Abstract

We present the first detector that is capable of recording high-bandwidth atom number density measurements of a Bose–Einstein condensate, with a readout of the data in real time. It is based on a shot-noise-limited unbalanced Mach–Zehnder interferometer designed for a minimally destructive measurement of the atom column density of a Bose–Einstein condensate. The shot-noise limit is reached by phase modulating the laser in one arm and phase locking the interferometer with a second-color laser. The detector is characterized, and its sensitivity for a fractional change in the column density of a Bose–Einstein condensate is calculated. With this detection system it may be possible to implement feedback to stabilize a Bose–Einstein condensate or an atom laser.

© 2006 Optical Society of America

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  1. M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, nondestructive observation of a Bose condensate," Science 273, 84-87 (1996).
    [CrossRef] [PubMed]
  2. S. Kadlecek, J. Sebby, R. Newell, and T. G. Walker, "Nondestructive spatial heterodyne imaging of cold atoms," Opt. Lett. 26, 137-139 (2001).
    [CrossRef]
  3. L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, "Off-resonant defocus-contrast imaging of cold atoms," Opt. Lett. 29, 232-234 (2004).
    [CrossRef] [PubMed]
  4. V. Savalli, G. Zs. K. Horvath, P. D. Featonby, L. Cognet, N. Westbrook, C. I. Westbrook, and A. Aspect, "Optical detection of cold atoms without spontaneous emission," Opt. Lett. 24, 1552-1554 (1999).
    [CrossRef]
  5. J. E. Lye, B. D. Cuthbertson, H.-A. Bachor, and J. D. Close, "Phase modulation spectroscopy: a non-destructive probe of Bose-Einstein condensates," J. Opt. B 1, 402-407 (1999).
    [CrossRef]
  6. J. E. Lye, J. J. Hope, and J. D. Close, "Rapid real-time detection of cold atoms with minimal destruction," Phys. Rev. A 69, 023601 (2004).
    [CrossRef]
  7. J. M. McGuirk, G. T. Foster, J. B. Fixler, and M. A. Kasevich, "Low-noise detection of ultracold atoms," Opt. Lett. 26, 364-366 (2001).
    [CrossRef]
  8. J. E. Lye, J. J. Hope, and J. D. Close, "Nondestructive dynamic detectors for Bose-Einstein condensates," Phys. Rev. A 67, 043609 (2003).
    [CrossRef]
  9. J. J. Hope and J. D. Close, "General limit to nondestructive optical detection of atoms," Phys. Rev. A 71, 043822 (2005).
    [CrossRef]
  10. M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
    [CrossRef]
  11. J. E. Lye, "Dynamic non-destructive detection of Bose-Einstein condensates and atom lasers," doctoral thesis (Australian National University, 2003).
  12. D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
    [CrossRef]

2005 (2)

J. J. Hope and J. D. Close, "General limit to nondestructive optical detection of atoms," Phys. Rev. A 71, 043822 (2005).
[CrossRef]

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

2004 (2)

J. E. Lye, J. J. Hope, and J. D. Close, "Rapid real-time detection of cold atoms with minimal destruction," Phys. Rev. A 69, 023601 (2004).
[CrossRef]

L. D. Turner, K. P. Weber, D. Paganin, and R. E. Scholten, "Off-resonant defocus-contrast imaging of cold atoms," Opt. Lett. 29, 232-234 (2004).
[CrossRef] [PubMed]

2003 (2)

J. E. Lye, "Dynamic non-destructive detection of Bose-Einstein condensates and atom lasers," doctoral thesis (Australian National University, 2003).

J. E. Lye, J. J. Hope, and J. D. Close, "Nondestructive dynamic detectors for Bose-Einstein condensates," Phys. Rev. A 67, 043609 (2003).
[CrossRef]

2001 (2)

1999 (2)

J. E. Lye, B. D. Cuthbertson, H.-A. Bachor, and J. D. Close, "Phase modulation spectroscopy: a non-destructive probe of Bose-Einstein condensates," J. Opt. B 1, 402-407 (1999).
[CrossRef]

V. Savalli, G. Zs. K. Horvath, P. D. Featonby, L. Cognet, N. Westbrook, C. I. Westbrook, and A. Aspect, "Optical detection of cold atoms without spontaneous emission," Opt. Lett. 24, 1552-1554 (1999).
[CrossRef]

1998 (1)

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

1996 (1)

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, nondestructive observation of a Bose condensate," Science 273, 84-87 (1996).
[CrossRef] [PubMed]

Alzar, C. L. Garrido

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

Andrews, M. R.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, nondestructive observation of a Bose condensate," Science 273, 84-87 (1996).
[CrossRef] [PubMed]

Aspect, A.

Bachor, H.-A.

J. E. Lye, B. D. Cuthbertson, H.-A. Bachor, and J. D. Close, "Phase modulation spectroscopy: a non-destructive probe of Bose-Einstein condensates," J. Opt. B 1, 402-407 (1999).
[CrossRef]

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Close, J. D.

J. J. Hope and J. D. Close, "General limit to nondestructive optical detection of atoms," Phys. Rev. A 71, 043822 (2005).
[CrossRef]

J. E. Lye, J. J. Hope, and J. D. Close, "Rapid real-time detection of cold atoms with minimal destruction," Phys. Rev. A 69, 023601 (2004).
[CrossRef]

J. E. Lye, J. J. Hope, and J. D. Close, "Nondestructive dynamic detectors for Bose-Einstein condensates," Phys. Rev. A 67, 043609 (2003).
[CrossRef]

J. E. Lye, B. D. Cuthbertson, H.-A. Bachor, and J. D. Close, "Phase modulation spectroscopy: a non-destructive probe of Bose-Einstein condensates," J. Opt. B 1, 402-407 (1999).
[CrossRef]

Cognet, L.

Cuthbertson, B. D.

J. E. Lye, B. D. Cuthbertson, H.-A. Bachor, and J. D. Close, "Phase modulation spectroscopy: a non-destructive probe of Bose-Einstein condensates," J. Opt. B 1, 402-407 (1999).
[CrossRef]

Durfee, D. S.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, nondestructive observation of a Bose condensate," Science 273, 84-87 (1996).
[CrossRef] [PubMed]

Featonby, P. D.

Fixler, J. B.

Foster, G. T.

Gray, M. B.

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Harb, C. C.

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Hope, J. J.

J. J. Hope and J. D. Close, "General limit to nondestructive optical detection of atoms," Phys. Rev. A 71, 043822 (2005).
[CrossRef]

J. E. Lye, J. J. Hope, and J. D. Close, "Rapid real-time detection of cold atoms with minimal destruction," Phys. Rev. A 69, 023601 (2004).
[CrossRef]

J. E. Lye, J. J. Hope, and J. D. Close, "Nondestructive dynamic detectors for Bose-Einstein condensates," Phys. Rev. A 67, 043609 (2003).
[CrossRef]

Horvath, G. Zs. K.

Kadlecek, S.

Kasevich, M. A.

Ketterle, W.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, nondestructive observation of a Bose condensate," Science 273, 84-87 (1996).
[CrossRef] [PubMed]

Kurn, D. M.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, nondestructive observation of a Bose condensate," Science 273, 84-87 (1996).
[CrossRef] [PubMed]

Lye, J. E.

J. E. Lye, J. J. Hope, and J. D. Close, "Rapid real-time detection of cold atoms with minimal destruction," Phys. Rev. A 69, 023601 (2004).
[CrossRef]

J. E. Lye, J. J. Hope, and J. D. Close, "Nondestructive dynamic detectors for Bose-Einstein condensates," Phys. Rev. A 67, 043609 (2003).
[CrossRef]

J. E. Lye, "Dynamic non-destructive detection of Bose-Einstein condensates and atom lasers," doctoral thesis (Australian National University, 2003).

J. E. Lye, B. D. Cuthbertson, H.-A. Bachor, and J. D. Close, "Phase modulation spectroscopy: a non-destructive probe of Bose-Einstein condensates," J. Opt. B 1, 402-407 (1999).
[CrossRef]

McGuirk, J. M.

Mewes, M.-O.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, nondestructive observation of a Bose condensate," Science 273, 84-87 (1996).
[CrossRef] [PubMed]

Mikkelsen, J. K.

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

Newell, R.

Oblak, D.

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

Paganin, D.

Petrov, P. G.

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

Polzik, E. S.

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

Savalli, V.

Scholten, R. E.

Sebby, J.

Shaddock, D. A.

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Sorensen, J. L.

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

Tittel, W.

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

Turner, L. D.

van Druten, N. J.

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, nondestructive observation of a Bose condensate," Science 273, 84-87 (1996).
[CrossRef] [PubMed]

Vershovski, A. K.

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

Walker, T. G.

Weber, K. P.

Westbrook, C. I.

Westbrook, N.

J. Opt. B (1)

J. E. Lye, B. D. Cuthbertson, H.-A. Bachor, and J. D. Close, "Phase modulation spectroscopy: a non-destructive probe of Bose-Einstein condensates," J. Opt. B 1, 402-407 (1999).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. A (4)

J. E. Lye, J. J. Hope, and J. D. Close, "Rapid real-time detection of cold atoms with minimal destruction," Phys. Rev. A 69, 023601 (2004).
[CrossRef]

J. E. Lye, J. J. Hope, and J. D. Close, "Nondestructive dynamic detectors for Bose-Einstein condensates," Phys. Rev. A 67, 043609 (2003).
[CrossRef]

J. J. Hope and J. D. Close, "General limit to nondestructive optical detection of atoms," Phys. Rev. A 71, 043822 (2005).
[CrossRef]

D. Oblak, P. G. Petrov, C. L. Garrido Alzar, W. Tittel, A. K. Vershovski, J. K. Mikkelsen, J. L. Sorensen, and E. S. Polzik, "Quantum-noise-limited interferometric measurement of atomic noise: towards spin squeezing on the Cs clock transition," Phys. Rev. A 71, 043807 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

M. B. Gray, D. A. Shaddock, C. C. Harb, and H.-A. Bachor, "Photodetector designs for low-noise, broadband, and high-power applications," Rev. Sci. Instrum. 69, 3755-3762 (1998).
[CrossRef]

Science (1)

M. R. Andrews, M.-O. Mewes, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, "Direct, nondestructive observation of a Bose condensate," Science 273, 84-87 (1996).
[CrossRef] [PubMed]

Other (1)

J. E. Lye, "Dynamic non-destructive detection of Bose-Einstein condensates and atom lasers," doctoral thesis (Australian National University, 2003).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental layout. The beams of the two lasers are drawn separated for clarity. The circle indicates where atoms would be placed. BS, 50–50 beam splitters; PD, photodetector; CG, color glass; DM, dichroic mirror.

Fig. 2
Fig. 2

Signal and noise at 2.5 MHz. Light powers and signal-to-noise ratios (SNR) are given in the graphs.

Fig. 3
Fig. 3

Noise amplitude spectral density at 2.5 MHz: local oscillator (○), locked interferometer (∗), and calculations (−) using Eq. (4).

Fig. 4
Fig. 4

Signal-to-noise ratio as a function of the probe-beam light power: measurement (∗), calculation including (. . .)∕without (- -) losses, and inaccuracies of calibration as given in the text.

Equations (5)

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

SNR max = 1 2 η P ab n ˜ σ 0 h ν B δ n ˜ n ˜ ,
δ ϕ / B = 1 Δ n ˜ σ 0 h ν η P ab .
i S = ± α η e 2 h ν P LO P Pt J 1 ( m ) sin ( ϕ γ ) ,
i shot = α e 2 η P LO B 2 h ν .
SNR = 2 J 1 ( m ) η P Pt h ν B δ ϕ = J 1 ( m ) η P ab n ˜ σ 0 h ν B δ n ˜ n ,

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