Coherent control and third-harmonic generation: theory and experiment Roberto Buffa 1, Stefano Cavalieri 2, Lorenzo Fini 2 Abstract. (1) Istituto Nazionale per la Fisica della Materia, Unità di Siena, Dipartimento di Fisica, Università di Siena, E-mail:[email protected] In the framework of the coherent control of photoreactions 1-10 we present an experimental study on the temporal coherent control on a process of twophoton-resonant third-harmonic (TH) generation in vapors of atomic sodium, where evidence of quantum interference in the TH generation is reported for the first time. (2) Istituto Nazionale per la Fisica della Materia, Unità di Firenze, Dipartimento di Fisica and European Laboratory for Non-Linear Spectroscopy (LENS), Università di Firenze, E-mail:[email protected], [email protected] The experimental results agree with the predictions of a theoretical model.8,9 Theory Experiment A sample of sodium vapors, generated in a cross-shaped oven cell operating at 350°C and filled with some mbar of argon as buffer gas, is exposed to pairs of laser pulses produced by a Nd:Yag-pumped dye laser. Each pulse has 5 ns duration, 31 GHz spectral bandwidth, linear polarization and wavelength tunable around the two-photon resonance of the 4 2D doublet of sodium. Pairs of collinear and identical laser pulses are obtained by passing the laser beam into a Michelson-type interferometer, which also allows to control the relative pulse delay t. The generated TH field is separated from the excitation field by a quartz prism followed by some dichroic filters and then detected by an UV photomultiplier. The evidence of quantum interference in the TH generation is shown by changing the relative pulse delay t. In the single atom approximation (arbitrary thin sample), the frequency integrated TH intensity Ig(t) around wg = 3wp is given by: w w Ig ( t ) | x1 ( t )x*2 ( t )|2 I p ( t ) g The Schrödinger equation provides the equations of motion a n x n exp( iwn t) for the probability amplitudes of the bound states. In the approximation of arbitrary weak field, the expression for the TH energy yield is: p t STH dt{| dt'[ E2p ( t' ) exp( it' )dt' ] |2 | Ep ( t ) |2 } Interaction scheme, showing the involved states of sodium where the expression of Ep(t) is given by Ep(t)=E0[fp(t)+fp(t-t)exp(-iwpt)] Experiment vs. Theory Measurement: Theory: TH energy yield vs. pulse delay t TH energy yield vs. pulse delay t The experimental results have been compared with the predictions of a theoretical model8,9 which makes use of a pair of identical Fourier-trasform-limited pulses. The spectral characteristics of the actual multimode laser pulses have been measured by a linear autocorrelation technique. The best fit for the power spectrum has been found when the electric field envelope of the laser pulses has been assumed to have a Lorentzian shape with a temporal width of 7.1 ps (FWHM). In the theoretical analysis we have then used such pulses. STH (arb. units) Contrast versus two-photon detuning (a) 1.5 t = 0 1 STH (arb. units) 2 2 (a) 1.5 1 0.5 0.5 0 0 0 0 1 2 3 4 5 6 7 8 9 1 2 3 4 Delay ( t - t) (fs) STH (arb. units) 0.35 STH Contrast 0.9 0.8 STH (arb. units) 0.4 1 (b) 0.6 0.3 0.2 0.5 0.15 0.4 0.1 0.3 t = 68 ps 0 0.1 1 2 3 4 5 6 7 8 9 10 Delay ( t - t) (fs) 0 50 100 150 8 9 10 0. 3 (c) 0. 2 0. 15 0. 1 0 0 0 7 0. 05 0.05 0.2 6 0. 25 0.25 0.7 5 Delay ( t - t) (fs) 10 0 1 2 3 4 5 6 7 8 9 10 Delay ( t - t) (fs) 200 Two-photon detuning (GHz) Dots represent the experimental results while lines reproduce theoretical calculations. The dashed line is obtained taking into account only the contribution of the second TH pulse, while in the case of the continuous line the computation has been performed on the whole TH field. Attività nel campo e prospettive future Conclusion The temporal coherent control of two-photon resonant TH generation into the continuum of ionization of sodium atoms has been experimentally investigated by using two delayed broadband laser pulses of identical electric-field shape. The experimental results have been compared with the theoretical predictions obtained using Fourier-transformlimited pulses of much shorter temporal duration but same spectral bandwidth. The good agreement confirms that coherent control of TH generation can be achieved through quantum interference even with broadband laser pulses, and that, for such purpose, broadband pulses are equivalent to Fourier-transform-limited pulses. References 1. L. Zhu, V. Kleinman, X. Li, S. P. Lu, K. Trentelman, and R. J. Gordon, Science 2. B. Sheehy, B. Walker, and L. F. DiMauro, Phys. Rev. Lett. 74, 4799 (1995). 3. T. Nakajima, P. Lambropoulos, S. Cavalieri and M. Matera, Phys. Rev. A 46, 7315 (1992). 4. E. Dupont, P. B. Corkum, H. C. Liu, M. Buchanan, and Z. R. Wasilewski, Phys. Rev. Lett. 74, 3596 (1995). 5. S. Cavalieri, R. Eramo, L. Fini, M. Materazzi, O. Faucher and D. Charalambidis, Phys. Rev. A 57, 2915 (1998). 6. V. Blanchet, C. Nicole, M. A. Bouchene and B. Girard, Phys. Rev. Lett. 78, 2716 (1997). 7. S. Cavalieri, M. Materazzi, R. Eramo, L. Fini and A. Giugni, Opt. Commun. 182, 161 (2000). 8. R. Buffa, S. Cavalieri, and L. Fini, Opt. Commun. 211, 167 (2002) 9. S. Cavalieri, L. Fini, R. Buffa, in stampa Journal of the Optical Society of America B, vol. 21 (2004) 10. S. Cavalieri, R. Eramo, M. Materazzi, C.Corsi, and M. Bellini, Phys. Rev. Lett. 89, 133002 (2002). Nel quadro più generale dell’interazione coerente radiazione-materia ci stiamo occupando anche di: Possibilità di variare caratteristiche temporali di un impulso tramite controllo della polarizzazione atomica ovvera tramite controllo della velocità di gruppo dell’impulso stesso. E’ stato condotto uno studio teorico che mostra questa possibilità (Roberto Buffa, Stefano Cavalieri, and Marco V. Tognetti: Coherent Control of Temporal Pulse Shaping by Electromagnetically Induced Transparency, Physical Review A, in stampa) E’ nostro obiettivo lo studio sperimentale della tematica: Applicazione di tecniche interferometriche per ottenere alta risoluzione spettrale con sorgenti a impulsi corti (<= 100fs) per superare il limite intriseco di purezza spettrale (vedi poster n. )

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