Abstract

Active control and cancellation of residual amplitude modulation (RAM) in phase modulation of an optical carrier is one of the key technologies for achieving the ultimate stability of a laser locked to an ultrastable optical cavity. Furthermore, such techniques are versatile tools in various frequency modulation-based spectroscopy applications. In this Letter we report a simple and robust approach to actively stabilize RAM in an optical phase modulation process. We employ a waveguide-based electro-optic modulator (EOM) to provide phase modulation and implement an active servo with both DC electric field and temperature feedback onto the EOM to cancel both the in-phase and quadrature components of the RAM. This technique allows RAM control on the parts-per-million level where RAM-induced frequency instability is comparable to or lower than the fundamental thermal noise limit of the best available optical cavities.

© 2014 Optical Society of America

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2014

2013

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, Nat. Photonics 7, 644 (2013).
[CrossRef]

2012

L. Li, F. Liu, C. Wang, and L. Chen, Rev. Sci. Instrum. 83, 043111 (2012).
[CrossRef]

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

C. Benko, A. Ruehl, M. J. Martin, K. S. E. Eikema, M. E. Fermann, I. Hartl, and J. Ye, Opt. Lett. 37, 2196 (2012).
[CrossRef]

B. Argence, E. Prevost, T. Lévèque, R. Le Goff, S. Bize, P. Lemonde, and G. Santarelli, Opt. Express 20, 25409 (2012).
[CrossRef]

2011

2010

S. Barke, M. Tröbs, B. Sheard, G. Heinzel, and K. Danzmann, Appl. Phys. B 98, 33 (2010).
[CrossRef]

2009

LIGO Scientific Collaboration, Rep. Prog. Phys. 72, 076901 (2009).
[CrossRef]

2008

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, Phys. Rev. A 77, 053809 (2008).
[CrossRef]

2007

2006

2003

H. Müller, S. Herrmann, T. Schuldt, M. Scholz, E. Kovalchuk, and A. Peters, Opt. Lett. 28, 2186 (2003).
[CrossRef]

F. Du Burck, O. Lopez, and A. El Basri, IEEE Trans. Instrum. Meas. 52, 288 (2003).
[CrossRef]

2000

1999

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

1998

1988

1985

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

1980

Adhikari, R. X.

Alnis, J.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Arai, K.

Argence, B.

Aspelmeyer, M.

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, Nat. Photonics 7, 644 (2013).
[CrossRef]

Barke, S.

S. Barke, M. Tröbs, B. Sheard, G. Heinzel, and K. Danzmann, Appl. Phys. B 98, 33 (2010).
[CrossRef]

Benko, C.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

C. Benko, A. Ruehl, M. J. Martin, K. S. E. Eikema, M. E. Fermann, I. Hartl, and J. Ye, Opt. Lett. 37, 2196 (2012).
[CrossRef]

Bergquist, J. C.

D. R. Leibrandt, M. J. Thorpe, J. C. Bergquist, and T. Rosenband, Opt. Express 19, 10278 (2011).
[CrossRef]

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

Bishof, M.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

Bize, S.

Bjorklund, G. C.

Blatt, S.

Bloom, B. J.

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

Boyd, M. M.

Campbell, S. L.

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

Chen, L.

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

L. Li, F. Liu, C. Wang, and L. Chen, Rev. Sci. Instrum. 83, 043111 (2012).
[CrossRef]

Cole, G. D.

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, Nat. Photonics 7, 644 (2013).
[CrossRef]

Cruz, F. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

Danzmann, K.

S. Barke, M. Tröbs, B. Sheard, G. Heinzel, and K. Danzmann, Appl. Phys. B 98, 33 (2010).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Du Burck, F.

F. Du Burck, O. Lopez, and A. El Basri, IEEE Trans. Instrum. Meas. 52, 288 (2003).
[CrossRef]

Eikema, K. S. E.

El Basri, A.

F. Du Burck, O. Lopez, and A. El Basri, IEEE Trans. Instrum. Meas. 52, 288 (2003).
[CrossRef]

Fermann, M. E.

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Foreman, S. M.

Gorshkov, A. V.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

Grebel, H.

Grebing, C.

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

Hagemann, C.

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

Hall, J. L.

J. Ye, L.-S. Ma, and J. L. Hall, J. Opt. Soc. Am. B 15, 6 (1998).
[CrossRef]

N. C. Wong and J. L. Hall, J. Opt. Soc. Am. B 2, 1527 (1985).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

C. Ishibashi, J. Ye, and J. L. Hall, in Quantum Electronics and Laser Science Conference, Long Beach, California, May19–24 (IEEE, 2002), paper QTuF27.

Hänsch, T. W.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Hartl, I.

Heinzel, G.

S. Barke, M. Tröbs, B. Sheard, G. Heinzel, and K. Danzmann, Appl. Phys. B 98, 33 (2010).
[CrossRef]

Helmcke, J.

Herrmann, S.

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Huang, X.

Ishibashi, C.

C. Ishibashi, J. Ye, and J. L. Hall, in Quantum Electronics and Laser Science Conference, Long Beach, California, May19–24 (IEEE, 2002), paper QTuF27.

Itano, W. M.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

Izumi, K.

Kasapi, S.

Kessler, T.

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

Kokeyama, K.

Kolachevsky, N.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Korth, W. Z.

Kovalchuk, E.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Lathi, S.

Le Goff, R.

Legero, T.

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

Leibrandt, D. R.

Lemonde, P.

Lévèque, T.

Li, L.

L. Li, F. Liu, C. Wang, and L. Chen, Rev. Sci. Instrum. 83, 043111 (2012).
[CrossRef]

Liu, F.

L. Li, F. Liu, C. Wang, and L. Chen, Rev. Sci. Instrum. 83, 043111 (2012).
[CrossRef]

Lopez, O.

F. Du Burck, O. Lopez, and A. El Basri, IEEE Trans. Instrum. Meas. 52, 288 (2003).
[CrossRef]

Lotem, H.

Ludlow, A. D.

Ma, L.-S.

Martin, M. J.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, Nat. Photonics 7, 644 (2013).
[CrossRef]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

C. Benko, A. Ruehl, M. J. Martin, K. S. E. Eikema, M. E. Fermann, I. Hartl, and J. Ye, Opt. Lett. 37, 2196 (2012).
[CrossRef]

Matveev, A.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Mensing, F.

Müller, H.

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Nicholson, T. L.

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

Notcutt, X. M.

Peters, A.

Prevost, E.

Rey, A. M.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

Riehle, F.

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

Rosenband, T.

Ruehl, A.

Santarelli, G.

Scholz, M.

Schuldt, T.

Sheard, B.

S. Barke, M. Tröbs, B. Sheard, G. Heinzel, and K. Danzmann, Appl. Phys. B 98, 33 (2010).
[CrossRef]

Shum, C. M.

Smith-Lefebvre, N.

Sterr, U.

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

H. Stoehr, F. Mensing, J. Helmcke, and U. Sterr, Opt. Lett. 31, 736 (2006).
[CrossRef]

Stoehr, H.

Swallows, M. D.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

Thorpe, M. J.

Tröbs, M.

S. Barke, M. Tröbs, B. Sheard, G. Heinzel, and K. Danzmann, Appl. Phys. B 98, 33 (2010).
[CrossRef]

Udem, T.

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, Phys. Rev. A 77, 053809 (2008).
[CrossRef]

von-Stecher, J.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

Wang, C.

L. Li, F. Liu, C. Wang, and L. Chen, Rev. Sci. Instrum. 83, 043111 (2012).
[CrossRef]

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

Whittaker, A.

Williams, J. R.

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

Wong, N. C.

Yamamoto, Y.

Ye, J.

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, Nat. Photonics 7, 644 (2013).
[CrossRef]

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

C. Benko, A. Ruehl, M. J. Martin, K. S. E. Eikema, M. E. Fermann, I. Hartl, and J. Ye, Opt. Lett. 37, 2196 (2012).
[CrossRef]

A. D. Ludlow, X. Huang, X. M. Notcutt, T. Zanon-Willette, S. M. Foreman, M. M. Boyd, S. Blatt, and J. Ye, Opt. Lett. 32, 641 (2007).
[CrossRef]

J. Ye, L.-S. Ma, and J. L. Hall, J. Opt. Soc. Am. B 15, 6 (1998).
[CrossRef]

C. Ishibashi, J. Ye, and J. L. Hall, in Quantum Electronics and Laser Science Conference, Long Beach, California, May19–24 (IEEE, 2002), paper QTuF27.

Young, B. C.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

Zanon-Willette, T.

Zhang, W.

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, Nat. Photonics 7, 644 (2013).
[CrossRef]

Zhang, X.

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

Appl. Phys. B

S. Barke, M. Tröbs, B. Sheard, G. Heinzel, and K. Danzmann, Appl. Phys. B 98, 33 (2010).
[CrossRef]

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, Appl. Phys. B 31, 97 (1983).
[CrossRef]

IEEE Trans. Instrum. Meas.

F. Du Burck, O. Lopez, and A. El Basri, IEEE Trans. Instrum. Meas. 52, 288 (2003).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nat. Photonics

T. Kessler, C. Hagemann, C. Grebing, T. Legero, U. Sterr, F. Riehle, M. J. Martin, L. Chen, and J. Ye, Nat. Photonics 6, 687 (2012).
[CrossRef]

G. D. Cole, W. Zhang, M. J. Martin, J. Ye, and M. Aspelmeyer, Nat. Photonics 7, 644 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

J. Alnis, A. Matveev, N. Kolachevsky, T. Udem, and T. W. Hänsch, Phys. Rev. A 77, 053809 (2008).
[CrossRef]

Phys. Rev. Lett.

B. C. Young, F. C. Cruz, W. M. Itano, and J. C. Bergquist, Phys. Rev. Lett. 82, 3799 (1999).
[CrossRef]

T. L. Nicholson, M. J. Martin, J. R. Williams, B. J. Bloom, M. Bishof, M. D. Swallows, S. L. Campbell, and J. Ye, Phys. Rev. Lett. 109, 230801 (2012).
[CrossRef]

Rep. Prog. Phys.

LIGO Scientific Collaboration, Rep. Prog. Phys. 72, 076901 (2009).
[CrossRef]

Rev. Sci. Instrum.

L. Li, F. Liu, C. Wang, and L. Chen, Rev. Sci. Instrum. 83, 043111 (2012).
[CrossRef]

Science

M. J. Martin, M. Bishof, M. D. Swallows, X. Zhang, C. Benko, J. von-Stecher, A. V. Gorshkov, A. M. Rey, and J. Ye, Science 341, 632 (2013).
[CrossRef]

Other

C. Ishibashi, J. Ye, and J. L. Hall, in Quantum Electronics and Laser Science Conference, Long Beach, California, May19–24 (IEEE, 2002), paper QTuF27.

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Figures (3)

Fig. 1.
Fig. 1.

Experimental scheme for active RAM stabilization. After passing through the phase modulator, a portion of the light is detected by PD1 for active RAM control, and PD2 is used for PDH signal and out-of-loop RAM measurement. EOM, waveguide-based electro-optic modulator; VRF, RF signal for phase modulation; VDC, direct current field applied to EOM for active RAM cancellation; IP, in-line polarizer; P, free-space polarizer; BS, beam splitter; PBS, polarization beam splitter; HW, half-wave plate; QW, quarter-wave plate; ISO, optical isolator; PD, photodetector; DBM, double-balanced mixer; I(Q) mixer in-phase (quadrature) port; φ, phase shifter; SA, spectrum analyzer; LO local oscillator (10.5 MHz); LF, loop filter; FFT, fast Fourier transform (FFT) analyzer.

Fig. 2.
Fig. 2.

(a) RAM reduction realized with the active cancellation scheme. The power spectrum of the in-loop RAM signal received by PD1 is recorded on a spectrum analyzer with 100 Hz resolution bandwidth. The RAM signal with active servo on (red line) is 56 dB lower than that without servo (black line). Blue line, shot noise floor. This remaining RAM is stable at the 3% level. (b) Left axis: power spectral density (PSD) of the out-of-loop RAM fluctuations, i.e., off-resonant PDH signal obtained from PD2. The noise corresponding to RAM with active cancellation (red and green lines) is approximately 20 times lower than the result without servo (black line) at 1 Hz. At low Fourier frequencies, simultaneous in-phase and quadrature servos (red line) achieve better stability than that with only in-phase servo (green line). The noise floor (blue line) is set by the shot noise of PD2. Right axis: corresponding PSD of the frequency noise for the cavity-stabilized 1.064 μm laser. The voltage noise is converted to frequency noise by the slope of the cavity frequency discrimination.

Fig. 3.
Fig. 3.

Out-of-loop RAM signal recorded with PD2 when the laser is detuned far off the cavity resonance. The linewidth of the 35 mm cavity is 28 kHz at a wavelength of 1.064 μm. The silicon cavity is 210 mm in length, resulting in a significantly reduced cavity linewidth of 3 kHz at 1.5 μm. (a) and (c) The modulation depth of the stabilized RAM based on the 35 mm cavity and the 210 mm silicon cavity, respectively. (b) and (d) RAM-induced fractional frequency instability corresponding to the data in (a) and (c), respectively. The black-dashed lines indicate the fractional frequency instability corresponding to 1 and 5 ppm RAM fluctuations, respectively, and the gray-dashed line is thermal-noise-limited frequency stability for each cavity.

Equations (2)

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I(ωm)=sin(2β)sin(2γ)|ϵ0|2J1(M)×sin(ωmt)sin(Δϕ+ΔϕDC).
σy=σRAM×κν.

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