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Millimeter-wave superconducting devices offer a platform for quantum experiments at temperatures above 1 K, and new avenues for studying light-matter interactions in the strong coupling regime. Using the intrinsic nonlinearity associated with kinetic inductance of thin film materials, we realize four-wave mixing at millimeter-wave frequencies, demonstrating a key component for superconducting quantum systems. We report on the performance of niobium nitride resonators around 100 GHz, patterned on thin (20-50 nm) films grown by atomic layer deposition, with sheet inductances up to 212 pH/ and critical temperatures up to 13.9 K. For films thicker than 20 nm, we measure quality factors from 1-6×10 4 , likely limited by two-level systems. Finally we measure degenerate parametric conversion for a 95 GHz device with a forward efficiency up to +16 dB, paving the way for the development of nonlinear quantum devices at millimeter-wave frequencies.For superconducting quantum circuits, the millimeterwave spectrum presents a fascinating frequency regime between microwaves and optics, giving access to a wider range of energy scales, and lower sensitivity to thermal background noise due to higher photon energies. Many advances have been made refining microwave quantum devices [1,2], typically relying on ultra-low temperatures in the millikelvin range to reduce sources of noise and quantum decoherence. Using millimeter-wave photons as building blocks for superconducting quantum devices offers transformative opportunities by allowing quantum experiments to be run at liquid Helium-4 temperatures, allowing higher device power dissipation and enabling large scale direct integration with semiconductor devices [2]. Millimeter-wave quantum devices could also provide new routes for studying strong-coupling light-matter interactions in this frequency regime [3][4][5][6][7], and present new opportunities for quantum-limited frequency conversion and detection [8,9].Recent interest in next-generation communication devices [10, 11] has led to important advances in sensitive millimeter-wave measurement technology around 100 GHz. Realizing quantum systems at these frequencies however requires both the demonstration of lowloss components -device materials with low absorption rates [12][13][14] and resonators with long photon lifetimes [15-20] -and most importantly, elements providing nonlinear interactions, which for circuit quantum optics can be realized with four-wave mixing Kerr terms in the Hamiltonian. One approach commonly used at microwave frequencies relies on aluminum Josephson junctions [2], which yield necessary four-wave mixing at low powers. However to avoid breaking Cooper pairs with high-frequency photons, devices at millimeter-wave frequencies are limited to materials with higher superconducting critical temperatures (T c ). Higher T c junctions have been implemented as high-frequency mixers for millimeter-wave detection [9,21,22], and ongoing efforts are improving losses for quantum applications [23,24].Kinetic inductance (KI)...

Interactions are essential for the creation of correlated quantum many-body states. While twobody interactions underlie most natural phenomena, three-and four-body interactions are important for the physics of nuclei [1], exotic few-body states in ultracold quantum gases [2], the fractional quantum Hall effect [3], quantum error correction [4], and holography [5,6]. Recently, a number of artificial quantum systems have emerged as simulators for many-body physics, featuring the ability to engineer strong interactions. However, the interactions in these systems have largely been limited to the two-body paradigm, and require building up multi-body interactions by combining two-body forces. Here, we demonstrate a pure N-body interaction between microwave photons stored in an arbitrary number of electromagnetic modes of a multimode cavity. The system is dressed such that there is collectively no interaction until a target total photon number is reached across multiple distinct modes, at which point they interact strongly. The microwave cavity features 9 modes with photon lifetimes of ∼ 2 ms coupled to a superconducting transmon circuit, forming a multimode circuit QED system with single photon cooperativities of ∼ 10 9 . We generate multimode interactions by using cavity photon number resolved drives on the transmon circuit to blockade any multiphoton state with a chosen total photon number distributed across the target modes. We harness the interaction for state preparation, preparing Fock states of increasing photon number via quantum optimal control pulses acting only on the cavity modes. We demonstrate multimode interactions by generating entanglement purely with uniform cavity drives and multimode photon blockade, and characterize the resulting two-and three-mode W states using a new protocol for multimode Wigner tomography.

The millimeter wave (mm-wave) frequency band provides exciting prospects for quantum science and devices, since many high-fidelity quantum emitters, including Rydberg atoms, molecules and silicon vacancies, exhibit resonances near 100 GHz. High-Q resonators at these frequencies would give access to strong interactions between emitters and single photons, leading to rich and unexplored quantum phenomena at temperatures above 1K. We report a 3D mmwave cavity with a measured single-photon internal quality factor of 3×10 7 and mode volume of 0.14×λ 3 at 98.2 GHz, sufficient to reach strong coupling in a Rydberg cavity QED system. An in-situ piezo tunability of 18 MHz facilitates coupling to specific atomic transitions. Our unique, seamless and optically accessible resonator design is enabled by the realization that intersections of 3D waveguides support tightly confined bound states below the waveguide cutoff frequency. Harnessing the features of our cavity design, we realize a hybrid mm-wave and optical cavity, designed for interconversion and entanglement of mm-wave and optical photons using Rydberg atoms. chemical sensing and effective medical diagnostics 25,26 . Recently, the search for higher bandwidth and lower latency communication brought mm-wave wave frequencies into the focus of the telecommunication industry 27,28 . Once prohibitively limited and expensive, mm-wave technology is be-arXiv:1911.00553v1 [quant-ph] 1 Nov 2019 109 GHz 98 GHz 92 GHz 30 GHz a. b. c. d. e.

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