Photon Subtraction by Many-Body Decoherence

We experimentally and theoretically investigate the scattering of a photonic quantum field from another stored in a strongly interacting atomic Rydberg ensemble. Considering the many-body limit of this problem, we derive an exact solution to the scattering-induced spatial decoherence of multiple stored photons, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis reveals a correlated coherence-protection process in which the scattering from one excitation can shield all others from spatial decoherence. We discuss how this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability.

Figure 1

(a) Schematics of the basic setting in which Rydberg spin wave excitations (blue) stored in an ultracold gas interact with secondary Rydberg polaritons formed by propagating photons (red), whose interaction-induced scattering causes decoherence of the stored spin waves. The underlying level scheme through which the initial gate (blue) and secondary source (red) photons are coupled to their respective Rydberg states $|c⟩$ and $|s⟩$ is shown in panel (b). Panel (c) shows the experimental pulse sequence for a complete cycle of storage, interaction, and retrieval stages. The blue and red curves show the gate and source field envelopes, respectively, where the light and dark traces indicate the incident and transmitted intensities. The gray curves show the control field envelopes (not to scale). Panel (d) shows the density matrix ${\rho }_5(x,r,y,r)$ of two stored gate excitations after scattering 5 source photons and illustrates the correlated nature of the associated decoherence process.

Figure 2

Normalized retrieval efficiency as a function of the number ${\overline{\alpha }}_s$ of scattered source photons for different indicated numbers ${\alpha }_g$ of stored gate excitations. The theoretical prediction of Eq. (5) (solid lines) is fitted to the experimental data (dots) with a common scattering probability of $p=0.5$ (errors bars showing SEM are smaller than the dots). Retrieval efficiencies are on the order of ${\eta }_R\sim 0.2$ for all measured data. The dashed lines indicate the expected scaling without decoherence protection.

Figure 3

Number ${\overline{\alpha }}_g$ of retrieved gate photons as a function of the number ${\alpha }_g$ of initially stored excitations for different incident source photon numbers ${\alpha }_s$. The measurements (dots) agree well with the prediction of Eq. (5) (solid lines) for the same value of $p$ as in Fig. 2. The black dashed line shows the prediction of Eq. (5) for $p=1$ and large source field intensity ${\alpha }_s\gg 1$, which are the ideal conditions for single-photon subtraction.

Figure 4

Single-photon subtraction efficiency, ${\mathcal{F}}_{\mathrm{opt}}$, for a coherent gate field with an average number of photons ${\alpha }_g=2$. The blue line shows the optimal efficiency of the current mechanism based on single-photon decoherence for perfect storage and retrieval, while the red dashed line shows the corresponding performance of photon subtraction by saturable absorption [54].