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...

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The recent work of Durnin, Miceli, and Eberly' on diAraction-free beams brings to mind the experiment which generates the Poisson spot. As normally observed by the diffraction of parallel light around a circular obstacle, the Poisson spot retains its intensity on axis as one recedes from the obstacle, while its radius increases linearly. However, if the obstacle is placed in the focal plane of a following lens, as was the case in Ref. 1, the illuminated spot which is observed in the center of the shadow exhibits the general characteristics which are de-scribed by Durnin, Miceli, and Eberly. For our experimental conditions, as described below, the spot retains its intensity and sharpness as the observation point is moved over the latter half of the 156-cm range on which it forms. However, we probably ought not to say that the spot constitutes a diff'ractionless propagating beam. It is rather a line image, as is shown by the fact that a new obstacle placed in its path does not obliterate the spot further along the axis. In Figs. 1(a) and 1(b) we show the shadow of a 0.8-cm ball bearing illuminated by a 1.5-cm-diam collimated He-Ne laser light beam as observed on a white card 150 cm from a 25-cm lens which is an~'. rugous to the lens in the apparatus of Ref. 1. Figure 1(a) shows the normal unblocked situation while Fig. 1(b) was obtained when a 0.3-cm-diam rod was inserted across the beam at a position 40 cm before the white card. The shadow of the rod is clearly visible as is the undisturbed Poisson spot. This shows that the energy in the spot did not get there by traveling along the axis.The rod only blocks that part of the image lying close enough to the rod that it cannot "see" the edge of the ball bearing. Further away, light skimming the edge of the ball bearing has a free path to the image position and hence it is not afrected We wish to thank F. W. Kantor for insightful comments and suggestions and E. Usadi for assistance in making the figures.

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