We demonstrate that yttrium iron garnet microspheres support optical whispering gallery modes similar to those in non-magnetic dielectric materials. The direction of the ferromagnetic moment tunes both the resonant frequency via the Voigt effect as well as the degree of polarization rotation via the Faraday effect. An understanding of the magneto-optical coupling in whispering gallery modes, where the propagation direction rotates with respect to the magnetization, is fundamental to the emerging field of cavity optomagnonics.

We demonstrate the long range strong coupling of magnetostatic modes in spatially separated ferromagnets mediated by a microwave frequency cavity. Two spheres of yttrium iron garnet are embedded in the cavity and their magnetostatic modes probed using a dispersive measurement technique. We find they are strongly coupled to each other even when detuned from the cavity modes. We investigate the dependence of the magnet-magnet coupling on the cavity detuning ∆, and find a 1/∆ dependence also characteristic of cavity-coupled superconducting qubits. Dark states of the coupled magnetostatic modes of the system are observed, and ascribed to mismatches between the symmetries of the modes and the drive field.

The big challenge in quantum computing is to realize scalable multi-qubit systems with cross-talk–free addressability and efficient coupling of arbitrarily selected qubits. Quantum networks promise a solution by integrating smaller qubit modules to a larger computing cluster. Such a distributed architecture, however, requires the capability to execute quantum-logic gates between distant qubits. Here we experimentally realize such a gate over a distance of 60 meters. We employ an ancillary photon that we successively reflect from two remote qubit modules, followed by a heralding photon detection, which triggers a final qubit rotation. We use the gate for remote entanglement creation of all four Bell states. Our nonlocal quantum-logic gate could be extended both to multiple qubits and many modules for a tailor-made multi-qubit computing register.

The long-lived, efficient storage and retrieval of a qubit encoded on a photon is an important ingredient for future quantum networks [1,2]. Although systems with intrinsically long coherence times have been demonstrated [3][4][5][6][7][8], the combination with an efficient light-matter interface [9][10][11][12][13][14] remains an outstanding challenge. In fact, the coherence times of memories for photonic qubits are currently limited to a few milliseconds [15,16]. Here we report on a qubit memory based on a single atom coupled to a highfinesse optical resonator. By mapping and remapping the qubit between a basis used for light-matter interfacing and a basis which is less susceptible to decoherence, a coherence time exceeding 100 ms has been measured with a time-independant storage-andretrieval efficiency of 22%. This demonstrates the first photonic qubit memory with a coherence time that exceeds the lower bound needed for teleporting qubits in a global quantum internet.Photons are convenient carriers for encoding both classical and quantum information. To transport a pulse of light between the most distant locations on earth, it has to travel about 20,000 km, which takes at least 66 ms. For future quantum networks allowing for distributed quantum computations, the exchange of quantum states between network nodes is indispensable. In principle, it can be achieved by using single photons, but unavoidable losses in glass fibres in combination with the impossibility to amplify a quantum state renders the direct distribution of quantum states over long distances extremely inefficient. A possible solution is the teleportation of qubits between the end nodes of a quantum repeater link [1,17]. While teleportation can be done deterministically, another challenge occurs: as quantum teleportation requires classical communication between the end nodes, the receiver has to preserve its quantum state for at least the time it takes for the classical information to arrive [18]. This establishes the above-mentioned 66 ms as a minimum requirement for global quantum-state distribution.A qubit memory for photons has to combine a lightmatter interface used to efficiently map the qubit between the photon and a material system with the ability to preserve quantum coherence for the duration of storage. It has been shown that neutral atoms are suitable systems for both requirements [19,20] by mapping the photonic qubit onto the atom and end by recreating the photon (upward pointing red wavy arrow). a, In an elementary store-and-retrieve experiment (red area) the qubit dephases within hundreds of microseconds. The dephasing is dominantly caused by magnetic field fluctuations. This is illustrated as the deformation of the Bloch sphere which represents the qubit. The labels |F, mF denote the qubit basis states. b, By temporarily mapping the qubit to a memory basis which is less sensitive to those fluctuations, the rate of dephasing can be drastically reduced (blue area). This allows for a total storage time on the order of tens of millise...

Thorough control of the optical mode of a single photon is essential for quantum information applications. We present a comprehensive experimental and theoretical study of a light-matter interface based on cavity quantum electrodynamics. We identify key parameters like the phases of the involved light fields and demonstrate absolute, flexible, and accurate control of the timedependent complex-valued wave function of a single photon over several orders of magnitude. This capability will be an important tool for the development of distributed quantum systems with multiple components that interact via photons.PACS numbers: 42.50.Dv, 42.50.Pq, 32.80.Qk Single photons are of paramount importance for modern quantum information science. Envisioned applications range from all-optical quantum computation [1, 2] to quantum communication in nonlocal quantum clouds [3, 4]. As all the conceived quantum information protocols involve, in one way or another, interference effects, coherent photons are mandatory for the implementation of these protocols [5,6]. This requirement includes the (relative) coherence within the photon wave packet as well as the (absolute) coherence with respect to a common network reference clock. Full control over amplitude and phase of the photon's temporal mode is a challenge [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23], as is the mode conversion for all regimes from narrow to broad-bandwidth single photons. Meeting these challenges would open up new possibilities like temporal mode matching in multimode quantum networks or information encoding in the optical mode of the photon.Here we exploit the arsenal of cavity quantum electrodynamics (CQED) [24] and demonstrate deterministic mode control over single optical photons. Toward this end, we extend previous models [25][26][27][28][29][30][31][32] and take into account the full energy-level structure of the atom that serves as photon emitter and photon receiver in a highfinesse optical resonator. We find a surprisingly strong frequency dependence of the process efficiency with a pronounced minimum that originates from destructive interference of transition amplitudes. We also show that the emission efficiency is not a reliable measure for photon coherence. We moreover shape the photon phase, demonstrate the mode selectivity of photon absorption, and stretch and compress a given single-photon wave packet by 3 orders of magnitude. All these achievements are realized in combination with a convenientto-implement coherence-testing method that outputs the time-dependent complex-valued temporal mode function with minimal resources [33]. As both the amplitude and the phase of the temporal mode are determined with respect to a commonly accepted reference, a phase-locked laser, we are now in a position to certify the (absolute) coherence of a network photon.Our system uses the quantum memory scheme described in Ref. [34] and therefore all the following results are also valid for single photons encoding a qubit in their polarization degr...