Abstract

We theoretically study macroscopic entanglement between a magnetically trapped Bose-Einstein condensate and a superconducting loop. We treat the superconducting loop in a quantum superposition of two different flux states coupling with the magnetic trap to generate macroscopic entanglement. The scheme also provides a platform to investigate interferometry with an entangled Bose Einstein condensate and to explore physics at the quantum-classical interface.

© 2009 Optical Society of America

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  1. W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, "Bose Einstein condensation on a microelectronic chip," Nature (London) 413, 498-501 (2001).
    [CrossRef]
  2. T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
    [CrossRef]
  3. S. Hofferberth, I. Lesanovsky, B. Fischer, J. Verdu, and J. Schmiedmayer, "Radiofrequency-dressed-state potentials for neutral atoms," Nat. Phys. 2, 710-716 (2006).
    [CrossRef]
  4. P. Treutlein, T. W. Hansch, J. Reichel, A. Negretti, M. A. Cirone, and T. Calarco, "Microwave potentials and optimal control for robust quantum gates on an atom chip," Phys. Rev. A 74, 022312 (2006).
    [CrossRef]
  5. P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, "Coherence in microchip traps," Phys. Rev. Lett. 92, 203005 (2004).
    [CrossRef] [PubMed]
  6. M. P. A. Jones, C. J. Vale, D. Sahagun, B. V. Hall, and E. A. Hinds, "Spin coupling between cold atoms and the thermal fluctuations of a metal surface," Phys. Rev. Lett. 91, 080401 (2003).
    [CrossRef] [PubMed]
  7. D. M. Harber, J. M. Obrecht, J. M. McGuirk, and E. A. Cornell, "Measurement of the Casimir-Polder force through centre-of-mass oscillations of a Bose Einstein condensate," Phys. Rev. A 72, 033610 (2005).
    [CrossRef]
  8. Y. Makhlin, G. Schon, and A. Shnirman, "Quantum-state engineering with Josephson-junction devices," Rev. Mod. Phys. 73, 357-400 (2001).
    [CrossRef]
  9. J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, "Josephson persistent current qubit," Science 285, 1036-1039 (1999).
    [CrossRef] [PubMed]
  10. J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, "Quantum superposition of distinct macroscopic states," Nature (London) 406, 43-46 (2000).
    [CrossRef]
  11. C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).
  12. I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, "Coherent quantum dynamics of a superconducting flux qubit," Science 299, 1869-1871 (2003).
    [CrossRef] [PubMed]
  13. A. D. Armour, M. P. Blencowe, and K. C. Schwab, "Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper pair box," Phys. Rev. Lett. 88, 148301 (2002).
    [CrossRef] [PubMed]
  14. P. Treutlein, D. Hunger, S. Camerer, T. W. H¨ansch, and J. Reichel, "A Bose Einstein condensate coupled to a nanomechanical resonator on an atom chip," Phys. Rev. Lett. 99, 140403 (2007).
    [CrossRef] [PubMed]
  15. A. S. Sørensen, C. H. van der Wal, L. I. Childress, and M. D. Lukin, "Capacitive coupling of atomic systems to mesoscopic conductors," Phys. Rev. Lett. 92, 063601 (2004).
    [CrossRef] [PubMed]
  16. T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
    [CrossRef] [PubMed]
  17. T. Mukai, C. Hufnagel, A. Kasper, T. Meno, A. Tsukada, K. Semba, and F. Shimizu, "Persistent supercurrent atom chip," Phys. Rev. Lett. 98, 260407 (2007).
    [CrossRef] [PubMed]
  18. P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, "De Broglie wavelength of a non-local four-photon Fock state," Nature (London) 429, 158-160 (2004).
    [CrossRef]
  19. M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, "Super-resolving phase measurements with a multiphoton entangled state," Nature (London) 429, 161-164 (2004).
    [CrossRef]
  20. K. Mølmer and A. Sørensen, "Multiparticle entanglement of hot trapped ions," Phys. Rev. Lett. 82, 1835 (1999).
    [CrossRef]
  21. C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
    [CrossRef]
  22. R. Bach and K. Rzazewski, "Correlations in atomic systems: Diagnosing coherent superpositions," Phys. Rev. Lett. 92, 200401 (2004).
    [CrossRef] [PubMed]
  23. Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard and A. E. Leanhardt, "Atom interferrometry with Bose Einstein condensates in a double well potential," Phys. Rev. Lett. 92,050405 (2004).
    [CrossRef] [PubMed]
  24. C. H. van der Wal, F. K. Wilhelm, C. J. P. M. Harmans and J. E. Mooij, "Engineering decoherence in Josephson persistent-current qubits," Eur. Phys. J. B 31, 111-124 (2003).
    [CrossRef]
  25. D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle and J. Fortagh, "Meissner effect in superconducting microtraps," Phys. Rev. Lett. 101, 183006 (2008).
    [CrossRef] [PubMed]
  26. J. Q. You and F. Nori, "Superconducting circuits and quantum information," Phys. Today 58, 42-47 (2005)
    [CrossRef]

2008 (1)

D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle and J. Fortagh, "Meissner effect in superconducting microtraps," Phys. Rev. Lett. 101, 183006 (2008).
[CrossRef] [PubMed]

2007 (2)

P. Treutlein, D. Hunger, S. Camerer, T. W. H¨ansch, and J. Reichel, "A Bose Einstein condensate coupled to a nanomechanical resonator on an atom chip," Phys. Rev. Lett. 99, 140403 (2007).
[CrossRef] [PubMed]

T. Mukai, C. Hufnagel, A. Kasper, T. Meno, A. Tsukada, K. Semba, and F. Shimizu, "Persistent supercurrent atom chip," Phys. Rev. Lett. 98, 260407 (2007).
[CrossRef] [PubMed]

2006 (3)

S. Hofferberth, I. Lesanovsky, B. Fischer, J. Verdu, and J. Schmiedmayer, "Radiofrequency-dressed-state potentials for neutral atoms," Nat. Phys. 2, 710-716 (2006).
[CrossRef]

P. Treutlein, T. W. Hansch, J. Reichel, A. Negretti, M. A. Cirone, and T. Calarco, "Microwave potentials and optimal control for robust quantum gates on an atom chip," Phys. Rev. A 74, 022312 (2006).
[CrossRef]

T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
[CrossRef] [PubMed]

2005 (3)

J. Q. You and F. Nori, "Superconducting circuits and quantum information," Phys. Today 58, 42-47 (2005)
[CrossRef]

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

D. M. Harber, J. M. Obrecht, J. M. McGuirk, and E. A. Cornell, "Measurement of the Casimir-Polder force through centre-of-mass oscillations of a Bose Einstein condensate," Phys. Rev. A 72, 033610 (2005).
[CrossRef]

2004 (6)

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, "Coherence in microchip traps," Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, "De Broglie wavelength of a non-local four-photon Fock state," Nature (London) 429, 158-160 (2004).
[CrossRef]

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, "Super-resolving phase measurements with a multiphoton entangled state," Nature (London) 429, 161-164 (2004).
[CrossRef]

R. Bach and K. Rzazewski, "Correlations in atomic systems: Diagnosing coherent superpositions," Phys. Rev. Lett. 92, 200401 (2004).
[CrossRef] [PubMed]

Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard and A. E. Leanhardt, "Atom interferrometry with Bose Einstein condensates in a double well potential," Phys. Rev. Lett. 92,050405 (2004).
[CrossRef] [PubMed]

A. S. Sørensen, C. H. van der Wal, L. I. Childress, and M. D. Lukin, "Capacitive coupling of atomic systems to mesoscopic conductors," Phys. Rev. Lett. 92, 063601 (2004).
[CrossRef] [PubMed]

2003 (3)

C. H. van der Wal, F. K. Wilhelm, C. J. P. M. Harmans and J. E. Mooij, "Engineering decoherence in Josephson persistent-current qubits," Eur. Phys. J. B 31, 111-124 (2003).
[CrossRef]

I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, "Coherent quantum dynamics of a superconducting flux qubit," Science 299, 1869-1871 (2003).
[CrossRef] [PubMed]

M. P. A. Jones, C. J. Vale, D. Sahagun, B. V. Hall, and E. A. Hinds, "Spin coupling between cold atoms and the thermal fluctuations of a metal surface," Phys. Rev. Lett. 91, 080401 (2003).
[CrossRef] [PubMed]

2002 (1)

A. D. Armour, M. P. Blencowe, and K. C. Schwab, "Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper pair box," Phys. Rev. Lett. 88, 148301 (2002).
[CrossRef] [PubMed]

2001 (2)

Y. Makhlin, G. Schon, and A. Shnirman, "Quantum-state engineering with Josephson-junction devices," Rev. Mod. Phys. 73, 357-400 (2001).
[CrossRef]

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, "Bose Einstein condensation on a microelectronic chip," Nature (London) 413, 498-501 (2001).
[CrossRef]

2000 (3)

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, "Quantum superposition of distinct macroscopic states," Nature (London) 406, 43-46 (2000).
[CrossRef]

C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

1999 (2)

K. Mølmer and A. Sørensen, "Multiparticle entanglement of hot trapped ions," Phys. Rev. Lett. 82, 1835 (1999).
[CrossRef]

J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, "Josephson persistent current qubit," Science 285, 1036-1039 (1999).
[CrossRef] [PubMed]

Andersson, L. M.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Armour, A. D.

A. D. Armour, M. P. Blencowe, and K. C. Schwab, "Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper pair box," Phys. Rev. Lett. 88, 148301 (2002).
[CrossRef] [PubMed]

Aspelmeyer, M.

P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, "De Broglie wavelength of a non-local four-photon Fock state," Nature (London) 429, 158-160 (2004).
[CrossRef]

Bach, R.

R. Bach and K. Rzazewski, "Correlations in atomic systems: Diagnosing coherent superpositions," Phys. Rev. Lett. 92, 200401 (2004).
[CrossRef] [PubMed]

Bar-Joseph, I.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Blencowe, M. P.

A. D. Armour, M. P. Blencowe, and K. C. Schwab, "Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper pair box," Phys. Rev. Lett. 88, 148301 (2002).
[CrossRef] [PubMed]

Brune, M.

T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
[CrossRef] [PubMed]

Calarco, T.

P. Treutlein, T. W. Hansch, J. Reichel, A. Negretti, M. A. Cirone, and T. Calarco, "Microwave potentials and optimal control for robust quantum gates on an atom chip," Phys. Rev. A 74, 022312 (2006).
[CrossRef]

Camerer, S.

P. Treutlein, D. Hunger, S. Camerer, T. W. H¨ansch, and J. Reichel, "A Bose Einstein condensate coupled to a nanomechanical resonator on an atom chip," Phys. Rev. Lett. 99, 140403 (2007).
[CrossRef] [PubMed]

Cano, D.

D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle and J. Fortagh, "Meissner effect in superconducting microtraps," Phys. Rev. Lett. 101, 183006 (2008).
[CrossRef] [PubMed]

Chen, W.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, "Quantum superposition of distinct macroscopic states," Nature (London) 406, 43-46 (2000).
[CrossRef]

Childress, L. I.

A. S. Sørensen, C. H. van der Wal, L. I. Childress, and M. D. Lukin, "Capacitive coupling of atomic systems to mesoscopic conductors," Phys. Rev. Lett. 92, 063601 (2004).
[CrossRef] [PubMed]

Chiorescu, I.

I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, "Coherent quantum dynamics of a superconducting flux qubit," Science 299, 1869-1871 (2003).
[CrossRef] [PubMed]

Cirone, M. A.

P. Treutlein, T. W. Hansch, J. Reichel, A. Negretti, M. A. Cirone, and T. Calarco, "Microwave potentials and optimal control for robust quantum gates on an atom chip," Phys. Rev. A 74, 022312 (2006).
[CrossRef]

Cornell, E. A.

D. M. Harber, J. M. Obrecht, J. M. McGuirk, and E. A. Cornell, "Measurement of the Casimir-Polder force through centre-of-mass oscillations of a Bose Einstein condensate," Phys. Rev. A 72, 033610 (2005).
[CrossRef]

Emmert, A.

T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
[CrossRef] [PubMed]

Fischer, B.

S. Hofferberth, I. Lesanovsky, B. Fischer, J. Verdu, and J. Schmiedmayer, "Radiofrequency-dressed-state potentials for neutral atoms," Nat. Phys. 2, 710-716 (2006).
[CrossRef]

Fort’agh, J.

D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle and J. Fortagh, "Meissner effect in superconducting microtraps," Phys. Rev. Lett. 101, 183006 (2008).
[CrossRef] [PubMed]

Friedman, J. R.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, "Quantum superposition of distinct macroscopic states," Nature (London) 406, 43-46 (2000).
[CrossRef]

Gasparoni, S.

P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, "De Broglie wavelength of a non-local four-photon Fock state," Nature (London) 429, 158-160 (2004).
[CrossRef]

Groth, S.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

H¨ansch, T. W.

P. Treutlein, D. Hunger, S. Camerer, T. W. H¨ansch, and J. Reichel, "A Bose Einstein condensate coupled to a nanomechanical resonator on an atom chip," Phys. Rev. Lett. 99, 140403 (2007).
[CrossRef] [PubMed]

P. Treutlein, T. W. Hansch, J. Reichel, A. Negretti, M. A. Cirone, and T. Calarco, "Microwave potentials and optimal control for robust quantum gates on an atom chip," Phys. Rev. A 74, 022312 (2006).
[CrossRef]

Hall, B. V.

M. P. A. Jones, C. J. Vale, D. Sahagun, B. V. Hall, and E. A. Hinds, "Spin coupling between cold atoms and the thermal fluctuations of a metal surface," Phys. Rev. Lett. 91, 080401 (2003).
[CrossRef] [PubMed]

Hansch, T. W.

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, "Coherence in microchip traps," Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, "Bose Einstein condensation on a microelectronic chip," Nature (London) 413, 498-501 (2001).
[CrossRef]

Hansel, W.

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, "Bose Einstein condensation on a microelectronic chip," Nature (London) 413, 498-501 (2001).
[CrossRef]

Harber, D. M.

D. M. Harber, J. M. Obrecht, J. M. McGuirk, and E. A. Cornell, "Measurement of the Casimir-Polder force through centre-of-mass oscillations of a Bose Einstein condensate," Phys. Rev. A 72, 033610 (2005).
[CrossRef]

Harmans, C. J. P. M.

I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, "Coherent quantum dynamics of a superconducting flux qubit," Science 299, 1869-1871 (2003).
[CrossRef] [PubMed]

C. H. van der Wal, F. K. Wilhelm, C. J. P. M. Harmans and J. E. Mooij, "Engineering decoherence in Josephson persistent-current qubits," Eur. Phys. J. B 31, 111-124 (2003).
[CrossRef]

C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).

Haroche, S.

T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
[CrossRef] [PubMed]

Hattermann, H.

D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle and J. Fortagh, "Meissner effect in superconducting microtraps," Phys. Rev. Lett. 101, 183006 (2008).
[CrossRef] [PubMed]

Hinds, E. A.

M. P. A. Jones, C. J. Vale, D. Sahagun, B. V. Hall, and E. A. Hinds, "Spin coupling between cold atoms and the thermal fluctuations of a metal surface," Phys. Rev. Lett. 91, 080401 (2003).
[CrossRef] [PubMed]

Hofferberth, S.

S. Hofferberth, I. Lesanovsky, B. Fischer, J. Verdu, and J. Schmiedmayer, "Radiofrequency-dressed-state potentials for neutral atoms," Nat. Phys. 2, 710-716 (2006).
[CrossRef]

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Hommelhoff, P.

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, "Coherence in microchip traps," Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, "Bose Einstein condensation on a microelectronic chip," Nature (London) 413, 498-501 (2001).
[CrossRef]

Hufnagel, C.

T. Mukai, C. Hufnagel, A. Kasper, T. Meno, A. Tsukada, K. Semba, and F. Shimizu, "Persistent supercurrent atom chip," Phys. Rev. Lett. 98, 260407 (2007).
[CrossRef] [PubMed]

Hunger, D.

P. Treutlein, D. Hunger, S. Camerer, T. W. H¨ansch, and J. Reichel, "A Bose Einstein condensate coupled to a nanomechanical resonator on an atom chip," Phys. Rev. Lett. 99, 140403 (2007).
[CrossRef] [PubMed]

Itano, W. M.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

Jones, M. P. A.

M. P. A. Jones, C. J. Vale, D. Sahagun, B. V. Hall, and E. A. Hinds, "Spin coupling between cold atoms and the thermal fluctuations of a metal surface," Phys. Rev. Lett. 91, 080401 (2003).
[CrossRef] [PubMed]

Kasch, B.

D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle and J. Fortagh, "Meissner effect in superconducting microtraps," Phys. Rev. Lett. 101, 183006 (2008).
[CrossRef] [PubMed]

Kasper, A.

T. Mukai, C. Hufnagel, A. Kasper, T. Meno, A. Tsukada, K. Semba, and F. Shimizu, "Persistent supercurrent atom chip," Phys. Rev. Lett. 98, 260407 (2007).
[CrossRef] [PubMed]

Ketterle, W.

Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard and A. E. Leanhardt, "Atom interferrometry with Bose Einstein condensates in a double well potential," Phys. Rev. Lett. 92,050405 (2004).
[CrossRef] [PubMed]

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C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

King, B. E.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

Kleiner, R.

D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle and J. Fortagh, "Meissner effect in superconducting microtraps," Phys. Rev. Lett. 101, 183006 (2008).
[CrossRef] [PubMed]

Koelle, D.

D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle and J. Fortagh, "Meissner effect in superconducting microtraps," Phys. Rev. Lett. 101, 183006 (2008).
[CrossRef] [PubMed]

Kruger, P.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Langer, C.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

Leanhardt, A. E.

Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard and A. E. Leanhardt, "Atom interferrometry with Bose Einstein condensates in a double well potential," Phys. Rev. Lett. 92,050405 (2004).
[CrossRef] [PubMed]

Lesanovsky, I.

S. Hofferberth, I. Lesanovsky, B. Fischer, J. Verdu, and J. Schmiedmayer, "Radiofrequency-dressed-state potentials for neutral atoms," Nat. Phys. 2, 710-716 (2006).
[CrossRef]

Levitov, L.

J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, "Josephson persistent current qubit," Science 285, 1036-1039 (1999).
[CrossRef] [PubMed]

Lloyd, S.

C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).

J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, "Josephson persistent current qubit," Science 285, 1036-1039 (1999).
[CrossRef] [PubMed]

Lukens, J. E.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, "Quantum superposition of distinct macroscopic states," Nature (London) 406, 43-46 (2000).
[CrossRef]

Lukin, M. D.

A. S. Sørensen, C. H. van der Wal, L. I. Childress, and M. D. Lukin, "Capacitive coupling of atomic systems to mesoscopic conductors," Phys. Rev. Lett. 92, 063601 (2004).
[CrossRef] [PubMed]

Lundeen, J. S.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, "Super-resolving phase measurements with a multiphoton entangled state," Nature (London) 429, 161-164 (2004).
[CrossRef]

Makhlin, Y.

Y. Makhlin, G. Schon, and A. Shnirman, "Quantum-state engineering with Josephson-junction devices," Rev. Mod. Phys. 73, 357-400 (2001).
[CrossRef]

McGuirk, J. M.

D. M. Harber, J. M. Obrecht, J. M. McGuirk, and E. A. Cornell, "Measurement of the Casimir-Polder force through centre-of-mass oscillations of a Bose Einstein condensate," Phys. Rev. A 72, 033610 (2005).
[CrossRef]

Meno, T.

T. Mukai, C. Hufnagel, A. Kasper, T. Meno, A. Tsukada, K. Semba, and F. Shimizu, "Persistent supercurrent atom chip," Phys. Rev. Lett. 98, 260407 (2007).
[CrossRef] [PubMed]

Meyer, V.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

Mitchell, M. W.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, "Super-resolving phase measurements with a multiphoton entangled state," Nature (London) 429, 161-164 (2004).
[CrossRef]

Mølmer, K.

K. Mølmer and A. Sørensen, "Multiparticle entanglement of hot trapped ions," Phys. Rev. Lett. 82, 1835 (1999).
[CrossRef]

Monroe, C.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

Mooij, J. E.

C. H. van der Wal, F. K. Wilhelm, C. J. P. M. Harmans and J. E. Mooij, "Engineering decoherence in Josephson persistent-current qubits," Eur. Phys. J. B 31, 111-124 (2003).
[CrossRef]

I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, "Coherent quantum dynamics of a superconducting flux qubit," Science 299, 1869-1871 (2003).
[CrossRef] [PubMed]

C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).

J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, "Josephson persistent current qubit," Science 285, 1036-1039 (1999).
[CrossRef] [PubMed]

Mukai, T.

T. Mukai, C. Hufnagel, A. Kasper, T. Meno, A. Tsukada, K. Semba, and F. Shimizu, "Persistent supercurrent atom chip," Phys. Rev. Lett. 98, 260407 (2007).
[CrossRef] [PubMed]

Myatt, C. J.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

Nakamura, Y.

I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, "Coherent quantum dynamics of a superconducting flux qubit," Science 299, 1869-1871 (2003).
[CrossRef] [PubMed]

Negretti, A.

P. Treutlein, T. W. Hansch, J. Reichel, A. Negretti, M. A. Cirone, and T. Calarco, "Microwave potentials and optimal control for robust quantum gates on an atom chip," Phys. Rev. A 74, 022312 (2006).
[CrossRef]

Nirrengarten, T.

T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
[CrossRef] [PubMed]

Nogues, G.

T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
[CrossRef] [PubMed]

Obrecht, J. M.

D. M. Harber, J. M. Obrecht, J. M. McGuirk, and E. A. Cornell, "Measurement of the Casimir-Polder force through centre-of-mass oscillations of a Bose Einstein condensate," Phys. Rev. A 72, 033610 (2005).
[CrossRef]

Orlando, T. P.

C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).

J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, "Josephson persistent current qubit," Science 285, 1036-1039 (1999).
[CrossRef] [PubMed]

Pan, J.-W.

P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, "De Broglie wavelength of a non-local four-photon Fock state," Nature (London) 429, 158-160 (2004).
[CrossRef]

Pasquini, T. A.

Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard and A. E. Leanhardt, "Atom interferrometry with Bose Einstein condensates in a double well potential," Phys. Rev. Lett. 92,050405 (2004).
[CrossRef] [PubMed]

Patel, V.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, "Quantum superposition of distinct macroscopic states," Nature (London) 406, 43-46 (2000).
[CrossRef]

Pritchard, D. E.

Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard and A. E. Leanhardt, "Atom interferrometry with Bose Einstein condensates in a double well potential," Phys. Rev. Lett. 92,050405 (2004).
[CrossRef] [PubMed]

Qarry, A.

T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
[CrossRef] [PubMed]

Raimond, J.-M.

T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
[CrossRef] [PubMed]

Reichel, J.

P. Treutlein, D. Hunger, S. Camerer, T. W. H¨ansch, and J. Reichel, "A Bose Einstein condensate coupled to a nanomechanical resonator on an atom chip," Phys. Rev. Lett. 99, 140403 (2007).
[CrossRef] [PubMed]

P. Treutlein, T. W. Hansch, J. Reichel, A. Negretti, M. A. Cirone, and T. Calarco, "Microwave potentials and optimal control for robust quantum gates on an atom chip," Phys. Rev. A 74, 022312 (2006).
[CrossRef]

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, "Coherence in microchip traps," Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

W. Hansel, P. Hommelhoff, T. W. Hansch, and J. Reichel, "Bose Einstein condensation on a microelectronic chip," Nature (London) 413, 498-501 (2001).
[CrossRef]

Roux, C.

T. Nirrengarten, A. Qarry, C. Roux, A. Emmert, G. Nogues, M. Brune, J.-M. Raimond and S. Haroche, "Realization of a superconducting atom chip," Phys. Rev. Lett. 97, 200405 (2006).
[CrossRef] [PubMed]

Rowe, M.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

Rza¸ ?zewski, K.

R. Bach and K. Rzazewski, "Correlations in atomic systems: Diagnosing coherent superpositions," Phys. Rev. Lett. 92, 200401 (2004).
[CrossRef] [PubMed]

Saba, M.

Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard and A. E. Leanhardt, "Atom interferrometry with Bose Einstein condensates in a double well potential," Phys. Rev. Lett. 92,050405 (2004).
[CrossRef] [PubMed]

Sackett, C. A.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

Sahagun, D.

M. P. A. Jones, C. J. Vale, D. Sahagun, B. V. Hall, and E. A. Hinds, "Spin coupling between cold atoms and the thermal fluctuations of a metal surface," Phys. Rev. Lett. 91, 080401 (2003).
[CrossRef] [PubMed]

Schmiedmayer, J.

S. Hofferberth, I. Lesanovsky, B. Fischer, J. Verdu, and J. Schmiedmayer, "Radiofrequency-dressed-state potentials for neutral atoms," Nat. Phys. 2, 710-716 (2006).
[CrossRef]

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Schon, G.

Y. Makhlin, G. Schon, and A. Shnirman, "Quantum-state engineering with Josephson-junction devices," Rev. Mod. Phys. 73, 357-400 (2001).
[CrossRef]

Schouten, R. N.

C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).

Schumm, T.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Schwab, K. C.

A. D. Armour, M. P. Blencowe, and K. C. Schwab, "Entanglement and decoherence of a micromechanical resonator via coupling to a Cooper pair box," Phys. Rev. Lett. 88, 148301 (2002).
[CrossRef] [PubMed]

Semba, K.

T. Mukai, C. Hufnagel, A. Kasper, T. Meno, A. Tsukada, K. Semba, and F. Shimizu, "Persistent supercurrent atom chip," Phys. Rev. Lett. 98, 260407 (2007).
[CrossRef] [PubMed]

Shimizu, F.

T. Mukai, C. Hufnagel, A. Kasper, T. Meno, A. Tsukada, K. Semba, and F. Shimizu, "Persistent supercurrent atom chip," Phys. Rev. Lett. 98, 260407 (2007).
[CrossRef] [PubMed]

Shin, Y.

Y. Shin, M. Saba, T. A. Pasquini, W. Ketterle, D. E. Pritchard and A. E. Leanhardt, "Atom interferrometry with Bose Einstein condensates in a double well potential," Phys. Rev. Lett. 92,050405 (2004).
[CrossRef] [PubMed]

Shnirman, A.

Y. Makhlin, G. Schon, and A. Shnirman, "Quantum-state engineering with Josephson-junction devices," Rev. Mod. Phys. 73, 357-400 (2001).
[CrossRef]

Sørensen, A.

K. Mølmer and A. Sørensen, "Multiparticle entanglement of hot trapped ions," Phys. Rev. Lett. 82, 1835 (1999).
[CrossRef]

Sørensen, A. S.

A. S. Sørensen, C. H. van der Wal, L. I. Childress, and M. D. Lukin, "Capacitive coupling of atomic systems to mesoscopic conductors," Phys. Rev. Lett. 92, 063601 (2004).
[CrossRef] [PubMed]

Steinberg, A. M.

M. W. Mitchell, J. S. Lundeen, and A. M. Steinberg, "Super-resolving phase measurements with a multiphoton entangled state," Nature (London) 429, 161-164 (2004).
[CrossRef]

Steinmetz, T.

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, "Coherence in microchip traps," Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

ter Haar, A. C. J.

C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).

Tian, L.

J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, "Josephson persistent current qubit," Science 285, 1036-1039 (1999).
[CrossRef] [PubMed]

Tolpygo, S. K.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, "Quantum superposition of distinct macroscopic states," Nature (London) 406, 43-46 (2000).
[CrossRef]

Treutlein, P.

P. Treutlein, D. Hunger, S. Camerer, T. W. H¨ansch, and J. Reichel, "A Bose Einstein condensate coupled to a nanomechanical resonator on an atom chip," Phys. Rev. Lett. 99, 140403 (2007).
[CrossRef] [PubMed]

P. Treutlein, T. W. Hansch, J. Reichel, A. Negretti, M. A. Cirone, and T. Calarco, "Microwave potentials and optimal control for robust quantum gates on an atom chip," Phys. Rev. A 74, 022312 (2006).
[CrossRef]

P. Treutlein, P. Hommelhoff, T. Steinmetz, T. W. Hansch, and J. Reichel, "Coherence in microchip traps," Phys. Rev. Lett. 92, 203005 (2004).
[CrossRef] [PubMed]

Tsukada, A.

T. Mukai, C. Hufnagel, A. Kasper, T. Meno, A. Tsukada, K. Semba, and F. Shimizu, "Persistent supercurrent atom chip," Phys. Rev. Lett. 98, 260407 (2007).
[CrossRef] [PubMed]

Turchette, Q. A.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

Ursin, R.

P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, "De Broglie wavelength of a non-local four-photon Fock state," Nature (London) 429, 158-160 (2004).
[CrossRef]

Vale, C. J.

M. P. A. Jones, C. J. Vale, D. Sahagun, B. V. Hall, and E. A. Hinds, "Spin coupling between cold atoms and the thermal fluctuations of a metal surface," Phys. Rev. Lett. 91, 080401 (2003).
[CrossRef] [PubMed]

van der Wal, C. H.

A. S. Sørensen, C. H. van der Wal, L. I. Childress, and M. D. Lukin, "Capacitive coupling of atomic systems to mesoscopic conductors," Phys. Rev. Lett. 92, 063601 (2004).
[CrossRef] [PubMed]

C. H. van der Wal, F. K. Wilhelm, C. J. P. M. Harmans and J. E. Mooij, "Engineering decoherence in Josephson persistent-current qubits," Eur. Phys. J. B 31, 111-124 (2003).
[CrossRef]

J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, "Josephson persistent current qubit," Science 285, 1036-1039 (1999).
[CrossRef] [PubMed]

van derWal, C. H.

C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).

Verdu, J.

S. Hofferberth, I. Lesanovsky, B. Fischer, J. Verdu, and J. Schmiedmayer, "Radiofrequency-dressed-state potentials for neutral atoms," Nat. Phys. 2, 710-716 (2006).
[CrossRef]

Walther, P.

P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, "De Broglie wavelength of a non-local four-photon Fock state," Nature (London) 429, 158-160 (2004).
[CrossRef]

Wildermuth, S.

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

Wilhelm, F. K.

C. H. van der Wal, F. K. Wilhelm, C. J. P. M. Harmans and J. E. Mooij, "Engineering decoherence in Josephson persistent-current qubits," Eur. Phys. J. B 31, 111-124 (2003).
[CrossRef]

C. H. van derWal, A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij, "Quantum superposition of macroscopic persistent current states," Science 209, 773-777 (2000).

Wineland, D. J.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland and C. Monroe, "Experimental entanglement of four particles," Nature (London) 404, 256-259 (2000).
[CrossRef]

You, J. Q.

J. Q. You and F. Nori, "Superconducting circuits and quantum information," Phys. Today 58, 42-47 (2005)
[CrossRef]

Zeilinger, A.

P. Walther, J.-W. Pan, M. Aspelmeyer, R. Ursin, S. Gasparoni, and A. Zeilinger, "De Broglie wavelength of a non-local four-photon Fock state," Nature (London) 429, 158-160 (2004).
[CrossRef]

Zimmermann, C.

D. Cano, B. Kasch, H. Hattermann, R. Kleiner, C. Zimmermann, D. Koelle and J. Fortagh, "Meissner effect in superconducting microtraps," Phys. Rev. Lett. 101, 183006 (2008).
[CrossRef] [PubMed]

Eur. Phys. J. B (1)

C. H. van der Wal, F. K. Wilhelm, C. J. P. M. Harmans and J. E. Mooij, "Engineering decoherence in Josephson persistent-current qubits," Eur. Phys. J. B 31, 111-124 (2003).
[CrossRef]

Nat. Phys. (2)

T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer and P. Kruger, "Matter-wave interferometry in a double well on an atom chip," Nat. Phys. 1, 57-62 (2005).
[CrossRef]

S. Hofferberth, I. Lesanovsky, B. Fischer, J. Verdu, and J. Schmiedmayer, "Radiofrequency-dressed-state potentials for neutral atoms," Nat. Phys. 2, 710-716 (2006).
[CrossRef]

Nature (London) (5)

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Figures (5)

Fig. 1.
Fig. 1.

Schematic showing a superconducting loop situated symmetrically above a Z-shaped wire magnetic trap. The persistent current in the loop can exist in a quantum superposition in the clockwise and anti-clockwise directions. The magnetic field produced by the persistent current can perturb the BEC trapping potential where the degree of perturbation can be increased by moving the trap center closer to the loop. The superconducting loop can be biased appropriately by applying an external magnetic field along the z-direction.

Fig. 2.
Fig. 2.

Magnetic field intensity profile along the axial direction of a Z-wire magnetic trap coupled to a superconducting loop when the persistent current flows (a) clockwise and (b) anti-clockwise. The dotted curve (red) represents the harmonic field profile without any coupling. The dashed curve (green) and solid line (blue) show the effect of perturbation when a persistent current in the loop generates a flux through the loop of magnitude one-quarter and one-half of a flux quantum, respectively.

Fig. 3.
Fig. 3.

Magnetic field intensity profile around the trap minimum when a clockwise flow of persistent current generates a flux through the loop of magnitude one-half of a flux quantum. Radial and axial axes lie in the horizontal plane passing through the trap minimum.

Fig. 4.
Fig. 4.

Density plot showing the magnetic field intensity in the horizontal plane. The colour scheme has one to one correspondence with that indicated in Fig. 3.

Fig. 5.
Fig. 5.

Perturbation amplitude as a function of distance (d) between the superconducting loop and the centre of the magnetic trap when the persistent current generates a flux through the loop of magnitude one-half of a flux quantum.

Equations (15)

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H S = E 0 0 0 + E 0 1 1 + J 1 0 + J 0 1
H T = Ψ ̂ ( r ) [ ( h ̄ 2 2 m 2 + V ( r ) ) I ̂ + Δ V 0 ( r , t ) 0 0 + Δ V 1 ( r , t ) 1 1 ] Ψ ̂ ( r ) d r
Ψ ̂ ( r , t ) = a ̂ 0 ϕ 0 ( r , t ) 0 0 + a ̂ 1 ϕ 1 ( r , t ) 1 1
H ( t ) = E 0 0 0 + E 0 1 1 + μ 0 ( t ) a ̂ 0 a ̂ 0 0 0 + μ 1 ( t ) a ̂ 1 a ̂ 1 1 1
μ 0 ( t ) = ϕ 0 ( r , t ) ( h ̄ 2 2 m 2 + V ( r ) + Δ V 0 ( r , t ) ) ϕ 0 ( r , t ) d r
μ 1 ( t ) = ϕ 1 ( r , t ) ( h ̄ 2 2 m 2 + V ( r ) + Δ V 1 ( r , t ) ) ϕ 1 ( r , t ) d r
Ψ , t = e i γ 0 ( t ) i ( E 0 t + N 0 t μ 0 ( t′ ) dt′ ) / h ̄ 2 × [ 0 N , ϕ 0 ( r , t ) + e Φ ( t ) 1 N , ϕ 1 ( r , t ) ]
Φ ( t ) = N 0 t μ 0 ( t′ ) μ 1 ( t′ ) h ̄ d t′ + γ 1 ( t ) γ 0 ( t )
e i h ̄ 0 t μ 0 ( t′ ) a ̂ 0 a ̂ 0 0 0 d t′ 0 N , ϕ ( r , t = 0 ) = e iN h ̄ 0 t μ 0 ( t′ ) d t′ e i γ 0 ( t ) 0 N , ϕ 0 ( r , t )
e i h ̄ 0 t μ 1 ( t′ ) a ̂ 1 a ̂ 1 1 1 d t′ 1 N , ϕ ( r , t = 0 ) = e iN h ̄ 0 t μ 1 ( t′ ) d t′ e i γ 1 ( t ) 1 N , ϕ 1 ( r , t )
n ( r , t ) = Ψ , t Ψ ̂ ( t ) Ψ ̂ ( t ) Ψ , t = 1 2 ( ϕ 0 ( r , t ) 2 + ϕ 1 ( r , t ) 2 )
Ψ , t = 1 2 [ + S + A ]
Ψ , t = 1 2 0 ( N , ϕ 0 ( r , t ) + e ( t ) N , ϕ 1 ( r , t ) )
V ( x , y , z , t ) = 1 2 m ω x 2 ( t ) x 2 + 1 2 m ω y 1 ( t ) y 2 + 1 2 m ω z 2 ( t ) ( z + z 0 ( t ) ) 2 + V 0 +
2 a ( t ) y σ 2 e y 2 σ 2 0 0 2 a ( t ) y σ 2 e y 2 σ 2 1 1

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