as well as the generation of phononic and photonic quantum states [3-10]."]Electromechanical systems realize this optomechanical interaction in the microwave regime. In this context, capacitive coupling arrangements demonstrated interaction rates of up to 280 Hz [11]. Complementary, early proposals [12-15] and experiments [16,17] suggest that inductive coupling schemes are tunable and have the potential to reach the vacuum strong-coupling regime. Here, we follow the latter approach by integrating a partly suspended superconducting quantum interference device (SQUID) into a microwave resonator. The mechanical displacement translates into a time varying flux in the SQUID loop, thereby providing an inductive electromechanical coupling. We demonstrate a sideband-resolved electromechanical system with a tunable vacuum coupling rate of up to 1.62 kHz, realizing sub-aN Hz-1/2 force sensitivities. Moreover, we study the frequency splitting of the microwave resonator for large mechanical amplitudes confirming the large coupling. The presented inductive coupling scheme shows the high potential of SQUID-based electromechanics for targeting the full wealth of the intrinsically nonlinear optomechanics Hamiltonian.
Ultrawide-range photon number calibration using a hybrid system combining nano-electromechanics and superconducting circuit quantum electrodynamics
We present a hybrid system consisting of a superconducting coplanar waveguide resonator coupled to a nanomechanical string and a transmon qubit acting as nonlinear circuit element.
We perform spectroscopy for both the transmon qubit and the nanomechanical string. Measuring the ac-Stark shift on the transmon qubit as well as the electromechanically induced absorption on the string allows us to determine the average photon number in the microwave resonator in both the low and high power regimes. In this way, we measure photon numbers that are up to nine orders of magnitude apart. We find a quantitative agreement between the calibration of photon numbers in the microwave resonator using the two methods. Our experiments demonstrate the successful combination of superconducting circuit quantum electrodynamics and nano-electromechanics on a single chip.
Scalable 3D quantum memory
Superconducting 3D microwave cavities offer state-of-the-art coherence times and a well controlled environment for superconducting qubits. In order to realize at the same time fast
readout and long-lived quantum information storage, one can couple the qubit both to a low-quality readout and a high-quality storage cavity. However, such systems are bulky compared to their less coherent 2D counterparts. A more compact and scalable approach is achieved by making use of the multimode structure of a 3D cavity. In our work, we investigate such a device where a transmon qubit is capacitively coupled to two modes of a single 3D cavity. The external coupling is engineered so that the memory mode has an about 100 times larger quality factor than the readout mode. Using an all-microwave second-order protocol, we realize a lifetime enhancement of the stored state over the qubit lifetime by a factor of 6 with a Z-fidelity of 82%. We also find that this enhancement is not limited by fundamental constraints.
Parity-engineered light-matter interaction
The concept of parity describes the inversion symmetry of a system and is of fundamental relevance in the standard model, quantum information processing, and field theory. In quantum
electrodynamics, parity is conserved and selection rules (SRs) appear when matter is probed with electromagnetic radiation. However, typically large field gradients are required to engineer the parity of the light-matter interaction operator for natural atoms. In this work, we instead irradiate a specifically designed superconducting artificial atom with spatially shaped microwave fields to select the interaction parity in situ. In this way, we observe dipole and quadrupole SRs for single state transitions and induce transparency via longitudinal coupling. Furthermore, we engineer an artificial potassium-like atom with adjustable wave function parity originating from an artificial orbital momentum provided by a resonator. Our work advances light-matter interaction to a new level with promising application perspectives in simulations of chemical compounds, quantum state engineering, and relativistic physics.
Flux-driven Josephson parametric amplifiers: Hysteretic flux response and nondegenerate gain measurements
Josephson parametric amplifiers (JPA) have become key devices in quantum science and technology with superconducting circuits. In particular, they can be utilized as quantum-limited
amplifiers or as a source of squeezed microwave fields. Here, we report on the detailed measurements of five flux-driven JPAs, three of them exhibiting a hysteretic dependence of the resonant frequency versus the applied magnetic flux. We model the measured characteristics by numerical simulations based on the two-dimensional potential landscape of the dc superconducting quantum interference devices (dc-SQUID), which provide the JPA nonlinearity, for a finite screening parameter βL>0 and demonstrate excellent agreement between the numerical results and the experimental data. Furthermore, we study the nondegenerate response of different JPAs and accurately describe the experimental results with our theory.
Loss mechanisms in superconducting thin film microwave resonators
We present a systematic analysis of the internal losses of superconducting coplanar waveguide microwave resonators based on niobium thin films on silicon substrates. At millikelvin
temperatures and low power, we find that the characteristic saturation power of two-level state (TLS) losses shows a pronounced temperature dependence. Furthermore, TLS losses can also be introduced by Nb/Al interfaces in the center conductor, when the interfaces are not positioned at current nodes of the resonator. In addition, we confirm that TLS losses can be reduced by proper surface treatment. For resonators including Al, quasiparticle losses become relevant above \SI{200}{\milli\kelvin}. Finally, we investigate how losses generated by eddy currents in the conductive material on the backside of the substrate can be minimized by using thick enough substrates or metals with high conductivity on the substrate backside.
Spin-boson model with an engineered reservoir in circuit quantum electrodynamics
A superconducting qubit coupled to an open transmission line represents an implementation of the spin-boson model with a broadband environment. We show that this environment can be
engineered by introducing partial reflectors into the transmission line, allowing to shape the spectral function, J({\omega}), of the spin-boson model. The spectral function can be accessed by measuring the resonance fluorescence of the qubit, which provides information on both the engineered environment and the coupling between qubit and transmission line. The spectral function of a transmission line without partial reflectors is found to be Ohmic over a wide frequency range, whereas a peaked spectral density is found for the shaped environment. Our work lays the ground for future quantum simulations of other, more involved, impurity models with superconducting circuits.
Control of microwave signals using circuit nano-electromechanics
and circuit quantum electrodynamics (cQED) [2]. Coupled to
artificial atoms in the form of superconducting"]qubits [3, 4], they now provide
a technologically promising and scalable platform for quantum information
processing tasks [2, 5-8]. Coupling these circuits, in situ, to other quantum
systems, such as molecules [9, 10], spin ensembles [11, 12], quantum dots [13]
or mechanical oscillators [14, 15] has been explored to realize hybrid systems
with extended functionality. Here, we couple a superconducting coplanar
waveguide resonator to a nano-coshmechanical oscillator, and demonstrate
all-microwave field controlled slowing, advancing and switching of microwave
signals. This is enabled by utilizing electromechanically induced transparency
[16-18], an effect analogous to electromagnetically induced transparency (EIT)
in atomic physics [19]. The exquisite temporal control gained over this
phenomenon provides a route towards realizing advanced protocols for storage of
both classical and quantum microwave signals [20-22], extending the toolbox of
control techniques of the microwave field.
Networks of nonlinear superconducting transmission line resonators
We investigate a network of coupled superconducting transmission line
resonators, each of them made nonlinear with a capacitively shunted Josephson
junction coupling to the odd flux
modes of the resonator. The resulting
eigenmode spectrum shows anticrossings between the plasma mode of the shunted
junction and the odd resonator modes. Notably, we find that the combined device
can inherit the complete nonlinearity of the junction, allowing for a
description as a harmonic oscillator with a Kerr nonlinearity. Using a dc SQUID
instead of a single junction, the nonlinearity can be tuned between 10 kHz and
4 MHz while maintaining resonance frequencies of a few gigahertz for realistic
device parameters. An array of such nonlinear resonators can be considered a
scalable superconducting quantum simulator for a Bose-Hubbard Hamiltonian. The
device would be capable of accessing the strongly correlated regime and be
particularly well suited for investigating quantum many-body dynamics of
interacting particles under the influence of drive and dissipation.