Abstract

We present a new method of laser frequency locking in which the feedback signal is directly proportional to the detuning from an atomic transition, even at detunings many times the natural linewidth of the transition. Our method is a form of sub-Doppler polarization spectroscopy, based on measuring two Stokes parameters (I2 and I3) of light transmitted through a vapor cell. It extends the linear capture range of the lock loop by as much as an order of magnitude and provides frequency discrimination equivalent to or better than those of other commonly used locking techniques.

© 2004 Optical Society of America

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References

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  1. W. Demtröder, Laser Spectroscopy, 2nd ed. (Springer-Verlag, Berlin, 1998).
  2. K. B. MacAdam, A. Steinbach, and C. Wieman, Am. J. Phys. 60, 1098 (1998).
    [CrossRef]
  3. A. White, IEEE J. Quantum Electron. QE-1, 349 (1965).
    [CrossRef]
  4. C. Wieman and T. Hänsch, Phys. Rev. Lett. 36, 1170 (1976).
    [CrossRef]
  5. T. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980).
    [CrossRef]
  6. C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
    [CrossRef]
  7. M. D. Harvey and A. G. White, Opt. Commun. 221, 163 (2003).
    [CrossRef]
  8. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
    [CrossRef]
  9. A. S. Arnold, S. J. Wilson, and M. G. Boshier, Rev. Sci. Instrum. 69, 1236 (1998).
    [CrossRef]

2003 (1)

M. D. Harvey and A. G. White, Opt. Commun. 221, 163 (2003).
[CrossRef]

2002 (1)

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[CrossRef]

1998 (2)

A. S. Arnold, S. J. Wilson, and M. G. Boshier, Rev. Sci. Instrum. 69, 1236 (1998).
[CrossRef]

K. B. MacAdam, A. Steinbach, and C. Wieman, Am. J. Phys. 60, 1098 (1998).
[CrossRef]

1980 (1)

T. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980).
[CrossRef]

1976 (1)

C. Wieman and T. Hänsch, Phys. Rev. Lett. 36, 1170 (1976).
[CrossRef]

1965 (1)

A. White, IEEE J. Quantum Electron. QE-1, 349 (1965).
[CrossRef]

Adams, C. S.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[CrossRef]

Arnold, A. S.

A. S. Arnold, S. J. Wilson, and M. G. Boshier, Rev. Sci. Instrum. 69, 1236 (1998).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
[CrossRef]

Boshier, M. G.

A. S. Arnold, S. J. Wilson, and M. G. Boshier, Rev. Sci. Instrum. 69, 1236 (1998).
[CrossRef]

Couillaud, B.

T. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980).
[CrossRef]

Cox, S. G.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[CrossRef]

Demtröder, W.

W. Demtröder, Laser Spectroscopy, 2nd ed. (Springer-Verlag, Berlin, 1998).

Griffin, P. F.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[CrossRef]

Hänsch, T.

T. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980).
[CrossRef]

C. Wieman and T. Hänsch, Phys. Rev. Lett. 36, 1170 (1976).
[CrossRef]

Harvey, M. D.

M. D. Harvey and A. G. White, Opt. Commun. 221, 163 (2003).
[CrossRef]

Hughes, I. G.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[CrossRef]

MacAdam, K. B.

K. B. MacAdam, A. Steinbach, and C. Wieman, Am. J. Phys. 60, 1098 (1998).
[CrossRef]

Pearman, C. P.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[CrossRef]

Smith, D. A.

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[CrossRef]

Steinbach, A.

K. B. MacAdam, A. Steinbach, and C. Wieman, Am. J. Phys. 60, 1098 (1998).
[CrossRef]

White, A.

A. White, IEEE J. Quantum Electron. QE-1, 349 (1965).
[CrossRef]

White, A. G.

M. D. Harvey and A. G. White, Opt. Commun. 221, 163 (2003).
[CrossRef]

Wieman, C.

K. B. MacAdam, A. Steinbach, and C. Wieman, Am. J. Phys. 60, 1098 (1998).
[CrossRef]

C. Wieman and T. Hänsch, Phys. Rev. Lett. 36, 1170 (1976).
[CrossRef]

Wilson, S. J.

A. S. Arnold, S. J. Wilson, and M. G. Boshier, Rev. Sci. Instrum. 69, 1236 (1998).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
[CrossRef]

Am. J. Phys. (1)

K. B. MacAdam, A. Steinbach, and C. Wieman, Am. J. Phys. 60, 1098 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. White, IEEE J. Quantum Electron. QE-1, 349 (1965).
[CrossRef]

J. Phys. B (1)

C. P. Pearman, C. S. Adams, S. G. Cox, P. F. Griffin, D. A. Smith, and I. G. Hughes, J. Phys. B 35, 5141 (2002).
[CrossRef]

Opt. Commun. (2)

M. D. Harvey and A. G. White, Opt. Commun. 221, 163 (2003).
[CrossRef]

T. Hänsch and B. Couillaud, Opt. Commun. 35, 441 (1980).
[CrossRef]

Phys. Rev. Lett. (1)

C. Wieman and T. Hänsch, Phys. Rev. Lett. 36, 1170 (1976).
[CrossRef]

Rev. Sci. Instrum. (1)

A. S. Arnold, S. J. Wilson, and M. G. Boshier, Rev. Sci. Instrum. 69, 1236 (1998).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, England, 1999).
[CrossRef]

W. Demtröder, Laser Spectroscopy, 2nd ed. (Springer-Verlag, Berlin, 1998).

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Figures (4)

Fig. 1
Fig. 1

Detector for measuring Stokes parameters Ii, i=1,2,3: PD, photodector; PBS, polarizing beam splitter; λi-plate, no, half-, and quarter–wave plates for i=1,2,3, respectively; Diff. Amp., differential amplifier.

Fig. 2
Fig. 2

Experimental setup for polarization quotient locking. A small fraction of light is split off the laser output and sent into a polarization spectrometer. The I2 and I3 Stokes parameters of the probe light are measured and used to provide feedback to lock the laser. BS, beam splitter; PBS, polarizing BS; NPBS, 50/50 nonpolarizing BS.

Fig. 3
Fig. 3

Spectra for the  87Rb 5S1/2 F=25P3/2 F=1,2,3 transition. Top trace (SA), regular saturated absorption spectrum; spectra of I2 and I3 are shown. Bottom trace, the quotient Qx. Shaded regions indicate the monotonic capture range of I2 (upper) and Qx (lower) locking.

Fig. 4
Fig. 4

Step responses of a laser locked by I2 and Qx locking after the dc lock point voltage is switched at t=0. Solid curves, measured error signal after switching; dashed curves, ideal response. Qx locking allows much larger jumps to be achieved without unlocking the laser.

Equations (7)

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

I0=ER2+EL2,
I1=2ERELcos ϕ,
I2=2ERELsin ϕ,
I3=ER2-EL2,
I2xΔnx=Δα0kx1+x2,
I3xΔαx=Δα01+x2,
Qx=I2xI3x=xk,

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