junction for Bose-Einstein condensates," Appl. Phys. B 82, 207 (2006).
[CrossRef]

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, "Direct observation of tunneling and nonlinear self-trapping in a single Bosonic Josephson junction," Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

Gerritsma, R.

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. C. Spreeuw, "Two-dimensional array of microtraps with atomic shift register on a chip," New J. Phys. 11, 023021 (2009).
[CrossRef]

Ghanbari, S.

S. Ghanbari, P. B. Blakie, P. Hannaford, and T. D. Kien, "Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice," Eur. Phys. J. B 70305 (2009).
[CrossRef]

S. Ghanbari, T. D. Kieu, and P. Hannaford, "A class of permanent magnetic lattices for ultracold atoms," J. Phys. B: At. Mol. Opt. Phys. 40, 1283 (2007).
[CrossRef]

S. Ghanbari, T. D Kieu, A. Sidorov, and P. Hannaford, "Permanent magnetic lattices for ultracold atoms and quantum degenerate gases," J. Phys. B 39, 847 (2006).
[CrossRef]

Giovanazzi, S.

S. Giovanazzi, A. Smerzi, and S. Fantoni, "Josephson effects in dilute Bose-Einstein condensates," Phys. Rev. Lett. 84, 4521 (2000).
[CrossRef] [PubMed]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, "Quantum coherent atomic tunneling between two Trapped Bose-Einstein condensates," Phys. Rev. Lett. 79, 4950 (1997).
[CrossRef]

Gossard, A. C.

L. V. Butov, A. C. Gossard, and D. S. Chemla, "Towards Bose-Einstein condensation of excitons in potential traps," Nature 47, 417 (2002).

Hall, B. V.

B.V. Hall, S. Whitlock, F. Scharnberg, P. Hannaford, and A. Sidorov, "A permanent magnetic film atom chip for Bose-Einstein condensation," J. Phys. B: At. Mol. Opt. Phys. 39, 27 (2006).
[CrossRef]

Hannaford, P.

S. Ghanbari, P. B. Blakie, P. Hannaford, and T. D. Kien, "Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice," Eur. Phys. J. B 70305 (2009).
[CrossRef]

M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, "One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip," J. Phys. B: At. Mol. Opt. Phys. 41, 065301 (2008).
[CrossRef]

S. Ghanbari, T. D. Kieu, and P. Hannaford, "A class of permanent magnetic lattices for ultracold atoms," J. Phys. B: At. Mol. Opt. Phys. 40, 1283 (2007).
[CrossRef]

B.V. Hall, S. Whitlock, F. Scharnberg, P. Hannaford, and A. Sidorov, "A permanent magnetic film atom chip for Bose-Einstein condensation," J. Phys. B: At. Mol. Opt. Phys. 39, 27 (2006).
[CrossRef]

S. Ghanbari, T. D Kieu, A. Sidorov, and P. Hannaford, "Permanent magnetic lattices for ultracold atoms and quantum degenerate gases," J. Phys. B 39, 847 (2006).
[CrossRef]

Holland, M.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, "Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate," Phys. Rev. A 59, R31 (1999).
[CrossRef]

Holthaus, M.

M. Holthaus and S. Stenholm, "Coherent control of the self-trapping transition," Eur. Phys. J. B 20, 451 (2001).
[CrossRef]

Inguscio, M.

A. Smerzi, A. Trombettoni, T. Lopez-Arias, C. Fort, P. Maddaloni, F. Minardi, and M. Inguscio, "Macroscopic oscillations between two weakly coupled Bose-Einstein condensates," Eur. Phys. J. B 31, 457 (2003).
[CrossRef]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

Inouye, S.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, "Spin domains in ground state spinor Bose-Einstein condensates," Nature 396, 345 (1998).
[CrossRef]

Javanainen, J.

J. Javanainen, "Oscillatory exchange of atoms between traps containing Bose condensates," Phys. Rev. Lett. 57, 3164 (1986).
[CrossRef] [PubMed]

Jessen, P. S.

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060 (1999).
[CrossRef]

Jo, G.-B.

Y. Shin, G.-B. Jo, M. Saba, T. A. Pasquini, W. Ketterle, and D. E. Pritchard, "Optical weak link between two spatially Separated Bose-Einstein Condensates," Phys. Rev. Lett. 95, 170402 (2005).
[CrossRef] [PubMed]

Josephson, B. D.

B. D. Josephson, "Tunneling Into Superconductors," Phys. Lett. 1, 251 (1962).
[CrossRef]

Kasevich, M. A.

B. P. Anderson and M. A. Kasevich, "Macroscopic quantum interference from atomic tunnel arrays," Science 282, 1686 (1998).
[CrossRef] [PubMed]

Ketterle, W.

Y. Shin, G.-B. Jo, M. Saba, T. A. Pasquini, W. Ketterle, and D. E. Pritchard, "Optical weak link between two spatially Separated Bose-Einstein Condensates," Phys. Rev. Lett. 95, 170402 (2005).
[CrossRef] [PubMed]

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, "Spin domains in ground state spinor Bose-Einstein condensates," Nature 396, 345 (1998).
[CrossRef]

Kien, T. D.

S. Ghanbari, P. B. Blakie, P. Hannaford, and T. D. Kien, "Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice," Eur. Phys. J. B 70305 (2009).
[CrossRef]

Kieu, T. D

S. Ghanbari, T. D Kieu, A. Sidorov, and P. Hannaford, "Permanent magnetic lattices for ultracold atoms and quantum degenerate gases," J. Phys. B 39, 847 (2006).
[CrossRef]

Kieu, T. D.

S. Ghanbari, T. D. Kieu, and P. Hannaford, "A class of permanent magnetic lattices for ultracold atoms," J. Phys. B: At. Mol. Opt. Phys. 40, 1283 (2007).
[CrossRef]

Konotop, V. V.

V. S. Shchesnovich and V. V. Konotop, "Nonlinear tunneling of Bose-Einstein condensates in an optical lattice: Signatures of quantum collapse and revival," Phys. Rev. A 75, 063628 (2007).
[CrossRef]

Lee, P. J.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, William D. Phillips, and J. V. Porto, "Controlled exchange interaction between pairs of neutral atoms in an optical lattice," Nature 448, 452 (2007).
[CrossRef] [PubMed]

Lopez-Arias, T.

A. Smerzi, A. Trombettoni, T. Lopez-Arias, C. Fort, P. Maddaloni, F. Minardi, and M. Inguscio, "Macroscopic oscillations between two weakly coupled Bose-Einstein condensates," Eur. Phys. J. B 31, 457 (2003).
[CrossRef]

Maddaloni, P.

A. Smerzi, A. Trombettoni, T. Lopez-Arias, C. Fort, P. Maddaloni, F. Minardi, and M. Inguscio, "Macroscopic oscillations between two weakly coupled Bose-Einstein condensates," Eur. Phys. J. B 31, 457 (2003).
[CrossRef]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

McLean, R.

M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, "One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip," J. Phys. B: At. Mol. Opt. Phys. 41, 065301 (2008).
[CrossRef]

Miesner, H.-J.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, "Spin domains in ground state spinor Bose-Einstein condensates," Nature 396, 345 (1998).
[CrossRef]

Milburn, G. J.

G. J. Milburn and J. Corney, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. Lett. 55, 4318 (1997).

Minardi, F.

A. Smerzi, A. Trombettoni, T. Lopez-Arias, C. Fort, P. Maddaloni, F. Minardi, and M. Inguscio, "Macroscopic oscillations between two weakly coupled Bose-Einstein condensates," Eur. Phys. J. B 31, 457 (2003).
[CrossRef]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

Pasquini, T. A.

Y. Shin, G.-B. Jo, M. Saba, T. A. Pasquini, W. Ketterle, and D. E. Pritchard, "Optical weak link between two spatially Separated Bose-Einstein Condensates," Phys. Rev. Lett. 95, 170402 (2005).
[CrossRef] [PubMed]

Perakis, L.

L. Perakis, "Condensed-matter physics: Exciton developments," Nature 33, 417 (2002).

Pritchard, D. E.

Y. Shin, G.-B. Jo, M. Saba, T. A. Pasquini, W. Ketterle, and D. E. Pritchard, "Optical weak link between two spatially Separated Bose-Einstein Condensates," Phys. Rev. Lett. 95, 170402 (2005).
[CrossRef] [PubMed]

Raghavan, S.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose- Einstein condensates: Josephson effects, p oscillations, and macroscopic quantum self-trapping," Phys. Rev. A 59, 620 (1999).
[CrossRef]

Rigol, M.

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective Oscillations of Strongly Correlated One- Dimensional Bosons on a Lattice," Phys. Rev. Lett. 95, 110402 (2005).
[CrossRef] [PubMed]

Ritsch, H.

H. Zoubi and H. Ritsch, "Bright and dark excitons in an atom-pairfilled optical lattice within a cavity," EPL 82, 14001 (2008).
[CrossRef]

Rousseau, V.

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective Oscillations of Strongly Correlated One- Dimensional Bosons on a Lattice," Phys. Rev. Lett. 95, 110402 (2005).
[CrossRef] [PubMed]

Saba, M.

Y. Shin, G.-B. Jo, M. Saba, T. A. Pasquini, W. Ketterle, and D. E. Pritchard, "Optical weak link between two spatially Separated Bose-Einstein Condensates," Phys. Rev. Lett. 95, 170402 (2005).
[CrossRef] [PubMed]

Scalettar, R. T.

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective Oscillations of Strongly Correlated One- Dimensional Bosons on a Lattice," Phys. Rev. Lett. 95, 110402 (2005).
[CrossRef] [PubMed]

Scharnberg, F.

B.V. Hall, S. Whitlock, F. Scharnberg, P. Hannaford, and A. Sidorov, "A permanent magnetic film atom chip for Bose-Einstein condensation," J. Phys. B: At. Mol. Opt. Phys. 39, 27 (2006).
[CrossRef]

Sebby-Strabley, J.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, William D. Phillips, and J. V. Porto, "Controlled exchange interaction between pairs of neutral atoms in an optical lattice," Nature 448, 452 (2007).
[CrossRef] [PubMed]

Shapiro, S.

S. Shapiro, "Josephson Currents in Superconducting Tunneling: The Effect of Microwaves and Other Observations," Phys. Rev. Lett. 11, 80 (1963).
[CrossRef]

Shchesnovich, V. S.

V. S. Shchesnovich and V. V. Konotop, "Nonlinear tunneling of Bose-Einstein condensates in an optical lattice: Signatures of quantum collapse and revival," Phys. Rev. A 75, 063628 (2007).
[CrossRef]

Shenoy, S. R.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose- Einstein condensates: Josephson effects, p oscillations, and macroscopic quantum self-trapping," Phys. Rev. A 59, 620 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, "Quantum coherent atomic tunneling between two Trapped Bose-Einstein condensates," Phys. Rev. Lett. 79, 4950 (1997).
[CrossRef]

Shin, Y.

Y. Shin, G.-B. Jo, M. Saba, T. A. Pasquini, W. Ketterle, and D. E. Pritchard, "Optical weak link between two spatially Separated Bose-Einstein Condensates," Phys. Rev. Lett. 95, 170402 (2005).
[CrossRef] [PubMed]

Sidorov, A.

M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, "One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip," J. Phys. B: At. Mol. Opt. Phys. 41, 065301 (2008).
[CrossRef]

B.V. Hall, S. Whitlock, F. Scharnberg, P. Hannaford, and A. Sidorov, "A permanent magnetic film atom chip for Bose-Einstein condensation," J. Phys. B: At. Mol. Opt. Phys. 39, 27 (2006).
[CrossRef]

S. Ghanbari, T. D Kieu, A. Sidorov, and P. Hannaford, "Permanent magnetic lattices for ultracold atoms and quantum degenerate gases," J. Phys. B 39, 847 (2006).
[CrossRef]

Singh, M.

M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, "One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip," J. Phys. B: At. Mol. Opt. Phys. 41, 065301 (2008).
[CrossRef]

Singh, R. R. P.

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective Oscillations of Strongly Correlated One- Dimensional Bosons on a Lattice," Phys. Rev. Lett. 95, 110402 (2005).
[CrossRef] [PubMed]

Smerzi, A.

A. Smerzi, A. Trombettoni, T. Lopez-Arias, C. Fort, P. Maddaloni, F. Minardi, and M. Inguscio, "Macroscopic oscillations between two weakly coupled Bose-Einstein condensates," Eur. Phys. J. B 31, 457 (2003).
[CrossRef]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

S. Giovanazzi, A. Smerzi, and S. Fantoni, "Josephson effects in dilute Bose-Einstein condensates," Phys. Rev. Lett. 84, 4521 (2000).
[CrossRef] [PubMed]

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose- Einstein condensates: Josephson effects, p oscillations, and macroscopic quantum self-trapping," Phys. Rev. A 59, 620 (1999).
[CrossRef]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, "Quantum coherent atomic tunneling between two Trapped Bose-Einstein condensates," Phys. Rev. Lett. 79, 4950 (1997).
[CrossRef]

Spreeuw, R. J. C.

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. C. Spreeuw, "Two-dimensional array of microtraps with atomic shift register on a chip," New J. Phys. 11, 023021 (2009).
[CrossRef]

Stamper-Kurn, D. M.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, "Spin domains in ground state spinor Bose-Einstein condensates," Nature 396, 345 (1998).
[CrossRef]

Stenger, J.

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, "Spin domains in ground state spinor Bose-Einstein condensates," Nature 396, 345 (1998).
[CrossRef]

Stenholm, S.

M. Holthaus and S. Stenholm, "Coherent control of the self-trapping transition," Eur. Phys. J. B 20, 451 (2001).
[CrossRef]

Trombettoni, A.

A. Smerzi, A. Trombettoni, T. Lopez-Arias, C. Fort, P. Maddaloni, F. Minardi, and M. Inguscio, "Macroscopic oscillations between two weakly coupled Bose-Einstein condensates," Eur. Phys. J. B 31, 457 (2003).
[CrossRef]

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

Volk, M.

M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, "One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip," J. Phys. B: At. Mol. Opt. Phys. 41, 065301 (2008).
[CrossRef]

Walser, R.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, "Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate," Phys. Rev. A 59, R31 (1999).
[CrossRef]

Whitlock, S.

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. C. Spreeuw, "Two-dimensional array of microtraps with atomic shift register on a chip," New J. Phys. 11, 023021 (2009).
[CrossRef]

B.V. Hall, S. Whitlock, F. Scharnberg, P. Hannaford, and A. Sidorov, "A permanent magnetic film atom chip for Bose-Einstein condensation," J. Phys. B: At. Mol. Opt. Phys. 39, 27 (2006).
[CrossRef]

William, J.

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, William D. Phillips, and J. V. Porto, "Controlled exchange interaction between pairs of neutral atoms in an optical lattice," Nature 448, 452 (2007).
[CrossRef] [PubMed]

Williams, J.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, "Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate," Phys. Rev. A 59, R31 (1999).
[CrossRef]

Yi, S.

W. Zhang, S. Yi, and L. You, "Bose-Einstein condensation of trapped interacting spin-1 atoms," Phys. Rev. A 70, 043611 (2004).
[CrossRef]

You, L.

W. Zhang, S. Yi, and L. You, "Bose-Einstein condensation of trapped interacting spin-1 atoms," Phys. Rev. A 70, 043611 (2004).
[CrossRef]

Zhang, W.

W. Zhang, S. Yi, and L. You, "Bose-Einstein condensation of trapped interacting spin-1 atoms," Phys. Rev. A 70, 043611 (2004).
[CrossRef]

Zoubi, H.

H. Zoubi and H. Ritsch, "Bright and dark excitons in an atom-pairfilled optical lattice within a cavity," EPL 82, 14001 (2008).
[CrossRef]

Appl. Phys. B (1)

R. Gati, M. Albiez, J. Folling, B. Hemmerling, and M. K. Oberthaler, "Realization of a single Josephson junction for Bose-Einstein condensates," Appl. Phys. B 82, 207 (2006).
[CrossRef]

EPL (1)

H. Zoubi and H. Ritsch, "Bright and dark excitons in an atom-pairfilled optical lattice within a cavity," EPL 82, 14001 (2008).
[CrossRef]

Eur. Phys. J. B (3)

S. Ghanbari, P. B. Blakie, P. Hannaford, and T. D. Kien, "Superfluid to Mott insulator quantum phase transition in a 2D permanent magnetic lattice," Eur. Phys. J. B 70305 (2009).
[CrossRef]

M. Holthaus and S. Stenholm, "Coherent control of the self-trapping transition," Eur. Phys. J. B 20, 451 (2001).
[CrossRef]

A. Smerzi, A. Trombettoni, T. Lopez-Arias, C. Fort, P. Maddaloni, F. Minardi, and M. Inguscio, "Macroscopic oscillations between two weakly coupled Bose-Einstein condensates," Eur. Phys. J. B 31, 457 (2003).
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J. Mod. Opt. (1)

B. J. Dalton, "Two-mode theory of BEC interferometry," J. Mod. Opt. 54, 615 (2007).
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J. Phys. B (1)

S. Ghanbari, T. D Kieu, A. Sidorov, and P. Hannaford, "Permanent magnetic lattices for ultracold atoms and quantum degenerate gases," J. Phys. B 39, 847 (2006).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys. (3)

B.V. Hall, S. Whitlock, F. Scharnberg, P. Hannaford, and A. Sidorov, "A permanent magnetic film atom chip for Bose-Einstein condensation," J. Phys. B: At. Mol. Opt. Phys. 39, 27 (2006).
[CrossRef]

M. Singh, M. Volk, A. Akulshin, A. Sidorov, R. McLean, and P. Hannaford, "One dimensional lattice of permanent magnetic microtraps for ultracold atoms on an atom chip," J. Phys. B: At. Mol. Opt. Phys. 41, 065301 (2008).
[CrossRef]

S. Ghanbari, T. D. Kieu, and P. Hannaford, "A class of permanent magnetic lattices for ultracold atoms," J. Phys. B: At. Mol. Opt. Phys. 40, 1283 (2007).
[CrossRef]

Nature (5)

L. Perakis, "Condensed-matter physics: Exciton developments," Nature 33, 417 (2002).

S. Folling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera1, T.Muller, and I. Bloch, "Direct observation of second-order atom tunnelling," Nature 448, 1029 (2007).
[CrossRef] [PubMed]

M. Anderlini, P. J. Lee, B. L. Brown, J. Sebby-Strabley, William D. Phillips, and J. V. Porto, "Controlled exchange interaction between pairs of neutral atoms in an optical lattice," Nature 448, 452 (2007).
[CrossRef] [PubMed]

J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, "Spin domains in ground state spinor Bose-Einstein condensates," Nature 396, 345 (1998).
[CrossRef]

L. V. Butov, A. C. Gossard, and D. S. Chemla, "Towards Bose-Einstein condensation of excitons in potential traps," Nature 47, 417 (2002).

New J. Phys. (1)

S. Whitlock, R. Gerritsma, T. Fernholz, and R. J. C. Spreeuw, "Two-dimensional array of microtraps with atomic shift register on a chip," New J. Phys. 11, 023021 (2009).
[CrossRef]

Phys. Lett. (1)

B. D. Josephson, "Tunneling Into Superconductors," Phys. Lett. 1, 251 (1962).
[CrossRef]

Phys. Rev. A (6)

S. Ashhab and Carlos Lobo, "External Josephson effect in Bose-Einstein condensates with a spin degree of freedom," Phys. Rev. A 66, 013609 (2002).
[CrossRef]

W. Zhang, S. Yi, and L. You, "Bose-Einstein condensation of trapped interacting spin-1 atoms," Phys. Rev. A 70, 043611 (2004).
[CrossRef]

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, "Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate," Phys. Rev. A 59, R31 (1999).
[CrossRef]

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose- Einstein condensates: Josephson effects, p oscillations, and macroscopic quantum self-trapping," Phys. Rev. A 59, 620 (1999).
[CrossRef]

V. S. Shchesnovich and V. V. Konotop, "Nonlinear tunneling of Bose-Einstein condensates in an optical lattice: Signatures of quantum collapse and revival," Phys. Rev. A 75, 063628 (2007).
[CrossRef]

B. Julia-Diaz, M. Guilleumas, M. Lewenstein, A. Polls, and A. Sanpera, "Josephson oscillations in binary mixtures of F=1 spinor Bose-Einstein condensates," Phys. Rev. A 80, 023616 (2009).
[CrossRef]

Phys. Rev. Lett. (9)

Y. Shin, G.-B. Jo, M. Saba, T. A. Pasquini, W. Ketterle, and D. E. Pritchard, "Optical weak link between two spatially Separated Bose-Einstein Condensates," Phys. Rev. Lett. 95, 170402 (2005).
[CrossRef] [PubMed]

M. Albiez, R. Gati, J. Folling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, "Direct observation of tunneling and nonlinear self-trapping in a single Bosonic Josephson junction," Phys. Rev. Lett. 95, 010402 (2005).
[CrossRef] [PubMed]

M. Rigol, V. Rousseau, R. T. Scalettar, and R. R. P. Singh, "Collective Oscillations of Strongly Correlated One- Dimensional Bosons on a Lattice," Phys. Rev. Lett. 95, 110402 (2005).
[CrossRef] [PubMed]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, "Quantum coherent atomic tunneling between two Trapped Bose-Einstein condensates," Phys. Rev. Lett. 79, 4950 (1997).
[CrossRef]

J. Javanainen, "Oscillatory exchange of atoms between traps containing Bose condensates," Phys. Rev. Lett. 57, 3164 (1986).
[CrossRef] [PubMed]

G. J. Milburn and J. Corney, "Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential," Phys. Rev. Lett. 55, 4318 (1997).

G. K. Brennen, C. M. Caves, P. S. Jessen, and I. H. Deutsch, "Quantum logic gates in optical lattices," Phys. Rev. Lett. 82, 1060 (1999).
[CrossRef]

S. Shapiro, "Josephson Currents in Superconducting Tunneling: The Effect of Microwaves and Other Observations," Phys. Rev. Lett. 11, 80 (1963).
[CrossRef]

S. Giovanazzi, A. Smerzi, and S. Fantoni, "Josephson effects in dilute Bose-Einstein condensates," Phys. Rev. Lett. 84, 4521 (2000).
[CrossRef] [PubMed]

Science (2)

F. S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, "Josephson junction arrays with Bose-Einstein condensates," Science 293, 843 (2001).
[CrossRef] [PubMed]

B. P. Anderson and M. A. Kasevich, "Macroscopic quantum interference from atomic tunnel arrays," Science 282, 1686 (1998).
[CrossRef] [PubMed]

Other (4)

H. Zoubi and H. Ritsch, "Excitons and cavity polaritons for cold-atoms in an optical lattice," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest (CD) (Optical Society of America, 2008), paper QThE3.

A. Abdelrahman, M. Vasiliev, K. Alameh, P. Hannaford, Yong-Tak Lee, and Byoung S. Ham, "Towards Bose- Einstein condensation of excitons in an asymmetric multi-quantum state magnetic lattice," Numerical Simulation of Optoelectronic Devices (NUSOD) (2009).

A. Abdelrahman, P. Hannaford, M. Vasiliev, and K. Alameh, "Asymmetric Two-dimensional Magnetic Lattices for Ultracold Atoms Trapping and Confinement," in progress, arXiv:0910.5032v1 [quant-ph] (2009).

D. R. Dounas-Frazer and L. D. Carr, "Tunneling resonances and entanglement dynamics of cold bosons in the double well," quant-ph/0610166 (2006).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic diagram of an 11×11 magnetic lattice surrounded by an unperturbed area. (b) The lattice parameters are specified by the hole size αh ×αh , the spacing as between the holes and the magnetic layer thickness τbtm . (c) 3D plot of the magnetic field (along the z-axis) of the distributed sites across the x-y plane simulated at a distance dmin from the surface. (d) Magnetic density plot of the simulated magnetic lattice sites in the z-x plane along the center of the lattice. The traps (dark color) are located at the effective z-distance, dmin, from the surface of the magnetic film (bright color). (e–f) Magnetic field density and contour plots across the x-y plane at dmin with no external magnetic bias fields, respectively. Simulation input parameters: αs =αh =7 µm Mz =2.80 kG, τbtm =2 µm and τp-wall =2 µm.

Fig. 2.
Fig. 2.

(a) Magnetic field density plot of the simulation of a 9×9 magnetic lattice where the magnetic local minima are located at dmin above the holes. The central sites of the lattice exhibit larger distances from the magnetic thin film surface than the edge sites. (b–d) Contour and magnetic field density plots of two adjacent edge sites showing the separating distance along the gravitational field z-axis and the magnetic potential tilt, δB, and the magnetic tunneling barriers, ΔB, between the two sites. The magnetic field is calculated across the two sites as indicated by the dashed line. (e) Comparison of the magnetic field local minima along the z-axis at the center and the edge sites. (f) Two different magnetic bands at the center and at the edge of the asymmetrical magnetic lattice. (g) Simulated Bz min for different values of αs where the width of the holes is fixed, αh =2 µm. (h) The effect of applying a varying external magnetic bias field on the non-zero local minima along the z-axis. (i) Tunneling barriers can adiabatically be controlled via applying the magnetic bias field Bz-bias along the z-axis. Simulation results show the effect of Bz-bias on ΔB and δB. Simulation inputs: αs =αh =7 µm Mz =2.80 kG, τbtm =2 µm and τn-wall =-0.5 µm.

Fig. 3.
Fig. 3.

(a–b) Schematic representation of the magnetic band structure (the pyramid-like distribution) where each band contains a set of magnetic minima. (c–d) Schematic representation of the two-modes configuration and a possible scenario of coupled spins between two magnetic bands hosting two different degrees of freedom of spins such a two-components spinor BECs or ultracold Fermions.

Fig. 4.
Fig. 4.

(a) Scanning Electron Microscope (SEM) and (b) Atomic Force Microscope (AFM) images of the fabricated two-dimensional magnetic lattice. (c) Magnetic field minima Bz min simulated across the surface of the magnetic lattice, where we simulate the application of in-situ bias field along the x-axis, Bx-bias =3 G.(d) Magnetic Force Microscope (MFM) image showing the phase across the surface with the same conditions applied in the simulation.

Fig. 5.
Fig. 5.

(a) Schematic representation of the two-mode system ϕg i , ϕe i . (b–c) Representation of the Josephson oscillation, i.e., adiabatically induced Josephson current, and the coupling between two different states at each pair of adjacent sites, respectively. The schematic representation shows only one site of the propagating Josephson currents.

Equations (29)

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B x = B ref sin ( β x ) e β [ z τ ] B ref 3 sin ( 3 β x ) e 3 β [ z τ ] + + B x bias
B y = B ref sin ( β y ) e β [ z τ ] B ref 3 sin ( 3 β y ) e 3 β [ z τ ] + + B y bias
B z = B ref [ cos ( β x ) + cos ( β y ) ] e β [ z τ ] B ref 3 [ cos ( 3 β x ) + cos ( 3 β y ) ] e 3 β ( z τ ) +
+ B z bias
B x = B o ( 1 e β τ ) e β [ z τ ] × sin ( βx ) + B x bias
B y = B o ( 1 e β τ ) e β [ z τ ] × sin ( βy ) + B y bias
B z = B o ( 1 e βτ ) e β [ z τ ] × [ cos ( βx ) + cos ( βy ) ] + B z bias
B = { B x bias 2 + B y bias 2 + B z bias 2 + 2 B ref 2 [ 1 + cos ( βx ) cos ( βy ) ] e 2 β [ z τ ] + 2 B ref ×
× e β [ z τ ] ( sin ( βx ) B x bias + sin ( βy ) B y bias + [ cos ( βx ) + cos ( βy ) ] B z bias ) } 1 / 2
δ B = B min i , l B min i + 1 , l + 1
Δ B = B max i , l B min i , l
Λ depth ( r ) = μ B g F m F k B Δ B ( x ) = μ B g F m F k B [ B max i , j ( x ) B min i , l ( x ) ]
H ̂ sys = d x Φ ̂ ( x ) ( 2 2 M 2 + B ( x ) ) Φ ̂ ( x )
+ 1 2 d x Φ ̂ ( x ) [ d x ́ Φ ̂ ( x ́ ) U int ( x x ́ ) Φ ̂ ( x ́ ) ] Φ ̂ ( x )
ϕ i [ k , m ] ( x x i ) = x i , k , m
H ̂ BH = Σ j i = 1 n J i , j [ k , m ] ( b ̂ i b ̂ j + b ̂ j b ̂ i ) + Σ j i = 1 n U i , j [ k , m ] 2 ( n ̂ i [ n ̂ i 1 ] + n ̂ j [ n ̂ j 1 ] ) +
+ δ B Σ i j ( b ̂ i [ k , m ] b ̂ j [ k′ , m ] + b ̂ j [ k′ , m ] b ̂ i [ k , m ] ) , k k′ { 0 , 1 }
J i , j [ k , m ] = d x ϕ i , j * [ k , m ] ( x x i ) ( 2 2 M 2 + B ( x , t ) ) ϕ i , j [ k , m ] ( x x j )
U i , j [ k , m ] = 3 g 8 d x ϕ i , j [ 0,0 ] ( x x j ) 4
Φ ̂ ( x ) = Σ i = 1 4 b ̂ i γ ϕ 1 , γ [ k , m ] ( x )
( 2 2 m 2 + Δ B ( x ) ) ϕ 1 , γ [ k , m ] = E 1 , γ ϕ 1 , γ [ k , m ]
N s U i , j [ 0,0 ] Δ E i , j [ k , m ] = 2 [ E i , j [ 1 , m ] E i , j [ 0 , m ] ] = ω
H ̂ 1 HB = Σ j i = 1 n J i , j [ 0,0 ] ( b ̂ i b ̂ j + b ̂ j b ̂ i ) + Σ j = i = 1 n U i , j [ 0,0 ] 2 ( n ̂ i [ n ̂ i 1 ] + n ̂ j [ n ̂ j 1 ] )
φ = Σ n i , j = 0 N + 1 c i , j [ 0,0 ] n i , n j
i φ i ( x , t ) t = [ 2 2 m 2 + B ( x ) + g φ i ( x , t ) 2 ] φ i ( x , t )
φ i ( x , t ) = N Σ i = 1 n ψ i ( x , t ) ϕ i g
i ψ i ( x , t ) t = [ Ω i , j ( x , t ) + U i , j [ 0 , m ] N ψ i 2 ] ψ i Σ i j n J i , j [ 0 , m ] ( x , t ) ψ j
Ω i , j ( x , t ) = d x [ 2 2 M ϕ i * g 2 + ϕ i * g B ( x , t ) ϕ i g ]
U i [ 0 , m ] U i [ 1 , m ] J i j [ 0 1 , m ]

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