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Abstract Coherence control in a λ-type three-level system having an ultrafast (<10 fs) dephasing time has been demonstrated. Coherences in the multilevel system were excited by an intense supercontinuum yielding terahertz Rabi frequencies. The coherence was controlled by changing the interaction phase between the excited coherences and the broadband light field in the double-pulse pumping scheme.
©2001 Optical Society of America
1. Introduction
The coherence can be excited in optical materials [1,2] when the Rabi frequency is greater than the absorption line width, i.e., ωR>ωa. Coherent transient phenomena in inhomogeneously broadened two level systems can be used in remarkable applications such as photon-echo data storage and processing [3] and spectroscopy [4]. In addition, quantum interference effects in multilevel systems have remarkable features: electromagnetically induced transparency, lasing without inversion [5], refractive-index enhancement [6], group-velocity control, etc.. Changing the coupling phase of the laser beam or the rf field [7], makes absorption and emission control and switching possible [8].
Until recently, these effects were demonstrated experimentally only in hyperfine structures [9], ultranarrow absorption lines in atomic gas media [10], solid hydrogen [11], or rare-earth-ion-doped crystals at liquid-helium temperature [12]. In the past few years, a femtosecond laser system has been used to demonstrate temporal coherent control in media having a dephasing time of several tens of picoseconds in two-photon transitions in Cs gas [13,14,15] and in a multilevel system based on a vibrational line in a molecular gas with a three-pulse photon echo technique [16,17].
In solid-state materials or organic dyes at room temperature, however, absorption bands have tens of terahertz and femtosecond dephasing time. So intense, quick, broadband excitation is required for their coherent excitation. In ultrafast excitation some technical problems, including temporal and spatial chirping in the medium, will arise. In this paper we demonstrate absorption and emission control in ultrafast (<10 fs) media by using the optical phase of broadband pump beams [18]. The intense ultrabroadband radiation covering the UV-IR spectral regions couples several energy levels in a medium, so multiple coherences are excited between these energy levels. By changing the Fourier amplitude or Fourier phase of the excitation, we can control population and coherence in the multilevel system.
2. Coherence control by broadband radiation
A time-dependent electrical field of the ultrabroadband light source is expressed as
where F(ω) and ϕ(ω) are the amplitudes of the Fourier component and the Fourier phase, respectively. The scope of integration assumes that the pump bandwidth is large enough in comparison with the absorption bands and includes all resonance frequencies of the λ-type three-level system shown in Fig. 1. When we have a transform-limited pulse, ϕ(ω)=constant is satisfied for any frequency component. In experiments, however, the medium should have strong absorption, i.e., should be highly dispersive so dϕ(ω)/dω varies with propagation distance.
Fig. 1. Energy-level configuration. ω 1 and ω 2 are coupling laser frequencies. L1 and L3 are nondegenerate sublevels of the ground state. L2 is a common excited state. δ is the detuning of the laser frequency from resonance.
When we apply the first pump pulse with field E 1(t 1), the medium that has resonances for the specific frequencies ω 1 and ω 2 is driven by an energy of µ E 1(t 1). Upon the second excitation at t 2(t 2-t 1<T 2, where T 2 is the dephasing time), the excited polarizations interact with field E 2(t 2), then change their amplitude. The ratio of amplitude of excited polarizations at these frequencies is given by S(ω 2,Δ)/S(ω 1,Δ), where the modulation depth S(ω,Δ)after the interactions is
Here Δ and T2i are the frequency difference from the center frequency of the pump and the dephasing time of the absorption line, respectively. The modulation depth is given by the delay time of the pump pulses and is independent of the frequency chirp. Let us consider an extremely chirped case, for example, two pump pulses separated by t 2-t 1=Ta(<T 2), with the frequency of the pump pulses slowly varying from ωL to ωU (ωL<ω 1<ωU) within a time Tb(≫T 2). This situation is also transient and can be considered a series of interactions: Each has the same phase of interaction ΔTa with temporally dependent detuning δ (t). The effect of chirp appears mainly in the generalized Rabi frequency . When the Rabi frequency exceeds the effective absorption full width ωR>2ωa=2δ, the condition for quasi-resonant excitation Ω≅ω R can be satisfied with broadband pumping.
As is shown in above argument, the pump source for ultrafast dephasing media should have a high intensity, but a transform-limited phase structure is not essential. To excite a few-cycle-time dephasing medium, the pump light must have a large bandwidth and sufficient fluence to saturate the absorbing medium within its dephasing time. An intense supercontinuum generated in rare gas covering the VUV-FIR spectrum was used as the pump light source. A total power of >1 TW with a flat spectral intensity of 1 GW/nm from the UV to IR spectral region has been generated by a self-trapped femtosecond laser pulse with a repetition rate of 10 Hz [19]. The frequency-dependent chirp characteristics of this supercontinuum have been measured [20] in the UV-IR region. The group delay of 1 fs/nm in the visible spectral region is quite small in comparison with the supercontinuum generated in solid-state materials. This supercontinuum is a quasi-transform-limited pulse when we select a spectral component confined to a ten-nm bandwidth.
3. Experiments
One of the other difficulties in superfast and multipulse coherent experiments is the angular dispersion of the broadband radiation emitted from the transient grating generated by the pump beams [16]. To explore this problem, symmetric and coaxial two-pulse pumping was carried out. The experimental setup is shown in Fig. 2. The optical system was designed to minimize spectral and spatial phase distortion. Two pairs of precisely made, thin, synthesized quartz plates were used as symmetric beam splitters for the ultrabroadband and intense laser beams. The plates were carefully polished to minimize phase distortion in both transmittance and reflection. The difference of thickness in optical length was measured to be less than 100 nm in the UV region. The beam splitters were placed at the Brewster angle to select linear polarization and enhance their surface reflection. Projecting an aperture image onto the sample medium avoids spatially varying spectral distortion due to diffraction. The temporal coherence of the pump beam, which had a diameter >1 cm in the 300–800-nm spectral window of the apparatus, was measured to be 1.4 fs, corresponding to a monocycle temporal resolution [21].
Throughout the following experiments, the relative Fourier phase between the pump beams was simultaneously measured in the frequency domain, interference fringes with a polychromator, providing a 1024-channels cooled-CCD array for the 300–800-nm spectral window. The phase-dependent absorption and emission in a 1-mm-thick sample were measured with a third beam (weak and off-axis white-light probe) at the termination of pumping as a function of the optical delay between the two pump pulses.
Fig. 2. Experimental setup for coherence control and monitoring with broadband light pulses. Thin quartz plates BS, located at the Brewster angle are used as broadband beam splitters and polarizing filters. The sample is located at the image plane of aperture A to avoid spatial chirp due to diffraction. The phase-sensitive absorption was measured by the off-axis probe beam by changing the optical delay between two pump pulses, t1. The dashed line (echo option) indicates a beam that is included for photon-echo experiments, but is not used for the absorption and emission measurements.
4. Results and discussion
Absorption and emission in several dye solutions were measured in the λ-type multilevel system. Because these organic dyes have a large absorption and emission cross section of the order of 10-15 to 10-16 cm2, a Rabi frequency of tens of terahertz can be obtained with a moderate laser intensity. The energy levels in Rhodamine 6G (Rh6G) dye are shown in Fig. 3. The probe is incoherent with the pump beams and is monitoring the population in the upper state just after the interactions. Figure 4 shows the frequency-resolved interference fringes of the pump pulses and the corresponding absorption and emission in the Rh6G dye. At a frequency of 545 THz, corresponding to the v=0-0 transition of the dye, the medium alternatively shows absorption and emission with delay time. Figure 5 represents the pump intensity dependence of absorption in the sample. A dephasing time of 10 fs in Fig. 5(a) is corresponds to an effective absorption linewidth of 30 THz. It is clear that a significant enhancement of the absorption saturation appears at an optical delay of ±5.1 fs when ωR≈2ωa. The optical delay at the maximum saturation (5.1 fs) corresponds to 196-THz fringe separation in the frequency domain. The phase of interaction to the Stokes shift ν 3 of 45 THz is measured to be Δϕ=2πΔt ν 3=π/2 at this delay time. In other words, the fist and the second pulses are in phase in the absorption band and have a π/2 phase difference in the emission band.
Fig. 3. Energy-level diagram for the λ system in an organic dye. ν 1, v 2, ΩR1, and ΩR1 are the absorption and emission optical frequencies and the corresponding Rabi frequencies, respectively. The vertical scale shows optical frequency for Rh6G dye.
The π phase difference (corresponding to a delay of 11 fs) gives the highest contrast between the absorption and the emission bands, with the maximum light intensity in the absorption band and no light in the emission band. In steady-state and the incoherent situation, the absorption saturation should be maximum at this time. The experimental result, however, is in disagreement with this spectral analysis. We have to discuss coherent transient effects as follows.
The first pulse excites the absorption band coherence ν1 and emission band coherence ν2. At t=0, the excitation is also strong, but the phase is the same as the single-pulse excitation. The two Rabi-flopping frequencies ΩR1 and ΩR2 interact with each other. The excited population is quickly transferred to other levels during the interaction. Sometimes two-photon coupling to the same upper state induces population trapping into dressed lower levels: Absorption vanishes. But this requires complete energy relaxation to a dressed lower level is because the upper-state energy lifetime of 3.9 ns in Rh6G is sufficiently long, absorption is still present at t=0.
At t=5.1 fs, because the phase difference between the coherence excited by the first pulse and that excited by the second pulse is π/2 for the emission band, the later interaction is orthogonal and disappears. Only the coherence in the absorption band can interact with the second pulse. In this situation, the second excitation becomes a simple two-level scheme. As a result of the strong interaction at ν1 and the suppression of induced emission at ν2, the absorption saturation takes a maximum value.
Fig. 4. Frequency-resolved mappings for (a) interference fringes as a function of optical delay between the two pump pulses, and (b) corresponding absorption and emission profiles in Rh6G dye. The shading in (b) represents transmittance, and its scale is shown on the right-hand side. The small-signal transmittance of the sample is 10-4. Weak absorption around 680 THz is attributed to excited-state absorption S 1–S 2.
Fig. 5. Intensity dependence of the absorption in 560–567 THz as a function of the optical delay between the pump pulses. (a) Weakly saturated and (b) strongly excited region.
5. Conclusion
In conclusion, we have demonstrated population and coherence control in a femtosecond-dephasing medium. The pumping scheme may be applicable to other broadband materials for the control of general material properties that are not limited to optical characteristics. Specifically, the UV and VUV broadband excitations’ coupling to the same continuum drastically changes ionization and reaction properties of the material. Applications for solid-state materials, or optical control of short-wavelength systems that are based on their short-lived and ultrabroadband nature are noteworthy possibilities for this scheme.
6. Acknowledgments
H. Nishioka thanks Kohzou Hakuta and Masayuki Katsuragawa for stimulating discussions. Part of this work is supported by a grand-in-aid for scientific research from the Ministry of Education, Science, Sports and Culture.
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