Attosecond beats in sodium vapor

Abstract

Transient, time-delayed, four-wave mixing (TDFWM) experiments have been performed on the Na D doublet with use of a novel angled-beam geometry. The effects of petahertz superposition-state modulations have been observed in the integrated TDFWM signal as a function of the time delay. As the time delay is varied, the lowest-order mixing signal modulates with a period of 980 as-corresponding to the sum frequency of the two Na D lines. Higher-diffraction-order mixing signals contain modulation components at integral multiples of the doublet sum frequency. PACS numbers: 42.65.Ma, 32.90.+a, 42.50.Md, 42.65.Ft Research on ultrafast phenomena is characterized by a mixture of techniques and instrumentation of varied nature. 1,2 Several practical schemes provide light pulses in the middle femtosecond regime and recent developments now yield excitation pulses with durations as short as 6 fs. 3 Less direct methods using broad-band light sources have the potential of exploiting short autocorrelation times in order to study ultrafast phenomena by way of transient four-wave mixing. 4 " 10 These latter experiments have been shown to be capable of obtaining both spectroscopic and relaxation information in the picosecond and femtosecond regimes. The extension of this technique to a much shorter time regime is promising. In the ultrafast regime, the establishment of a well defined delay time poses a potential difficulty because of . E-Eo{e-is "[e /k, + e \+e 'fe i'ki-r I /kj-r- -rewhere the primed and unprimed k vectors correspond to the frequencies a and a', and r is a variable relative delay between the prompt and delayed fields which are indicated by the subscripts 1 and 2, respectively. The optics were adjusted so that ki -k2 = k{ -k2. u A mixing signal is generated with wave vector 2k2~ki which modulates at the difference frequency ft'-ftasa function of r. In the case of the Na /Mine excitations the difference frequency is 530 GHz resulting in a modulation with a period of 1.9 ps. Similar results have been seen with use of broad-bandwidth excitations in atomic vapors of both Na 10 and Rb. 7 In the case of the Rb D line the difference frequency is much larger yielding a beat with a period of 139 fs. To see such beats in the attosecond regime the difference frequency would have to be in the petahertz regime. Alternatively, attosecond beats can be realized by the adjustment of the beams so that ki-k2"" -(kj-ki), whereupon the modulation frequency is the sum rather than the difference of the individual excitation frequencies. The penalty is that mixing signals are no longer (see Ref. 11) produced when the angling of the excitation beams with respect to each other. This problem is relevant, however, only when we make relaxation measurements, not when we look at modulation effects.The observation of high-frequency modulation effects in time-delayed four-wave mixing (TDFWM) does not require the use of broad-band excitation pulses when relaxation times are long. This is best seen by our viewing the modulation process not as a conse...

Quasiresonant nonlinear optical processes involving excited and ionized atoms

“…Указанное обстоятельство напоминает процесс образования ударной волны в не линейной акустике, где дисперсия среды мала и возможна генерация многих гармоник. Напомним, что образование осцилляции с коротким периодом (30 фс) уже наблюдалось экспериментально в работе [126], где интерферировали две далеко отстоящие друг от друга линии излу чения аргонового лазера (488 и 514,5 нм); в работе [127] наблюдались биения атто секундной длительности. В рамках рассматриваемой моде ли эти эксперименты соответствуют наличию в спектре интерфери рующих полей только двух первых гармоник соизмеримой интенсив ности.…”

Intermixing between four-wave mixing and six-wave mixing in a four-level atomic system

“…−ω 2 −−→ ρ (3) 10 (I). Next, we apply two coupling laser fields with same frequency ω 3 (≈ 3 ), both of which propagate along beam 2, to drive the transition |2 to |3 .…”

“…The strong coupling fields E 3 and E 3 create dressed atomic states |+ and |− from the level |2 (figure 1(c)), which are the coherent superpositions of the states |2 and |3 . Physically, in the dressed-state picture, the suppression and enhancement of the dressed FWM signals are due to destructive and constructive interference between the two FWM channels: (3) 10 (FWM + ) and ρ (0) 00 (3) 10 (FWM − ), respectively. On the other hand, in the bare-state picture, the simultaneous interactions of atoms with E 1 of beam 1, as well as E 2 and E 3 of beam 2, can induce atomic coherence between |0 and |3 through resonant two-photon or resonant three-photon transition [10] under particular conditions (figure 1(b)).…”

“…. Note that ρ 10 is not a purely third-order nonlinearity ρ (3) 10 , instead it denotes the dressed FWM, including fifth-order nonlinear responses.…”

“…Under assumption ζ 1 (ζ = G 2 /ψ, ψ = 20 30 , = 20 + 30 ), the dressed FWM intensity becomes the sum of two separate FWMs, |ρ 10 | 2 ≈ ρ (3) + 2 + |ρ (3) − | 2 where…”