**In quantum computing, dense atomic clouds can efficiently map “flying” photonic qubits onto stationary qubits. The absorbed photons, however, end up encoded in delocalized atomic excitations which impede local processing. A Team of researchers from Innsbruck, Oxford, Singapore and Harvard came up with a new concept – a so-called “Quantum Spin Lens” – which could focus delocalized excitations onto single atoms. This would allow the manipulation and processing of “flying” qubits using the well-developed quantum computing toolbox.**

Due to the robustness against decoherence and their negligible scattering rate, photons are perfect candidates for fast and reliable long-distance quantum communication. In photonic quantum networks, ‘flying’ qubits can be mapped onto stationary (atomic) qubits using a dense cloud of atoms, which absorbs photons with high probability. The absorbed photon, however, ends up encoded in an atomic excitation which is delocalized over the atomic ensemble. The spatial extent of the delocalized qubit impedes local operations required for further manipulation and processing of the qubit. “Ultimately, the goal is to map photonic qubits with high efficiency onto single atoms, such that the well-developed quantum computing toolbox with single and two-qubit gates becomes available – as demonstrated e.g. with laser excited Rydberg atoms or ions” explains Alexander Glätzle from the IQOQI Innsbruck who recently moved to the University of Oxford.

The researchers, including Alexander Glätzle, Kilian Ender and Peter Zoller, have now proposed an elegant solution for coherently converting delocalized qubits into localized ones in an array of atoms. They identified spin Hamiltonians —implementable, for example, through suitable laser fields applied to an ensemble of Rydberg atoms — which act as a ‘quantum spin lens’. This is of immediate interest as a novel quantum light-matter interface which has potential applications in coherent quantum spintronic to design and exploit coherent spin transport.

The researchers from Innsbruck, Oxford, Singapore and Harvard design such quantum spin lenses in close analogy to optical lenses: “Typically, optical lenses consist of a transparent material which delays an incident wave front by an amount proportional to the thickness of the lens”, explains Kilian Enders from Peter Zoller’s group. “A light beam passing through the lens can then be collimated to a focal point.” The proposed ‘Quantum Spin Lens’ mimics the refractive material of the lens by imprinting a position dependent energy shift on the atomic spins in the atomic ensemble. This allows one to sequentially store flying qubits in an atomic array and to focus them to a quantum register of spatially localized spin qubits represented by single atoms. “Creating such strong and nonlinear interactions between individual photons is a long-standing goal in quantum optics and photonics” says Alexander Glätzle. “The ability to engineer such interactions synthetically would hold profound implications for both fundamental and applied science.”

The physicists present several variants of their lenses, including multifocal ones, where a single delocalized spin excitation is transformed into a state with entanglement between excitations at spatially separated focal points. By adding finite range spin-spin interactions in the atomic ensemble the focusing dynamics will be conditional on the number of initial photons. Thus, an initial quantum superposition state of photons will be laid out in space corresponding to a superposition of spatial spin patterns. This provides a tool to manipulate the individual terms (corresponding to a specific excitation number) in the superposition state by spatially addressing in the atomic medium.