Free-Space Quantum Electrodynamics with a Single Rydberg Superatom

The interaction of a single photon with an individual two-level system is the textbook example of quantum electrodynamics. Achieving strong coupling in this system has so far required confinement of the light field inside resonators or waveguides. Here, we demonstrate strong coherent coupling between a single Rydberg superatom, consisting of thousands of atoms behaving as a single two-level system because of the Rydberg blockade, and a propagating light pulse containing only a few photons. The strong light-matter coupling, in combination with the direct access to the outgoing field, allows us to observe, for the first time, the effect of the interactions on the driving field at the single-photon level. We find that all our results are in quantitative agreement with the predictions of the theory of a single two-level system strongly coupled to a single quantized propagating light mode.

Popular Summary

Interactions between particles of light (photons) and objects that emit those photons is fundamental in both nature and technology. Vision, photosynthesis, and even high-speed transfer of data across the Internet depend on these exchanges. The fundamental processes involved—absorption and emission—happen on the level of individual photons interacting with the most basic elements of matter: atoms, molecules, or even artificial atoms. This interaction strength can be boosted by confining the light in an optical resonator or a waveguide, which has enabled the observation and even manipulation of quantized light fields. Here, we present a free-space system interacting so strongly with a few photons that the absorption and re-emission of a single photon is measurable, without the need for any light-confining structures.

Our system is made of approximately 10,000 atoms acting as a single superatom thanks to the strong interaction that arises when the atoms are driven to a highly excited (Rydberg) state. We study the coherent interaction of this single two-level system coupled to a single propagating light mode both as Rabi oscillations between the two levels of the superatom and as a periodic modulation of the light field. In particular, we study how the absorption and stimulated emission of single photons by the superatom results in photon-photon correlations in the transmitted light over multiple Rabi cycles.

It is straightforward to scale our system up to complex arrangements of multiple superatoms, which paves the way toward quantum optical networks and strongly correlated states of light and matter.

Figure 1

Experimental setup and level scheme. (a) An ensemble of laser-cooled atoms is confined within a blockade volume using an optical dipole trap. Single-photon counting modules (SPCMs) are used to detect the light that interacts with the atoms, while a multichannel plate (MCP) detects the Rydberg atoms after ionization. (b) A few-photon probe field (red) and a strong control field (blue) couple the single-atom ground state $|g⟩$ to a Rydberg state $|r⟩$. Their respective Rabi frequencies are $g_0\sqrt{{\mathcal{R}}_{\mathrm{in}}}$ and $\mathrm{\Omega }$, where $g_0$ is the single-atom coupling constant for the probe field and ${\mathcal{R}}_{\mathrm{in}}$ is the photon rate. (c) Because of the Rydberg blockade, the whole ensemble collectively behaves like a two-level system with many-body states $|G⟩$ and $|W⟩$, including a loss channel to a set of collective dark states ${\{|D_i⟩\}}_{i=1}^{N-1}$.

Figure 2

Time evolution of the photon signal and Rydberg population. (a,b) Time traces of the outgoing probe photon rate (blue points) and Rydberg population (orange points) for input pulses (dashed gray line) with peak photon rates ${\mathcal{R}}_{\mathrm{in}}=12.4\mu {\mathrm{s}}^{-1}$ (a) and ${\mathcal{R}}_{\mathrm{in}}=2.6\mu {\mathrm{s}}^{-1}$ (b), corresponding to a mean number ${\overline{N}}_{\mathrm{ph}}$ of 71.6 and 15.1 photons in the pulse. The Rabi oscillation of the single superatom is visible both in the excited-state population and in the modulation of the transmitted probe light. Solid lines are fits to the data using our model. (c) Difference signal $\mathrm{\Delta }\mathcal{R}(t)$ between the incoming and outgoing pulses (dots) for different input photon rates ${\mathcal{R}}_{\mathrm{in}}$. Each data set is vertically shifted by the corresponding ${\mathcal{R}}_{\mathrm{in}}$. Solid lines are again the result of fitting the full data set with our theory model using a single set of fit parameters. Dashed lines indicate the expected positions of the Rabi oscillation peaks based on the fitted parameters, showing the scaling of the Rabi period with $1/\sqrt{{\overline{N}}_{\mathrm{ph}}}$. Error bars in (a)–(c) are SEM and are smaller than the data points.

Figure 3

Dynamical phase diagram of a driven atom in free space. (Bottom panel) The diagram shows the visibility of Rabi oscillations, defined as ${\max }_{0\le t\le \tau }[{\rho }_{WW}(t)]-{\rho }_{WW}(t=\infty )$, of an ideal ($\mathrm{\Gamma }={\gamma }_D=0$) atom driven by a propagating field. In contrast to cavity QED, the coupling and the decay of photons from the system are not independent in free-space and waveguide QED. For large coupling to the propagating mode ($\lambda =\kappa \tau \gg 1$), the enhanced emission into this mode results in an overdamped system, where the number of photons required to observe Rabi oscillations increases with coupling strength. For $\lambda \ll 1$, a large number of photons is required to drive the system with a $\pi$ pulse, defining a crossover (dashed line) between the regime of damped Rabi oscillations and the weak driving regime at lower mean photon number. For our experiment, we find $\lambda =2.2$. (Top panels) Examples of the variation of the Rydberg population with time for the points indicated in the main diagram.

Figure 4

Correlations of the outgoing probe field. (a,b) Measured two-time correlations $g^{(2)}(t_1,t_2)$ for pulses with ${\mathcal{R}}_{\mathrm{in}}=12.4\mu {\mathrm{s}}^{-1}$ and ${\mathcal{R}}_{\mathrm{in}}=2.5\mu {\mathrm{s}}^{-1}$ corresponding to the time traces in Figs. 2 and 2. (c,d) Corresponding calculated correlation functions using the values of $\kappa$, $\mathrm{\Gamma }$, and ${\gamma }_D$ obtained by fitting the time traces in Fig. 2 and 2. (e,f) Measured (dotted line) and simulated (solid line) $\mathrm{\Delta }{\mathcal{R}}_{\mathrm{in}}$ together with scaled input pulses (dashed gray) for reference.