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Optics Letters

Carrier-wave Rabi flopping: role of the carrier-envelope phase

Oliver D. Mücke, Thorsten Tritschler, Martin Wegener, Uwe Morgner, Franz X. Käertner, G. Khitrova, Hyatt M. Gibbs

Published Sep 15, 2004• 51 citations
Publisher

Abstract

Recently, a dependence of Rabi flopping on the carrier-envelope phase of the exciting laser pulses was predicted theoretically [Phys. Rev. Lett. 89, 127401 (2002)] for excitation of a thin semiconductor film with intense few-cycle pulses. Here, we report corresponding experiments on 50-100-nm thin GaAs films excited with 5-fs pulses. We find a dependence on the carrier-envelope phase arising from the interference of sidebands from the fundamental or the third-harmonic Mollow triplet, respectively, with surface second-harmonic generation.

DOI
10.1364/ol.29.002160

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Recently, a dependence of Rabi flopping on the carrier-envelope phase of the exciting laser pulses was predicted theoretically [Phys. Rev. Lett. 89, 127401 (2002)] for excitation of a thin semiconductor film with intense few-cycle pulses. Here, we report corresponding experiments on 50-100-nm thin GaAs films excited with 5-fs pulses. We find a dependence on the carrier-envelope phase arising from the interference of sidebands from the fundamental or the third-harmonic Mollow triplet, respectively, with surface second-harmonic generation.
Summary form only given. Illuminating a semiconductor with a constant light intensity can lead to a periodic oscillation of the inversion, a phenomenon which is known as Rabi flopping. Using pulsed excitation, Rabi flopping has been observed on semiconductors and exhibited periods in the range from 100 fs to 1 ps. Hughes (Phys. Rev. Lett. vol. 81, p. 3363, 1998) theoretically investigated the question of what happens when the light intensity becomes so high that the period of one Rabi oscillation becomes comparable with that of only one cycle of light, 2.7 fs for the band edge of GaAs, and predicted a new phenomenon: carrier-wave Rabi flopping. During a carrier-wave Rabi oscillation, the optical polarization becomes strongly distorted, which can lead to a double-peak structure (the Fourier-transform of the Rabi oscillation) in the third-harmonic (3/spl omega/) spectra. This characteristic shape is quite different from the well-known off-resonant third-harmonic generation. Importantly, resonant effects contain information on the dynamics of electronic resonances-potentially on the timescale of a single optical cycle. It is clear that, under these conditions, the usual envelope approximation breaks down, i.e. both the rotating wave approximation (RWA) as well as the slowly varying envelope approximation (SVEA) must not be used. This paper investigates carrier-wave Rabi flopping experimentally.
Summary form only given. In our recent experiments on the model semiconductor GaAs using 5 fs pulses, the Rabi period became as short as 3 fs, which is comparable to the period of light of 2.9 fs at the GaAs band edge. Hence, the medium's dynamics significantly distort the optical polarization within one optical cycle, which can be measured by a characteristic shape of the harmonics of the emitted light. In this paper we summarize our efforts to obtain a detailed understanding of these experiments by simulations based on a finite difference time-domain algorithm, solving the coupled Maxwell-Bloch equations in one dimension without using either the rotating wave approximation or the slowly varying envelope approximation. We consider not only transitions close to the band edge but also transitions up to 5.8 eV photon energy in a realistic fashion, i.e. comprising the known E/sub 1/ and E/sub 2/ resonances in GaAs which are due to band structure effects.
Recently the shortest pulses directly out of a Ti:sapphire laser as short as 6.5fs has been generated by use of single quantum well (SQW) GaAs absorber [1]. Since this laser produces pulses with durations shorter than or comparable to the polarization dephasing time and sufficient power for Rabi flopping of the excited carrier density, the noninstantaneous response of the absorber polarization has to be taken into account. We develope the theory of coherent absorber mode locking taking into account also inhomogeneous broadening of the semiconductor transition by freely movable carriers and Coulomb renormalization of the transition frequency in the scope of semiconductor Bloch equations. Photo-echo measurements in highly excited GaAs yield a decreasing of the effective dephasing with increasing of the laser excited carrier density as T2 ∝ N-1/3. In the SQW absorber the center wavelength of 750nm is well above the bandedge of the GaAs SQW at 870nm and the broad pulse spectrum excites mainly 3D carriers above the confinement depth. We have shown that Rabi-flopping is self-consistently produced due to sub10fs pulse formation at TW/cm2 intensities corresponding to an excited carrier density up to 1020cm-3.
By solving Maxwell's curl equations coupled to a two-level atom, a theoretical study of carrier-wave Rabi flopping of femtosecond optical pulses of only several carrier-cycles time duration is reported. For pulse areas of $2\ensuremath{\pi}$, the usual self-induced transparency regime is essentially recovered. However, for larger pulse areas, carrier-wave Rabi flopping occurs that manifests in local carrier reshaping and subsequently to the production of significantly higher spectral components on the propagating pulse. These new features are not predicted by employing the area theorem or a slowly-varying-envelope approximation for the amplitude and phase terms---which is the usual approach.