Abstract

We consider Bloch oscillations of ultracold atoms stored in a one-dimensional vertical optical lattice and simultaneously interacting with a unidirectionally pumped optical ring cavity whose vertical arm is collinear with the optical lattice. We find that the feedback provided by the cavity field on the atomic motion synchronizes Bloch oscillations via a mode-locking mechanism, steering the atoms to the lowest Bloch band. It also stabilizes Bloch oscillations against noise, and even suppresses dephasing due to atom-atom interactions. Furthermore, it generates periodic bursts of light emitted into the counter-propagating cavity mode, providing a non-destructive monitor of the atomic dynamics. All these features may be crucial for future improvements of the design of atomic gravimeters based on recording Bloch oscillations.

© 2015 Optical Society of America

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  1. M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508 (1996).
    [Crossref] [PubMed]
  2. E. Peik, M. B. Dahan, I. Bouchoule, Y. Castin, and C. Salomon, “Bloch oscillations of atoms, adiabatic rapid passage, and monokinetic atomic beams,” Phys. Rev. A 55, 2989 (1997).
    [Crossref]
  3. P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave,” Europhys. Lett. 71, 730 (2005).
    [Crossref]
  4. G. Ferrari, N. Poli, F. Sorrentino, and G.M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
    [Crossref] [PubMed]
  5. B. M. Peden, D. Meiser, M. L. Chiofalo, and M. J. Holland, “Nondestructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms,” Phys. Rev. A 80, 043803 (2009).
    [Crossref]
  6. B. P. Venkatesh, M. Trupke, E. A. Hinds, and D. H. J. O’Dell, “Atomic Bloch–Zener oscillations for sensitive force measurements in a cavity,” Phys. Rev. A 80, 063834 (2009).
    [Crossref]
  7. J. Goldwin, B. P. Venkatesh, and D. H. J. O’Dell, “Backaction-driven transport of Bloch oscillating atoms in ring cavities,” Phys. Rev. Lett. 113, 073003 (2014).
    [Crossref] [PubMed]
  8. M. Samoylova, N. Piovella, D. Hunter, G. R. M. Robb, R. Bachelard, and Ph. W. Courteille, “Mode-locked Bloch oscillations in a ring cavity,” Laser Phys. Lett. 11, 126005 (2015).
    [Crossref]
  9. R. Bonifacio, L. DeSalvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716 (1994).
    [Crossref] [PubMed]
  10. B. P. Venkatesh and D. H. J. O’Dell, “Bloch oscillations of cold atoms in a cavity: effects of quantum noise,” Phys. Rev. A 88, 013848 (2013).
    [Crossref]
  11. M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, “Control of interaction-induced dephasing of Bloch oscillations,” Phys. Rev. Lett. 100, 080404 (2008).
    [Crossref] [PubMed]
  12. F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
    [Crossref] [PubMed]
  13. D. Kruse, C. von Cube, C. Zimmermann, and Ph. W. Courteille, “Observation of lasing mediated by collective atomic recoil,” Phys. Rev. Lett. 91, 183601 (2003).
    [Crossref] [PubMed]
  14. B. Nagorny, Th. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91, 153003 (2003).
    [Crossref] [PubMed]
  15. S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
    [Crossref] [PubMed]
  16. N. Piovella, M. Gatelli, and R. Bonifacio, “Quantum effects in the collective light scattering by coherent atomic recoil in a Bose-Einstein condensate,” Opt. Commun. 194, 167 (2001).
    [Crossref]
  17. M. Glück, A. R. Kolovsky, and H. Jürgen Korsch, “Wannier-Stark resonances in optical and semiconductor superlattices,” Phys. Rep. 366 (3), 103 (2002).
    [Crossref]
  18. N. Piovella, L. Salasnich, R. Bonifacio, and G. R. M. Robb, “Atomic interaction effects in the superradiant light scattering from a Bose–Einstein condensate,” Las. Phys. 14, 278 (2004).
  19. S. Giovanazzi, D. O’Dell, and G. Kurizki, “Density modulations of Bose–Einstein condensates via laser-induced interactions,” Phys. Rev. Lett. 88, 130402 (2002).
    [Crossref]
  20. D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, “Rotons in gaseous Bose–Einstein condensates irradiated by a laser,” Phys. Rev. Lett. 90, 110402 (2003).
    [Crossref]
  21. I. E. Mazets, D. H. J. O’Dell, G. Kurizki, N. Davidson, and W. P. Schleich, “Depletion of a Bose–Einstein condensate by laser-induced dipoledipole interactions,” J. Phys. B: At. Mol. Opt. Phys. 37, S155 (2004).
    [Crossref]
  22. M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
    [Crossref]
  23. T. Hartmann, F. Keck, H. J. Korsch, and S. Mossmann, “Dynamics of Bloch oscillations,” New J. Phys. 6, 2 (2004).
    [Crossref]
  24. D. Jaksch, S. A. Gardiner, K. Schulze, J. I. Cirac, and P. Zoller, “Uniting Bose–Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4733 (2001).
    [Crossref] [PubMed]

2015 (1)

M. Samoylova, N. Piovella, D. Hunter, G. R. M. Robb, R. Bachelard, and Ph. W. Courteille, “Mode-locked Bloch oscillations in a ring cavity,” Laser Phys. Lett. 11, 126005 (2015).
[Crossref]

2014 (2)

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
[Crossref] [PubMed]

J. Goldwin, B. P. Venkatesh, and D. H. J. O’Dell, “Backaction-driven transport of Bloch oscillating atoms in ring cavities,” Phys. Rev. Lett. 113, 073003 (2014).
[Crossref] [PubMed]

2013 (1)

B. P. Venkatesh and D. H. J. O’Dell, “Bloch oscillations of cold atoms in a cavity: effects of quantum noise,” Phys. Rev. A 88, 013848 (2013).
[Crossref]

2010 (1)

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
[Crossref]

2009 (2)

B. M. Peden, D. Meiser, M. L. Chiofalo, and M. J. Holland, “Nondestructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms,” Phys. Rev. A 80, 043803 (2009).
[Crossref]

B. P. Venkatesh, M. Trupke, E. A. Hinds, and D. H. J. O’Dell, “Atomic Bloch–Zener oscillations for sensitive force measurements in a cavity,” Phys. Rev. A 80, 063834 (2009).
[Crossref]

2008 (1)

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, “Control of interaction-induced dephasing of Bloch oscillations,” Phys. Rev. Lett. 100, 080404 (2008).
[Crossref] [PubMed]

2007 (1)

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref] [PubMed]

2006 (1)

G. Ferrari, N. Poli, F. Sorrentino, and G.M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref] [PubMed]

2005 (1)

P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave,” Europhys. Lett. 71, 730 (2005).
[Crossref]

2004 (3)

T. Hartmann, F. Keck, H. J. Korsch, and S. Mossmann, “Dynamics of Bloch oscillations,” New J. Phys. 6, 2 (2004).
[Crossref]

N. Piovella, L. Salasnich, R. Bonifacio, and G. R. M. Robb, “Atomic interaction effects in the superradiant light scattering from a Bose–Einstein condensate,” Las. Phys. 14, 278 (2004).

I. E. Mazets, D. H. J. O’Dell, G. Kurizki, N. Davidson, and W. P. Schleich, “Depletion of a Bose–Einstein condensate by laser-induced dipoledipole interactions,” J. Phys. B: At. Mol. Opt. Phys. 37, S155 (2004).
[Crossref]

2003 (3)

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, “Rotons in gaseous Bose–Einstein condensates irradiated by a laser,” Phys. Rev. Lett. 90, 110402 (2003).
[Crossref]

D. Kruse, C. von Cube, C. Zimmermann, and Ph. W. Courteille, “Observation of lasing mediated by collective atomic recoil,” Phys. Rev. Lett. 91, 183601 (2003).
[Crossref] [PubMed]

B. Nagorny, Th. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91, 153003 (2003).
[Crossref] [PubMed]

2002 (2)

M. Glück, A. R. Kolovsky, and H. Jürgen Korsch, “Wannier-Stark resonances in optical and semiconductor superlattices,” Phys. Rep. 366 (3), 103 (2002).
[Crossref]

S. Giovanazzi, D. O’Dell, and G. Kurizki, “Density modulations of Bose–Einstein condensates via laser-induced interactions,” Phys. Rev. Lett. 88, 130402 (2002).
[Crossref]

2001 (2)

D. Jaksch, S. A. Gardiner, K. Schulze, J. I. Cirac, and P. Zoller, “Uniting Bose–Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4733 (2001).
[Crossref] [PubMed]

N. Piovella, M. Gatelli, and R. Bonifacio, “Quantum effects in the collective light scattering by coherent atomic recoil in a Bose-Einstein condensate,” Opt. Commun. 194, 167 (2001).
[Crossref]

1997 (1)

E. Peik, M. B. Dahan, I. Bouchoule, Y. Castin, and C. Salomon, “Bloch oscillations of atoms, adiabatic rapid passage, and monokinetic atomic beams,” Phys. Rev. A 55, 2989 (1997).
[Crossref]

1996 (1)

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508 (1996).
[Crossref] [PubMed]

1994 (1)

R. Bonifacio, L. DeSalvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716 (1994).
[Crossref] [PubMed]

Bachelard, R.

M. Samoylova, N. Piovella, D. Hunter, G. R. M. Robb, R. Bachelard, and Ph. W. Courteille, “Mode-locked Bloch oscillations in a ring cavity,” Laser Phys. Lett. 11, 126005 (2015).
[Crossref]

Biraben, F.

P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave,” Europhys. Lett. 71, 730 (2005).
[Crossref]

Bonifacio, R.

N. Piovella, L. Salasnich, R. Bonifacio, and G. R. M. Robb, “Atomic interaction effects in the superradiant light scattering from a Bose–Einstein condensate,” Las. Phys. 14, 278 (2004).

N. Piovella, M. Gatelli, and R. Bonifacio, “Quantum effects in the collective light scattering by coherent atomic recoil in a Bose-Einstein condensate,” Opt. Commun. 194, 167 (2001).
[Crossref]

R. Bonifacio, L. DeSalvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716 (1994).
[Crossref] [PubMed]

Bouchoule, I.

E. Peik, M. B. Dahan, I. Bouchoule, Y. Castin, and C. Salomon, “Bloch oscillations of atoms, adiabatic rapid passage, and monokinetic atomic beams,” Phys. Rev. A 55, 2989 (1997).
[Crossref]

Bux, S.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref] [PubMed]

Castin, Y.

E. Peik, M. B. Dahan, I. Bouchoule, Y. Castin, and C. Salomon, “Bloch oscillations of atoms, adiabatic rapid passage, and monokinetic atomic beams,” Phys. Rev. A 55, 2989 (1997).
[Crossref]

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508 (1996).
[Crossref] [PubMed]

Chiofalo, M. L.

B. M. Peden, D. Meiser, M. L. Chiofalo, and M. J. Holland, “Nondestructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms,” Phys. Rev. A 80, 043803 (2009).
[Crossref]

Cirac, J. I.

D. Jaksch, S. A. Gardiner, K. Schulze, J. I. Cirac, and P. Zoller, “Uniting Bose–Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4733 (2001).
[Crossref] [PubMed]

Cladé, P.

P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave,” Europhys. Lett. 71, 730 (2005).
[Crossref]

Courteille, Ph. W.

M. Samoylova, N. Piovella, D. Hunter, G. R. M. Robb, R. Bachelard, and Ph. W. Courteille, “Mode-locked Bloch oscillations in a ring cavity,” Laser Phys. Lett. 11, 126005 (2015).
[Crossref]

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref] [PubMed]

D. Kruse, C. von Cube, C. Zimmermann, and Ph. W. Courteille, “Observation of lasing mediated by collective atomic recoil,” Phys. Rev. Lett. 91, 183601 (2003).
[Crossref] [PubMed]

D’Angelo, E. J.

R. Bonifacio, L. DeSalvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716 (1994).
[Crossref] [PubMed]

Dahan, M. B.

E. Peik, M. B. Dahan, I. Bouchoule, Y. Castin, and C. Salomon, “Bloch oscillations of atoms, adiabatic rapid passage, and monokinetic atomic beams,” Phys. Rev. A 55, 2989 (1997).
[Crossref]

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508 (1996).
[Crossref] [PubMed]

Daley, A. J.

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
[Crossref]

Danzl, J. G.

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
[Crossref]

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, “Control of interaction-induced dephasing of Bloch oscillations,” Phys. Rev. Lett. 100, 080404 (2008).
[Crossref] [PubMed]

Davidson, N.

I. E. Mazets, D. H. J. O’Dell, G. Kurizki, N. Davidson, and W. P. Schleich, “Depletion of a Bose–Einstein condensate by laser-induced dipoledipole interactions,” J. Phys. B: At. Mol. Opt. Phys. 37, S155 (2004).
[Crossref]

DeSalvo, L.

R. Bonifacio, L. DeSalvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716 (1994).
[Crossref] [PubMed]

Elsässer, Th.

B. Nagorny, Th. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91, 153003 (2003).
[Crossref] [PubMed]

Ferrari, G.

G. Ferrari, N. Poli, F. Sorrentino, and G.M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref] [PubMed]

Gardiner, S. A.

D. Jaksch, S. A. Gardiner, K. Schulze, J. I. Cirac, and P. Zoller, “Uniting Bose–Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4733 (2001).
[Crossref] [PubMed]

Gatelli, M.

N. Piovella, M. Gatelli, and R. Bonifacio, “Quantum effects in the collective light scattering by coherent atomic recoil in a Bose-Einstein condensate,” Opt. Commun. 194, 167 (2001).
[Crossref]

Giovanazzi, S.

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, “Rotons in gaseous Bose–Einstein condensates irradiated by a laser,” Phys. Rev. Lett. 90, 110402 (2003).
[Crossref]

S. Giovanazzi, D. O’Dell, and G. Kurizki, “Density modulations of Bose–Einstein condensates via laser-induced interactions,” Phys. Rev. Lett. 88, 130402 (2002).
[Crossref]

Glück, M.

M. Glück, A. R. Kolovsky, and H. Jürgen Korsch, “Wannier-Stark resonances in optical and semiconductor superlattices,” Phys. Rep. 366 (3), 103 (2002).
[Crossref]

Goldwin, J.

J. Goldwin, B. P. Venkatesh, and D. H. J. O’Dell, “Backaction-driven transport of Bloch oscillating atoms in ring cavities,” Phys. Rev. Lett. 113, 073003 (2014).
[Crossref] [PubMed]

Gröbner, M.

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
[Crossref] [PubMed]

Guellati-Khélifa, S.

P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave,” Europhys. Lett. 71, 730 (2005).
[Crossref]

Gustavsson, M.

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
[Crossref]

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, “Control of interaction-induced dephasing of Bloch oscillations,” Phys. Rev. Lett. 100, 080404 (2008).
[Crossref] [PubMed]

Haller, E.

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
[Crossref]

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, “Control of interaction-induced dephasing of Bloch oscillations,” Phys. Rev. Lett. 100, 080404 (2008).
[Crossref] [PubMed]

Hart, R.

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
[Crossref]

Hartmann, T.

T. Hartmann, F. Keck, H. J. Korsch, and S. Mossmann, “Dynamics of Bloch oscillations,” New J. Phys. 6, 2 (2004).
[Crossref]

Hemmerich, A.

B. Nagorny, Th. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91, 153003 (2003).
[Crossref] [PubMed]

Hinds, E. A.

B. P. Venkatesh, M. Trupke, E. A. Hinds, and D. H. J. O’Dell, “Atomic Bloch–Zener oscillations for sensitive force measurements in a cavity,” Phys. Rev. A 80, 063834 (2009).
[Crossref]

Holland, M. J.

B. M. Peden, D. Meiser, M. L. Chiofalo, and M. J. Holland, “Nondestructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms,” Phys. Rev. A 80, 043803 (2009).
[Crossref]

Hunter, D.

M. Samoylova, N. Piovella, D. Hunter, G. R. M. Robb, R. Bachelard, and Ph. W. Courteille, “Mode-locked Bloch oscillations in a ring cavity,” Laser Phys. Lett. 11, 126005 (2015).
[Crossref]

Jaksch, D.

D. Jaksch, S. A. Gardiner, K. Schulze, J. I. Cirac, and P. Zoller, “Uniting Bose–Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4733 (2001).
[Crossref] [PubMed]

Julien, L.

P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave,” Europhys. Lett. 71, 730 (2005).
[Crossref]

Jürgen Korsch, H.

M. Glück, A. R. Kolovsky, and H. Jürgen Korsch, “Wannier-Stark resonances in optical and semiconductor superlattices,” Phys. Rep. 366 (3), 103 (2002).
[Crossref]

Keck, F.

T. Hartmann, F. Keck, H. J. Korsch, and S. Mossmann, “Dynamics of Bloch oscillations,” New J. Phys. 6, 2 (2004).
[Crossref]

Kirilov, E.

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
[Crossref] [PubMed]

Kolovsky, A. R.

M. Glück, A. R. Kolovsky, and H. Jürgen Korsch, “Wannier-Stark resonances in optical and semiconductor superlattices,” Phys. Rep. 366 (3), 103 (2002).
[Crossref]

Korsch, H. J.

T. Hartmann, F. Keck, H. J. Korsch, and S. Mossmann, “Dynamics of Bloch oscillations,” New J. Phys. 6, 2 (2004).
[Crossref]

Krenz, G.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref] [PubMed]

Kruse, D.

D. Kruse, C. von Cube, C. Zimmermann, and Ph. W. Courteille, “Observation of lasing mediated by collective atomic recoil,” Phys. Rev. Lett. 91, 183601 (2003).
[Crossref] [PubMed]

Kurizki, G.

I. E. Mazets, D. H. J. O’Dell, G. Kurizki, N. Davidson, and W. P. Schleich, “Depletion of a Bose–Einstein condensate by laser-induced dipoledipole interactions,” J. Phys. B: At. Mol. Opt. Phys. 37, S155 (2004).
[Crossref]

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, “Rotons in gaseous Bose–Einstein condensates irradiated by a laser,” Phys. Rev. Lett. 90, 110402 (2003).
[Crossref]

S. Giovanazzi, D. O’Dell, and G. Kurizki, “Density modulations of Bose–Einstein condensates via laser-induced interactions,” Phys. Rev. Lett. 88, 130402 (2002).
[Crossref]

Lauber, K.

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
[Crossref] [PubMed]

Mark, M. J.

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
[Crossref] [PubMed]

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
[Crossref]

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, “Control of interaction-induced dephasing of Bloch oscillations,” Phys. Rev. Lett. 100, 080404 (2008).
[Crossref] [PubMed]

Mazets, I. E.

I. E. Mazets, D. H. J. O’Dell, G. Kurizki, N. Davidson, and W. P. Schleich, “Depletion of a Bose–Einstein condensate by laser-induced dipoledipole interactions,” J. Phys. B: At. Mol. Opt. Phys. 37, S155 (2004).
[Crossref]

Meinert, F.

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
[Crossref] [PubMed]

Meiser, D.

B. M. Peden, D. Meiser, M. L. Chiofalo, and M. J. Holland, “Nondestructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms,” Phys. Rev. A 80, 043803 (2009).
[Crossref]

Mossmann, S.

T. Hartmann, F. Keck, H. J. Korsch, and S. Mossmann, “Dynamics of Bloch oscillations,” New J. Phys. 6, 2 (2004).
[Crossref]

Nägerl, H.-C.

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
[Crossref] [PubMed]

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
[Crossref]

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, “Control of interaction-induced dephasing of Bloch oscillations,” Phys. Rev. Lett. 100, 080404 (2008).
[Crossref] [PubMed]

Nagorny, B.

B. Nagorny, Th. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91, 153003 (2003).
[Crossref] [PubMed]

Narducci, L. M.

R. Bonifacio, L. DeSalvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716 (1994).
[Crossref] [PubMed]

Nez, F.

P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave,” Europhys. Lett. 71, 730 (2005).
[Crossref]

O’Dell, D.

S. Giovanazzi, D. O’Dell, and G. Kurizki, “Density modulations of Bose–Einstein condensates via laser-induced interactions,” Phys. Rev. Lett. 88, 130402 (2002).
[Crossref]

O’Dell, D. H. J.

J. Goldwin, B. P. Venkatesh, and D. H. J. O’Dell, “Backaction-driven transport of Bloch oscillating atoms in ring cavities,” Phys. Rev. Lett. 113, 073003 (2014).
[Crossref] [PubMed]

B. P. Venkatesh and D. H. J. O’Dell, “Bloch oscillations of cold atoms in a cavity: effects of quantum noise,” Phys. Rev. A 88, 013848 (2013).
[Crossref]

B. P. Venkatesh, M. Trupke, E. A. Hinds, and D. H. J. O’Dell, “Atomic Bloch–Zener oscillations for sensitive force measurements in a cavity,” Phys. Rev. A 80, 063834 (2009).
[Crossref]

I. E. Mazets, D. H. J. O’Dell, G. Kurizki, N. Davidson, and W. P. Schleich, “Depletion of a Bose–Einstein condensate by laser-induced dipoledipole interactions,” J. Phys. B: At. Mol. Opt. Phys. 37, S155 (2004).
[Crossref]

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, “Rotons in gaseous Bose–Einstein condensates irradiated by a laser,” Phys. Rev. Lett. 90, 110402 (2003).
[Crossref]

Peden, B. M.

B. M. Peden, D. Meiser, M. L. Chiofalo, and M. J. Holland, “Nondestructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms,” Phys. Rev. A 80, 043803 (2009).
[Crossref]

Peik, E.

E. Peik, M. B. Dahan, I. Bouchoule, Y. Castin, and C. Salomon, “Bloch oscillations of atoms, adiabatic rapid passage, and monokinetic atomic beams,” Phys. Rev. A 55, 2989 (1997).
[Crossref]

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508 (1996).
[Crossref] [PubMed]

Piovella, N.

M. Samoylova, N. Piovella, D. Hunter, G. R. M. Robb, R. Bachelard, and Ph. W. Courteille, “Mode-locked Bloch oscillations in a ring cavity,” Laser Phys. Lett. 11, 126005 (2015).
[Crossref]

N. Piovella, L. Salasnich, R. Bonifacio, and G. R. M. Robb, “Atomic interaction effects in the superradiant light scattering from a Bose–Einstein condensate,” Las. Phys. 14, 278 (2004).

N. Piovella, M. Gatelli, and R. Bonifacio, “Quantum effects in the collective light scattering by coherent atomic recoil in a Bose-Einstein condensate,” Opt. Commun. 194, 167 (2001).
[Crossref]

Poli, N.

G. Ferrari, N. Poli, F. Sorrentino, and G.M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref] [PubMed]

Reichel, J.

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508 (1996).
[Crossref] [PubMed]

Robb, G. R. M.

M. Samoylova, N. Piovella, D. Hunter, G. R. M. Robb, R. Bachelard, and Ph. W. Courteille, “Mode-locked Bloch oscillations in a ring cavity,” Laser Phys. Lett. 11, 126005 (2015).
[Crossref]

N. Piovella, L. Salasnich, R. Bonifacio, and G. R. M. Robb, “Atomic interaction effects in the superradiant light scattering from a Bose–Einstein condensate,” Las. Phys. 14, 278 (2004).

Rojas-Kopeinig, G.

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, “Control of interaction-induced dephasing of Bloch oscillations,” Phys. Rev. Lett. 100, 080404 (2008).
[Crossref] [PubMed]

Salasnich, L.

N. Piovella, L. Salasnich, R. Bonifacio, and G. R. M. Robb, “Atomic interaction effects in the superradiant light scattering from a Bose–Einstein condensate,” Las. Phys. 14, 278 (2004).

Salomon, C.

E. Peik, M. B. Dahan, I. Bouchoule, Y. Castin, and C. Salomon, “Bloch oscillations of atoms, adiabatic rapid passage, and monokinetic atomic beams,” Phys. Rev. A 55, 2989 (1997).
[Crossref]

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508 (1996).
[Crossref] [PubMed]

Samoylova, M.

M. Samoylova, N. Piovella, D. Hunter, G. R. M. Robb, R. Bachelard, and Ph. W. Courteille, “Mode-locked Bloch oscillations in a ring cavity,” Laser Phys. Lett. 11, 126005 (2015).
[Crossref]

Schleich, W. P.

I. E. Mazets, D. H. J. O’Dell, G. Kurizki, N. Davidson, and W. P. Schleich, “Depletion of a Bose–Einstein condensate by laser-induced dipoledipole interactions,” J. Phys. B: At. Mol. Opt. Phys. 37, S155 (2004).
[Crossref]

Schulze, K.

D. Jaksch, S. A. Gardiner, K. Schulze, J. I. Cirac, and P. Zoller, “Uniting Bose–Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4733 (2001).
[Crossref] [PubMed]

Schwob, C.

P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave,” Europhys. Lett. 71, 730 (2005).
[Crossref]

Slama, S.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref] [PubMed]

Sorrentino, F.

G. Ferrari, N. Poli, F. Sorrentino, and G.M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref] [PubMed]

Tino, G.M.

G. Ferrari, N. Poli, F. Sorrentino, and G.M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref] [PubMed]

Trupke, M.

B. P. Venkatesh, M. Trupke, E. A. Hinds, and D. H. J. O’Dell, “Atomic Bloch–Zener oscillations for sensitive force measurements in a cavity,” Phys. Rev. A 80, 063834 (2009).
[Crossref]

Venkatesh, B. P.

J. Goldwin, B. P. Venkatesh, and D. H. J. O’Dell, “Backaction-driven transport of Bloch oscillating atoms in ring cavities,” Phys. Rev. Lett. 113, 073003 (2014).
[Crossref] [PubMed]

B. P. Venkatesh and D. H. J. O’Dell, “Bloch oscillations of cold atoms in a cavity: effects of quantum noise,” Phys. Rev. A 88, 013848 (2013).
[Crossref]

B. P. Venkatesh, M. Trupke, E. A. Hinds, and D. H. J. O’Dell, “Atomic Bloch–Zener oscillations for sensitive force measurements in a cavity,” Phys. Rev. A 80, 063834 (2009).
[Crossref]

von Cube, C.

D. Kruse, C. von Cube, C. Zimmermann, and Ph. W. Courteille, “Observation of lasing mediated by collective atomic recoil,” Phys. Rev. Lett. 91, 183601 (2003).
[Crossref] [PubMed]

Weinmann, P.

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
[Crossref] [PubMed]

Zimmermann, C.

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref] [PubMed]

D. Kruse, C. von Cube, C. Zimmermann, and Ph. W. Courteille, “Observation of lasing mediated by collective atomic recoil,” Phys. Rev. Lett. 91, 183601 (2003).
[Crossref] [PubMed]

Zoller, P.

D. Jaksch, S. A. Gardiner, K. Schulze, J. I. Cirac, and P. Zoller, “Uniting Bose–Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4733 (2001).
[Crossref] [PubMed]

Europhys. Lett. (1)

P. Cladé, S. Guellati-Khélifa, C. Schwob, F. Nez, L. Julien, and F. Biraben, “A promising method for the measurement of the local acceleration of gravity using Bloch oscillations of ultracold atoms in a vertical standing wave,” Europhys. Lett. 71, 730 (2005).
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (1)

I. E. Mazets, D. H. J. O’Dell, G. Kurizki, N. Davidson, and W. P. Schleich, “Depletion of a Bose–Einstein condensate by laser-induced dipoledipole interactions,” J. Phys. B: At. Mol. Opt. Phys. 37, S155 (2004).
[Crossref]

Las. Phys. (1)

N. Piovella, L. Salasnich, R. Bonifacio, and G. R. M. Robb, “Atomic interaction effects in the superradiant light scattering from a Bose–Einstein condensate,” Las. Phys. 14, 278 (2004).

Laser Phys. Lett. (1)

M. Samoylova, N. Piovella, D. Hunter, G. R. M. Robb, R. Bachelard, and Ph. W. Courteille, “Mode-locked Bloch oscillations in a ring cavity,” Laser Phys. Lett. 11, 126005 (2015).
[Crossref]

New J. Phys. (2)

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, R. Hart, A. J. Daley, and H.-C. Nägerl, “Interference of interacting matter waves,” New J. Phys. 12, 065029 (2010).
[Crossref]

T. Hartmann, F. Keck, H. J. Korsch, and S. Mossmann, “Dynamics of Bloch oscillations,” New J. Phys. 6, 2 (2004).
[Crossref]

Opt. Commun. (1)

N. Piovella, M. Gatelli, and R. Bonifacio, “Quantum effects in the collective light scattering by coherent atomic recoil in a Bose-Einstein condensate,” Opt. Commun. 194, 167 (2001).
[Crossref]

Phys. Rep. (1)

M. Glück, A. R. Kolovsky, and H. Jürgen Korsch, “Wannier-Stark resonances in optical and semiconductor superlattices,” Phys. Rep. 366 (3), 103 (2002).
[Crossref]

Phys. Rev. A (5)

B. M. Peden, D. Meiser, M. L. Chiofalo, and M. J. Holland, “Nondestructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms,” Phys. Rev. A 80, 043803 (2009).
[Crossref]

B. P. Venkatesh, M. Trupke, E. A. Hinds, and D. H. J. O’Dell, “Atomic Bloch–Zener oscillations for sensitive force measurements in a cavity,” Phys. Rev. A 80, 063834 (2009).
[Crossref]

E. Peik, M. B. Dahan, I. Bouchoule, Y. Castin, and C. Salomon, “Bloch oscillations of atoms, adiabatic rapid passage, and monokinetic atomic beams,” Phys. Rev. A 55, 2989 (1997).
[Crossref]

R. Bonifacio, L. DeSalvo, L. M. Narducci, and E. J. D’Angelo, “Exponential gain and self-bunching in a collective atomic recoil laser,” Phys. Rev. A 50, 1716 (1994).
[Crossref] [PubMed]

B. P. Venkatesh and D. H. J. O’Dell, “Bloch oscillations of cold atoms in a cavity: effects of quantum noise,” Phys. Rev. A 88, 013848 (2013).
[Crossref]

Phys. Rev. Lett. (11)

M. Gustavsson, E. Haller, M. J. Mark, J. G. Danzl, G. Rojas-Kopeinig, and H.-C. Nägerl, “Control of interaction-induced dephasing of Bloch oscillations,” Phys. Rev. Lett. 100, 080404 (2008).
[Crossref] [PubMed]

F. Meinert, M. J. Mark, E. Kirilov, K. Lauber, P. Weinmann, M. Gröbner, and H.-C. Nägerl, “Interaction-induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic Bloch oscillations,” Phys. Rev. Lett. 112, 193003 (2014).
[Crossref] [PubMed]

D. Kruse, C. von Cube, C. Zimmermann, and Ph. W. Courteille, “Observation of lasing mediated by collective atomic recoil,” Phys. Rev. Lett. 91, 183601 (2003).
[Crossref] [PubMed]

B. Nagorny, Th. Elsässer, and A. Hemmerich, “Collective atomic motion in an optical lattice formed inside a high finesse cavity,” Phys. Rev. Lett. 91, 153003 (2003).
[Crossref] [PubMed]

S. Slama, S. Bux, G. Krenz, C. Zimmermann, and Ph. W. Courteille, “Superradiant Rayleigh scattering and collective atomic recoil lasing in a ring cavity,” Phys. Rev. Lett. 98, 053603 (2007).
[Crossref] [PubMed]

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508 (1996).
[Crossref] [PubMed]

G. Ferrari, N. Poli, F. Sorrentino, and G.M. Tino, “Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at the micrometer scale,” Phys. Rev. Lett. 97, 060402 (2006).
[Crossref] [PubMed]

J. Goldwin, B. P. Venkatesh, and D. H. J. O’Dell, “Backaction-driven transport of Bloch oscillating atoms in ring cavities,” Phys. Rev. Lett. 113, 073003 (2014).
[Crossref] [PubMed]

D. Jaksch, S. A. Gardiner, K. Schulze, J. I. Cirac, and P. Zoller, “Uniting Bose–Einstein condensates in optical resonators,” Phys. Rev. Lett. 86, 4733 (2001).
[Crossref] [PubMed]

S. Giovanazzi, D. O’Dell, and G. Kurizki, “Density modulations of Bose–Einstein condensates via laser-induced interactions,” Phys. Rev. Lett. 88, 130402 (2002).
[Crossref]

D. H. J. O’Dell, S. Giovanazzi, and G. Kurizki, “Rotons in gaseous Bose–Einstein condensates irradiated by a laser,” Phys. Rev. Lett. 90, 110402 (2003).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Scheme of a ring cavity consisting of two high-reflecting mirrors (HR) and one output coupler (OC) interacting with a Bose-Einstein condensate (BEC) stored in the vertical arm of the ring cavity. Only one cavity mode is pumped (Ωp, k0), the counter-propagating probe mode (α) is populated by backscattering from the atoms. Two lasers (K1,2) crossing the cavity mode at the location of the BEC under angles ±β/2 generate an optical lattice whose periodicity is commensurate with the standing wave created by the pump and probe modes.

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Fig. 2
Fig. 2 (a): Average atomic momentum in the laboratory frame as a function of scaled time νbt for a sudden switch-on of the optical lattice without (red dash-dotted) and with (plain blue) the cavity, compared to an adiabatic switch-on without the cavity (dashed black); (b): average number of photons |α|2 in the cavity field; (c): phase of the cavity mode α for a sudden switch-on of the optical lattice in the presence of the cavity. The parameters of the simulations are provided in the body of the text.

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Fig. 3
Fig. 3 Time evolution of the momentum populations |Cn|2 for (a): adiabatic switch-on of the lattice without the cavity, and (b): abrupt switch-on of the lattice in the presence of the cavity. The same parameters as in Fig. 2 are used, except for the lattice depth W0 = 1.68ωr and N = 3 · 104. The different colors chosen for adjacent momentum states are meant to facilitate their visual distinction.

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Fig. 4
Fig. 4 Impact of collisions on the evolution of the populations of the momentum states |Cn|2 (a) without the cavity and (b) in the presence of the cavity. The other parameters are the same as in Fig. 2 with an adiabatic rise of the optical lattice in both cases and β = ωr. (c) Average momentum for the same conditions as in (a). The assumption made for the interaction strengths, β ≃ ωr, corresponds to typical experimental situations, as = 110aB for 87Rb, N = 2 × 104 and Σ ≃ 300 μm2.

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Fig. 5
Fig. 5 Evolution of the populations of the momentum states |Cn|2 when the atoms are initially distributed over several states ( C 0 2 = 70 %, C − 1 2 = C + 1 2 = 15 %) in the case of (a) adiabatic switch-on of the lattice without the cavity, (b) abrupt switch-on of the lattice in the presence of the cavity. The other parameters are the same as in Fig. 2.

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Fig. 6
Fig. 6 Dephasing induced by phase-fluctuations of the lattice potential. Simulations are realized with the adiabatic rise of the optical lattice in both cases with (solid black) and without the cavity (dashed red) and three sequential phase kicks at times νbt = 3.6, 11.9, 22.3, with the respective amplitudes δϕ = 0.16π, 0.37π, 0.46π.

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Fig. 7
Fig. 7 Comparison of the average atomic momentum 〈p〉 given in units of 2ħk0 obtained from the ARP solution (red) of Eq. (15) and numerical solution (blue) of Eqs. (6) and (7) in the accelerated frame. The parameters are the same as in Fig. 2.

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Equations (15)

Equations on this page are rendered with MathJax. Learn more.

i ℏ ∂ ψ ( x , t ) ∂ t = − ℏ 2 2 m ∂ 2 ψ ( x , t ) ∂ x 2 − i ℏ U 0 [ α ( t ) e 2 i k 0 x − α * ( t ) e − 2 i k 0 x ] ψ ( x , t ) − m g x ψ ( x , t ) + ℏ W 0 2 sin ( 2 k 0 x ) ψ ( x , t ) ,
d α ( t ) d t = N U 0 ∫ | ψ ( x , t ) | 2 e − 2 i k 0 x d ( 2 k 0 x ) + ( i δ − κ ) α ( t ) ,
∂ ψ ˜ ∂ t = i ℏ 2 m ( ∂ ∂ x + i m g t ℏ ) 2 ψ ˜ − U 0 ( α ˜ e 2 i k 0 x − α ˜ * e − 2 i k 0 x ) ψ ˜ ,
d α ˜ d t = N U 0 ∫ | ψ ˜ | 2 e − 2 i k 0 x d ( 2 k 0 x ) + ( i δ − κ ) ( α ˜ − α 0 ) .
ψ ˜ ( x , t ) = 1 2 π ∑ n C n ( t ) e 2 i n k 0 x ,
d C n d t = − 4 i ω r ( n + ν b t ) 2 C n + U 0 ( α ˜ * C n + 1 − α ˜ C n − 1 ) ,
d α ˜ d t = U 0 N ∑ n C n − 1 * C n + ( i δ − κ ) ( α ˜ − α 0 ) .
F RP ( t ) = ℏ k 0 Γ 4 Δ 2 ( Ω p 2 − Ω 1 2 | α ( t ) | 2 ) .
ψ ( x , t ) = ψ ˜ ( x , t ) exp ( i m g x t ℏ − i ℏ x ∫ 0 t F R P ( t ′ ) d t ′ ) .
d C n d t = − 4 i ω r [ n + ν b t − Γ 8 Δ 2 ( Ω p 2 t + Ω 1 2 ∫ 0 t | α ( t ′ ) | 2 d t ′ ) ] 2 C n + U 0 ( α ˜ * C n + 1 − α ˜ C n + 1 ) .
〈 p 〉 lab = ∑ n n | C n | 2 + ν b t − Γ 8 Δ 2 ( Ω p 2 t + Ω 1 2 ∫ 0 t | α ( t ′ ) | 2 d t ′ ) .
d S d t = − i Λ n S + U 0 α ˜ W ,
d W d t = − 2 U 0 ( α ˜ S * + α ˜ * S ) ,
d α ˜ d t = U 0 N S + ( i δ − κ ) ( α ˜ − α 0 ) ,
W = Λ n 4 U 0 2 α 0 2 + Λ n 2 ,                   S = − i U 0 α 0 4 U 0 2 α 0 2 + Λ n 2 .

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