## Carrier-envelope phase-sensitive inversion in two-level systems

JOSA B, Vol. 22, Issue 10, pp. 2065-2075 (2005)

http://dx.doi.org/10.1364/JOSAB.22.002065

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### Abstract

We theoretically study the carrier-envelope phase-dependent inversion generated in a two-level system by excitation with a few-cycle pulse. On the basis of the invariance of the inversion under time reversal of the exciting field, parameters are introduced to characterize the phase sensitivity of the induced inversion. Linear and nonlinear phase effects are numerically studied for rectangular and sinc-shaped pulses. Furthermore, analytical results are obtained in the limits of weak fields, as well as strong dephasing, and by nearly degenerate perturbation theory for sinusoidal excitation. The results show that the phase-sensitive inversion in the ideal two-level system is a promising route for constructing carrier-envelope phase detectors.

© 2005 Optical Society of America

**OCIS Codes**

(020.0020) Atomic and molecular physics : Atomic and molecular physics

(020.1670) Atomic and molecular physics : Coherent optical effects

(190.7110) Nonlinear optics : Ultrafast nonlinear optics

(320.7120) Ultrafast optics : Ultrafast phenomena

**ToC Category:**

Atomic and Molecular Physics

**Citation**

Christian Jirauschek, Lingze Duan, Oliver D. Mücke, Franz X. Kärtner, Martin Wegener, and Uwe Morgner, "Carrier-envelope phase-sensitive inversion in two-level systems," J. Opt. Soc. Am. B **22**, 2065-2075 (2005)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-22-10-2065

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### References

- L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, 1975).
- S. Hughes, "Breakdown of the area theorem: carrier-wave Rabi flopping of femtosecond optical pulses," Phys. Rev. Lett. 81, 3363-3366 (1998). [CrossRef]
- J. H. Shirley, "Solution of the Schrödinger equation with a Hamiltonian periodic in time," Phys. Rev. 138, B979-B987 (1965). [CrossRef]
- R. Gush and H. P. Gush, "Scattering of intense light by a two-level system," Phys. Rev. A 6, 129-140 (1972). [CrossRef]
- F. Ahmad, "Semiclassical electrodynamics of a two-level system," Phys. Rev. A 12, 1539-1545 (1975). [CrossRef]
- J. V. Moloney and W. J. Meath, "Phase and temporal average transition probabilities for a multi-level system in a sinusoidal field," Mol. Phys. 31, 1537-1548 (1976). [CrossRef]
- J. V. Moloney and W. J. Meath, "Induced transition probabilities and energies for the strongly coupled two-level system," Phys. Rev. A 17, 1550-1554 (1978). [CrossRef]
- W. M. Griffith, M. W. Noel, and T. F. Gallagher, "Phase and rise-time dependence using rf pulses in multiphoton processes," Phys. Rev. A 57, 3698-3704 (1998). [CrossRef]
- L. Xu, C. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T. W. Hänsch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996). [CrossRef] [PubMed]
- A. Apolonski, A. Poppe, G. Tempea, C. Spielmann, T. Udem, R. Holzwarth, T. W. Hänsch, and F. Krausz, "Controlling the phase evolution of few-cycle light pulses," Phys. Rev. Lett. 85, 740-743 (2000). [CrossRef] [PubMed]
- D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000). [CrossRef] [PubMed]
- U. Morgner, R. Ell, G. Metzler, T. R. Schibli, F. X. Kärtner, J. G. Fujimoto, H. A. Haus, and E. P. Ippen, "Nonlinear optics with phase-controlled pulses in the sub-two-cycle regime," Phys. Rev. Lett. 86, 5462-5465 (2001). [CrossRef] [PubMed]
- O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, "Determining the carrier-envelope offset frequency of 5-fs pulses with extreme nonlinear optics in ZnO," Opt. Lett. 27, 2127-2129 (2002). [CrossRef]
- T. M. Fortier, P. A. Roos, D. J. Jones, S. T. Cundiff, R. D. R. Bhat, and J. E. Sipe, "Carrier-envelope phase-controlled quantum interference of injected photocurrents in semiconductors," Phys. Rev. Lett. 92, 147403 (2004). [CrossRef] [PubMed]
- A. Apolonski, P. Dombi, G. G. Paulus, M. Kakehata, R. Holzwarth, T. Udem, C. Lemell, K. Torizuka, J. Burgdörfer, T. W. Hänsch, and F. Krausz, "Observation of light-phase-sensitive photoemission from a metal," Phys. Rev. Lett. 92, 073902 (2004). [CrossRef] [PubMed]
- G. G. Paulus, F. Lindner, H. Walther, A. Baltuska, E. Goulielmakis, M. Lezius, and F. Krausz, "Measurement of the phase of few-cycle laser pulses," Phys. Rev. Lett. 91, 253004 (2003). [CrossRef]
- M. Y. Ivanov, P. B. Corkum, and P. Dietrich, "Coherent control and collapse of symmetry in a two-level system in an intense laser field," Laser Phys. 3, 375-380 (1993).
- O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, "Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics," Phys. Rev. Lett. 89, 127401 (2002). [CrossRef] [PubMed]
- O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, F. X. Kärtner, G. Khitrova, and H. M. Gibbs, "Carrier-wave Rabi flopping: role of the carrier-envelope phase," Opt. Lett. 29, 2160-2162 (2004). [CrossRef] [PubMed]
- G. F. Thomas, "Dipole interaction of a multilevel system with a continuous-wave or Gaussian-pulsed laser," Phys. Rev. A 32, 1515-1525 (1985). [CrossRef] [PubMed]
- A. Brown and W. J. Meath, "On the effects of absolute laser phase on the interaction of a pulsed laser with polar versus nonpolar molecules," J. Chem. Phys. 109, 9351-9365 (1998). [CrossRef]
- V. M. Akulin and N. V. Karlov, Intense Resonant Interactions in Quantum Electronics (Springer-Verlag, 1992). [CrossRef]
- A. J. Jerri, Introduction to Integral Equations with Applications (Wiley, 1999).
- O. Mitrofanov, L. N. Pfeiffer, and K. W. West, "Generation of low-frequency components due to phase-amplitude modulation of subcycle far-infrared pulses in near-field diffraction," Appl. Phys. Lett. 81, 1579-1581 (2002). [CrossRef]
- U. Morgner, F. X. Kärtner, S. H. Cho, Y. Chen, H. A. Haus, J. G. Fujimoto, E. P. Ippen, V. Scheuer, G. Angelow, and T. Tschudi, "Sub-two-cycle pulses from a Kerr-lens mode-locked Ti:sapphire laser," Opt. Lett. 24, 411-413 (1999). [CrossRef]
- P. R. Certain and J. O. Hirschfelder, "New partitioning perturbation theory. I. General formalism," J. Chem. Phys. 52, 5977-5987 (1970). [CrossRef]
- J. O. Hirschfelder, "Almost degenerate perturbation theory," Chem. Phys. Lett. 54, 1-3 (1978). [CrossRef]
- P. K. Aravind and J. O. Hirschfelder, "Two-state systems in semiclassical and quantized fields," J. Phys. Chem. 88, 4788-4801 (1984). [CrossRef]
- B. Misra and E. C. G. Sudarshan, "The Zeno's paradox in quantum theory," J. Math. Phys. 18, 756-763 (1977). [CrossRef]

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