Abstract

We demonstrate a waveplate for a pseudo-spin-1/2 Bose–Einstein condensate (BEC) using a two-photon Raman interaction. The angle of the waveplate is set by the relative phase of the optical fields, and the retardance is controlled by the pulse area. The waveplate allows us to image maps of the Stokes parameters of a BEC and thereby measure its relative ground-state phase. We demonstrate the waveplate by measuring the Stokes parameters of a coreless vortex.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
    [CrossRef]
  2. Y.-J. Lin, R. L. Compton, K. Jiménez-Garca, J. V. Porto, and I. B. Spielman, Nature 462, 628 (2009).
    [CrossRef]
  3. K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
    [CrossRef]
  4. L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, Phys. Rev. Lett. 103, 250401 (2009).
  5. J. Choi, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 108, 035301 (2012).
    [CrossRef]
  6. J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 111, 245301 (2013).
    [CrossRef]
  7. M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, Nature 505, 657 (2014).
    [CrossRef]
  8. P. Meystre, Atom Optics (Springer, 2001).
  9. A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Rev. Mod. Phys. 81, 1051 (2009).
    [CrossRef]
  10. R. A. Beth, Phys. Rev. 50, 115 (1936).
    [CrossRef]
  11. A. H. S. Holbourn, Nature 137, 31 (1936).
    [CrossRef]
  12. U. Fano, Phys. Rev. 93, 121 (1954).
    [CrossRef]
  13. H. G. Jerrard, Opt. Laser Technol. 14, 309 (1982).
    [CrossRef]
  14. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).
  15. K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 78, 053412 (2008).
    [CrossRef]
  16. B. W. Shore, The Theory of Coherent Atomic Excitations (Wiley, 1990), Vol. 2.
  17. E. Brion, L. H. Pedersen, and K. Mølmer, J. Phys. A: Math Theor. 40, 1033 (2007).
    [CrossRef]
  18. M. P. Fewell, Opt. Commun. 253, 125 (2005).
    [CrossRef]
  19. K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, Phys. Rev. Lett. 102, 030405 (2009).
    [CrossRef]
  20. A. M. Beckley, T. G. Brown, and M. A. Alonso, Opt. Express 18, 10777 (2010).
    [CrossRef]
  21. G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
    [CrossRef]
  22. I. G. Da Paz, P. L. Saldanha, M. C. Nemes, and J. G. P. de Faria, New J. Phys. 13, 125005 (2011).
    [CrossRef]
  23. A. Hansen, J. T. Schultz, and N. P. Bigelow, in The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement Meeting, OSA Technical Digest (Optical Society of America, 2013), paper M6.64.

2014 (1)

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, Nature 505, 657 (2014).
[CrossRef]

2013 (1)

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 111, 245301 (2013).
[CrossRef]

2012 (1)

J. Choi, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 108, 035301 (2012).
[CrossRef]

2011 (3)

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

I. G. Da Paz, P. L. Saldanha, M. C. Nemes, and J. G. P. de Faria, New J. Phys. 13, 125005 (2011).
[CrossRef]

2010 (1)

2009 (4)

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, Phys. Rev. Lett. 102, 030405 (2009).
[CrossRef]

Y.-J. Lin, R. L. Compton, K. Jiménez-Garca, J. V. Porto, and I. B. Spielman, Nature 462, 628 (2009).
[CrossRef]

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, Phys. Rev. Lett. 103, 250401 (2009).

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Rev. Mod. Phys. 81, 1051 (2009).
[CrossRef]

2008 (2)

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[CrossRef]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 78, 053412 (2008).
[CrossRef]

2007 (1)

E. Brion, L. H. Pedersen, and K. Mølmer, J. Phys. A: Math Theor. 40, 1033 (2007).
[CrossRef]

2005 (1)

M. P. Fewell, Opt. Commun. 253, 125 (2005).
[CrossRef]

1982 (1)

H. G. Jerrard, Opt. Laser Technol. 14, 309 (1982).
[CrossRef]

1954 (1)

U. Fano, Phys. Rev. 93, 121 (1954).
[CrossRef]

1936 (2)

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

A. H. S. Holbourn, Nature 137, 31 (1936).
[CrossRef]

Alfano, R. R.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Alonso, M. A.

Beckley, A. M.

Beth, R. A.

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Bigelow, N. P.

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, Phys. Rev. Lett. 103, 250401 (2009).

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, Phys. Rev. Lett. 102, 030405 (2009).
[CrossRef]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 78, 053412 (2008).
[CrossRef]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[CrossRef]

A. Hansen, J. T. Schultz, and N. P. Bigelow, in The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement Meeting, OSA Technical Digest (Optical Society of America, 2013), paper M6.64.

Brion, E.

E. Brion, L. H. Pedersen, and K. Mølmer, J. Phys. A: Math Theor. 40, 1033 (2007).
[CrossRef]

Brown, T. G.

Choi, J.

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 111, 245301 (2013).
[CrossRef]

J. Choi, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 108, 035301 (2012).
[CrossRef]

Compton, R. L.

Y.-J. Lin, R. L. Compton, K. Jiménez-Garca, J. V. Porto, and I. B. Spielman, Nature 462, 628 (2009).
[CrossRef]

Cronin, A. D.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Rev. Mod. Phys. 81, 1051 (2009).
[CrossRef]

Da Paz, I. G.

I. G. Da Paz, P. L. Saldanha, M. C. Nemes, and J. G. P. de Faria, New J. Phys. 13, 125005 (2011).
[CrossRef]

Dalibard, J.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

de Faria, J. G. P.

I. G. Da Paz, P. L. Saldanha, M. C. Nemes, and J. G. P. de Faria, New J. Phys. 13, 125005 (2011).
[CrossRef]

Deutsch, B. M.

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, Phys. Rev. Lett. 103, 250401 (2009).

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

Fano, U.

U. Fano, Phys. Rev. 93, 121 (1954).
[CrossRef]

Fewell, M. P.

M. P. Fewell, Opt. Commun. 253, 125 (2005).
[CrossRef]

Gerbier, F.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Hall, D. S.

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, Nature 505, 657 (2014).
[CrossRef]

Hansen, A.

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, Phys. Rev. Lett. 102, 030405 (2009).
[CrossRef]

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, Phys. Rev. Lett. 103, 250401 (2009).

A. Hansen, J. T. Schultz, and N. P. Bigelow, in The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement Meeting, OSA Technical Digest (Optical Society of America, 2013), paper M6.64.

Holbourn, A. H. S.

A. H. S. Holbourn, Nature 137, 31 (1936).
[CrossRef]

Jerrard, H. G.

H. G. Jerrard, Opt. Laser Technol. 14, 309 (1982).
[CrossRef]

Jiménez-Garca, K.

Y.-J. Lin, R. L. Compton, K. Jiménez-Garca, J. V. Porto, and I. B. Spielman, Nature 462, 628 (2009).
[CrossRef]

Juzeliunas, G.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Kandel, S.

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, Nature 505, 657 (2014).
[CrossRef]

Kang, S.

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 111, 245301 (2013).
[CrossRef]

Kwon, W. J.

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 111, 245301 (2013).
[CrossRef]

J. Choi, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 108, 035301 (2012).
[CrossRef]

Leslie, L. S.

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, Phys. Rev. Lett. 102, 030405 (2009).
[CrossRef]

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, Phys. Rev. Lett. 103, 250401 (2009).

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 78, 053412 (2008).
[CrossRef]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[CrossRef]

Lin, Y.-J.

Y.-J. Lin, R. L. Compton, K. Jiménez-Garca, J. V. Porto, and I. B. Spielman, Nature 462, 628 (2009).
[CrossRef]

Meystre, P.

P. Meystre, Atom Optics (Springer, 2001).

Milione, G.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Mølmer, K.

E. Brion, L. H. Pedersen, and K. Mølmer, J. Phys. A: Math Theor. 40, 1033 (2007).
[CrossRef]

Möttönen, M.

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, Nature 505, 657 (2014).
[CrossRef]

Nemes, M. C.

I. G. Da Paz, P. L. Saldanha, M. C. Nemes, and J. G. P. de Faria, New J. Phys. 13, 125005 (2011).
[CrossRef]

Nolan, D. A.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Öhberg, P.

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

Pedersen, L. H.

E. Brion, L. H. Pedersen, and K. Mølmer, J. Phys. A: Math Theor. 40, 1033 (2007).
[CrossRef]

Porto, J. V.

Y.-J. Lin, R. L. Compton, K. Jiménez-Garca, J. V. Porto, and I. B. Spielman, Nature 462, 628 (2009).
[CrossRef]

Pritchard, D. E.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Rev. Mod. Phys. 81, 1051 (2009).
[CrossRef]

Ray, M. W.

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, Nature 505, 657 (2014).
[CrossRef]

Ruokokoski, E.

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, Nature 505, 657 (2014).
[CrossRef]

Saldanha, P. L.

I. G. Da Paz, P. L. Saldanha, M. C. Nemes, and J. G. P. de Faria, New J. Phys. 13, 125005 (2011).
[CrossRef]

Schmiedmayer, J.

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Rev. Mod. Phys. 81, 1051 (2009).
[CrossRef]

Schultz, J. T.

A. Hansen, J. T. Schultz, and N. P. Bigelow, in The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement Meeting, OSA Technical Digest (Optical Society of America, 2013), paper M6.64.

Seo, S. W.

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 111, 245301 (2013).
[CrossRef]

Shin, Y.

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 111, 245301 (2013).
[CrossRef]

J. Choi, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 108, 035301 (2012).
[CrossRef]

Shore, B. W.

B. W. Shore, The Theory of Coherent Atomic Excitations (Wiley, 1990), Vol. 2.

Spielman, I. B.

Y.-J. Lin, R. L. Compton, K. Jiménez-Garca, J. V. Porto, and I. B. Spielman, Nature 462, 628 (2009).
[CrossRef]

Sztul, H. I.

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Wright, K. C.

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, Phys. Rev. Lett. 103, 250401 (2009).

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, Phys. Rev. Lett. 102, 030405 (2009).
[CrossRef]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 78, 053412 (2008).
[CrossRef]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[CrossRef]

J. Phys. A: Math Theor. (1)

E. Brion, L. H. Pedersen, and K. Mølmer, J. Phys. A: Math Theor. 40, 1033 (2007).
[CrossRef]

Nature (3)

A. H. S. Holbourn, Nature 137, 31 (1936).
[CrossRef]

Y.-J. Lin, R. L. Compton, K. Jiménez-Garca, J. V. Porto, and I. B. Spielman, Nature 462, 628 (2009).
[CrossRef]

M. W. Ray, E. Ruokokoski, S. Kandel, M. Möttönen, and D. S. Hall, Nature 505, 657 (2014).
[CrossRef]

New J. Phys. (1)

I. G. Da Paz, P. L. Saldanha, M. C. Nemes, and J. G. P. de Faria, New J. Phys. 13, 125005 (2011).
[CrossRef]

Opt. Commun. (1)

M. P. Fewell, Opt. Commun. 253, 125 (2005).
[CrossRef]

Opt. Express (1)

Opt. Laser Technol. (1)

H. G. Jerrard, Opt. Laser Technol. 14, 309 (1982).
[CrossRef]

Phys. Rev. (2)

U. Fano, Phys. Rev. 93, 121 (1954).
[CrossRef]

R. A. Beth, Phys. Rev. 50, 115 (1936).
[CrossRef]

Phys. Rev. A (2)

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 78, 053412 (2008).
[CrossRef]

K. C. Wright, L. S. Leslie, and N. P. Bigelow, Phys. Rev. A 77, 041601 (2008).
[CrossRef]

Phys. Rev. Lett. (5)

L. S. Leslie, A. Hansen, K. C. Wright, B. M. Deutsch, and N. P. Bigelow, Phys. Rev. Lett. 103, 250401 (2009).

J. Choi, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 108, 035301 (2012).
[CrossRef]

J. Choi, S. Kang, S. W. Seo, W. J. Kwon, and Y. Shin, Phys. Rev. Lett. 111, 245301 (2013).
[CrossRef]

K. C. Wright, L. S. Leslie, A. Hansen, and N. P. Bigelow, Phys. Rev. Lett. 102, 030405 (2009).
[CrossRef]

G. Milione, H. I. Sztul, D. A. Nolan, and R. R. Alfano, Phys. Rev. Lett. 107, 053601 (2011).
[CrossRef]

Rev. Mod. Phys. (2)

J. Dalibard, F. Gerbier, G. Juzeliūnas, and P. Öhberg, Rev. Mod. Phys. 83, 1523 (2011).
[CrossRef]

A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Rev. Mod. Phys. 81, 1051 (2009).
[CrossRef]

Other (4)

P. Meystre, Atom Optics (Springer, 2001).

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987).

B. W. Shore, The Theory of Coherent Atomic Excitations (Wiley, 1990), Vol. 2.

A. Hansen, J. T. Schultz, and N. P. Bigelow, in The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement Meeting, OSA Technical Digest (Optical Society of America, 2013), paper M6.64.

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 (3)

Fig. 1.
Fig. 1.

(a) The Bloch sphere. (b) Three-level Lambda system.

Fig. 2.
Fig. 2.

Polarizing beamsplitter for atoms. The first two columns of (a) are averages of two-to-three highly similar absorption images of the outputs of the atom polarizing beamsplitter (|a|2, |a|2) for essentially identical coreless vortices. The first two rows correspond to ϕ=π/2 and 0 of the Raman waveplate, and the third row is without the waveplate operation. The final column shows the Stokes maps Si i{1,2,3}, which are the differences of the two beamsplitter outputs. The Si are arranged such that the index i corresponds to the row number. (b) shows the corresponding theory when the coreless vortex is created with a radial phase.

Fig. 3.
Fig. 3.

Stokes maps and relative ground-state phase of (a) ideal coreless vortex (theory), (b) coreless vortex with a radial phase (theory), and (c) experimentally created coreless vortex. (d) shows a theoretical relative ground-state phase for a coreless vortex with opposite handedness to that in (b), and (e) is the relative ground-state phase of the experimentally created coreless vortex.

Equations (3)

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

S0=c2+c2,S1=cccosφ,S2=ccsinφ,S3=c2c2.
a˙=i2ΩA*ae,a˙=i2ΩB*ae+iΔABa,a˙e=iΔAaei2ΩAai2ΩBa.
ψ⃗(t)=eiΩt2[cosΩt2ieiϕsinΩt2ieiϕsinΩt2cosΩt2]ψ⃗(t=0),

Metrics