IV. CONCLUSION 5 -391.5 -391 -390.5 -390 -389.5 -389 -391.5 -391.2 -390.9 -390.6 389 390 391 -391.5 -391 -390.5 -390 -389.5 -389 0 0.2 0.4 0.6 0.8 1 390.5 390.8 391.1 391.4 -391.5 -391.2 -390.9 -390.6 0 0.2 0.4 0.6 0.8 1 ➢ ➤ ➥ ➦ ➧ ➨ ➩ ➫ ➭ ➯ ➲ ➳ ➵ ➸ ➺ ➻ ➼ ➽ ➾ ➚ ➪ ➶ ➹ ➘ ➴ ➷ ➬ ➮ ➱ ✃ ❐ ❒ ❮ ❰ GLYPH<a207> GLYPH<a208> GLYPH<a209> GLYPH<a210> GLYPH<a211> GLYPH<a212> GLYPH<a213> GLYPH<a214> GLYPH<a215> GLYPH<a216> GLYPH<a217> GLYPH<a218> GLYPH<a219> GLYPH<a220> GLYPH<a221> GLYPH<a222>GLYPH<a223> GLYPH<a224> GLYPH<a225>GLYPH<a226> GLYPH<a227> GLYPH<a228>GLYPH<a229> GLYPH<a230> GLYPH<a231> GLYPH<a232> GLYPH<a233> GLYPH<a234> GLYPH<a235> GLYPH<a236> GLYPH<a237> GLYPH<a238> GLYPH<a239> GLYPH<a240> GLYPH<a241> GLYPH<a242> GLYPH<a243> GLYPH<a244> GLYPH<a245> S$_{I}$ ( ω$_{τ}$ , T, ω$_{t}$ ) and S$_{II}$ ( ω$_{τ}$ , T, ω$_{t}$ ) 2DFT spectra for potassium vapor have been obtained using a multi- dimensional nonlinear spectrometer. Numerical sim- ulation based on the optical Bloch equations repro- duce the experimental spectra giving excellent agree- ment. Purely absorptive spectra are obtained by sum- ming S$_{I}$ ( ω$_{τ}$ , T, ω$_{t}$ ) and S$_{II}$ ( ω$_{τ}$ , T, ω$_{t}$ ). We also experi- mentally isolated Raman coherences by projecting the 2DFT signal along ω$_{T}$ and ω$_{t}$ instead of ω$_{τ}$ and ω$_{t}$ . Fi- nally, the expected distortion of 2DFT spectra due to propagation effect is observed at higher vapor tempera- tures. 2DFT spectroscopy has been proved to be a powerful tool to show interactions and coupling in complex sys- tems, it can also be used to investigate simple atomic and small molecular systems. As we have demonstrated, 2DFT spectroscopy of simple systems can be useful to validate the various techniques and theory for 2DFT spectroscopy. to propagation can then be observed. S$_{I}$ ( ω$_{τ}$ , T, ω$_{t}$ ) spec - tra of potassium vapor at 220 ◦ C and 270 ◦ C are show n in Fig. 7, where the absorbance αL is ∼ 0 . 2 and ∼ 1 . 3 for the D$_{2}$ transition, respectively. At the lower tempera- ture, the diagonal D$_{2}$ feature is a symmetric star shape, while at high temperature it is elongated along the emis- sion photon axis. This change has been predicted [38–40], although the expected change in peak strength ratio is not observed [38]. FIG. 7: (color) Distortion of the peak shapes due to propa- gation effects. Left two panels are the S$_{I}$ ( ω$_{τ}$ , T, ω$_{t}$ ) spectr a of the potassium vapor at 220 ◦ C (top) and 270 ◦ C (bottom) . Right two panels are the zoomed pictures of the diagonal peaks corresponding to the D 2 transition at 220 ◦ C (top) an d 2 70 ◦ C (bottom). Acknowledgments The authors thank T. Asnicar and H. Green for techni- cal assistance. The financial support is provided by NIST and the National Science Foundation’s Physics Frontier Center Program. S.T.C. is a staff member in the NIST Quantum Physics Division. sions (Oxford Science Publications, Oxford, 1987). [1] I. Bloch, J. Dalibard, and W. Zwerger, Rev. Mod. Phys. 80 , 885 (2008). [2] M. Fleischhauer, A. Imamoglu, and J. Marangos, Rev. Mod. Phys. 77 , 633 (2005). [3] A. Flusberg, T. Mossberg, R. Kachru, and S. R. Hart- mann, Phys. Rev. Lett. 41 , 305 (1978). [4] O. Kinrot and Y. Prior, Phys. Rev. A 50 , R1999 (1994). [14] Y. Tanimura and S. Mukamel, J. Chem. Phys. 99 , 9496 (1993). [15] M. Cho, Chem. Rev. 108 , 1331 (2008). [16] M. D. Fayer, D. E. Moilanen, D. Wong, D. E. Rosen- feld, E. E. Fenn, and S. Park, Acc. Chem. Res. 42 , 1210 (2009). [17] T. Elsaesser, Acc. Chem. Res. 42 , 1220 (2009). [18] N. S. Ginsberg, Y.-C. Cheng, and G. R. Fleming, Acc. Chem. Res. 42 , 1352 (2009). [19] S. T. Cundiff, T. Zhang, A. D. Bristow, D. Karaiskaj, and X. Dai, Acc. Chem. Res. 42 , 1423 (2009). [5] O. Kinrot and Y. Prior, Phys. Rev. A 51 , 4996 (1995). [6] J. Golub and T. Mossberg, J. Opt. Soc. Am. B 3 , 554 (1986). [7] F. Shen, J. Gao, A. A. Senin, C. J. Zhu, J. R. Allen, Z. H. Lu, Y. Xiao, and J. G. Eden, Phys. Rev. Lett. 99 , 143201 (2007). [20] A. D. Bristow, D. Karaiskaj, X. Dai, T. Zhang, C. Carls- son, K. R. Hagen, R. Jimenez, and S. T. Cundiff, Rev. Sci. Instrum. 80 , 073108 (2009). [21] L. Yang, T. Zhang, A. D. Bristow, S. T. Cundiff, and S. Mukamel, J. Chem. Phys. 129 , 234711 (2008). [22] A. D. Bristow, D. Karaiskaj, X. Dai, and S. T. Cundiff, Opt. Express 16 , 18017 (2008). [23] A. D. Bristow, D. Karaiskaj, X. Dai, R. P. Mirin, and S. T. Cundiff, Phys. Rev. B 79 , 161305(R) (2009). [24] K. W. Stone, K. Gundogdu, D. B. Turner, X. Li, S. T. Cundiff, and K. A. Nelson, Science 324 , 1169 (2009). [25] L. Yang and S. Mukamel, Phys. Rev. Lett. 100 , 057402 (2008). [8] V. Lorenz and S. Cundiff, Phys. Rev. Lett. 95 , 163601 (2005). [9] V. O. Lorenz, S. Mukamel, W. Zhuang, and S. T. Cundiff, Phys. Rev. Lett. 100 , 013603 (2008). [10] P. Tian, D. Keusters, Y. Suzaki, and W. Warren, Science 300 , 1553 (2003). [11] J. C. Vaughan, T. Hornung, K. W. Stone, and K. A. Nelson, J. Phys. Chem. A 111 , 4873 (2007). [12] P. F. Tekavec, G. A. Lott, and A. H. Marcus, J. Chem. Phys. 127 , 214307 (2007). [13] R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimen-