Collective optical effects of ultra-cold Rydberg atoms in optical cavities

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The project aims at studying the influence of strong intermediate-range dipole-dipole interactions of Rydberg atoms on the collective external and internal dynamics of ultracold atoms inside an optical cavity. Atoms in cavities are known to self-organize in periodic structures when they are illuminated from the side of the cavity by laser light. The self-organization process is triggered by the light which is collectively scattered into the cavity, recycled by the cavity mirrors, and mechanically back acts on the atoms. This cavity-mediated interaction between the atoms is infinite-range. New physics comes into play by the additional interactions of Rydberg atoms. At intermediate distance dipole-dipole interactions between Rydberg atoms suppress the excitation of more than one Rydberg atom, i.e. Rydberg blockade. Thus, within a Rydberg bubble light scattering is a highly nonlinear process, and scattering of light into the cavity is a collective phenomenon of the individual Rydberg bubbles rather than of the individual atoms. We will study the effect of Rydberg blockade on the emerging self-organized structures and on the intensity and phase of the light scattered into the cavity. Furthermore, we will study if the additional interaction can lead to new stable phases of the atom cloud, depending on the size of the blockade radius and of the atom cloud as a whole.The internal dynamics is governed by the fact that the cavity mode is near-resonant to the transition from the atomic ground state to an intermediate level, with collectively enhanced coupling. The intermediate state in turn is coupled to a Rydberg state by a strong external coupling laser field. For large detuning from the intermediate level, the dynamics is that of an effective two-level system, where the coupling between the atoms and the cavity is mediated by a two-photon transition. The coupling strength can thus be tuned by the intensity of the coupling laser, whereas the cavity is only resonant to the photons of the lower transition. This fact is remarkable and makes a difference to the usual case where the cavity field is resonant to a single photon transition. Using two-photon transitions the coupling strength can be externally controlled both in time and in space, which is a very interesting feature for applications in quantum technology, as for instance quantum memories. We will lay the fundament for such future applications by demonstrating strong collective coupling of cavity light and atomic two-photon transitions between the ground state and Rydberg states. This will be achieved by observing vacuum Rabi oscillations using pulsed excitation schemes.