Ultralow-Power Four-Wave Mixing with Rb in a Hollow-Core Photonic Band-Gap Fiber

We demonstrate extremely efficient four-wave mixing with gains greater than 100 at microwatt pump powers and signal-to-idler conversion of 50% in Rb vapor confined to a hollow-core photonic band-gap fiber. We present a theoretical model that demonstrates such efficiency is consistent with the dimensions of the fiber and the optical depths attained. This is, to our knowledge, the largest four-wave mixing gain observed at such low total pump powers and the first demonstrated example of four-wave mixing in an alkali-metal vapor system with a large ($\sim 30\mathrm{MHz}$) ground state decoherence rate.

Figure 1

Transmission electron microscope image of the cross section of the fiber used in these experiments. Light-induced atomic desorption is used to generate rubidium vapor in the core region, which then interacts with light fields coupled into the core.

Figure 2

Energy-level diagram of the FWM scheme. Pump fields of Rabi frequency ${\Omega }_1$ and ${\Omega }_2$ mix with the signal field $E_s$ and the generated corresponding idler field $E_i$. Pump ${\Omega }_1$ is on resonance, while ${\Omega }_2$ is blue-detuned from the excited state by $\Delta$. The signal field is detuned from the excited state by ${\Delta }^{\prime }$ and thus from the two-photon Raman resonance by $\delta ={\Delta }^{\prime }-\Delta$. This generates an idler field $E_i$ which is detuned from its Raman resonance by $-\delta$.

Figure 3

Experimental setup for the FWM experiments. Pump fields ${\Omega }_1$ and ${\Omega }_2$ are combined with a cross-polarized signal field on a PBS propagate collinearly through the PBGF. The fiber is sealed to two vacuum cells, the leftmost of which contains Rb vapor which enters the core of the fiber and attaches to the fiber walls. The vapor density is controlled by a counterpropagating desorption beam of a chosen duration and power. The signal and idler fields are separated from the pump fields by a PBS and from each other by an etalon.

Figure 4

(a) Probe transmission through the fiber as its frequency is scanned across the D1 line after generating a Rb vapor by desorption. (b) Idler power versus frequency as detected while scanning the probe detuning. (c) Gain experienced by the signal field as a function of detuning.

Figure 5

Probe gain for Rb vapor generated from a 2.5-s desorption pulse. A gain of more than 100 is observed. Inset: At lower gains, the bandwidth can exceed 300 MHz.