Abstract

We demonstrate minimization of ion micromotion in a linear Paul trap with the use of a high finesse cavity. The excess ion micromotion projected along the optical cavity axis or along the laser propagation direction manifests itself as sideband peaks around the carrier in the ion-cavity emission spectrum. By minimizing the sideband height in the emission spectrum, we are able to reduce the micromotion amplitude along two directions to approximately the spread of the ground state wave function. This method is useful for cavity QED experiments as it describes the possibility of efficient 3-D micromotion compensation despite optical access limitations imposed by the cavity mirrors. We also show that, in principle, sub-nanometer micromotion compensation is achievable with our current system.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  23. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983). .
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    [CrossRef] [PubMed]
  27. H. Doerk, Z. Idziaszek, and T. Calarco, “Atom-ion quantum gate,” Phys. Rev. A81, 012708 (2010).
    [CrossRef]
  28. L. H. Nguyên, A. Kalev, M. D. Barrett, and B.-G. Englert, “Micromotion in trapped atom-ion systems,” Phys. Rev. A85, 052718 (2012).
    [CrossRef]

2012

A. Stute, B. Casabone, B. Brandsttter, D. Habicher, H. Barros, P. Schmidt, T. Northup, and R. Blatt, “Toward an ionphoton quantum interface in an optical cavity,” Appl. Phys. B107, 1145–1157 (2012).
[CrossRef]

L. H. Nguyên, A. Kalev, M. D. Barrett, and B.-G. Englert, “Micromotion in trapped atom-ion systems,” Phys. Rev. A85, 052718 (2012).
[CrossRef]

N. C. Lewty, B. L. Chuah, R. Cazan, B. K. Sahoo, and M. D. Barrett, “Spectroscopy on a single trapped 137Ba+ion for nuclear magnetic octupole moment determination,” Opt. Express20, 21379–21384 (2012).
[CrossRef] [PubMed]

2011

P. F. Herskind, S. X. Wang, M. Shi, Y. Ge, M. Cetina, and I. L. Chuang, “Microfabricated surface ion trap on a high-finesse optical mirror,” Opt. Lett.36, 3045–3047 (2011).
[CrossRef] [PubMed]

B. L. Chuah, N. C. Lewty, and M. D. Barrett, “State detection using coherent raman repumping and two-color raman transfers,” Phys. Rev. A84, 013411 (2011).
[CrossRef]

Y. Ibaraki, U. Tanaka, and S. Urabe, “Detection of parametric resonance of trapped ions for micromotion compensation,” Appl. Phys. B105, 219–223 (2011). .
[CrossRef]

S. Narayanan, N. Daniilidis, S. A. Moller, R. Clark, F. Ziesel, K. Singer, F. Schmidt-Kaler, and H. Haffner, “Electric field compensation and sensing with a single ion in a planar trap,” J. Appl. Phys.110, 114909 (2011).
[CrossRef]

D. Wineland and D. Leibfried, “Quantum information processing and metrology with trapped ions,” Laser Phys. Lett.8, 175–188 (2011).
[CrossRef]

2010

L.-M. Duan and C. Monroe, “Colloquium: Quantum networks with trapped ions,” Rev. Mod. Phys.82, 1209–1224 (2010).
[CrossRef]

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+optical clocks,” Phys. Rev. Lett.104, 070802 (2010).
[CrossRef] [PubMed]

H. Doerk, Z. Idziaszek, and T. Calarco, “Atom-ion quantum gate,” Phys. Rev. A81, 012708 (2010).
[CrossRef]

2009

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity sideband cooling of a single trapped ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, and D. J. Wineland, “Complete methods set for scalable ion trap quantum information processing,” Science325, 1227–1230 (2009).
[CrossRef] [PubMed]

2008

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

2003

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

2002

D. J. Berkeland, “Linear paul trap for strontium ions,” Rev. Sci. Instrum.73, 2856–2860 (2002).
[CrossRef]

2001

R. Jáuregui, J. Récamier, and P. A. Quinto-Su, “On decoherence and nonlinear effects in the generation of quantum states of motion in paul traps,” J. Opt. B: Quantum Semiclass. Opt.3, 194 (2001).
[CrossRef]

S. Brouard and J. Plata, “Heating of a trapped ion by random fields: The influence of the micromotion,” Phys. Rev. A63, 043402 (2001).
[CrossRef]

2000

C. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett.85, 538–541 (2000).
[CrossRef] [PubMed]

1998

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a paul trap,” J. Appl. Phys.83, 5025–5033 (1998).
[CrossRef]

D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol.103, 259 (1998).
[CrossRef]

1997

J. Höffges, H. Baldauf, T. Eichler, S. Helmfrid, and H. Walther, “Heterodyne measurement of the fluorescent radiation of a single trapped ion,” Opt. Commun.133, 170–174 (1997).
[CrossRef]

1995

J. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett.74, 4091–4094 (1995).
[CrossRef] [PubMed]

1989

J. D. Prestage, G. J. Dick, and L. Maleki, “New ion trap for frequency standard applications,” J. Appl. Phys.66, 1013–1017 (1989).
[CrossRef]

1983

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983). .
[CrossRef]

Amini, J. M.

J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, and D. J. Wineland, “Complete methods set for scalable ion trap quantum information processing,” Science325, 1227–1230 (2009).
[CrossRef] [PubMed]

Baldauf, H.

J. Höffges, H. Baldauf, T. Eichler, S. Helmfrid, and H. Walther, “Heterodyne measurement of the fluorescent radiation of a single trapped ion,” Opt. Commun.133, 170–174 (1997).
[CrossRef]

Barrett, M. D.

N. C. Lewty, B. L. Chuah, R. Cazan, B. K. Sahoo, and M. D. Barrett, “Spectroscopy on a single trapped 137Ba+ion for nuclear magnetic octupole moment determination,” Opt. Express20, 21379–21384 (2012).
[CrossRef] [PubMed]

L. H. Nguyên, A. Kalev, M. D. Barrett, and B.-G. Englert, “Micromotion in trapped atom-ion systems,” Phys. Rev. A85, 052718 (2012).
[CrossRef]

B. L. Chuah, N. C. Lewty, and M. D. Barrett, “State detection using coherent raman repumping and two-color raman transfers,” Phys. Rev. A84, 013411 (2011).
[CrossRef]

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Barros, H.

A. Stute, B. Casabone, B. Brandsttter, D. Habicher, H. Barros, P. Schmidt, T. Northup, and R. Blatt, “Toward an ionphoton quantum interface in an optical cavity,” Appl. Phys. B107, 1145–1157 (2012).
[CrossRef]

Becher, C.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Bergquist, J. C.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a paul trap,” J. Appl. Phys.83, 5025–5033 (1998).
[CrossRef]

Berkeland, D. J.

D. J. Berkeland, “Linear paul trap for strontium ions,” Rev. Sci. Instrum.73, 2856–2860 (2002).
[CrossRef]

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a paul trap,” J. Appl. Phys.83, 5025–5033 (1998).
[CrossRef]

Blatt, R.

A. Stute, B. Casabone, B. Brandsttter, D. Habicher, H. Barros, P. Schmidt, T. Northup, and R. Blatt, “Toward an ionphoton quantum interface in an optical cavity,” Appl. Phys. B107, 1145–1157 (2012).
[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

C. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett.85, 538–541 (2000).
[CrossRef] [PubMed]

Bolle, J.

C. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett.85, 538–541 (2000).
[CrossRef] [PubMed]

Brandsttter, B.

A. Stute, B. Casabone, B. Brandsttter, D. Habicher, H. Barros, P. Schmidt, T. Northup, and R. Blatt, “Toward an ionphoton quantum interface in an optical cavity,” Appl. Phys. B107, 1145–1157 (2012).
[CrossRef]

Britton, J.

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Brouard, S.

S. Brouard and J. Plata, “Heating of a trapped ion by random fields: The influence of the micromotion,” Phys. Rev. A63, 043402 (2001).
[CrossRef]

Brusch, A.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Calarco, T.

H. Doerk, Z. Idziaszek, and T. Calarco, “Atom-ion quantum gate,” Phys. Rev. A81, 012708 (2010).
[CrossRef]

Casabone, B.

A. Stute, B. Casabone, B. Brandsttter, D. Habicher, H. Barros, P. Schmidt, T. Northup, and R. Blatt, “Toward an ionphoton quantum interface in an optical cavity,” Appl. Phys. B107, 1145–1157 (2012).
[CrossRef]

Cazan, R.

Cetina, M.

Chiaverini, J.

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Chou, C. W.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+optical clocks,” Phys. Rev. Lett.104, 070802 (2010).
[CrossRef] [PubMed]

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Chuah, B. L.

N. C. Lewty, B. L. Chuah, R. Cazan, B. K. Sahoo, and M. D. Barrett, “Spectroscopy on a single trapped 137Ba+ion for nuclear magnetic octupole moment determination,” Opt. Express20, 21379–21384 (2012).
[CrossRef] [PubMed]

B. L. Chuah, N. C. Lewty, and M. D. Barrett, “State detection using coherent raman repumping and two-color raman transfers,” Phys. Rev. A84, 013411 (2011).
[CrossRef]

Chuang, I. L.

P. F. Herskind, S. X. Wang, M. Shi, Y. Ge, M. Cetina, and I. L. Chuang, “Microfabricated surface ion trap on a high-finesse optical mirror,” Opt. Lett.36, 3045–3047 (2011).
[CrossRef] [PubMed]

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity sideband cooling of a single trapped ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

Cirac, J.

J. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett.74, 4091–4094 (1995).
[CrossRef] [PubMed]

Clark, R.

S. Narayanan, N. Daniilidis, S. A. Moller, R. Clark, F. Ziesel, K. Singer, F. Schmidt-Kaler, and H. Haffner, “Electric field compensation and sensing with a single ion in a planar trap,” J. Appl. Phys.110, 114909 (2011).
[CrossRef]

Daniilidis, N.

S. Narayanan, N. Daniilidis, S. A. Moller, R. Clark, F. Ziesel, K. Singer, F. Schmidt-Kaler, and H. Haffner, “Electric field compensation and sensing with a single ion in a planar trap,” J. Appl. Phys.110, 114909 (2011).
[CrossRef]

DeMarco, B.

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Deuschle, T.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Dick, G. J.

J. D. Prestage, G. J. Dick, and L. Maleki, “New ion trap for frequency standard applications,” J. Appl. Phys.66, 1013–1017 (1989).
[CrossRef]

Diddams, S. A.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Doerk, H.

H. Doerk, Z. Idziaszek, and T. Calarco, “Atom-ion quantum gate,” Phys. Rev. A81, 012708 (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, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983). .
[CrossRef]

Drullinger, R. E.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Duan, L.-M.

L.-M. Duan and C. Monroe, “Colloquium: Quantum networks with trapped ions,” Rev. Mod. Phys.82, 1209–1224 (2010).
[CrossRef]

Eichler, T.

J. Höffges, H. Baldauf, T. Eichler, S. Helmfrid, and H. Walther, “Heterodyne measurement of the fluorescent radiation of a single trapped ion,” Opt. Commun.133, 170–174 (1997).
[CrossRef]

Englert, B.-G.

L. H. Nguyên, A. Kalev, M. D. Barrett, and B.-G. Englert, “Micromotion in trapped atom-ion systems,” Phys. Rev. A85, 052718 (2012).
[CrossRef]

Eschner, J.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

C. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett.85, 538–541 (2000).
[CrossRef] [PubMed]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983). .
[CrossRef]

Fortier, T. M.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Ge, Y.

Gulde, S.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Habicher, D.

A. Stute, B. Casabone, B. Brandsttter, D. Habicher, H. Barros, P. Schmidt, T. Northup, and R. Blatt, “Toward an ionphoton quantum interface in an optical cavity,” Appl. Phys. B107, 1145–1157 (2012).
[CrossRef]

Haffner, H.

S. Narayanan, N. Daniilidis, S. A. Moller, R. Clark, F. Ziesel, K. Singer, F. Schmidt-Kaler, and H. Haffner, “Electric field compensation and sensing with a single ion in a planar trap,” J. Appl. Phys.110, 114909 (2011).
[CrossRef]

Häffner, H.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Hall, J. L.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983). .
[CrossRef]

Hanneke, D.

J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, and D. J. Wineland, “Complete methods set for scalable ion trap quantum information processing,” Science325, 1227–1230 (2009).
[CrossRef] [PubMed]

Helmfrid, S.

J. Höffges, H. Baldauf, T. Eichler, S. Helmfrid, and H. Walther, “Heterodyne measurement of the fluorescent radiation of a single trapped ion,” Opt. Commun.133, 170–174 (1997).
[CrossRef]

Herschbach, N.

K. Pyka, N. Herschbach, J. Keller, and T. Mehlstäubler, “A high-precision rf trap with minimized micromotion for an In+multiple-ion clock,” arXiv preprint arXiv:1206.5111 (2012).

Herskind, P. F.

Höffges, J.

J. Höffges, H. Baldauf, T. Eichler, S. Helmfrid, and H. Walther, “Heterodyne measurement of the fluorescent radiation of a single trapped ion,” Opt. Commun.133, 170–174 (1997).
[CrossRef]

Home, J. P.

J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, and D. J. Wineland, “Complete methods set for scalable ion trap quantum information processing,” Science325, 1227–1230 (2009).
[CrossRef] [PubMed]

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983). .
[CrossRef]

Hume, D. B.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+optical clocks,” Phys. Rev. Lett.104, 070802 (2010).
[CrossRef] [PubMed]

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Ibaraki, Y.

Y. Ibaraki, U. Tanaka, and S. Urabe, “Detection of parametric resonance of trapped ions for micromotion compensation,” Appl. Phys. B105, 219–223 (2011). .
[CrossRef]

Idziaszek, Z.

H. Doerk, Z. Idziaszek, and T. Calarco, “Atom-ion quantum gate,” Phys. Rev. A81, 012708 (2010).
[CrossRef]

Itano, W.

D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol.103, 259 (1998).
[CrossRef]

Itano, W. M.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a paul trap,” J. Appl. Phys.83, 5025–5033 (1998).
[CrossRef]

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Jáuregui, R.

R. Jáuregui, J. Récamier, and P. A. Quinto-Su, “On decoherence and nonlinear effects in the generation of quantum states of motion in paul traps,” J. Opt. B: Quantum Semiclass. Opt.3, 194 (2001).
[CrossRef]

Jelenkovic, B.

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Jost, J. D.

J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, and D. J. Wineland, “Complete methods set for scalable ion trap quantum information processing,” Science325, 1227–1230 (2009).
[CrossRef] [PubMed]

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Kalev, A.

L. H. Nguyên, A. Kalev, M. D. Barrett, and B.-G. Englert, “Micromotion in trapped atom-ion systems,” Phys. Rev. A85, 052718 (2012).
[CrossRef]

Keller, J.

K. Pyka, N. Herschbach, J. Keller, and T. Mehlstäubler, “A high-precision rf trap with minimized micromotion for an In+multiple-ion clock,” arXiv preprint arXiv:1206.5111 (2012).

King, B.

D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol.103, 259 (1998).
[CrossRef]

Koelemeij, J. C. J.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+optical clocks,” Phys. Rev. Lett.104, 070802 (2010).
[CrossRef] [PubMed]

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983). .
[CrossRef]

Labaziewicz, J.

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity sideband cooling of a single trapped ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

Lancaster, G.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Langer, C.

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Leibfried, D.

D. Wineland and D. Leibfried, “Quantum information processing and metrology with trapped ions,” Laser Phys. Lett.8, 175–188 (2011).
[CrossRef]

J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, and D. J. Wineland, “Complete methods set for scalable ion trap quantum information processing,” Science325, 1227–1230 (2009).
[CrossRef] [PubMed]

D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol.103, 259 (1998).
[CrossRef]

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Leibrandt, D. R.

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity sideband cooling of a single trapped ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

Lewty, N. C.

N. C. Lewty, B. L. Chuah, R. Cazan, B. K. Sahoo, and M. D. Barrett, “Spectroscopy on a single trapped 137Ba+ion for nuclear magnetic octupole moment determination,” Opt. Express20, 21379–21384 (2012).
[CrossRef] [PubMed]

B. L. Chuah, N. C. Lewty, and M. D. Barrett, “State detection using coherent raman repumping and two-color raman transfers,” Phys. Rev. A84, 013411 (2011).
[CrossRef]

Lorini, L.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Maleki, L.

J. D. Prestage, G. J. Dick, and L. Maleki, “New ion trap for frequency standard applications,” J. Appl. Phys.66, 1013–1017 (1989).
[CrossRef]

Meekhof, D.

D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol.103, 259 (1998).
[CrossRef]

Mehlstäubler, T.

K. Pyka, N. Herschbach, J. Keller, and T. Mehlstäubler, “A high-precision rf trap with minimized micromotion for an In+multiple-ion clock,” arXiv preprint arXiv:1206.5111 (2012).

Meyer, V.

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Miller, J. D.

D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, “Minimization of ion micromotion in a paul trap,” J. Appl. Phys.83, 5025–5033 (1998).
[CrossRef]

Moller, S. A.

S. Narayanan, N. Daniilidis, S. A. Moller, R. Clark, F. Ziesel, K. Singer, F. Schmidt-Kaler, and H. Haffner, “Electric field compensation and sensing with a single ion in a planar trap,” J. Appl. Phys.110, 114909 (2011).
[CrossRef]

Monroe, C.

L.-M. Duan and C. Monroe, “Colloquium: Quantum networks with trapped ions,” Rev. Mod. Phys.82, 1209–1224 (2010).
[CrossRef]

D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol.103, 259 (1998).
[CrossRef]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983). .
[CrossRef]

Narayanan, S.

S. Narayanan, N. Daniilidis, S. A. Moller, R. Clark, F. Ziesel, K. Singer, F. Schmidt-Kaler, and H. Haffner, “Electric field compensation and sensing with a single ion in a planar trap,” J. Appl. Phys.110, 114909 (2011).
[CrossRef]

Newbury, N. R.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Nguyên, L. H.

L. H. Nguyên, A. Kalev, M. D. Barrett, and B.-G. Englert, “Micromotion in trapped atom-ion systems,” Phys. Rev. A85, 052718 (2012).
[CrossRef]

Northup, T.

A. Stute, B. Casabone, B. Brandsttter, D. Habicher, H. Barros, P. Schmidt, T. Northup, and R. Blatt, “Toward an ionphoton quantum interface in an optical cavity,” Appl. Phys. B107, 1145–1157 (2012).
[CrossRef]

Oberst, H.

C. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett.85, 538–541 (2000).
[CrossRef] [PubMed]

Oskay, W. H.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Plata, J.

S. Brouard and J. Plata, “Heating of a trapped ion by random fields: The influence of the micromotion,” Phys. Rev. A63, 043402 (2001).
[CrossRef]

Prestage, J. D.

J. D. Prestage, G. J. Dick, and L. Maleki, “New ion trap for frequency standard applications,” J. Appl. Phys.66, 1013–1017 (1989).
[CrossRef]

Purcell, E.

E. Purcell, “Spontaneous emission probabilities at radio frequencies,” in “Confined Electrons and Photons,” vol. 340 of NATO ASI Series, E. Burstein and C. Weisbuch, eds. (SpringerUS, 1995), pp. 839–839.
[CrossRef]

Pyka, K.

K. Pyka, N. Herschbach, J. Keller, and T. Mehlstäubler, “A high-precision rf trap with minimized micromotion for an In+multiple-ion clock,” arXiv preprint arXiv:1206.5111 (2012).

Quinto-Su, P. A.

R. Jáuregui, J. Récamier, and P. A. Quinto-Su, “On decoherence and nonlinear effects in the generation of quantum states of motion in paul traps,” J. Opt. B: Quantum Semiclass. Opt.3, 194 (2001).
[CrossRef]

Raab, C.

C. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett.85, 538–541 (2000).
[CrossRef] [PubMed]

Récamier, J.

R. Jáuregui, J. Récamier, and P. A. Quinto-Su, “On decoherence and nonlinear effects in the generation of quantum states of motion in paul traps,” J. Opt. B: Quantum Semiclass. Opt.3, 194 (2001).
[CrossRef]

Riebe, M.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Roos, C.

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

Rosenband, T.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+optical clocks,” Phys. Rev. Lett.104, 070802 (2010).
[CrossRef] [PubMed]

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Sahoo, B. K.

Schaetz, T.

M. D. Barrett, B. DeMarco, T. Schaetz, V. Meyer, D. Leibfried, J. Britton, J. Chiaverini, W. M. Itano, B. Jelenković, J. D. Jost, C. Langer, T. Rosenband, and D. J. Wineland, “Sympathetic cooling of 9Be+and 24Mg+for quantum logic,” Phys. Rev. A68, 042302.

Schmidt, P.

A. Stute, B. Casabone, B. Brandsttter, D. Habicher, H. Barros, P. Schmidt, T. Northup, and R. Blatt, “Toward an ionphoton quantum interface in an optical cavity,” Appl. Phys. B107, 1145–1157 (2012).
[CrossRef]

Schmidt, P. O.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Schmidt-Kaler, F.

S. Narayanan, N. Daniilidis, S. A. Moller, R. Clark, F. Ziesel, K. Singer, F. Schmidt-Kaler, and H. Haffner, “Electric field compensation and sensing with a single ion in a planar trap,” J. Appl. Phys.110, 114909 (2011).
[CrossRef]

F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, and R. Blatt, “Realization of the cirac–zoller controlled-not quantum gate,” Nature422, 408–411 (2003).
[CrossRef] [PubMed]

C. Raab, J. Eschner, J. Bolle, H. Oberst, F. Schmidt-Kaler, and R. Blatt, “Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,” Phys. Rev. Lett.85, 538–541 (2000).
[CrossRef] [PubMed]

Shi, M.

Singer, K.

S. Narayanan, N. Daniilidis, S. A. Moller, R. Clark, F. Ziesel, K. Singer, F. Schmidt-Kaler, and H. Haffner, “Electric field compensation and sensing with a single ion in a planar trap,” J. Appl. Phys.110, 114909 (2011).
[CrossRef]

Stalnaker, J. E.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Stute, A.

A. Stute, B. Casabone, B. Brandsttter, D. Habicher, H. Barros, P. Schmidt, T. Northup, and R. Blatt, “Toward an ionphoton quantum interface in an optical cavity,” Appl. Phys. B107, 1145–1157 (2012).
[CrossRef]

Swann, W. C.

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

Tanaka, U.

Y. Ibaraki, U. Tanaka, and S. Urabe, “Detection of parametric resonance of trapped ions for micromotion compensation,” Appl. Phys. B105, 219–223 (2011). .
[CrossRef]

Urabe, S.

Y. Ibaraki, U. Tanaka, and S. Urabe, “Detection of parametric resonance of trapped ions for micromotion compensation,” Appl. Phys. B105, 219–223 (2011). .
[CrossRef]

Vuletic, V.

D. R. Leibrandt, J. Labaziewicz, V. Vuletić, and I. L. Chuang, “Cavity sideband cooling of a single trapped ion,” Phys. Rev. Lett.103, 103001 (2009).
[CrossRef] [PubMed]

Walther, H.

J. Höffges, H. Baldauf, T. Eichler, S. Helmfrid, and H. Walther, “Heterodyne measurement of the fluorescent radiation of a single trapped ion,” Opt. Commun.133, 170–174 (1997).
[CrossRef]

Wang, S. X.

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical resonator,” Appl. Phys. B31, 97–105 (1983). .
[CrossRef]

Wineland, D.

D. Wineland and D. Leibfried, “Quantum information processing and metrology with trapped ions,” Laser Phys. Lett.8, 175–188 (2011).
[CrossRef]

D. Wineland, C. Monroe, W. Itano, D. Leibfried, B. King, and D. Meekhof, “Experimental issues in coherent quantum-state manipulation of trapped atomic ions,” J. Res. Natl. Inst. Stand. Technol.103, 259 (1998).
[CrossRef]

Wineland, D. J.

C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, and T. Rosenband, “Frequency comparison of two high-accuracy Al+optical clocks,” Phys. Rev. Lett.104, 070802 (2010).
[CrossRef] [PubMed]

J. P. Home, D. Hanneke, J. D. Jost, J. M. Amini, D. Leibfried, and D. J. Wineland, “Complete methods set for scalable ion trap quantum information processing,” Science325, 1227–1230 (2009).
[CrossRef] [PubMed]

T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou, A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Diddams, W. C. Swann, N. R. Newbury, W. M. Itano, D. J. Wineland, and J. C. Bergquist, “Frequency ratio of Al+and Hg+single-ion optical clocks; metrology at the 17th decimal place,” Science319, 1808–1812 (2008).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

The schematic of the setup. A single 138Ba+ is trapped at the RF trap center and coupled to a high finesse cavity. Two laser beams are used for fluorescence detection and Doppler cooling at 493nm (D1) and 650nm (D2) respectively, indicated by the purple arrow. A magnetic field is applied to define the quantization axis, indicated by the green arrow (). The ion-cavity emission spectrum is probed by a 493nm beam (Rp), indicated by the blue arrow (). The photons emitted from the cavity are collected into a fiber-coupled single-photon counting module (SPCM). A CCD camera, interchangeable with another free-space SPCM, detects the fluorescence of the ion in the direction indicated by the black arrow. The cavity length is stabilized to a 650nm laser, indicated by a red arrow which is aligned to the cavity axis (ŷ).

Fig. 2
Fig. 2

The relevant transitions and level structure for 138Ba+. Doppler cooling is achieved by driving the 6S1/2 → 6P1/2 transitions at 493nm (D1) and repumping on the 5D3/2 → 6P1/2 transitions at 650nm (D2). The ion-cavity coupling is driven by the cavity probing beam (Rp) with Rabi rate ΩL and the intra-cavity field with coupling strength g. Δ is the detuning of the laser frequency from the S1/2 ↔ P1/2 transition while Δc is the relative detuning between the laser and the cavity resonance. To obtain the ion-cavity emission profiles, Δc is swept ±12MHz over the transition carrier (Δc = 0) while Δ is kept constant at −110MHz.

Fig. 3
Fig. 3

(a), (b) and (c) are the ion-cavity emission profiles obtained at the cavity antinode while (d) is obtained at the cavity node. All plots are normalized to their respective carrier peaks except (d), which is normalized to the carrirer peak in (c). First and second order micromotion sidebands at ±Ω and ±2Ω are clearly visible in (a) before any micromotion compensation. After compensating the micromotion along the probe direction (), the first order sidebands are eliminated as shown in (b). The persistence of the second order sidebands at ±2Ω is due to the coupling of the micromotion along the cavity axis (ŷ). Compensating the micromotion along this direction eliminates the second order peaks as shown in (c). For greater detection sensitivity, the ion is shifted to the cavity node. Consequently, the residual micromotion along the cavity axis manifests as sidebands with a much higher amplitude at ±Ω as shown in (d). In the same plot, the peak at resonance is due to a residual offset from the cavity node. The other two peaks are motional sidebands due to the secular motion of the ion.

Fig. 4
Fig. 4

The ion-cavity emission profiles for an ion located at the cavity antinode with the micromotion fully compensated. The inset shows the data near to the RF sideband frequency which is statistically flat with no clear signature of a sideband present consistent with a signal to noise ratio of one.

Equations (8)

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H I = Ω R exp ( i Δ c t ) a + Ω R * exp ( i Δ c t ) a ,
Ω R = g Ω L Δ exp ( i k x ) sin ( k y + ϕ )
H I = g Ω L Δ { sin ( ϕ ) [ exp ( i Δ c t ) + β x 2 ( exp ( i ( Δ c + Ω ) t ) exp ( i ( Δ c Ω ) t ) ) + β x 2 + β y 2 8 ( exp ( i ( Δ c + 2 Ω ) t ) + exp ( i ( Δ c 2 Ω ) t ) ) ] + cos ( ϕ ) [ β y 2 ( exp ( i ( Δ c + Ω ) t ) + exp ( i ( Δ c Ω ) t ) ) + β x β y 4 ( exp ( i ( Δ c + 2 Ω ) t ) exp ( i ( Δ c 2 Ω ) t ) ) ] } a + h . c . ,
( ρ ) = κ ( 2 a ρ a ρ a a a a ) ,
I c = I c 0 [ κ 2 κ 2 + Δ c 2 + β x 2 4 ( κ 2 κ 2 + ( Δ c + Ω ) 2 + κ 2 κ 2 + ( Δ c Ω ) 2 ) + ( β x 2 + β y 2 8 ) 2 ( κ 2 κ 2 + ( Δ c + 2 Ω ) 2 + κ 2 κ 2 + ( Δ c 2 Ω ) 2 ) ]
I c = I c 0 [ β y 2 4 ( κ 2 κ 2 + ( Δ c + Ω ) 2 + κ 2 κ 2 + ( Δ c Ω ) 2 ) + β x 2 β y 2 16 ( κ 2 κ 2 + ( Δ c + 2 Ω ) 2 + κ 2 κ 2 + ( Δ c 2 Ω ) 2 ) ] ,
SNR = N s Δ N b = β x 2 4 N c N b .
β x , min = 2 N b N c .

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