The University of Tokyo (Yasunobu Nakamura)

Nippon Telegraph and Telephone Corporation

Tokyo Medical and Dental University

Tohoku University

Quantum repeater is an indispensable technology for constructing long-distance secure photonic network in the presence of finite loss in optical fibers. To distribute entanglement between remote parties, entanglement swapping operations at quantum repeater nodes in between are required. To this end, we developed technologies based on superconducting quantum circuits hybridized with other quantum degrees of freedom. Our project consisted of the following two subthemes.

**Subtheme 1**: Superconducting circuits for entanglement manipulation- The rapid progress on quantum information processing technology in superconducting circuits makes it promising for high-fidelity entanglement manipulation demanded in the quantum repeater applications. The recent improvement of the coherence time beyond 100 μs has boosted up the achievable gate fidelity. It also allows high-fidelity quantum nondemolition readout of qubits with an aid of low-noise devices in the quantum limit, such as Josephson parametric amplifiers. In the circuit quantum electrodynamics (circuit QED) architecture consisting of qubits and resonators, we demonstrated various novel tools for microwave quantum optical applications.
**Subtheme 2**: Quantum interface between superconducting circuits and other quantum mechanical systems- Superconducting circuits work fine in the microwave domain. However, all the excellent properties are lost in the optical domain. Therefore, to interface quantum information in the superconducting circuits with that in the optical communication network and vice versa, a quantum transducer based on other quantum degrees of freedom is needed. The additional degrees of freedom need to couple with both microwave and optical modes coherently. The candidates include spin ensembles in solid, phonons in nanomechanics, and magnons in ferromagnets, for example. In such hybrid quantum systems, advantages from each system can be exploited to achieve the functionality.
- Quantum interface between superconducting circuits and other quantum mechanical systems is also useful for constructing quantum networks between superconducting quantum information processors as well as for quantum measurements with ultimate sensitivity. Our goal is to establish basic concepts and technologies versatile and robust enough for all such applications.

**Fig. 1**Superconducting circuits and quantum transducers for quantum interface between microwave and optical domains.

Josephson parametric amplifires and their applicaions

Josephson parametric amplifier (JPA) is a versatile tool for microwave quantum optics. We characterized the squeezed vacuum generated by a flux-driven JPA [1] as well as demonstrated the path entanglement produced by combining the squeezed vacuum and a vacuum state in a beam splitter [2]. We also used a JPA for dispersive readout of a superconducting qubit and observed quantum jumps by monitoring the qubit continuously [3]. We further operated the JPA at the parametric oscillation threshold. Then, the device worked as a phase-sensitive threshold detector and allowed us to implement binary-phase-shifted-keying demodulation of a weak microwave signal as well as fast qubit readout [4].

- [1] L. Zhong et al., New J. Phys.
**15**, 125013 (2013). - [2] E. P. Menzel et al., Phys. Rev. Lett.
**109**, 250502 (2012). - [3] Z. R. Lin et al., Appl. Phys. Lett.
**103**, 132602 (2013). - [4] Z. R. Lin et al., Nature Commun.
**5**, 4480 (2014).

Microwave single photon detector

Impedance matching is a key concept in microwave engineering as well as in quantum transducers. We proposed and implemented an impedance-matched Λ-type three-level system in a driven circuit-QED architecture [1, 2]. The Λ-system absorbs an incoming microwave photon with 100% efficiency. The subsequent high-fidelity qubit readout signals the detection of a single photon [3]. We achieved a quantum efficiency of 66±6 % [4] and expect further improvement with a better coherence time of the qubit used in the detector.

- [1] K. Koshino et al., Phys. Rev. Lett.
**111**, 153601 (2013). - [2] K. Inomata et al., Phys. Rev. Lett.
**113**, 063604 (2014). - [3] K. Koshino et al., Phys. Rev. A
**91**, 043805 (2015). - [4] K. Inomata et al., Nature Commun.
**7**, 12303 (2016).

Quantum memory using an ensemble of NV centers in diamond

One approach to hybrid quantum systems is to use an ensemble of non-interacting spins in a bulk crystal. We demonstrated storage and retrieval of quantum states of a superconducting qubit into and out of a spin ensemble in diamond [1,2] as well as found a dark state involving collective spin excitations [3]. As an alternative spin ensemble, we also investigated Er ions doped in yttrium silicate and detected electron spin resonance via a SQUID [4].

- [1] X. Zhu et al., Nature
**478**, 221 (2011). - [2] S. Saito et al., Phys. Rev. Lett.
**111**, 107008 (2013). - [3] X. Zhu et al., Nature Commun.
**5**, 3524 (2014). - [4] H. Toida et al., Appl. Phys. Lett.
**108**, 052601 (2016).

Coherent control of magnons in a ferromagnetic crystal

In contrast to paramagnetic spin ensembles, spins in ferromagnetic materials are high-density and strongly interacting each other by the exchange interaction. Therefore, only collective spin excitations such as long-wavelength spin waves remain as low-energy excitations. Magnons are quanta of such collective modes. We used a single-crystalline sphere of yttrium iron garnet and coherently coupled the ferromagnetic resonance mode, i.e., a spatially uniform spin precession mode in the sphere, to an electromagnetic mode in a microwave cavity [1]. Furthermore, we put a superconducting qubit in the cavity together with the YIG sphere. The qubit and the single-magnon excitation in the sphere were coupled coherently via the virtual excitation of microwave photons in the cavity. We observed Rabi splitting of the qubit induced by the magnon vacuum in the millimeter-sized ferromagnetic sphere containing ~10^{18} net electron spins [2,3]. Our work initiated the new direction of quantum magnonics.

- [1] Y. Tabuchi et al., Phys. Rev. Lett.
**113**, 083603 (2014). - [2] Y. Tabuchi et al., Science
**349**, 405 (2015). - [3] Y. Tabuchi et al., C. R. Physique
**17**, 729 (2016).

Optomagnonics

Following the successful coherent coupling of magnons and a superconducting qubit, we studied interaction between magnons in YIG crystals and optical light at the communication wavelength. We demonstrated coherent bidirectional conversions of light and microwaves in a classical sense: Microwave-driven magnons are converted to optical signals via Faraday effect, while the optically generated magnons via stimulated magnon Brillouin scattering are converted into microwaves through a cavity mode [1]. We also developed cavity optomagnonics using a whispering-gallery resonator mode on the YIG sphere, where the chirality of the light mode plays an interesting role to produce nonreciprocity in the magnon Billouin scattering [2]. An issue remaining in those experiments is the weak interaction between the magnons and the light. An enhanced coupling strength is needed for reaching a higher efficiency for the quantum transduction.

- [1] R. Hisatomi et al., Phys. Rev. B
**93**, 174427 (2016). - [2] A. Osada et al., Phys. Rev. Lett.
**116**, 223601 (2016).

Hybrid quantum system with nanomechanics

As another candidate for a quantum transducer between microwave and optics, we investigated a nanomechanical system consisting of a silicon-nitride membrane and its hybridization with a microwave cavity. We developed a novel 3D cavity architecture to minimize the parasitic capacitance and enhance the electromechanical coupling strength. Using the device, we demonstrated electromechanical sideband cooling of the membrane mode to the ground state, i.e., the average phonon occupancy ~0.5 [1].

- [1] A. Noguchi et al., New J. Phys.
**18**, 103036 (2016).

Hybrid quantum systems combining various quantum systems will open many applications in quantum information science. For example, they will remove barriers across a large difference in energy scales, such as the one between superconducting quantum circuits and optical quantum networks. In our project, we developed numerous concepts and techniques related to hybrid quantum systems. The concept of impedance matching is fundamental and ubiquitous in efficient quantum state transfer from one system to the other. It works quite well in hybrid systems within the microwave domain where one can easily obtain strong coupling strengths. The demonstrations of a microwave single photon detector and coherent coupling between a qubit and magnon excitations in a ferromagnetic sphere are good examples. On the other hand, interfacing with the optical domain is not straightforward. The energy difference more than 10,000 times has to be parametrically overcome, while the coupling strength is typically very small. Explorations of better hybrid systems with an enhanced coupling strength are ongoing. Nevertheless, the concepts and techniques developed in our project will be useful in future works.