Abstract

We demonstrate modulation-based frequency locking of an external cavity diode laser, utilizing a piezo-electrically actuated mirror, external to the laser cavity, to create an error signal from saturated absorption spectroscopy. With this method, a laser stabilized to a rubidium hyperfine transition has a FWHM of 130kHz over seconds, making the locked laser suitable for experiments in atomic physics, such as creating and manipulating Bose–Einstein condensates. This technique combines the advantages of low-amplitude modulation, simplicity, performance, and price, factors that are usually considered to be mutually exclusive.

© 2008 Optical Society of America

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  1. W. Demtroder, Laser Spectroscopy (Springer-Verlag, 1998).
  2. W. Lu, D. Milic, M. D. Hoogerland, M. Jacka, K. G. H. Baldwin, and S. J. Buckman, “A practical direct current discharge helium absorption cell for laser frequency locking at 1083 nm,” Rev. Sci. Instrum. 67, 3003-3004 (1996).
    [CrossRef]
  3. We find that even for small modulation depth, the linewidth of an inherently narrow ECDL is broadened by using this technique.
  4. K. L. Corwin, Z.-T. Lu, C. F. Hand, R. J. Epstein, and C. E. Wieman, “Frequency-stabilized diode laser with the zeeman shift in an atomic vapor,” Appl. Opt. 37, 3295-3298 (1998).
    [CrossRef]
  5. C. I. Sukenik, H. C. Busch, and M. Shiddiq, “Laser frequency stabilization and detuning,” Opt. Commun. 203, 133-137 (2002).
    [CrossRef]
  6. S. E. Park, H. S. Lee, T. Y. Kwon, and H. Cho, “Dispersion-like signals in velocity-selective saturated-absorption spectroscopy,” Opt. Commun. 192, 49-55 (2001).
    [CrossRef]
  7. N. P. Robins, B. J. J. Slagmolen, D. A. Shaddock, J. D. Close, and M. B. Gray, “Interferometric, modulation-free laser stabilization,” Opt. Lett. 27, 1905-1907 (2002).
    [CrossRef]
  8. P. V. der Straten, E. D. V. Ooijen, and G. Katgert, “Laser frequency stabilization using Doppler-free bichromatic spectroscopy,” Appl. Phys. B 79, 57-59 (2004).
    [CrossRef]
  9. C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141-5151 (2002).
    [CrossRef]
  10. Y. Yoshikawa, T. Umeki, T. Mukae, Y. Torii, and T. Kuga, “Frequency stabilization of a laser diode with use of light-induced birefringence in an atomic vapor,” Appl. Opt. 42, 6645-6649 (2003).
    [CrossRef] [PubMed]
  11. Q. M. Zhang, W. Y. Pan, and L. E. Cross, “Laser interferometer for the study of piezo electric and electrostrictive strains,” J. Appl. Phys. 63, 2492-2496 (1988).
    [CrossRef]
  12. W. Y. Pan and L. E. Cross, “A sensitive double beam laser interferometer for studying high-frequency piezoelectric and electrostrictive strains,” Rev. Sci. Instrum. 60, 2701-2705 (1989).
    [CrossRef]
  13. J.-F. Li, P. Moses, and D. Viehland, “Simple, high-resolution interferometer for the measurement of frequency dependent complex piezoelectric responses in ferroelectric ceramics,” Rev. Sci. Instrum. 66, 215-221 (1995).
    [CrossRef]
  14. R. Yimnirun, P. J. Moses, R. J. Meyer, Jr., and R. E. Newnham, “A single-beam interferometer with sub-ångström displacement resolution for electrostriction measurements,” Meas. Sci. Technol. 14, 766-772 (2003).
    [CrossRef]
  15. See Stanford Research Systems, http://www.thinksrs.com/products/SR510530.htm.
  16. See Piezomechanik GmbH, http://piezomechanik.com/f/core/frontend/http/http.php?dl=50-file-1.
  17. This estimate is calculated based on a typical saturated absorption signal with 300 μW of power focused onto the photodetector. We assume a Lorenzian absorption profile and use Beer's law with Eq. to calculate a theoretical error signal for a modulation frequency of 100 kHz. The absolute lower limit of 1 Å is based on a feedback bandwidth of 200 Hz, a value that is typical for two of our three BEC lasers, whereas a value of 10 Å is the lower limit required for a feedback bandwidth of 20 kHz. Both of these values result in a signal-to-noise ratio of approximately 5 relative to the shot noise, leading to theoretical stability in the lock point of 200 kHz in the laser output frequency.
  18. Diode laser purchased from TOPTICA Photonics AG, Model DL 100; see http://www.toptica.com/page/scientific_lasers.php.
  19. This value is based on a 50 mm focal length for the lens in Fig. and a tilt angle of 50 μrad, calculated assuming a 200 nm arclength due to the tilt. We feel this estimate of arclength is a more than generous number, given the previously measured piezo displacements referenced in the paper.
  20. N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close., “A pumped atom laser,” Nat. Phys. 4, 731-736 (2008).
    [CrossRef]
  21. See Noliac, http://www.noliac.com/Ring_actuators_-56.aspx.
  22. The self-heterodyne beat measurement uses an AOM to scatter a portion of the laser beam into the first order, producing a frequency-shifted beam (~200 MHz for our AOM). The unscattered zeroth order is then launched into a single-mode optical fiber before being mixed with the first order on a beam splitter. The length of the fiber should be significantly longer than the coherence length of the laser, rendering the zeroth-order beam incoherent relative to the first order. Upon mixing the two beams, a beat signal is obtained at the AOM drive frequency, and as long as the two beams are sufficiently incoherent, this results in a reliable measurement of the laser linewidth without the need for locking two identical lasers. Note that a laser with a 100 kHz linewidth has a coherence length of about 2 km, which is significantly shorter than the 3 km of fiber used in our setup.

2008

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close., “A pumped atom laser,” Nat. Phys. 4, 731-736 (2008).
[CrossRef]

2004

P. V. der Straten, E. D. V. Ooijen, and G. Katgert, “Laser frequency stabilization using Doppler-free bichromatic spectroscopy,” Appl. Phys. B 79, 57-59 (2004).
[CrossRef]

2003

Y. Yoshikawa, T. Umeki, T. Mukae, Y. Torii, and T. Kuga, “Frequency stabilization of a laser diode with use of light-induced birefringence in an atomic vapor,” Appl. Opt. 42, 6645-6649 (2003).
[CrossRef] [PubMed]

R. Yimnirun, P. J. Moses, R. J. Meyer, Jr., and R. E. Newnham, “A single-beam interferometer with sub-ångström displacement resolution for electrostriction measurements,” Meas. Sci. Technol. 14, 766-772 (2003).
[CrossRef]

2002

N. P. Robins, B. J. J. Slagmolen, D. A. Shaddock, J. D. Close, and M. B. Gray, “Interferometric, modulation-free laser stabilization,” Opt. Lett. 27, 1905-1907 (2002).
[CrossRef]

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141-5151 (2002).
[CrossRef]

C. I. Sukenik, H. C. Busch, and M. Shiddiq, “Laser frequency stabilization and detuning,” Opt. Commun. 203, 133-137 (2002).
[CrossRef]

2001

S. E. Park, H. S. Lee, T. Y. Kwon, and H. Cho, “Dispersion-like signals in velocity-selective saturated-absorption spectroscopy,” Opt. Commun. 192, 49-55 (2001).
[CrossRef]

1998

1996

W. Lu, D. Milic, M. D. Hoogerland, M. Jacka, K. G. H. Baldwin, and S. J. Buckman, “A practical direct current discharge helium absorption cell for laser frequency locking at 1083 nm,” Rev. Sci. Instrum. 67, 3003-3004 (1996).
[CrossRef]

1995

J.-F. Li, P. Moses, and D. Viehland, “Simple, high-resolution interferometer for the measurement of frequency dependent complex piezoelectric responses in ferroelectric ceramics,” Rev. Sci. Instrum. 66, 215-221 (1995).
[CrossRef]

1989

W. Y. Pan and L. E. Cross, “A sensitive double beam laser interferometer for studying high-frequency piezoelectric and electrostrictive strains,” Rev. Sci. Instrum. 60, 2701-2705 (1989).
[CrossRef]

1988

Q. M. Zhang, W. Y. Pan, and L. E. Cross, “Laser interferometer for the study of piezo electric and electrostrictive strains,” J. Appl. Phys. 63, 2492-2496 (1988).
[CrossRef]

Adams, C. S.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141-5151 (2002).
[CrossRef]

Baldwin, K. G. H.

W. Lu, D. Milic, M. D. Hoogerland, M. Jacka, K. G. H. Baldwin, and S. J. Buckman, “A practical direct current discharge helium absorption cell for laser frequency locking at 1083 nm,” Rev. Sci. Instrum. 67, 3003-3004 (1996).
[CrossRef]

Buckman, S. J.

W. Lu, D. Milic, M. D. Hoogerland, M. Jacka, K. G. H. Baldwin, and S. J. Buckman, “A practical direct current discharge helium absorption cell for laser frequency locking at 1083 nm,” Rev. Sci. Instrum. 67, 3003-3004 (1996).
[CrossRef]

Busch, H. C.

C. I. Sukenik, H. C. Busch, and M. Shiddiq, “Laser frequency stabilization and detuning,” Opt. Commun. 203, 133-137 (2002).
[CrossRef]

Cho, H.

S. E. Park, H. S. Lee, T. Y. Kwon, and H. Cho, “Dispersion-like signals in velocity-selective saturated-absorption spectroscopy,” Opt. Commun. 192, 49-55 (2001).
[CrossRef]

Close, J. D.

Corwin, K. L.

Cox, S. G.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141-5151 (2002).
[CrossRef]

Cross, L. E.

W. Y. Pan and L. E. Cross, “A sensitive double beam laser interferometer for studying high-frequency piezoelectric and electrostrictive strains,” Rev. Sci. Instrum. 60, 2701-2705 (1989).
[CrossRef]

Q. M. Zhang, W. Y. Pan, and L. E. Cross, “Laser interferometer for the study of piezo electric and electrostrictive strains,” J. Appl. Phys. 63, 2492-2496 (1988).
[CrossRef]

Demtroder, W.

W. Demtroder, Laser Spectroscopy (Springer-Verlag, 1998).

Dennis, G. R.

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close., “A pumped atom laser,” Nat. Phys. 4, 731-736 (2008).
[CrossRef]

der Straten, P. V.

P. V. der Straten, E. D. V. Ooijen, and G. Katgert, “Laser frequency stabilization using Doppler-free bichromatic spectroscopy,” Appl. Phys. B 79, 57-59 (2004).
[CrossRef]

Epstein, R. J.

Figl, C.

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close., “A pumped atom laser,” Nat. Phys. 4, 731-736 (2008).
[CrossRef]

Gray, M. B.

Griffin, P. F.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141-5151 (2002).
[CrossRef]

Hand, C. F.

Hoogerland, M. D.

W. Lu, D. Milic, M. D. Hoogerland, M. Jacka, K. G. H. Baldwin, and S. J. Buckman, “A practical direct current discharge helium absorption cell for laser frequency locking at 1083 nm,” Rev. Sci. Instrum. 67, 3003-3004 (1996).
[CrossRef]

Hughes, I. G.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141-5151 (2002).
[CrossRef]

Jacka, M.

W. Lu, D. Milic, M. D. Hoogerland, M. Jacka, K. G. H. Baldwin, and S. J. Buckman, “A practical direct current discharge helium absorption cell for laser frequency locking at 1083 nm,” Rev. Sci. Instrum. 67, 3003-3004 (1996).
[CrossRef]

Jeppesen, M.

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close., “A pumped atom laser,” Nat. Phys. 4, 731-736 (2008).
[CrossRef]

Katgert, G.

P. V. der Straten, E. D. V. Ooijen, and G. Katgert, “Laser frequency stabilization using Doppler-free bichromatic spectroscopy,” Appl. Phys. B 79, 57-59 (2004).
[CrossRef]

Kuga, T.

Kwon, T. Y.

S. E. Park, H. S. Lee, T. Y. Kwon, and H. Cho, “Dispersion-like signals in velocity-selective saturated-absorption spectroscopy,” Opt. Commun. 192, 49-55 (2001).
[CrossRef]

Lee, H. S.

S. E. Park, H. S. Lee, T. Y. Kwon, and H. Cho, “Dispersion-like signals in velocity-selective saturated-absorption spectroscopy,” Opt. Commun. 192, 49-55 (2001).
[CrossRef]

Li, J.-F.

J.-F. Li, P. Moses, and D. Viehland, “Simple, high-resolution interferometer for the measurement of frequency dependent complex piezoelectric responses in ferroelectric ceramics,” Rev. Sci. Instrum. 66, 215-221 (1995).
[CrossRef]

Lu, W.

W. Lu, D. Milic, M. D. Hoogerland, M. Jacka, K. G. H. Baldwin, and S. J. Buckman, “A practical direct current discharge helium absorption cell for laser frequency locking at 1083 nm,” Rev. Sci. Instrum. 67, 3003-3004 (1996).
[CrossRef]

Lu, Z.-T.

Meyer, R. J.

R. Yimnirun, P. J. Moses, R. J. Meyer, Jr., and R. E. Newnham, “A single-beam interferometer with sub-ångström displacement resolution for electrostriction measurements,” Meas. Sci. Technol. 14, 766-772 (2003).
[CrossRef]

Milic, D.

W. Lu, D. Milic, M. D. Hoogerland, M. Jacka, K. G. H. Baldwin, and S. J. Buckman, “A practical direct current discharge helium absorption cell for laser frequency locking at 1083 nm,” Rev. Sci. Instrum. 67, 3003-3004 (1996).
[CrossRef]

Moses, P.

J.-F. Li, P. Moses, and D. Viehland, “Simple, high-resolution interferometer for the measurement of frequency dependent complex piezoelectric responses in ferroelectric ceramics,” Rev. Sci. Instrum. 66, 215-221 (1995).
[CrossRef]

Moses, P. J.

R. Yimnirun, P. J. Moses, R. J. Meyer, Jr., and R. E. Newnham, “A single-beam interferometer with sub-ångström displacement resolution for electrostriction measurements,” Meas. Sci. Technol. 14, 766-772 (2003).
[CrossRef]

Mukae, T.

Newnham, R. E.

R. Yimnirun, P. J. Moses, R. J. Meyer, Jr., and R. E. Newnham, “A single-beam interferometer with sub-ångström displacement resolution for electrostriction measurements,” Meas. Sci. Technol. 14, 766-772 (2003).
[CrossRef]

Ooijen, E. D. V.

P. V. der Straten, E. D. V. Ooijen, and G. Katgert, “Laser frequency stabilization using Doppler-free bichromatic spectroscopy,” Appl. Phys. B 79, 57-59 (2004).
[CrossRef]

Pan, W. Y.

W. Y. Pan and L. E. Cross, “A sensitive double beam laser interferometer for studying high-frequency piezoelectric and electrostrictive strains,” Rev. Sci. Instrum. 60, 2701-2705 (1989).
[CrossRef]

Q. M. Zhang, W. Y. Pan, and L. E. Cross, “Laser interferometer for the study of piezo electric and electrostrictive strains,” J. Appl. Phys. 63, 2492-2496 (1988).
[CrossRef]

Park, S. E.

S. E. Park, H. S. Lee, T. Y. Kwon, and H. Cho, “Dispersion-like signals in velocity-selective saturated-absorption spectroscopy,” Opt. Commun. 192, 49-55 (2001).
[CrossRef]

Pearman, C. P.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141-5151 (2002).
[CrossRef]

Robins, N. P.

Shaddock, D. A.

Shiddiq, M.

C. I. Sukenik, H. C. Busch, and M. Shiddiq, “Laser frequency stabilization and detuning,” Opt. Commun. 203, 133-137 (2002).
[CrossRef]

Slagmolen, B. J. J.

Smith, D. A.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141-5151 (2002).
[CrossRef]

Sukenik, C. I.

C. I. Sukenik, H. C. Busch, and M. Shiddiq, “Laser frequency stabilization and detuning,” Opt. Commun. 203, 133-137 (2002).
[CrossRef]

Torii, Y.

Umeki, T.

Viehland, D.

J.-F. Li, P. Moses, and D. Viehland, “Simple, high-resolution interferometer for the measurement of frequency dependent complex piezoelectric responses in ferroelectric ceramics,” Rev. Sci. Instrum. 66, 215-221 (1995).
[CrossRef]

Wieman, C. E.

Yimnirun, R.

R. Yimnirun, P. J. Moses, R. J. Meyer, Jr., and R. E. Newnham, “A single-beam interferometer with sub-ångström displacement resolution for electrostriction measurements,” Meas. Sci. Technol. 14, 766-772 (2003).
[CrossRef]

Yoshikawa, Y.

Zhang, Q. M.

Q. M. Zhang, W. Y. Pan, and L. E. Cross, “Laser interferometer for the study of piezo electric and electrostrictive strains,” J. Appl. Phys. 63, 2492-2496 (1988).
[CrossRef]

Appl. Opt.

Appl. Phys. B

P. V. der Straten, E. D. V. Ooijen, and G. Katgert, “Laser frequency stabilization using Doppler-free bichromatic spectroscopy,” Appl. Phys. B 79, 57-59 (2004).
[CrossRef]

J. Appl. Phys.

Q. M. Zhang, W. Y. Pan, and L. E. Cross, “Laser interferometer for the study of piezo electric and electrostrictive strains,” J. Appl. Phys. 63, 2492-2496 (1988).
[CrossRef]

J. Phys. B

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, “Polarization spectroscopy of a closed atomic transition: applications to laser frequency locking,” J. Phys. B 35, 5141-5151 (2002).
[CrossRef]

Meas. Sci. Technol.

R. Yimnirun, P. J. Moses, R. J. Meyer, Jr., and R. E. Newnham, “A single-beam interferometer with sub-ångström displacement resolution for electrostriction measurements,” Meas. Sci. Technol. 14, 766-772 (2003).
[CrossRef]

Nat. Phys.

N. P. Robins, C. Figl, M. Jeppesen, G. R. Dennis, and J. D. Close., “A pumped atom laser,” Nat. Phys. 4, 731-736 (2008).
[CrossRef]

Opt. Commun.

C. I. Sukenik, H. C. Busch, and M. Shiddiq, “Laser frequency stabilization and detuning,” Opt. Commun. 203, 133-137 (2002).
[CrossRef]

S. E. Park, H. S. Lee, T. Y. Kwon, and H. Cho, “Dispersion-like signals in velocity-selective saturated-absorption spectroscopy,” Opt. Commun. 192, 49-55 (2001).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

W. Lu, D. Milic, M. D. Hoogerland, M. Jacka, K. G. H. Baldwin, and S. J. Buckman, “A practical direct current discharge helium absorption cell for laser frequency locking at 1083 nm,” Rev. Sci. Instrum. 67, 3003-3004 (1996).
[CrossRef]

W. Y. Pan and L. E. Cross, “A sensitive double beam laser interferometer for studying high-frequency piezoelectric and electrostrictive strains,” Rev. Sci. Instrum. 60, 2701-2705 (1989).
[CrossRef]

J.-F. Li, P. Moses, and D. Viehland, “Simple, high-resolution interferometer for the measurement of frequency dependent complex piezoelectric responses in ferroelectric ceramics,” Rev. Sci. Instrum. 66, 215-221 (1995).
[CrossRef]

Other

See Stanford Research Systems, http://www.thinksrs.com/products/SR510530.htm.

See Piezomechanik GmbH, http://piezomechanik.com/f/core/frontend/http/http.php?dl=50-file-1.

This estimate is calculated based on a typical saturated absorption signal with 300 μW of power focused onto the photodetector. We assume a Lorenzian absorption profile and use Beer's law with Eq. to calculate a theoretical error signal for a modulation frequency of 100 kHz. The absolute lower limit of 1 Å is based on a feedback bandwidth of 200 Hz, a value that is typical for two of our three BEC lasers, whereas a value of 10 Å is the lower limit required for a feedback bandwidth of 20 kHz. Both of these values result in a signal-to-noise ratio of approximately 5 relative to the shot noise, leading to theoretical stability in the lock point of 200 kHz in the laser output frequency.

Diode laser purchased from TOPTICA Photonics AG, Model DL 100; see http://www.toptica.com/page/scientific_lasers.php.

This value is based on a 50 mm focal length for the lens in Fig. and a tilt angle of 50 μrad, calculated assuming a 200 nm arclength due to the tilt. We feel this estimate of arclength is a more than generous number, given the previously measured piezo displacements referenced in the paper.

We find that even for small modulation depth, the linewidth of an inherently narrow ECDL is broadened by using this technique.

See Noliac, http://www.noliac.com/Ring_actuators_-56.aspx.

The self-heterodyne beat measurement uses an AOM to scatter a portion of the laser beam into the first order, producing a frequency-shifted beam (~200 MHz for our AOM). The unscattered zeroth order is then launched into a single-mode optical fiber before being mixed with the first order on a beam splitter. The length of the fiber should be significantly longer than the coherence length of the laser, rendering the zeroth-order beam incoherent relative to the first order. Upon mixing the two beams, a beat signal is obtained at the AOM drive frequency, and as long as the two beams are sufficiently incoherent, this results in a reliable measurement of the laser linewidth without the need for locking two identical lasers. Note that a laser with a 100 kHz linewidth has a coherence length of about 2 km, which is significantly shorter than the 3 km of fiber used in our setup.

W. Demtroder, Laser Spectroscopy (Springer-Verlag, 1998).

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of one setup used for creating externally phase modulated light for saturated absorption spectroscopy. PBS, polarizing beam splitter; λ / 4 , quarter-wave plate; λ / 2 , half-wave plate; ND, neutral-density filter; LD, laser diode; M1, M2, and M3, mirrors. For the version shown, both the probe and the pump beams are modulated. Removing the top of the system ( λ / 4 and M1) and modulating just the probe beam (placing the external PZT on M2) yields error signals similar to those produced by the above configuration and minimizes the amount of optics devoted to locking. We have included a schematic of the ECDL to emphasize that the grating PZT, shown behind the grating mount cantilever, is not used to produce phase modulated light.

Fig. 2
Fig. 2

Saturated absorption of the 5 2 S 1 / 2 F = 2 5 2 P 3 / 2 transition for Rb 87 (lower trace) and the corresponding error signal. The transitions are labeled, F F , and the frequency axis is relative to the D2 transition frequency equivalent to 780.24 nm . For clarity, the saturated absorption signal’s Doppler background has been subtracted; it has been offset from zero and multiplied by 20.

Fig. 3
Fig. 3

Self-heterodyne beat signal obtained for an ECDL locked to the 5 2 S 1 / 2 F = 2 5 2 P 3 / 2 F = 3 transition using an error signal produced by a 100 kHz external PZT drive frequency. The beat signal is measured on an RF spectrum analyzer using a 20 ms sweep time averaged over 100 sweeps, and thus represents a 2   s integration time. The linewidth for this integration time is calculated from the beat signal to be 126.6 kHz . A video bandwidth and resolution bandwidth of 10 kHz are used.

Equations (2)

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E = E 0 cos ( ω t + δ cos ω m t ) .
E E 0 [ cos ω t δ 2 [ sin ( ω + ω m ) t + sin ( ω ω m ) t ] ,

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