Figure 1

The interference of an absorptive resonance and an amplifying resonance can lead to an enhanced refractive index with vanishing absorption. (a) The most straightforward way to achieve such an interference. Because of various difficulties, the scheme in (a) is not practical (see text for details). (b) An equivalent scheme that we experimentally demonstrate in this work. With an atom starting in the ground state $|g⟩$, a Raman transition involves absorption of one photon and emission of another photon of different frequency such that the two-photon resonance condition is satisfied. By changing the order at which the probe laser, $E_p$, is involved in the process, such a Raman resonance can be made absorptive or amplifying. (c) shows the real part, ${\chi }^{\prime }$, and the imaginary part of the susceptibility, ${\chi }^{\prime \prime }$, as a function of frequency. Here, we take the two resonances to be of equal strength with a width of 0.1 MHz and assume the spacing between resonances to be 0.2 MHz.Reuse & Permissions

Figure 2

Simplified experimental setup and the energy level diagram (not to scale) for the two isotopes. The experiment is performed in a magnetically shielded, natural abundance Rb vapor cell. Two optical pumping lasers optically pump the two species to the $F=2$ hyperfine state in the ground electronic state. With the atoms optically pumped, three experimental laser beams, $E_p$, $E_{c1}$, and $E_{c2}$ drive two Raman transitions, one in each isotope. The interference of these two resonances lead to enhanced refractive index with vanishing absorption. All three laser beams are far-detuned from the single-photon electronic resonance.Reuse & Permissions

Figure 3

The peak intensity of the probe laser measured after the cell as a function of the frequency of the probe laser. With the control lasers, we induce a gain resonance and an absorption resonance on the probe laser. When the probe laser is resonant with the $F=2\to F=1$ Raman transition in ${}^{87}\mathrm{Rb}$, the beam experiences gain. When it is resonant with $F=2\to F=3$ Raman transition in ${}^{85}\mathrm{Rb}$, the beam experiences loss. By changing the frequencies of the control lasers, we can tune each of the Raman resonances. In plots (a),(b),(c), and (d), the two resonances are spaced by 0.8, 0.4, $-0.4$, and $-0.8\mathrm{MHz}$, respectively.Reuse & Permissions

Figure 4

Experimental demonstration of the refractive index enhancement at the point of vanishing absorption. (a) The peak intensity of the probe beam and (b) the transmission through a pinhole as a function of probe laser frequency. The transmission through the pinhole changes as a result of focusing or defocusing of the beam due to spatial dependence of the refractive index. The pinhole transmission and therefore the refractive index is maximized at the point of vanishing absorption. The solid line in (a) is a fit that assumes the two resonances to be Lorentzian. The solid line in (b) is the calculated refractive index change at the peak of the spatial profile based on the fit of (a). We see good qualitative agreement between pinhole transmission data and our calculation.Reuse & Permissions