Abstract

We measure and stabilize the relative angle of parallel and antiparallel laser beams to 5nradHz resolution by comparing the phases of radio frequency beat notes on a quadrant photodetector. The absolute accuracy is 5.1 and 2.1μrad for antiparallel and parallel beams, respectively, which is more than 6 and 16 times below the Rayleigh criterion.

© 2005 Optical Society of America

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References

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  1. C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, Phys. Rev. Lett. 88, 010401 (2002).
    [Crossref]
  2. H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, Phys. Rev. Lett. 91, 020401 (2003).
    [Crossref]
  3. H. Müller, S.-w. Chiow, Q. Long, and S. Chu, “Phase-locked, low-noise, frequency-agile titanium:sapphire lasers for simultaneous atom interferometers,” Opt. Lett. (to be published).
  4. S. Chu, Nature 416, 206 (2002).
    [Crossref] [PubMed]
  5. S. Chu, in Coherent Atomic Matter Waves, R. Kaiser, C. Westbrook, and F. David, eds. (Springer-Verlag, 2001), p. 317.
    [Crossref]
  6. P. Berman, Atom Interferometry (Academic, 1997).
  7. M. Kasevich, D. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
    [Crossref] [PubMed]
  8. M. Kasevich and S. Chu, Phys. Rev. Lett. 67, 181 (1991).
    [Crossref] [PubMed]
  9. A. Wicht, J. M. Hensley, E. Sarajlic, and S. Chu, Phys. Scr. T102, 82 (2002).
    [Crossref]
  10. Lord Rayleigh, Philos. Mag. 8, 261–274 (1879).
    [Crossref]
  11. P. C. D. Hobbs, Building Electro-Optical Systems (Wiley, 2000).
    [Crossref]
  12. E. Morrison, B. J. Meers, D. I. Robertson, and H. Ward, Appl. Opt. 33, 5041 (1994).
    [Crossref] [PubMed]
  13. G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
    [Crossref]

2004 (1)

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

2003 (1)

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, Phys. Rev. Lett. 91, 020401 (2003).
[Crossref]

2002 (3)

S. Chu, Nature 416, 206 (2002).
[Crossref] [PubMed]

A. Wicht, J. M. Hensley, E. Sarajlic, and S. Chu, Phys. Scr. T102, 82 (2002).
[Crossref]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, Phys. Rev. Lett. 88, 010401 (2002).
[Crossref]

1994 (1)

1991 (2)

M. Kasevich, D. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

M. Kasevich and S. Chu, Phys. Rev. Lett. 67, 181 (1991).
[Crossref] [PubMed]

1879 (1)

Lord Rayleigh, Philos. Mag. 8, 261–274 (1879).
[Crossref]

Berman, P.

P. Berman, Atom Interferometry (Academic, 1997).

Braxmaier, C.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, Phys. Rev. Lett. 91, 020401 (2003).
[Crossref]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, Phys. Rev. Lett. 88, 010401 (2002).
[Crossref]

Chiow, S.-w.

H. Müller, S.-w. Chiow, Q. Long, and S. Chu, “Phase-locked, low-noise, frequency-agile titanium:sapphire lasers for simultaneous atom interferometers,” Opt. Lett. (to be published).

Chu, S.

S. Chu, Nature 416, 206 (2002).
[Crossref] [PubMed]

A. Wicht, J. M. Hensley, E. Sarajlic, and S. Chu, Phys. Scr. T102, 82 (2002).
[Crossref]

M. Kasevich, D. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

M. Kasevich and S. Chu, Phys. Rev. Lett. 67, 181 (1991).
[Crossref] [PubMed]

H. Müller, S.-w. Chiow, Q. Long, and S. Chu, “Phase-locked, low-noise, frequency-agile titanium:sapphire lasers for simultaneous atom interferometers,” Opt. Lett. (to be published).

S. Chu, in Coherent Atomic Matter Waves, R. Kaiser, C. Westbrook, and F. David, eds. (Springer-Verlag, 2001), p. 317.
[Crossref]

Danzmann, K.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Garcya, A.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Heinzel, G.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Hensley, J. M.

A. Wicht, J. M. Hensley, E. Sarajlic, and S. Chu, Phys. Scr. T102, 82 (2002).
[Crossref]

Herrmann, S.

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, Phys. Rev. Lett. 91, 020401 (2003).
[Crossref]

Hobbs, P. C. D.

P. C. D. Hobbs, Building Electro-Optical Systems (Wiley, 2000).
[Crossref]

Hoyland, D.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Jennrich, O.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Johann, U.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Kasapi, S.

M. Kasevich, D. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

Kasevich, M.

M. Kasevich and S. Chu, Phys. Rev. Lett. 67, 181 (1991).
[Crossref] [PubMed]

M. Kasevich, D. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

Long, Q.

H. Müller, S.-w. Chiow, Q. Long, and S. Chu, “Phase-locked, low-noise, frequency-agile titanium:sapphire lasers for simultaneous atom interferometers,” Opt. Lett. (to be published).

Meers, B. J.

Middleton, K.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Mlynek, J.

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, Phys. Rev. Lett. 88, 010401 (2002).
[Crossref]

Moler, K.

M. Kasevich, D. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

Morrison, E.

Müller, H.

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, Phys. Rev. Lett. 91, 020401 (2003).
[Crossref]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, Phys. Rev. Lett. 88, 010401 (2002).
[Crossref]

H. Müller, S.-w. Chiow, Q. Long, and S. Chu, “Phase-locked, low-noise, frequency-agile titanium:sapphire lasers for simultaneous atom interferometers,” Opt. Lett. (to be published).

Peters, A.

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, Phys. Rev. Lett. 91, 020401 (2003).
[Crossref]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, Phys. Rev. Lett. 88, 010401 (2002).
[Crossref]

Pradl, O.

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, Phys. Rev. Lett. 88, 010401 (2002).
[Crossref]

Rayleigh, Lord

Lord Rayleigh, Philos. Mag. 8, 261–274 (1879).
[Crossref]

Riis, E.

M. Kasevich, D. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

Robertson, D.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Robertson, D. I.

Rüdiger, A.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Sarajlic, E.

A. Wicht, J. M. Hensley, E. Sarajlic, and S. Chu, Phys. Scr. T102, 82 (2002).
[Crossref]

Schiller, S.

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, Phys. Rev. Lett. 91, 020401 (2003).
[Crossref]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, Phys. Rev. Lett. 88, 010401 (2002).
[Crossref]

Schilling, R.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Wand, V.

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Ward, H.

Weiss, D.

M. Kasevich, D. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

Wicht, A.

A. Wicht, J. M. Hensley, E. Sarajlic, and S. Chu, Phys. Scr. T102, 82 (2002).
[Crossref]

Appl. Opt. (1)

Class. Quantum Grav. (1)

G. Heinzel, V. Wand, A. Garcya, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, Class. Quantum Grav. 21, S581 (2004).
[Crossref]

Nature (1)

S. Chu, Nature 416, 206 (2002).
[Crossref] [PubMed]

Philos. Mag. (1)

Lord Rayleigh, Philos. Mag. 8, 261–274 (1879).
[Crossref]

Phys. Rev. Lett. (4)

M. Kasevich, D. Weiss, E. Riis, K. Moler, S. Kasapi, and S. Chu, Phys. Rev. Lett. 66, 2297 (1991).
[Crossref] [PubMed]

M. Kasevich and S. Chu, Phys. Rev. Lett. 67, 181 (1991).
[Crossref] [PubMed]

C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, Phys. Rev. Lett. 88, 010401 (2002).
[Crossref]

H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, and A. Peters, Phys. Rev. Lett. 91, 020401 (2003).
[Crossref]

Phys. Scr. (1)

A. Wicht, J. M. Hensley, E. Sarajlic, and S. Chu, Phys. Scr. T102, 82 (2002).
[Crossref]

Other (4)

P. C. D. Hobbs, Building Electro-Optical Systems (Wiley, 2000).
[Crossref]

H. Müller, S.-w. Chiow, Q. Long, and S. Chu, “Phase-locked, low-noise, frequency-agile titanium:sapphire lasers for simultaneous atom interferometers,” Opt. Lett. (to be published).

S. Chu, in Coherent Atomic Matter Waves, R. Kaiser, C. Westbrook, and F. David, eds. (Springer-Verlag, 2001), p. 317.
[Crossref]

P. Berman, Atom Interferometry (Academic, 1997).

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Figures (4)

Fig. 1
Fig. 1

(Color online) Schematic of the setup for antiparallel beams.

Fig. 2
Fig. 2

(Color online) Tests for systematic influences: (a) parallel shift of the corner cube, (b) PBS alignment, (c) rotation of the corner cube.

Fig. 3
Fig. 3

Noise spectral density (SD) of the angle measurement.

Fig. 4
Fig. 4

(Color online) 12 h operation of the system.

Equations (1)

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I 1 = 2 E 1 E 2 0 R π 4 π 4 r exp ( 2 r 2 w 0 2 ) cos ( β k r cos θ ω t ) d θ d r ,

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