Abstract

Superradiant active clocks operating on narrow linewidth clock transitions are predicted to achieve precision orders of magnitude higher than any currently existing optical atomic clocks. We introduce a theory of superradiant lasing and implement it for the example of 40Ca atoms. The presented model, however, is valid for any two- or three-level system in an optical lattice. We perform a feasibility analysis and suggest a set of parameters for the experimental fulfillment of superradiant lasing in Ca. Moreover, we present an overview of different magic wavelengths for the 4s2 1S0 ↔ 4s4p 3P1 (mJ = 0) transition in Ca for different polarizations and a robustness analysis of these magic conditions. We also report the magic-zero wavelengths for the 4s4p 3P1, mJ = 0 state.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Superradiant cooling, trapping, and lasing of dipole-interacting clock atoms

Christoph Hotter, David Plankensteiner, Laurin Ostermann, and Helmut Ritsch
Opt. Express 27(22) 31193-31206 (2019)

A superradiant clock laser on a magic wavelength optical lattice

Thomas Maier, Sebastian Kraemer, Laurin Ostermann, and Helmut Ritsch
Opt. Express 22(11) 13269-13279 (2014)

References

  • View by:
  • |
  • |
  • |

  1. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93(1), 99–110 (1954).
    [Crossref]
  2. K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93(25), 250602 (2004).
    [Crossref]
  3. J. Chen, “Active optical clock,” Chin. Sci. Bull. 54(3), 348–352 (2009).
    [Crossref]
  4. D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett. 102(16), 163601 (2009).
    [Crossref]
  5. D. Yu and J. Chen, “Laser theory with finite atom-field interacting time,” Phys. Rev. A 78(1), 013846 (2008).
    [Crossref]
  6. W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
    [Crossref]
  7. D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
    [Crossref]
  8. H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76(1), 127–137 (1998).
    [Crossref]
  9. M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, “Superradiance on the millihertz linewidth strontium clock transition,” Sci. Adv. 2(10), e1601231 (2016).
    [Crossref]
  10. G. A. Kazakov and T. Schumm, “Active optical frequency standard using sequential coupling of atomic ensembles,” Phys. Rev. A 87(1), 013821 (2013).
    [Crossref]
  11. T. Laske, H. Winter, and A. Hemmerich, “Pulse delay time statistics in a superradiant laser with calcium atoms,” Phys. Rev. Lett. 123(10), 103601 (2019).
    [Crossref]
  12. S. A. Schäffer, M. Tang, M. R. Henriksen, A. A. Jørgensen, B. T. R. Christensen, and J. W. Thomsen, “Lasing on a narrow transition in a cold thermal strontium ensemble,” Phys. Rev. A 101(1), 013819 (2020).
    [Crossref]
  13. C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, “Wavelength-dependent ac stark shift of the 1S0-3P1 transition at 657 nm in Ca,” Phys. Rev. A 70(2), 023414 (2004).
    [Crossref]
  14. L. J. LeBlanc and J. H. Thywissen, “Species-specific optical lattices,” Phys. Rev. A 75(5), 053612 (2007).
    [Crossref]
  15. C. Gardiner and P. Zoller, Quantum Noise (Springer, 2004).
  16. G. A. Kazakov and T. Schumm, “Stability analysis for bad cavity lasers using inhomogeneously broadened spin-1/2 atoms as a gain medium,” Phys. Rev. A 95(2), 023839 (2017).
    [Crossref]
  17. C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
    [Crossref]
  18. C. Lisdat, J. S. R. V. Winfred, T. Middelmann, F. Riehle, and U. Sterr, “Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons,” Phys. Rev. Lett. 103(9), 090801 (2009).
    [Crossref]
  19. X. Zhou, X. Xu, X. Chen, and J. Chen, “Magic wavelengths for terahertz clock transitions,” Phys. Rev. A 81(1), 012115 (2010).
    [Crossref]

2020 (1)

S. A. Schäffer, M. Tang, M. R. Henriksen, A. A. Jørgensen, B. T. R. Christensen, and J. W. Thomsen, “Lasing on a narrow transition in a cold thermal strontium ensemble,” Phys. Rev. A 101(1), 013819 (2020).
[Crossref]

2019 (1)

T. Laske, H. Winter, and A. Hemmerich, “Pulse delay time statistics in a superradiant laser with calcium atoms,” Phys. Rev. Lett. 123(10), 103601 (2019).
[Crossref]

2017 (3)

G. A. Kazakov and T. Schumm, “Stability analysis for bad cavity lasers using inhomogeneously broadened spin-1/2 atoms as a gain medium,” Phys. Rev. A 95(2), 023839 (2017).
[Crossref]

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

2016 (1)

M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, “Superradiance on the millihertz linewidth strontium clock transition,” Sci. Adv. 2(10), e1601231 (2016).
[Crossref]

2013 (1)

G. A. Kazakov and T. Schumm, “Active optical frequency standard using sequential coupling of atomic ensembles,” Phys. Rev. A 87(1), 013821 (2013).
[Crossref]

2010 (1)

X. Zhou, X. Xu, X. Chen, and J. Chen, “Magic wavelengths for terahertz clock transitions,” Phys. Rev. A 81(1), 012115 (2010).
[Crossref]

2009 (3)

C. Lisdat, J. S. R. V. Winfred, T. Middelmann, F. Riehle, and U. Sterr, “Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons,” Phys. Rev. Lett. 103(9), 090801 (2009).
[Crossref]

J. Chen, “Active optical clock,” Chin. Sci. Bull. 54(3), 348–352 (2009).
[Crossref]

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett. 102(16), 163601 (2009).
[Crossref]

2008 (1)

D. Yu and J. Chen, “Laser theory with finite atom-field interacting time,” Phys. Rev. A 78(1), 013846 (2008).
[Crossref]

2007 (1)

L. J. LeBlanc and J. H. Thywissen, “Species-specific optical lattices,” Phys. Rev. A 75(5), 053612 (2007).
[Crossref]

2005 (1)

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

2004 (2)

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, “Wavelength-dependent ac stark shift of the 1S0-3P1 transition at 657 nm in Ca,” Phys. Rev. A 70(2), 023414 (2004).
[Crossref]

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93(25), 250602 (2004).
[Crossref]

1998 (1)

H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76(1), 127–137 (1998).
[Crossref]

1954 (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93(1), 99–110 (1954).
[Crossref]

Benko, C.

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

Camp, J.

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93(25), 250602 (2004).
[Crossref]

Carlson, D. R.

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett. 102(16), 163601 (2009).
[Crossref]

Chen, J.

X. Zhou, X. Xu, X. Chen, and J. Chen, “Magic wavelengths for terahertz clock transitions,” Phys. Rev. A 81(1), 012115 (2010).
[Crossref]

J. Chen, “Active optical clock,” Chin. Sci. Bull. 54(3), 348–352 (2009).
[Crossref]

D. Yu and J. Chen, “Laser theory with finite atom-field interacting time,” Phys. Rev. A 78(1), 013846 (2008).
[Crossref]

Chen, X.

X. Zhou, X. Xu, X. Chen, and J. Chen, “Magic wavelengths for terahertz clock transitions,” Phys. Rev. A 81(1), 012115 (2010).
[Crossref]

Christensen, B. T. R.

S. A. Schäffer, M. Tang, M. R. Henriksen, A. A. Jørgensen, B. T. R. Christensen, and J. W. Thomsen, “Lasing on a narrow transition in a cold thermal strontium ensemble,” Phys. Rev. A 101(1), 013819 (2020).
[Crossref]

Cline, J. R. K.

M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, “Superradiance on the millihertz linewidth strontium clock transition,” Sci. Adv. 2(10), e1601231 (2016).
[Crossref]

Degenhardt, C.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, “Wavelength-dependent ac stark shift of the 1S0-3P1 transition at 657 nm in Ca,” Phys. Rev. A 70(2), 023414 (2004).
[Crossref]

Dicke, R. H.

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93(1), 99–110 (1954).
[Crossref]

Gardiner, C.

C. Gardiner and P. Zoller, Quantum Noise (Springer, 2004).

Grebing, C.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

Häfner, S.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

Hall, J. L.

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

Helmcke, J.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

Hemmerich, A.

T. Laske, H. Winter, and A. Hemmerich, “Pulse delay time statistics in a superradiant laser with calcium atoms,” Phys. Rev. Lett. 123(10), 103601 (2019).
[Crossref]

Henriksen, M. R.

S. A. Schäffer, M. Tang, M. R. Henriksen, A. A. Jørgensen, B. T. R. Christensen, and J. W. Thomsen, “Lasing on a narrow transition in a cold thermal strontium ensemble,” Phys. Rev. A 101(1), 013819 (2020).
[Crossref]

Holland, M. J.

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett. 102(16), 163601 (2009).
[Crossref]

Jørgensen, A. A.

S. A. Schäffer, M. Tang, M. R. Henriksen, A. A. Jørgensen, B. T. R. Christensen, and J. W. Thomsen, “Lasing on a narrow transition in a cold thermal strontium ensemble,” Phys. Rev. A 101(1), 013819 (2020).
[Crossref]

Kazakov, G. A.

G. A. Kazakov and T. Schumm, “Stability analysis for bad cavity lasers using inhomogeneously broadened spin-1/2 atoms as a gain medium,” Phys. Rev. A 95(2), 023839 (2017).
[Crossref]

G. A. Kazakov and T. Schumm, “Active optical frequency standard using sequential coupling of atomic ensembles,” Phys. Rev. A 87(1), 013821 (2013).
[Crossref]

Kemery, A.

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93(25), 250602 (2004).
[Crossref]

Kimble, H. J.

H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76(1), 127–137 (1998).
[Crossref]

Laske, T.

T. Laske, H. Winter, and A. Hemmerich, “Pulse delay time statistics in a superradiant laser with calcium atoms,” Phys. Rev. Lett. 123(10), 103601 (2019).
[Crossref]

LeBlanc, L. J.

L. J. LeBlanc and J. H. Thywissen, “Species-specific optical lattices,” Phys. Rev. A 75(5), 053612 (2007).
[Crossref]

Legero, T.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

Lipphardt, B.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

Lisdat, C.

C. Lisdat, J. S. R. V. Winfred, T. Middelmann, F. Riehle, and U. Sterr, “Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons,” Phys. Rev. Lett. 103(9), 090801 (2009).
[Crossref]

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, “Wavelength-dependent ac stark shift of the 1S0-3P1 transition at 657 nm in Ca,” Phys. Rev. A 70(2), 023414 (2004).
[Crossref]

Matei, D. G.

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

Meiser, D.

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett. 102(16), 163601 (2009).
[Crossref]

Middelmann, T.

C. Lisdat, J. S. R. V. Winfred, T. Middelmann, F. Riehle, and U. Sterr, “Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons,” Phys. Rev. Lett. 103(9), 090801 (2009).
[Crossref]

Nazarova, T.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

Norcia, M. A.

M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, “Superradiance on the millihertz linewidth strontium clock transition,” Sci. Adv. 2(10), e1601231 (2016).
[Crossref]

Numata, K.

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93(25), 250602 (2004).
[Crossref]

Oelker, E.

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

Pottie, P.-E.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

Riehle, F.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

C. Lisdat, J. S. R. V. Winfred, T. Middelmann, F. Riehle, and U. Sterr, “Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons,” Phys. Rev. Lett. 103(9), 090801 (2009).
[Crossref]

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, “Wavelength-dependent ac stark shift of the 1S0-3P1 transition at 657 nm in Ca,” Phys. Rev. A 70(2), 023414 (2004).
[Crossref]

Robinson, J. M.

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

Schäffer, S. A.

S. A. Schäffer, M. Tang, M. R. Henriksen, A. A. Jørgensen, B. T. R. Christensen, and J. W. Thomsen, “Lasing on a narrow transition in a cold thermal strontium ensemble,” Phys. Rev. A 101(1), 013819 (2020).
[Crossref]

Schnatz, H.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

Schumm, T.

G. A. Kazakov and T. Schumm, “Stability analysis for bad cavity lasers using inhomogeneously broadened spin-1/2 atoms as a gain medium,” Phys. Rev. A 95(2), 023839 (2017).
[Crossref]

G. A. Kazakov and T. Schumm, “Active optical frequency standard using sequential coupling of atomic ensembles,” Phys. Rev. A 87(1), 013821 (2013).
[Crossref]

Sonderhouse, L.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

Sterr, U.

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

C. Lisdat, J. S. R. V. Winfred, T. Middelmann, F. Riehle, and U. Sterr, “Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons,” Phys. Rev. Lett. 103(9), 090801 (2009).
[Crossref]

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, “Wavelength-dependent ac stark shift of the 1S0-3P1 transition at 657 nm in Ca,” Phys. Rev. A 70(2), 023414 (2004).
[Crossref]

Stoehr, H.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, “Wavelength-dependent ac stark shift of the 1S0-3P1 transition at 657 nm in Ca,” Phys. Rev. A 70(2), 023414 (2004).
[Crossref]

Tang, M.

S. A. Schäffer, M. Tang, M. R. Henriksen, A. A. Jørgensen, B. T. R. Christensen, and J. W. Thomsen, “Lasing on a narrow transition in a cold thermal strontium ensemble,” Phys. Rev. A 101(1), 013819 (2020).
[Crossref]

Thompson, J. K.

M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, “Superradiance on the millihertz linewidth strontium clock transition,” Sci. Adv. 2(10), e1601231 (2016).
[Crossref]

Thomsen, J. W.

S. A. Schäffer, M. Tang, M. R. Henriksen, A. A. Jørgensen, B. T. R. Christensen, and J. W. Thomsen, “Lasing on a narrow transition in a cold thermal strontium ensemble,” Phys. Rev. A 101(1), 013819 (2020).
[Crossref]

Thywissen, J. H.

L. J. LeBlanc and J. H. Thywissen, “Species-specific optical lattices,” Phys. Rev. A 75(5), 053612 (2007).
[Crossref]

V. Winfred, J. S. R.

C. Lisdat, J. S. R. V. Winfred, T. Middelmann, F. Riehle, and U. Sterr, “Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons,” Phys. Rev. Lett. 103(9), 090801 (2009).
[Crossref]

Weyrich, R.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

Wilpers, G.

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

Winchester, M. N.

M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, “Superradiance on the millihertz linewidth strontium clock transition,” Sci. Adv. 2(10), e1601231 (2016).
[Crossref]

Winter, H.

T. Laske, H. Winter, and A. Hemmerich, “Pulse delay time statistics in a superradiant laser with calcium atoms,” Phys. Rev. Lett. 123(10), 103601 (2019).
[Crossref]

Xu, X.

X. Zhou, X. Xu, X. Chen, and J. Chen, “Magic wavelengths for terahertz clock transitions,” Phys. Rev. A 81(1), 012115 (2010).
[Crossref]

Ye, J.

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett. 102(16), 163601 (2009).
[Crossref]

Yu, D.

D. Yu and J. Chen, “Laser theory with finite atom-field interacting time,” Phys. Rev. A 78(1), 013846 (2008).
[Crossref]

Zhang, W.

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

Zhou, X.

X. Zhou, X. Xu, X. Chen, and J. Chen, “Magic wavelengths for terahertz clock transitions,” Phys. Rev. A 81(1), 012115 (2010).
[Crossref]

Zoller, P.

C. Gardiner and P. Zoller, Quantum Noise (Springer, 2004).

Chin. Sci. Bull. (1)

J. Chen, “Active optical clock,” Chin. Sci. Bull. 54(3), 348–352 (2009).
[Crossref]

Phys. Rev. (1)

R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev. 93(1), 99–110 (1954).
[Crossref]

Phys. Rev. A (8)

D. Yu and J. Chen, “Laser theory with finite atom-field interacting time,” Phys. Rev. A 78(1), 013846 (2008).
[Crossref]

S. A. Schäffer, M. Tang, M. R. Henriksen, A. A. Jørgensen, B. T. R. Christensen, and J. W. Thomsen, “Lasing on a narrow transition in a cold thermal strontium ensemble,” Phys. Rev. A 101(1), 013819 (2020).
[Crossref]

C. Degenhardt, H. Stoehr, U. Sterr, F. Riehle, and C. Lisdat, “Wavelength-dependent ac stark shift of the 1S0-3P1 transition at 657 nm in Ca,” Phys. Rev. A 70(2), 023414 (2004).
[Crossref]

L. J. LeBlanc and J. H. Thywissen, “Species-specific optical lattices,” Phys. Rev. A 75(5), 053612 (2007).
[Crossref]

G. A. Kazakov and T. Schumm, “Active optical frequency standard using sequential coupling of atomic ensembles,” Phys. Rev. A 87(1), 013821 (2013).
[Crossref]

G. A. Kazakov and T. Schumm, “Stability analysis for bad cavity lasers using inhomogeneously broadened spin-1/2 atoms as a gain medium,” Phys. Rev. A 95(2), 023839 (2017).
[Crossref]

C. Degenhardt, H. Stoehr, C. Lisdat, G. Wilpers, H. Schnatz, B. Lipphardt, T. Nazarova, P.-E. Pottie, U. Sterr, J. Helmcke, and F. Riehle, “Calcium optical frequency standard with ultracold atoms: Approaching 10−15 relative uncertainty,” Phys. Rev. A 72(6), 062111 (2005).
[Crossref]

X. Zhou, X. Xu, X. Chen, and J. Chen, “Magic wavelengths for terahertz clock transitions,” Phys. Rev. A 81(1), 012115 (2010).
[Crossref]

Phys. Rev. Lett. (6)

C. Lisdat, J. S. R. V. Winfred, T. Middelmann, F. Riehle, and U. Sterr, “Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons,” Phys. Rev. Lett. 103(9), 090801 (2009).
[Crossref]

T. Laske, H. Winter, and A. Hemmerich, “Pulse delay time statistics in a superradiant laser with calcium atoms,” Phys. Rev. Lett. 123(10), 103601 (2019).
[Crossref]

W. Zhang, J. M. Robinson, L. Sonderhouse, E. Oelker, C. Benko, J. L. Hall, T. Legero, D. G. Matei, F. Riehle, U. Sterr, and J. Ye, “Ultrastable silicon cavity in a continuously operating closed-cycle cryostat at 4 K,” Phys. Rev. Lett. 119(24), 243601 (2017).
[Crossref]

D. G. Matei, T. Legero, S. Häfner, C. Grebing, R. Weyrich, W. Zhang, L. Sonderhouse, J. M. Robinson, J. Ye, F. Riehle, and U. Sterr, “1.5 µm lasers with sub-10 mHz linewidth,” Phys. Rev. Lett. 118(26), 263202 (2017).
[Crossref]

K. Numata, A. Kemery, and J. Camp, “Thermal-noise limit in the frequency stabilization of lasers with rigid cavities,” Phys. Rev. Lett. 93(25), 250602 (2004).
[Crossref]

D. Meiser, J. Ye, D. R. Carlson, and M. J. Holland, “Prospects for a millihertz-linewidth laser,” Phys. Rev. Lett. 102(16), 163601 (2009).
[Crossref]

Phys. Scr. (1)

H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T76(1), 127–137 (1998).
[Crossref]

Sci. Adv. (1)

M. A. Norcia, M. N. Winchester, J. R. K. Cline, and J. K. Thompson, “Superradiance on the millihertz linewidth strontium clock transition,” Sci. Adv. 2(10), e1601231 (2016).
[Crossref]

Other (1)

C. Gardiner and P. Zoller, Quantum Noise (Springer, 2004).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1. (a) Magic wavelength lattice confines atoms in a cavity in lattice sites. Applied magnetic field is parallel to the $x$-axis, the superradiant pulse is generated along the cavity axis $z$. (b) Level diagram of $j$-th atom, interacting with a clock transition laser field $\Omega ^j$, cavity mode $g^j$. Atoms are either initially prepared at the state 2 or are prepared at state 3 and incoherently pumped to state 2 by the rate $W(t)$.
Fig. 2.
Fig. 2. (a) Generated SR pulse flux for different values of the atom number (inset shows the number of atoms). (b) Populations of the states 1 (blue - $^1S_0$), 2 (red - $^3P_1$) and 3 (magenta - $^3P_0$) for $N = 69 000$ atoms. The solid curves show the averaged populations over all lattice sites. Populations of ground and excited states in different lattice sites is within the range between the blue and red dotted curves, correspondingly. The cyan dotted curve is the sum of the populations of the ground and excited states. The black dashed curve is the scaled shape of the pumping pulse $W(t)$. See the text for the rest of parameters.
Fig. 3.
Fig. 3. Influence of the number of atoms on (a) the peak value of the pulse; (b) the photon number; (c) the pulse width; (d) the temporal position of the pulse peak value. The red curves correspond to the case when atoms are pumped from the state 3 to the state 2 with the pumping rate of $W(t)$ and the cyan curves correspond to the emission when the atoms are pumped instantaneously. The magenta and black dashed curves are functions fitted to the red and cyan curves, correspondingly. In (a) a quadratic function is fitted, while in (b) a linear function is fitted. Other relevant parameters are the same as in Fig. 2.
Fig. 4.
Fig. 4. SR pulse peak value dependence on the number of atoms for the regime $\sqrt {N}g_0\;>\;\kappa$ for instantaneous pumping. Parameters are the same as in Fig. 3. Dashed curves are quadratic and linear fits for small and large number of atoms, correspondingly.
Fig. 5.
Fig. 5. Impact of the cavity finesse on (a) the peak value of the pulse; (b) photon number; (c) pulse width; (d) temporal position of the pulse peak value. The number of atoms is taken $N = 69 000$. The rest of the parameters are the same as in Fig. 2. The black dashed curves are $a/x + b$ function fits.
Fig. 6.
Fig. 6. Realisation of "pure" types of linear polarization. (a): $\pi$-polarization, where the amplitude $\vec {E}_0$ of electric component of the laser field is polarized along the quantization axis defined by the external magnetic field $\vec {B}$; (b) and (c): $xy$-polarization, where $\vec {B}\perp \vec {E}_0$.
Fig. 7.
Fig. 7. Ac Stark shifts for ${}^1S_0$ (black) and ${}^3P_1,m_J=0$ (red) states of Ca atom in the running-wave laser field with $xy$- (a) and $\pi$-polarization (b), whose intensity $I=10~\textrm {kW/cm}^2$, versus frequency $\omega$ (bottom scale) or wavelength $\lambda$ (top scale) of the field. Blue circles indicate “magic” points, where the ac Stark shifts are equal, and green diamonds indicate “zero-magic” points, where the ${}^3P_{1}(m_J=0)$ state is not trapped.

Tables (1)

Tables Icon

Table 1. Characterization of magic wavelengths for the 1 S 0 3 P 1 ( m J = 0 ) transition in bosonic isotopes of Ca

Equations (14)

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

d n out ( t ) d t = c ^ out ( t ) c ^ out ( t ) ,
c ^ out ( t ) + c ^ in ( t ) = κ c ^ ( t )
d n out ( t ) d t = κ c ^ ( t ) c ^ ( t ) .
d ρ d t = i [ H ^ , ρ ] + d ρ d t | r e l ,
d ρ d t | r e l = κ L [ c ^ ] ρ + j ( γ 2 L [ σ ^ 12 j ] ρ + W ( t ) L [ σ ^ 23 j ] ρ ) + d ρ d t | d e p h ,
H ^ = j = 1 N [ Δ j σ ^ 22 j + ( g j σ ^ 21 j c ^ + Ω j σ ^ 21 j + H . c . ) ] ,
g ( x , y , z ) = g 0 exp ( x 2 + y 2 w c 2 ) cos ( k z ) ,
g ~ ( z ) = g 0 w c 2 w c 2 + w r 2 / 2 cos k z 0 ,
n = n 0 exp ( 2 r 2 w r 2 2 ( z z 0 ) 2 w z 2 ) ,
c ^ ˙ = i j = 1 M [ ( i κ + Δ j ) c ^ + N j g ~ j σ ^ 21 ( j ) c ^ ] ,
W ( t ) = W 0 2 ( tanh [ C s ( t t 1 ) ] tanh [ C s ( t t 2 ) ] ) ,
Δ i S ( λ ) = α ( i , p , λ ) E 0 2 4 = α ( i , p , λ ) 2 π I c ,
α ( i , p , λ ) = 3 c 3 2 k , m k A J k i ( 2 J k + 1 ) ω J k i 2 ( ω J k i 2 ω 2 ) ( J i 1 J k m i p m k ) 2 .
α φ ( i , ϕ , λ ) = α ( i , 1 , λ ) + α ( i , 1 , λ ) ) 2 sin 2 φ + α ( i , 0 , λ ) cos 2 φ .

Metrics