Coupling of four-wave mixing and Raman scattering by ground-state atomic coherence

We demonstrate coupling of light resonant to transition between two excited states of rubidium and long-lived ground-state atomic coherence. In our proof-of-principle experiment a nonlinear process of four-wave mixing is used to achieve light emission proportional to independently prepared ground-state atomic coherence. Strong correlations between stimulated Raman-scattering light heralding the generation of ground-state coherence and the four-wave mixing signal are measured and shown to survive the storage period, which is promising in terms of quantum memory applications. The process is characterized as a function of laser detunings.

Figure 1

(a) Configuration of atomic levels and fields we use to realize the four-photon interface, (b) pulse sequence used in the experiment, (c) the central part of the experimental setup demonstrating phase-matching geometry, and (d) trace of the 1-GHz FSR Fabry-Pérot interferometer signal showing the frequency of 4Ph field being different from what one would expect from the closed-loop process. Rows in panel (b) correspond to different beam paths presented in panel (c).

Figure 2

(a, b) Averaged signal intensities (solid lines) with several single realizations (dashed lines), denoted by same colors in panels (a) and (b), demonstrating visible strong correlations. (c) Calculated cross correlation $C\left(t\right)$ between signals of four-photon (4Ph) and two-photon (2Ph) processes.

Figure 3

Joint statistics $P({\mathcal{E}}_{2\mathrm{Ph}},{\mathcal{E}}_{4\mathrm{Ph}})$ together with marginal distributions of registered pulse energies for (a) a short driving time of 200 ns, yield nearly single-mode thermal statistics (note the logarithmic scale in this plot), and (b) a longer driving time of $4\mu \mathrm{s}$ with observable pulse energy stabilization well described by multimode thermal statistics with a mode number $\mathcal{M}$ of 4.1 for 2Ph pulses and 1.6 for 4Ph pulses. Solid curves correspond to fitted thermal distributions.

Figure 4

(a) Scheme of experiment to demonstrate storage of ground-state atomic coherence for $\tau =450$ ns. (b) Measured two-point correlation $C(t_1,t_2)$ between 2Ph and 4Ph signals with average registered signal powers. Off-diagonal elements of the correlation map demonstrate that light fields interact with the same atomic coherence before and after the time delay.

Figure 5

(a) Averaged (over 500 realizations) pulse shapes for the intensities of the 2Ph and the 4Ph signals for a set of single-photon detunings ${\mathrm{\Delta }}_g$ for constant $\delta /2\pi =-50$ MHz and ${\mathrm{\Delta }}_h/2\pi =1500$ MHz, (b) pulses full width at half maximum (FWHM), (c) their energies, and (d) pulse energy correlation between the two processes as a function of the field $a$ single photon detuning ${\mathrm{\Delta }}_g$. Subsequent plots of 2Ph (4Ph) signals in panel (a) are shifted by $120\mu \mathrm{W}$ (40 nW).

Figure 6

Experimental average pulse energies of 2Ph and 4Ph signals as a function of the field $a$ detuning ${\mathrm{\Delta }}_g$ (measured from $F=1\to F^{\prime }=1$ resonance) and the field $b$ detuning $\delta -{\mathrm{\Delta }}_g$ around the two-photon resonance. As we change the field $a$ detuning both the single-photon detuning ${\mathrm{\Delta }}_g$ and the two-photon detuning $\delta$ change accordingly. Dots (squares) represent maxima (minima) of the 4Ph (2Ph) signal, while the $\delta =0$ line indicates the two-photon absorption resonance.

Figure 7

Four-photon signal pulse energy as a function of the detuning ${\mathrm{\Delta }}_h$ (measured from $F=2\to F^{\prime }=2$ resonance) of field $c$ for optimal conditions of other lasers $({\mathrm{\Delta }}_g/2\pi =900$ MHz and $\delta /2\pi =-50$ MHz). Absorption line corresponds to the $F=2$ hyperfine component of the ground state, where the right side of the plot is the red-detuned side. Drop at around ${\mathrm{\Delta }}_h/2\pi =-900$ MHz corresponds exactly to 6.8 GHz detuning between the two 780-nm lasers, or ${\mathrm{\Delta }}_g+{\mathrm{\Delta }}_h=0$.