The combination of low mass density, high frequency, and high quality-factor of mechanical resonators made of two-dimensional crystals such as graphene 1-8 make them attractive for applications in force sensing/mass sensing, and exploring the quantum regime of mechanical motion. Microwave optomechanics with superconducting cavities 9-14 offers exquisite position sensitivity 10 and enables the preparation and detection of mechanical systems in the quantum ground state 15,16 . Here, we demonstrate coupling between a multilayer graphene resonator with quality factors up to 220,000 and a high-Q superconducting cavity. Using thermo-mechanical noise as calibration, we achieve a displacement sensitivity of 17 fm/ √ Hz. Optomechanical coupling is demonstrated by optomechanically induced reflection (OMIR) and absorption (OMIA) of microwave photons [17][18][19] . We observe 17 dB of mechanical microwave amplification 13 and signatures of strong optomechanical backaction. We extract the cooperativity C, a characterization of coupling strength, quantitatively from the measurement with no free parameters and find C = 8, promising for the quantum regime of graphene motion. Here, we present a multilayer graphene mechanical resonator coupled to a superconducting cavity. Using a deterministic all-dry transfer technique 22 and a novel microwave coupling design, we are able to combine these two without sacrificing the exceptional intrinsic properties of either. Although multilayer graphene has a higher mass than a monolayer, it could be advantageous for coupling to a superconducting cavity due to its lower electrical resistance. In Figure 2, we characterize the mechanical properties of the multilayer graphene resonator using a homodyne measurement scheme 9 . Here, the cavity is used as an interferometer to detect motion while injecting a microwave signal near ω c and exciting the mechanical resonator with an AC voltage applied to the gate. The mechanical resonance frequency is much larger than the cavity linewidth (ω m /κ ∼ 150), placing us in the sideband resolved limit, a prerequisite for ground state cooling. The cavity can also be used to detect the undriven motion, such as thermomechanical noise of the drum shown in the inset of Figure 2(a) corresponding to a mechanical mode temperature of 96 mK (see SI for additional details). The thermal motion peak serves as a calibration for the displacement sensitivity. While driving the cavity at its resonance and utilizing its full dynamic range before the electrical nonlinearity set in (-41 dBm injected power) we estimate a displacement sensitivity for mechanical motion of 17 fm/ √ Hz. Using a DC voltage applied to the gate electrode, we can also tune the frequency of the multilayer graphene resonator shown in Figure 2(b). The decrease in resonance frequency ω m for non-zero gate voltage is due to electrostatic softening of the spring constant and has been observed before 3 .In Figure 3, we demonstrate optomechanical coupling between the multilayer graphene mechanical resona...

With the introduction of superconducting circuits into the field of quantum optics, many experimental demonstrations of the quantum physics of an artificial atom coupled to a single-mode light field have been realized. Engineering such quantum systems offers the opportunity to explore extreme regimes of light-matter interaction that are inaccessible with natural systems. For instance the coupling strength g can be increased until it is comparable with the atomic or mode frequency ω a,m and the atom can be coupled to multiple modes which has always challenged our understanding of light-matter interaction. Here, we experimentally realize a transmon qubit in the ultra-strong coupling regime, reaching coupling ratios of g/ω m = 0.19 and we measure multi-mode interactions through a hybridization of the qubit up to the fifth mode of the resonator. This is enabled by a qubit with 88% of its capacitance formed by a vacuum-gap capacitance with the center conductor of a coplanar waveguide resonator. In addition to potential applications in quantum information technologies due to its small size, this architecture offers the potential to further explore the regime of multi-mode ultra-strong coupling. With strong coupling, 3 where the coupling is larger than the dissipation rates γ and κ of the atom and mode respectively, experiments such as photon-number resolution 4 or Schrödinger-cat revivals 5 have beautifully displayed the quantum physics of a single-atom coupled to the electromagnetic field of a single mode. As the field matures, circuits of larger complexity are explored, 6-8 opening the prospect of controllably studying systems that are theoretically and numerically difficult to understand.One example is the interaction between an (artificial) atom and an electromagnetic mode where the coupling rate becomes a considerable fraction of the atomic or mode eigen-frequency. This ultra-strong coupling (USC) regime, described by the quantum Rabi model, shows the breakdown of excitation number as conserved quantity, resulting in a significant theoretical challenge. 9,10 In the regime of g=ω a;m ' 1, known as deep-strong coupling (DSC), a symmetry breaking of the vacuum is predicted 11 (i.e., qualitative change of the ground state), similar to the Higgs mechanism or Jahn-Teller instability. To date, U/DSC with superconducting circuits has only been realized with flux qubits 6,12 or in the context of quantum simulations. 13,14 Using transmon qubits for USC is interesting due to their higher coherence rates 15 as well as their weakly-anharmonic nature, allowing the exploration of a different Hamiltonian than with flux qubits. 16 Since transmon qubits are currently a standard in quantum computing efforts, [17][18][19] implementing USC in a transmon architecture could also have technological applications by

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Superconducting microwave resonators (SMR) with high quality factors have become an important technology in a wide range of applications. Molybdenum-Rhenium (MoRe) is a disordered superconducting alloy with a noble surface chemistry and a relatively high transition temperature.These properties make it attractive for SMR applications, but characterization of MoRe SMR has not yet been reported. Here, we present the fabrication and characterization of SMR fabricated with a MoRe 60-40 alloy. At low drive powers, we observe internal quality-factors as high as 700,000. Temperature and power dependence of the internal quality-factors suggest the presence of the two level systems from the dielectric substrate dominating the internal loss at low temperatures. We further test the compatibility of these resonators with high temperature processes such as for carbon nanotube CVD growth, and their performance in the magnetic field, an important characterization for hybrid systems. The SMR were designed in a coplanar waveguide geometry and fabricated on a sapphire wafer (substrate thickness ∼ 430 µm) in order to minimize dielectric losses. As cleaning of the substrate surface seems to play an important role in minimizing two-level systems 24 , an extensive cleaning of the sapphire wafer is performed with phosphoric acid (H 3 PO 4 )at 75 ℃ for 30 minutes followed by rinsing in DI water for 2 hours. After exposing the fresh surface of the wafer, it was immediately loaded in the vacuum chamber for MoRe film 2 deposition. Using an RF sputtering system, we deposit a 145 nm thick MoRe film with a continuous flow of Ar (pressure 1.5 × 10 −3 mTorr) from a ∼ 99.95 % purity, single target of MoRe. The SMR designs were patterned using e-beam lithography on a three layer mask (S1813/W(Tungsten)/PMMA-950) followed by the etching of MoRe by SF 6 /He plasma. We use a frequency multiplexing scheme to side-couple multiple quarter wavelength resonators of different frequencies to a common transmission line. Figure 1(a) shows an optical microscope image of such a resonator after the fabrication process. The quarter-wavelength coplanar waveguide resonator is formed by terminating a transmission line (characteristic impedance of 50 Ω and 10 µm wide trace) to the ground plane. For microwave measurements, the samples were mounted in a light-tight microwave box and were cooled down in a dilution fridge or a He-3 cryostat with sufficient attenuation at each temperature stage to thermalize the microwave photons reaching the sample. A schematic of the attenuation scheme in the dilution refrigerator is shown in Figure 1(b). For these sputtered thin films, we measure a typical room temperature resistivity of 88 µΩ-cm, RRR ∼ 1.2 and T c ∼ 9.2 K.The low power transmission response S 21 for a side-coupled quarter wavelength resonator near its resonance frequency f 0 can be modeled bywhereis the loaded quality-factor, Q c is the coupling quality-factor and Q i is the internal quality-factor of the resonator. Figure 1(c) shows the measurement of the tr...

In this experiment, we couple a superconducting transmon qubit to a high-impedance 645 microwave resonator. Doing so leads to a large qubit-resonator coupling rate g, measured through a large vacuum Rabi splitting of 2g 910 MHz. The coupling is a significant fraction of the qubit and resonator oscillation frequencies ω, placing our system close to the ultrastrong coupling regime (ḡ = g/ω = 0.071 on resonance). Combining this setup with a vacuum-gap transmon architecture shows the potential of reaching deep into the ultrastrong couplingḡ ∼ 0.45 with transmon qubits.