Tunable Three-Body Loss in a Nonlinear Rydberg Medium

Long-range Rydberg interactions, in combination with electromagnetically induced transparency (EIT), give rise to strongly interacting photons where the strength, sign, and form of the interactions are widely tunable and controllable. Such control can be applied to both coherent and dissipative interactions, which provides the potential for generating novel few-photon states. Recently it has been shown that Rydberg-EIT is a rare system in which three-body interactions can be as strong or stronger than two-body interactions. In this work, we study three-body scattering loss for Rydberg-EIT in a wide regime of single and two-photon detunings. Our numerical simulations of the full three-body wave function and analytical estimates based on Fermi’s golden rule strongly suggest that the observed features in the outgoing photonic correlations are caused by the resonant enhancement of the three-body losses.

Figure 1

(a) Atomic structure: A weak probe, with collectively enhanced single-photon coupling $g$, and a classical field, with Rabi frequency ${\mathrm{\Omega }}_c$, couple the ground state, $|G⟩=|5S_{1/2},F=2,m_F=2⟩$, to the Rydberg state $|S⟩=|82S_{1/2},m_J=1/2⟩$ via an intermediate state $|P⟩=|5P_{3/2},F=3,m_F=3⟩$. (b) Experimental setup: The probe and control beams are overlapped along the propagation axis. After exiting the atomic medium, the probe beam is sent to a generalized Hanbury Brown–Twiss setup to measure the photon correlation functions. (c) Dispersion of polaritons in the limit $\mathrm{\Gamma }\ll |\delta |$, with $\delta /(2\pi )=25\mathrm{MHz}$, ${\delta }_s/(2\pi )=0$, ${\mathrm{\Omega }}_c/(2\pi )=23.5\mathrm{MHz}$, for a homogeneous cloud of length $L=4.2{\sigma }_z$ [15], with ${\omega }_c\equiv {\mathrm{\Omega }}_c^2/4|\mathrm{\Delta }|$ and $k_c\equiv {\omega }_c/v_g\approx g^2/c|\mathrm{\Delta }|$. The black curve is the dark-state branch ($D$), while the blue and green curves are the bright states ($U$ and $L$). The diagram depicts the allowed three-body loss process for three polaritons initially near the EIT resonance at ${\omega }_j=q_j=0$ ($j=1$, 2, 3 labels the three polaritons). ${\omega }_{+}$ is the energy where ${\omega }_D$ and ${\omega }_U$ become approximately flat. (d) Allowed final momenta $q_1$ and $q_2$ for the three-body loss with $q_3=-q_1-q_2$. Only the process depicted in (c) is relevant for ${\delta }_s\approx 0$. For the plotted momenta, there is no two-body loss process allowed because there are no final states with $q_1=0$ or $q_2=0$.

Figure 2

(a)–(c) Measured (a) $g^{(2)}(\tau )$, (b) $g^{(3)}({\tau }_1,{\tau }_2)$, and (c) ${\eta }_3({\tau }_1,{\tau }_2)$ for the experimental parameters indicated in the text with $\delta /(2\pi )=15$ and ${\delta }_s/(2\pi )=-2\mathrm{MHz}$, where ${\eta }_3(0,0)<0$. (d)–(f) Measured (d) $g^{(2)}(\tau )$, (e), $g^{(3)}({\tau }_1,{\tau }_2)$, and (f) ${\eta }_3({\tau }_1,{\tau }_2)$ for $\delta /(2\pi )=22.5$ and ${\delta }_s/(2\pi )=2\mathrm{MHz}$, where ${\eta }_3(0,0)>0$.

Figure 3

(a)–(c) Experimental data of the second-order $g^{(2)}(0)$, third-order $g^{(3)}(0,0)$, and connected ${\eta }_3(0,0)$ correlation functions with ${\mathrm{\Omega }}_c/(2\pi )=23.5\pm 1.5\mathrm{MHz}$, for a cloud with $\mathrm{OD}=37\pm 4$ and ${\sigma }_z=42\pm 4\mu \mathrm{m}$. (d)–(f) Numerical simulations for the same correlation functions. Parameters used for the simulations are $\mathrm{OD}=37$, ${\mathrm{\Omega }}_c/2\pi =25\mathrm{MHz}$, $\mathrm{\Gamma }/2\pi =7\mathrm{MHz}$, $\gamma /2\pi =0.3\mathrm{MHz}$, and ${\sigma }_z=40\mu \mathrm{m}$. Regions with ${\eta }_3(0,0)>0$ indicate excess of three-body loss with respect to two-body loss. The dashed lines indicate enhanced three-body loss predicted by Fermi’s golden rule calculation (see text).

Figure 4

Lowest-order diagrams that contribute to three-body loss. The black lines indicate polaritons in the dark branch, and the blue lines indicate polaritons scattered to the upper-bright branch. Dotted-wiggly lines indicate the effective pairwise interactions. We use the full propagator for the $S$ states in the virtual state (black-arrowed line), which includes contributions from all branches. Additionally, five similar diagrams (total of six) for both (a)–(b) are obtained by permuting inputs and outputs.