Signatures of Carrier-Wave Rabi Flopping in GaAs

Mücke, Oliver D.; Tritschler, T.; Wegener, Martin; Morgner, Uwe; Kärtner, Franz X.

doi:10.1103/physrevlett.87.057401

Cited by 200 publications

(134 citation statements)

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“…This brings one close to Rabi frequencies approaching the frequency of light -a regime which has previously been referred to as carrier-wave Rabi flopping [10]. In this regime, a splitting in the third-harmonic spectra has been observed [11]. However, as the measurements have been compared only with calculations on the basis of two-level systems [11], skepticism has been expressed whether this interpretation was correct indeed.…”

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confidence: 98%

“…In this regime, a splitting in the third-harmonic spectra has been observed [11]. However, as the measurements have been compared only with calculations on the basis of two-level systems [11], skepticism has been expressed whether this interpretation was correct indeed. Furthermore, later theoretical work [12] showed that the original experimental data of the four resulting bands is superimposed onto them by a gray scale: Black corresponds to 1, white to 0.…”

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confidence: 99%

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Light-Induced Gaps in Semiconductor Band-to-Band Transitions

Haug

Mücke

et al. 2004

Phys. Rev. Lett.

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We observe a triplet around the third harmonic of the semiconductor band gap when exciting 50 -100 nm thin GaAs films with 5 fs pulses at 3 10 12 W=cm 2 . The comparison with solutions of the semiconductor Bloch equations allows us to interpret the observed peak structure as being due to a twoband Mollow triplet. This triplet in the optical spectrum is a result of light-induced gaps in the band structure, which arise from coherent band mixing. The theory is formulated for full tight-binding bands and uses no rotating-wave approximation. DOI: 10.1103/PhysRevLett.92.217403 PACS numbers: 78.20.Bh, 42.50.Md, 42.65.Re, 78.47.+p When an intense light field at frequency ! 0 excites band-to-band transitions in a semiconductor, additional energy gaps can evolve within the original bands [ Fig. 1(b)]. These so-called light-induced gaps [1][2][3][4][5] are the analog of the induced doublets, split by the Rabi frequency R , in a resonantly excited two-level system [ Fig. 1(a)]. Here, two out of the four possible optical transitions are energetically degenerate. Hence, the optical spectrum consists of three peaks -the famous Mollow triplet for atoms [6,7] or excitons [8,9]. In the semiconductor band case, the light-induced gap in, e.g., the conduction band arises because the original conduction band and the one-photon sideband of the valence band lead to an avoided crossing. The corresponding Hopfield coefficients [1] determine the amount of conduction band admixture. It is crucial to note that this admixture can be finite even far away from the fictitious crossing point. This statement becomes particularly important for Rabi energies h R approaching the photon energy h! 0 , while it can be neglected for small Rabi energies. The latter case is tacitly assumed in previous graphical representations of calculated light-induced gaps. Importantly, as a result of this finite admixture, optical transitions between the induced bands are possible throughout an appreciable fraction of momentum space. Consequently, the transitions acquire considerable spectral weight. Again, two out of the four sets of possible optical transitions are energetically degenerate and a triplet results, which we will refer to as the two-band Mollow triplet in what follows.Light-induced gaps in semiconductor bands have not unambiguously been observed yet. In order to observe the splitting, it clearly has to be larger than the damping. As typical electron dephasing times under relevant conditions are on the order of 10 fs or less, the Rabi oscillation period has to be shorter than this value. This brings one close to Rabi frequencies approaching the frequency of light -a regime which has previously been referred to as carrier-wave Rabi flopping [10]. In this regime, a splitting in the third-harmonic spectra has been observed [11]. However, as the measurements have been compared only with calculations on the basis of two-level systems [11], skepticism has been expressed whether this interpretation was correct indeed. Furthermore, later theoretical work [12...

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confidence: 98%

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Light-Induced Gaps in Semiconductor Band-to-Band Transitions

Haug

Mücke

et al. 2004

Phys. Rev. Lett.

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“…For each slice, this approach offers a simple analytical formula for the ratio of level population amplitudes, resulting in equally simple analytical formulae for population inversion, induced dipole moment, and spectrum of the radiation emitted by this dipole. A good quality of the method is proved by showing that the resulting photon-emission spectra reproduce the numerically calculated ones available in literature [8,9,[13][14][15][16][17][18][19]. Moreover, the method indicates weak points of the square--wave solution of Tritschler et al [23] and is shown to be particularly useful in the area of extreme nonlinear optics [23], i.e., when few-cycle, strong pulses stimulate significant population dynamics in a two-level system on a timescale of half the optical cycle.…”

Section: Introductionmentioning

confidence: 67%

“…The latter is known [8,9,12,[24][25][26][27] to be a relevant quantity determining the response of the system in the regime of few-cycle pulses. Traditionally, there has been solved in different coupling regimes either a set of two linear differential equations for b k with no RWA applied (e.g.…”

Section: The Analytical Solution For Short Time Intervals and Iteratimentioning

confidence: 99%

An Iterative Method for Extreme Optics of Two-Level Systems

2004

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We formulate the problem of a two-level system in a linearly polarized laser field in terms of a nonlinear Riccati-type differential equation and solve the equation analytically in time intervals much shorter than half the optical period. The analytical solutions for subsequent intervals are then stuck together in an iterative procedure to cover the whole scale time of the laser pulse. Very good quality of the iterative method is shown by recovering with it a number of subtle effects met in earlier numerically calculated photon--emission spectra from model molecular ions, double quantum wells, atoms, and semiconductors. The method is used to describe novel, carrier-envelope offset phase effects in the region of extreme nonlinear optics, i.e., when two--level systems are exposed to pulses of only a few cycles in duration and strength ensuring the Rabi frequency to approach the laser light frequence.

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“…When the resonant interaction is considered, it has been demonstrated both theoretically and experimentally that the conventional Rabi flopping is greatly modified. A new type of carrierwave Rabi flopping occurs, which results in the formation of higher spectral components in the transmitted laser spectra [13,14]. Secondly, the spectral width of a few-cycle ultrashort pulse is very large.…”

Section: Introductionmentioning

confidence: 99%

Carrier-envelope phase-dependent transmitted spectra in inversion-asymmetric media with permanent dipole moments

Yang¹,

Xia²,

Zhang³

et al. 2009

J. Phys. B: At. Mol. Opt. Phys.

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We investigate the transmitted spectra of a few-cycle ultrashort pulse in an inversion-asymmetric medium with a permanent dipole moment (PDM). Our results show that even-order harmonics can be generated in this medium. Moreover, the generated even-order harmonics depend strongly on the carrier-envelope phase (CEP) of initial incident few-cycle ultrashort pulses. Physical analysis of the re-emitted spectra of the medium reveals that the CEP-dependent spectral effect is originated from the inversion-asymmetric structure and the corresponding PDM effects: two-photon transition dominates in the nonlinear process and further induces the generations of the even-order harmonics. Furthermore, the orientation relation between the electric field peak of the pulse and the PDM results in even-order harmonic generations depending on the CEP.

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Signatures of Carrier-Wave Rabi Flopping in GaAs

Cited by 200 publications

References 14 publications

Light-Induced Gaps in Semiconductor Band-to-Band Transitions

Light-Induced Gaps in Semiconductor Band-to-Band Transitions

An Iterative Method for Extreme Optics of Two-Level Systems

Carrier-envelope phase-dependent transmitted spectra in inversion-asymmetric media with permanent dipole moments

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