1. Refractive index enhancement with vanishing absorption in an atomic vapor Deniz Yavuz, Nick Proite, Brett Unks, Tyler Green Department of Physics, University of Wisconsin Madison, WI

2. Key Question  How much can we increase the refractive index, n, of an atomic medium while maintaining vanishing absorption?  When an electromagnetic wave is in a medium with refractive index n, the wavelength of the wave is /n. As a result the resolution is increased.  Over the last two decades, there has been a growing interest in techniques that modify the optical properties of a medium.

3.  A laser beam tuned close to a two level resonance can experience a large refractive index. However, such a large index is accompanied by large absorption. Two-level atoms atomic medium  It was first pointed out by Scully that using atomic coherence in a three level system, one can obtain an enhanced refractive index with vanishing absorption. M. O. Scully, Phys. Rev. Lett. 67, 1855 (1991); Phys. Rev. Lett. 69, 1360 (1992). M. Fleischhauer et al., Phys. Rev. A 46, 1468 (1992). U. Rathe et al., Phys. Rev. A 47, 4994 (1993). A. S. Zibrov et al., Phys. Rev. Lett. 76, 3935 (1996).

4. +  The interference between an absorptive resonance and an amplifying resonance can result in a large refractive index with vanishing absorption. M. Fleischhauer et. al. Phys. Rev. A 46, 1468 (1992). Multiple two-level scheme  + D. D. Yavuz, Phys. Rev. Lett. 95, 223601 (2005).

5. Susceptibility curves Susceptibility (a. u.) Frequency/  real part,  imaginary part,   How much can the refractive index be increased by using this approach? D. D. Yavuz, Phys. Rev. Lett. 95, 223601 (2005). P. Anisimov and O. Kocharovskaya, PQE 2008, invited talk.

6. Noise  Although the beam experiences vanishing absorption, the beam becomes noisier as it travels through the index enhanced medium. index-enhanced medium n EpEp E p +noise L D. D. Yavuz and N. A. Proite, Phys. Rev. A 78, 053811 (2008).

7. Rb vapor cell E c1 EpEp E c2 probe detection 85 Rb pump 87 Rb pump EpEp E c1 optical pump F=1 F=2 16 GHz 87 Rb EpEp E c2 optical pump F=2 F=3 85 Rb Experimental-setup

9. Resonance tuning Frequency (MHz) intensity 87 Rb 85 Rb Frequency (MHz)  By changing the frequencies of the control lasers, we can tune the position of the gain and absorption resonances for the probe beam.

10. pinhole transmission intensity refractive index,  n  10 -6 -0.2 0.2 Frequency (MHz) Refractive index enhancement with vanishing absorption N. A. Proite, B. E. Unks, J. T. Green, and D. D. Yavuz, Phys. Rev. Lett. 101, 147401 (2008). absorption, gain refractive index

11. 10 11 10 13 10 15 10 17 10 -6 10 -4 10 -2 1 Density (atoms/cm 3 ) Susceptibility,   How large of a refractive index can we obtain in Rb? Maximum refractive index hot vapor ultra-cold cloud n=1.3 n=3.2 P. Anisimov and O. Kocharovskaya, PQE 2008, invited talk.

12. 7 mm photograph of our MOT 10 9 Rb atoms at a temperature of 50  K. EpEp atomic cloud E c1,E c2 intensity pattern refractive index pattern I(x) n(x) an all optical device

13. Conclusions and outlook  We have demonstrated a new approach for increasing the refractive index of a medium while maintaining vanishing absorption of the beam.  Our first goal will be to obtain a refractive index that is large enough to be of practical importance (n=2) inside Rb vapor.  Our ultimate goal is to obtain n=10 with vanishing absorption in a gas and integrate such an approach to a practical optical microscope.  We expect applications of our technique in various fields including quantum computing and all-optical information processing.