Abstract

In optical dipole traps, the excited rotational states of a molecule may experience a very different light shift than the ground state. For particles with two polarizability components (parallel and perpendicular), such as linear 1Σ molecules, the differential shift can be nulled by choice of elliptical polarization. When one component of the polarization vector is ±i2 times the orthogonal component, the light shift for a sublevel of excited rotational states ±approaches that of the ground state at high optical intensity. In this case, fluctuating trap intensity need not limit coherence between ground and excited rotational states.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Floquet theory for atomic light-shift engineering with near-resonant polychromatic fields

Simon Coop, Silvana Palacios, Pau Gomez, Y. Natali Martinez de Escobar, Thomas Vanderbruggen, and Morgan W. Mitchell
Opt. Express 25(26) 32550-32559 (2017)

Magnetic resonance line shapes in optical pumping and light-shift experiments in alkali atomic vapors

J. Skalla, S. Lang, and G. Wäckerle
J. Opt. Soc. Am. B 12(5) 772-781 (1995)

Dynamic effects in nonlinear magneto-optics of atoms and molecules: review

Evgeniy B. Alexandrov, Marcis Auzinsh, Dmitry Budker, Derek F. Kimball, Simon M. Rochester, and Valeriy V. Yashchuk
J. Opt. Soc. Am. B 22(1) 7-20 (2005)

References

  • View by:
  • |
  • |
  • |

  1. B. Cagnac, A. Izraël, and M. Nogaret, “Spectroscopie Hertzienne,” Comptes Rendus Acad. Sci. Sér. B 267, 274–277 (1968).
  2. W. Happer, “Light propagation and light shifts in optical pumping experiments,” Prog. Quant. Elec. 151–103 (1970).
    [Crossref]
  3. D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics (Oxford University Press, 2004).
  4. S. Kotochigova and D. DeMille, “Electric-field-dependent dynamic polarizability and state-insensitive conditions for optical trapping of diatomic polar molecules,” Phys. Rev. A 82063421 (2010).
    [Crossref]
  5. B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
    [Crossref]
  6. P. D. Gregory, J. A. Blackmore, J. Aldegunde, J. M. Hutson, and S. L. Cornish, “ac Stark effect in ultracold polar 87Rb133Cs molecules,” Phys. Rev. A 96021402 (2017).
    [Crossref]
  7. H. Kim, H. S. Han, and D. Cho, “Magic Polarization for Optical Trapping of Atoms without Stark-Induced Dephasing,” Phys. Rev. Lett. 111243004 (2013).
    [Crossref]
  8. A. V. Taichenachev, V. I. Yudin, V. D. Ovsiannikov, and V. G. Pal’chikov, “Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions,” Phys. Rev. Lett. 97173601 (2006).
    [Crossref] [PubMed]
  9. V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Second Edition) (Butterworth-Heinemann, 1982), §61.
  10. T. C. James and W. Klemperer, “Line Intensities in the Raman Effect of 1Σ Diatomic Molecules,” J. Chem. Phys. 31130–134 (1959).
    [Crossref]
  11. K. D. Bonin and V. V. Kresin, Electric-Dipole Polarizabilities of Atoms, Molecules, and Clusters (World Scientific, 1997), p. 43.
  12. B. Friedrich and D. Herschbach, “Alignment and Trapping of Molecules in Intense Laser Fields,” Phys. Rev. Lett. 744623–4626 (1995).
    [Crossref] [PubMed]
  13. H. Stapelfeldt and T. Seideman, “Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75543–557 (2003).
    [Crossref]
  14. J. Aldegunde and J. M. Hutson, “Hyperfine structure of alkali-metal diatomic molecules,” Phys. Rev. A 96042506 (2017).
    [Crossref]
  15. R. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, 1988).
  16. M. Zwierlein, Private communication (2018).
  17. Polarization with ellipticity ϵ=i(x^ory^)2/3±z^1/3 in the xz or yz plane rather than xy causes the diagonal elements of β^ to be zero in Eq. 7, making it apparent that for all J, β^ is singular with a zero eigenvalue.
  18. B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
    [Crossref] [PubMed]
  19. R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
    [Crossref]
  20. L. Viola and S. Lloyd, “Dynamical suppression of decoherence in two-state quantum systems,” Phys. Rev. A 582733–2744 (1998).
    [Crossref]

2017 (3)

P. D. Gregory, J. A. Blackmore, J. Aldegunde, J. M. Hutson, and S. L. Cornish, “ac Stark effect in ultracold polar 87Rb133Cs molecules,” Phys. Rev. A 96021402 (2017).
[Crossref]

J. Aldegunde and J. M. Hutson, “Hyperfine structure of alkali-metal diatomic molecules,” Phys. Rev. A 96042506 (2017).
[Crossref]

R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
[Crossref]

2013 (2)

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

H. Kim, H. S. Han, and D. Cho, “Magic Polarization for Optical Trapping of Atoms without Stark-Induced Dephasing,” Phys. Rev. Lett. 111243004 (2013).
[Crossref]

2012 (1)

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

2010 (1)

S. Kotochigova and D. DeMille, “Electric-field-dependent dynamic polarizability and state-insensitive conditions for optical trapping of diatomic polar molecules,” Phys. Rev. A 82063421 (2010).
[Crossref]

2006 (1)

A. V. Taichenachev, V. I. Yudin, V. D. Ovsiannikov, and V. G. Pal’chikov, “Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions,” Phys. Rev. Lett. 97173601 (2006).
[Crossref] [PubMed]

2003 (1)

H. Stapelfeldt and T. Seideman, “Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75543–557 (2003).
[Crossref]

1998 (1)

L. Viola and S. Lloyd, “Dynamical suppression of decoherence in two-state quantum systems,” Phys. Rev. A 582733–2744 (1998).
[Crossref]

1995 (1)

B. Friedrich and D. Herschbach, “Alignment and Trapping of Molecules in Intense Laser Fields,” Phys. Rev. Lett. 744623–4626 (1995).
[Crossref] [PubMed]

1970 (1)

W. Happer, “Light propagation and light shifts in optical pumping experiments,” Prog. Quant. Elec. 151–103 (1970).
[Crossref]

1968 (1)

B. Cagnac, A. Izraël, and M. Nogaret, “Spectroscopie Hertzienne,” Comptes Rendus Acad. Sci. Sér. B 267, 274–277 (1968).

1959 (1)

T. C. James and W. Klemperer, “Line Intensities in the Raman Effect of 1Σ Diatomic Molecules,” J. Chem. Phys. 31130–134 (1959).
[Crossref]

Aldegunde, J.

P. D. Gregory, J. A. Blackmore, J. Aldegunde, J. M. Hutson, and S. L. Cornish, “ac Stark effect in ultracold polar 87Rb133Cs molecules,” Phys. Rev. A 96021402 (2017).
[Crossref]

J. Aldegunde and J. M. Hutson, “Hyperfine structure of alkali-metal diatomic molecules,” Phys. Rev. A 96042506 (2017).
[Crossref]

Aymar, M.

R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
[Crossref]

Berestetskii, V. B.

V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Second Edition) (Butterworth-Heinemann, 1982), §61.

Blackmore, J. A.

P. D. Gregory, J. A. Blackmore, J. Aldegunde, J. M. Hutson, and S. L. Cornish, “ac Stark effect in ultracold polar 87Rb133Cs molecules,” Phys. Rev. A 96021402 (2017).
[Crossref]

Bonin, K. D.

K. D. Bonin and V. V. Kresin, Electric-Dipole Polarizabilities of Atoms, Molecules, and Clusters (World Scientific, 1997), p. 43.

Borsalino, D.

R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
[Crossref]

Bouloufa-Maafa, N.

R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
[Crossref]

Budker, D.

D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics (Oxford University Press, 2004).

Cagnac, B.

B. Cagnac, A. Izraël, and M. Nogaret, “Spectroscopie Hertzienne,” Comptes Rendus Acad. Sci. Sér. B 267, 274–277 (1968).

Cho, D.

H. Kim, H. S. Han, and D. Cho, “Magic Polarization for Optical Trapping of Atoms without Stark-Induced Dephasing,” Phys. Rev. Lett. 111243004 (2013).
[Crossref]

Chotia, A.

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

Cornish, S. L.

P. D. Gregory, J. A. Blackmore, J. Aldegunde, J. M. Hutson, and S. L. Cornish, “ac Stark effect in ultracold polar 87Rb133Cs molecules,” Phys. Rev. A 96021402 (2017).
[Crossref]

Covey, J. P.

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

DeMille, D.

S. Kotochigova and D. DeMille, “Electric-field-dependent dynamic polarizability and state-insensitive conditions for optical trapping of diatomic polar molecules,” Phys. Rev. A 82063421 (2010).
[Crossref]

DeMille, D. P.

D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics (Oxford University Press, 2004).

Dulieu, O.

R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
[Crossref]

Friedrich, B.

B. Friedrich and D. Herschbach, “Alignment and Trapping of Molecules in Intense Laser Fields,” Phys. Rev. Lett. 744623–4626 (1995).
[Crossref] [PubMed]

Gadway, B.

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

Gregory, P. D.

P. D. Gregory, J. A. Blackmore, J. Aldegunde, J. M. Hutson, and S. L. Cornish, “ac Stark effect in ultracold polar 87Rb133Cs molecules,” Phys. Rev. A 96021402 (2017).
[Crossref]

Han, H. S.

H. Kim, H. S. Han, and D. Cho, “Magic Polarization for Optical Trapping of Atoms without Stark-Induced Dephasing,” Phys. Rev. Lett. 111243004 (2013).
[Crossref]

Happer, W.

W. Happer, “Light propagation and light shifts in optical pumping experiments,” Prog. Quant. Elec. 151–103 (1970).
[Crossref]

Hazzard, K. R. A.

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

Herschbach, D.

B. Friedrich and D. Herschbach, “Alignment and Trapping of Molecules in Intense Laser Fields,” Phys. Rev. Lett. 744623–4626 (1995).
[Crossref] [PubMed]

Hutson, J. M.

J. Aldegunde and J. M. Hutson, “Hyperfine structure of alkali-metal diatomic molecules,” Phys. Rev. A 96042506 (2017).
[Crossref]

P. D. Gregory, J. A. Blackmore, J. Aldegunde, J. M. Hutson, and S. L. Cornish, “ac Stark effect in ultracold polar 87Rb133Cs molecules,” Phys. Rev. A 96021402 (2017).
[Crossref]

Izraël, A.

B. Cagnac, A. Izraël, and M. Nogaret, “Spectroscopie Hertzienne,” Comptes Rendus Acad. Sci. Sér. B 267, 274–277 (1968).

James, T. C.

T. C. James and W. Klemperer, “Line Intensities in the Raman Effect of 1Σ Diatomic Molecules,” J. Chem. Phys. 31130–134 (1959).
[Crossref]

Jin, D. S.

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

Kim, H.

H. Kim, H. S. Han, and D. Cho, “Magic Polarization for Optical Trapping of Atoms without Stark-Induced Dephasing,” Phys. Rev. Lett. 111243004 (2013).
[Crossref]

Kimball, D. F.

D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics (Oxford University Press, 2004).

Klemperer, W.

T. C. James and W. Klemperer, “Line Intensities in the Raman Effect of 1Σ Diatomic Molecules,” J. Chem. Phys. 31130–134 (1959).
[Crossref]

Kotochigova, S.

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

S. Kotochigova and D. DeMille, “Electric-field-dependent dynamic polarizability and state-insensitive conditions for optical trapping of diatomic polar molecules,” Phys. Rev. A 82063421 (2010).
[Crossref]

Kresin, V. V.

K. D. Bonin and V. V. Kresin, Electric-Dipole Polarizabilities of Atoms, Molecules, and Clusters (World Scientific, 1997), p. 43.

Lepers, M.

R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
[Crossref]

Lifshitz, E. M.

V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Second Edition) (Butterworth-Heinemann, 1982), §61.

Lloyd, S.

L. Viola and S. Lloyd, “Dynamical suppression of decoherence in two-state quantum systems,” Phys. Rev. A 582733–2744 (1998).
[Crossref]

Moses, S. A.

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

Neyenhuis, B.

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

Nogaret, M.

B. Cagnac, A. Izraël, and M. Nogaret, “Spectroscopie Hertzienne,” Comptes Rendus Acad. Sci. Sér. B 267, 274–277 (1968).

Orbán, A.

R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
[Crossref]

Ovsiannikov, V. D.

A. V. Taichenachev, V. I. Yudin, V. D. Ovsiannikov, and V. G. Pal’chikov, “Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions,” Phys. Rev. Lett. 97173601 (2006).
[Crossref] [PubMed]

Pal’chikov, V. G.

A. V. Taichenachev, V. I. Yudin, V. D. Ovsiannikov, and V. G. Pal’chikov, “Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions,” Phys. Rev. Lett. 97173601 (2006).
[Crossref] [PubMed]

Petrov, A.

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

Pitaevskii, L. P.

V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Second Edition) (Butterworth-Heinemann, 1982), §61.

Rey, A. M.

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

Seideman, T.

H. Stapelfeldt and T. Seideman, “Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75543–557 (2003).
[Crossref]

Stapelfeldt, H.

H. Stapelfeldt and T. Seideman, “Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75543–557 (2003).
[Crossref]

Taichenachev, A. V.

A. V. Taichenachev, V. I. Yudin, V. D. Ovsiannikov, and V. G. Pal’chikov, “Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions,” Phys. Rev. Lett. 97173601 (2006).
[Crossref] [PubMed]

Vexiau, R.

R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
[Crossref]

Viola, L.

L. Viola and S. Lloyd, “Dynamical suppression of decoherence in two-state quantum systems,” Phys. Rev. A 582733–2744 (1998).
[Crossref]

Yan, B.

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

Ye, J.

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

Yudin, V. I.

A. V. Taichenachev, V. I. Yudin, V. D. Ovsiannikov, and V. G. Pal’chikov, “Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions,” Phys. Rev. Lett. 97173601 (2006).
[Crossref] [PubMed]

Zare, R.

R. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, 1988).

Zwierlein, M.

M. Zwierlein, Private communication (2018).

Comptes Rendus Acad. Sci. Sér. B (1)

B. Cagnac, A. Izraël, and M. Nogaret, “Spectroscopie Hertzienne,” Comptes Rendus Acad. Sci. Sér. B 267, 274–277 (1968).

International Reviews in Physical Chemistry (1)

R. Vexiau, D. Borsalino, M. Lepers, A. Orbán, M. Aymar, O. Dulieu, and N. Bouloufa-Maafa, “Dynamic dipole polarizabilities of heteronuclear alkali dimers: optical response, trapping and control of ultracold molecules,” International Reviews in Physical Chemistry,  36709–750 (2017).
[Crossref]

J. Chem. Phys. (1)

T. C. James and W. Klemperer, “Line Intensities in the Raman Effect of 1Σ Diatomic Molecules,” J. Chem. Phys. 31130–134 (1959).
[Crossref]

Nature (1)

B. Yan, S. A. Moses, B. Gadway, J. P. Covey, K. R. A. Hazzard, A. M. Rey, D. S. Jin, and J. Ye, “Observation of dipolar spin-exchange interactions with lattice-confined polar molecules,” Nature 501521–525 (2013).
[Crossref] [PubMed]

Phys. Rev. A (4)

L. Viola and S. Lloyd, “Dynamical suppression of decoherence in two-state quantum systems,” Phys. Rev. A 582733–2744 (1998).
[Crossref]

J. Aldegunde and J. M. Hutson, “Hyperfine structure of alkali-metal diatomic molecules,” Phys. Rev. A 96042506 (2017).
[Crossref]

S. Kotochigova and D. DeMille, “Electric-field-dependent dynamic polarizability and state-insensitive conditions for optical trapping of diatomic polar molecules,” Phys. Rev. A 82063421 (2010).
[Crossref]

P. D. Gregory, J. A. Blackmore, J. Aldegunde, J. M. Hutson, and S. L. Cornish, “ac Stark effect in ultracold polar 87Rb133Cs molecules,” Phys. Rev. A 96021402 (2017).
[Crossref]

Phys. Rev. Lett. (4)

H. Kim, H. S. Han, and D. Cho, “Magic Polarization for Optical Trapping of Atoms without Stark-Induced Dephasing,” Phys. Rev. Lett. 111243004 (2013).
[Crossref]

A. V. Taichenachev, V. I. Yudin, V. D. Ovsiannikov, and V. G. Pal’chikov, “Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions,” Phys. Rev. Lett. 97173601 (2006).
[Crossref] [PubMed]

B. Neyenhuis, B. Yan, S. A. Moses, J. P. Covey, A. Chotia, A. Petrov, S. Kotochigova, J. Ye, and D. S. Jin, “Anisotropic Polarizability of Ultracold Polar 40K87Rb Molecules,” Phys. Rev. Lett. 109230403 (2012).
[Crossref]

B. Friedrich and D. Herschbach, “Alignment and Trapping of Molecules in Intense Laser Fields,” Phys. Rev. Lett. 744623–4626 (1995).
[Crossref] [PubMed]

Prog. Quant. Elec. (1)

W. Happer, “Light propagation and light shifts in optical pumping experiments,” Prog. Quant. Elec. 151–103 (1970).
[Crossref]

Rev. Mod. Phys. (1)

H. Stapelfeldt and T. Seideman, “Aligning molecules with strong laser pulses,” Rev. Mod. Phys. 75543–557 (2003).
[Crossref]

Other (6)

K. D. Bonin and V. V. Kresin, Electric-Dipole Polarizabilities of Atoms, Molecules, and Clusters (World Scientific, 1997), p. 43.

R. Zare, Angular Momentum: Understanding Spatial Aspects in Chemistry and Physics (Wiley, 1988).

M. Zwierlein, Private communication (2018).

Polarization with ellipticity ϵ=i(x^ory^)2/3±z^1/3 in the xz or yz plane rather than xy causes the diagonal elements of β^ to be zero in Eq. 7, making it apparent that for all J, β^ is singular with a zero eigenvalue.

D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics (Oxford University Press, 2004).

V. B. Berestetskii, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Second Edition) (Butterworth-Heinemann, 1982), §61.

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 (2)

Fig. 1
Fig. 1 Eigenvalues of β ^ ( γ ), as defined in Eq. (8), in units of Δ vs. ellipticity parameter γ. Linear polarization corresponds to γ = 0 or ±π/2 where two values are negative and one positive. Circular polarization corresponds to γ = ±π/4 where two values are positive and one negative. Between these extremes are zero-crossings where one J = 1 state has no differential light shift with respect to the J = 0 state. Polarizations are depicted with horizontal x ^ and vertical y ^ directions.
Fig. 2
Fig. 2 Difference of energy eigenvalues between J = 1 and J = 0 as a function of J = 0 light shift for an example molecule (NaCs with 10 Gauss magnetic field along z ^) where the offset of 3.48 GHz due to rotational energy is removed. The polarizability of the rotation state ( | 1 , 1 | 1 , 1 ) / 2 approaches that of the ground state for high intensity when the polarization vector is ϵ = x ^ 2 / 3 + i y ^ / 3, as described in the text. We add the molecular Hamiltonian H0 [14] to the light shift of Eq. (7), to make the 32 molecular hyperfine states visible. Tensor coupling between nuclear magnetic dipoles is neglected due to smallness. The hyperfine coupling and Zeeman energies of H0 must be small compared to 2 E 0 2 Δ / 15 for the deep-trap limit to apply. A polarizability anisotropy of α = α/4 is used, corresponding to NaCs at a wavelength of 1064 nm [19], but the exact values do not affect the main result. The eigenstates for deep traps are labeled in terms of superpositions of |J, m〉 basis states. We have neglected J = 2 states in this calculation, and their energy difference with the ground state sets an upper bound for the range of trap depths where the results are valid.

Equations (8)

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

A ˜ = ( α 0 0 0 α 0 0 0 α ) ,
R ˜ x = ( 1 0 0 0 cos θ sin θ 0 sin θ cos θ ) , R ˜ z ( cos ϕ sin ϕ 0 sin ϕ cos ϕ 0 0 0 1 )
α ˜ ( θ , ϕ ) = R ˜ z R ˜ x A ˜ R ˜ x R ˜ z .
V ( θ , ϕ ) = 1 2 E 0 2 ϵ α ˜ ( θ , ϕ ) ϵ
β ( γ , θ , ϕ ) = Δ ( 1 3 + 1 2 sin 2 θ 1 2 cos ( 2 γ ) cos ( 2 ϕ ) sin 2 θ )
= Δ 2 π 15 m = 2 2 c m Y 2 , m ( θ , ϕ )
J , m | β ^ ( γ ) | J , m Y J , m ( θ , ϕ ) * Y j , m ( θ , ϕ ) β ( γ , θ , ϕ ) d Ω = Δ ( 1 ) m ( 2 J + 1 ) ( 2 J + 1 ) 6 ( 2 J J 0 0 0 ) × c m m ( 2 J J m m m m )
β ^ ( γ ) = Δ 15 ( 1 0 3 cos ( 2 γ ) 0 2 0 3 cos ( 2 γ ) 0 1 ) .

Metrics