Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Spatial and spectral coherent control with frequency combs

Abstract

Quantum coherent control1,2,3,4,5,6 is a powerful tool for steering the outcome of quantum processes towards a desired final state by the accurate manipulation of quantum interference between multiple pathways. Although coherent control techniques have found applications in many fields of science7,8,9,10,11,12, the possibilities for spatial and high-resolution frequency control have remained limited. Here, we show that the use of counter-propagating broadband pulses enables the generation of fully controlled spatial excitation patterns. This spatial control approach also provides decoherence reduction, which allows the use of the high-frequency resolution of an optical frequency comb13,14. We exploit the counter-propagating geometry to perform spatially selective excitation of individual species in a multicomponent gas mixture, as well as frequency determination of hyperfine constants of atomic rubidium with unprecedented accuracy. The combination of spectral and spatial coherent control adds a new dimension to coherent control, with applications in nonlinear spectroscopy, microscopy and high-precision frequency metrology, among others.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Level diagram and schematic of the experimental set-up.
Figure 2: Experimental demonstration of spatial coherent control using four different phase masks.
Figure 3: Spatial coherent control of different atomic species.
Figure 4: Direct frequency comb spectroscopy of atomic rubidium with spatial coherent control.

Similar content being viewed by others

References

  1. Warren, W. S., Rabitz, H. & Dahleh, M. Coherent control of quantum dynamics: the dream is alive. Science 259, 1581–1589 (1993).

    Article  ADS  MathSciNet  Google Scholar 

  2. Weiner, A. M., Leaird, D. E., Wiederrecht, G. P. & Nelson, K. A. Femtosecond pulse sequences used for optical manipulation of molecular motion. Science 247, 1317–1319 (1990).

    Article  ADS  Google Scholar 

  3. Silberberg, Y. Quantum coherent control for nonlinear spectroscopy and microscopy. Annu. Rev. Phys. Chem. 60, 277–292 (2009).

    Article  ADS  Google Scholar 

  4. Brif, C., Chakrabarti, R. & Rabitz, H. Control of quantum phenomena: past, present and future. New J. Phys. 12, 075008 (2010).

    Article  ADS  Google Scholar 

  5. Broers, B., van Linden van den Heuvell, H. B. & Noordam, L. D. Large interference effects of small chirp observed in two-photon absorption. Opt. Commun. 91, 57–61 (1992).

    Article  ADS  Google Scholar 

  6. Chatel, B., Degert, J., Stock, S. & Girard, B. Competition between sequential and direct paths in a two-photon transition. Phys. Rev. A 68, 041402 (2003).

    Article  ADS  Google Scholar 

  7. Bartels, R. et al. Shaped-pulse optimization of coherent emission of high-harmonic soft X-rays. Nature 406, 164–166 (2000).

    Article  ADS  Google Scholar 

  8. Dela Cruz, J. M., Pastirk, I., Comstock, M., Lozovoy, V. V. & Dantus, M. Use of coherent control methods through scattering biological tissue to achieve functional imaging. Proc. Natl Acad. Sci. USA 101, 16996–17001 (2004).

    Article  ADS  Google Scholar 

  9. Papagiakoumou, E. et al. Scanless two-photon excitation of channelrhodopsin-2. Nature Methods 7, 848–854 (2010).

    Article  Google Scholar 

  10. Prokhorenko, V. I. et al. Coherent control of retinal isomerization in bacteriorhodopsin. Science 313, 1257–1261 (2006).

    Article  ADS  Google Scholar 

  11. Herek, J. L., Wohlleben, W., Cogdell, R. J., Zeidler, D. & Motzkus, M. Quantum control of energy flow in light harvesting. Nature 417, 533–535 (2002).

    Article  ADS  Google Scholar 

  12. Nuernberger, P., Wolpert, D., Weiss, H. & Gerber, G. Femtosecond quantum control of molecular bond formation. Proc. Natl Acad. Sci. USA 107, 10366–10370 (2010).

    Article  ADS  Google Scholar 

  13. Holzwarth, R. et al. Optical frequency synthesizer for precision spectroscopy. Phys. Rev. Lett. 85, 2264–2267 (2000).

    Article  ADS  Google Scholar 

  14. Jones, D. J. et al. Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis. Science 288, 635–639 (2000).

    Article  ADS  Google Scholar 

  15. Weiner, A. M. Femtosecond pulse shaping using spatial light modulators. Rev. Sci. Instrum. 71, 1929–1960 (2000).

    Article  ADS  Google Scholar 

  16. Stowe, M. C., Pe'er, A. & Ye, J. Control of four-level quantum coherence via discrete spectral shaping of an optical frequency comb. Phys. Rev. Lett. 100, 203001 (2008).

    Article  ADS  Google Scholar 

  17. Meshulach, D. & Silberberg, Y. Coherent quantum control of two-photon transitions by a femtosecond laser pulse. Nature 396, 239–242 (1998).

    Article  ADS  Google Scholar 

  18. Hänsch, T. W., Harvey, K. C., Meisel, G. & Schawlow, A. L. Two-photon spectroscopy of Na 3s–4d without Doppler broadening using a CW dye laser. Opt. Commun. 11, 50–53 (1974).

    Article  ADS  Google Scholar 

  19. Levenson, M. D. & Bloembergen, N. Observation of two-photon absorption without Doppler broadening on the 3S–5S transition in sodium vapor. Phys. Rev. Lett. 32, 645–648 (1974).

    Article  ADS  Google Scholar 

  20. Witte, S., Zinkstok, R. Th., Ubachs, W., Hogervorst, W. & Eikema, K. S. E. Deep-ultraviolet quantum interference metrology with ultrashort laser pulses. Science 307, 400–403 (2005).

    Article  ADS  Google Scholar 

  21. Marian, A., Stowe, M. C., Lawall, J. R., Felinto, D. & Ye, J. United time-frequency spectroscopy for dynamics and global structure. Science 306, 2063–2068 (2004).

    Article  ADS  Google Scholar 

  22. Wolf, A. L., van den Berg, S. A., Ubachs, W. & Eikema, K. S. E. Direct frequency comb spectroscopy of trapped ions. Phys. Rev. Lett. 102, 223901 (2009).

    Article  ADS  Google Scholar 

  23. Gerginov, V., Tanner, C. E., Diddams, S. A., Bartels, A. & Hollberg L. High-resolution spectroscopy with a femtosecond laser frequency comb. Opt. Lett. 30, 1734–1736 (2005).

    Article  ADS  Google Scholar 

  24. Marian, A., Stowe, M. C., Felinto, D. & Ye, J. Direct frequency comb measurements of absolute optical frequencies and population transfer dynamics. Phys. Rev. Lett. 95, 023001 (2005).

    Article  ADS  Google Scholar 

  25. Ozawa, A. & Kobayashi, Y. Chirped-pulse direct frequency-comb spectroscopy of two-photon transitions. Phys. Rev. A 86, 022514 (2012).

    Article  ADS  Google Scholar 

  26. Chui, H. C. et al. Absolute frequency measurement of rubidium 5S–7S two-photon transitions with a femtosecond laser comb. Opt. Lett. 30, 842–844 (2005).

    Article  ADS  Google Scholar 

  27. Cundiff, S. T. & Weiner, A. M. Optical arbitrary waveform generation. Nature Photon. 4, 760–766 (2010).

    Article  ADS  Google Scholar 

  28. Kirchner, M. S. & Diddams, S. A. Grism-based pulse shaper for line-by-line control of more than 600 optical frequency comb lines. Opt. Lett. 35, 3264–3266 (2010).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

S.W. acknowledges support from the Netherlands Organization for Scientific Research (NWO Veni grant 680-47-402). K.S.E.E. acknowledges support from the NWO (VICI grant no. 680-47-310), the Foundation for Fundamental Research on Matter (FOM) through its programme ‘Broken Mirrors and Drifting Constants’, and Laserlab Europe (JRA ALADIN and INREX). The authors thank M. Sheinman for helpful discussions in the development of the theoretical model.

Author information

Authors and Affiliations

Authors

Contributions

K.S.E.E. conceived the V-shape phase concept for frequency comb spectroscopy. I.B. extended this concept to full spatial coherent control and provided the theoretical description. I.B. performed the experiments (with assistance from S.W and K.S.E.E.) and data analysis. K.S.E.E. supervised the project. All authors participated in the design of the experiments, interpretation of the results and writing of the manuscript.

Corresponding author

Correspondence to Kjeld S. E. Eikema.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 731 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barmes, I., Witte, S. & Eikema, K. Spatial and spectral coherent control with frequency combs. Nature Photon 7, 38–42 (2013). https://doi.org/10.1038/nphoton.2012.299

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2012.299

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing