We present a detailed beyond-mean-field analysis of a weakly interacting Bose gas in the crossover from three to low dimensions. We find an analytical solution for the energy and provide a clear qualitative picture of the crossover in the case of a box potential with periodic boundary conditions. We show that the leading contribution of the confinement-induced resonance is of beyond-mean-field order and calculate the leading corrections in the three-and low-dimensional limits. We also characterize the crossover for harmonic potentials in a model system with particularly chosen short-and long-range interactions and show the limitations of the local-density approximation. Our analysis is applicable to Bose-Bose mixtures and gives a starting point for developing the beyond-mean-field theory in inhomogeneous systems with long-range interactions such as dipolar particles or Rydbergdressed atoms.
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 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 due to 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.The interaction between a single emitter and individual photons is a fundamental process in nature [1], underlying many phenomena such as vision and photosynthesis as well as applications including imaging, spectroscopy or optical information processing and communication. In the strong coupling limit, where the coherent interaction between a single photon and an individual emitter exceeds all decoherence and loss rates, a single emitter can function as interface between stationary and flying qubits, a central building block for future quantum networks [2,3]. Such a quantum optical node is able to mediate effective photon-photon interactions, thus enabling deterministic all-optical quantum gates [4][5][6].One groundbreaking scheme to achieve strong coupling is the use of electromagnetic (EM) cavities, where the photons are trapped within the finite volume of a high-finesse resonator. The physics of these systems is captured by the seminal Jaynes-Cummings model [7], which has been experimentally realized and extensively studied in atomic cavity quantum electrodynamics (QED) [8] and more recently in circuit QED systems combining on-chip microwave resonators with superconducting two-level systems [9,10]. Achieving a strong interaction between a propagating photon and a single emitter opens the possibility to realize novel quantumoptical devices where atoms process photonic qubits on the fly and facilitate the preparation of non-classical states of light [11]. However, mode matching between the input field and the dipolar emission pattern of the quantum emitter in free space is challenging and has so far limited the achievable coupling strength [12][13][14]. Waveguide QED systems seek to overcome this limitation by transversely confining the propagating EM mode coupled to one or more emitters [15][16][17][18][19][20][21].Here we report on the realization of coherent coupling between a propagating few-photon optical field and a single Rydberg superatom in free space. By exploiting the Rydberg blockade effect in an atomic ensemble [22][23][24][25], which allows at most a single excitation shared among all N constituents, we turn ∼ 10 4 individual ultra...
We report on the experimental observation of nontrivial three-photon correlations imprinted onto initially uncorrelated photons through an interaction with a single Rydberg superatom. Exploiting the Rydberg blockade mechanism, we turn a cold atomic cloud into a single effective emitter with collectively enhanced coupling to a focused photonic mode which gives rise to clear signatures in the connected part of the three-body correlation function of the outgoing photons. We show that our results are in good agreement with a quantitative model for a single, strongly coupled Rydberg superatom. Furthermore, we present an idealized but exactly solvable model of a single two-level system coupled to a photonic mode, which allows for an interpretation of our experimental observations in terms of bound states and scattering states.
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