Circuit Quantum Electrodynamics Experiments Research Articles

Circuit quantum electrodynamics

Quantum mechanical effects at the macroscopic level were first explored in Josephson junction-based superconducting circuits in the 1980's. In the last twenty years, the emergence of quantum information science has intensified research toward using these circuits as qubits in quantum information processors. The realization that superconducting qubits can be made to strongly and controllably interact with microwave photons, the quantized electromagnetic fields stored in superconducting circuits, led to the creation of the field of circuit quantum electrodynamics (QED), the topic of this review. While atomic cavity QED inspired many of the early developments of circuit QED, the latter has now become an independent and thriving field of research in its own right. Circuit QED allows the study and control of light-matter interaction at the quantum level in unprecedented detail. It also plays an essential role in all current approaches to quantum information processing with superconducting circuits. In addition, circuit QED enables the study of hybrid quantum systems interacting with microwave photons. Here, we review the coherent coupling of superconducting qubits to microwave photons in high-quality oscillators focussing on the physics of the Jaynes-Cummings model, its dispersive limit, and the different regimes of light-matter interaction in this system. We discuss coupling of superconducting circuits to their environment, which is necessary for coherent control and measurements in circuit QED, but which also invariably leads to decoherence. Dispersive qubit readout, a central ingredient in almost all circuit QED experiments, is also described. Following an introduction to these fundamental concepts that are at the heart of circuit QED, we discuss important use cases of these ideas in quantum information processing and in quantum optics.

Magnetic field resilient high kinetic inductance superconducting niobium nitride coplanar waveguide resonators

We characterize niobium nitride (NbN) λ/2 coplanar waveguide resonators, which were fabricated from a 10-nm-thick film on silicon dioxide grown by sputter deposition. For films grown at 180 °C, we report a superconducting critical temperature of 7.4 K associated with a normal square resistance of 1 kΩ, leading to a kinetic inductance of 192 pH/◻. We fabricated resonators with a characteristic impedance up to 4.1 kΩ and internal quality factors Qi>104 in the single photon regime at zero magnetic field. Moreover, in the many photon regime, the resonators present a high magnetic field resilience with Qi>104 in a 6 T in-plane magnetic field and in a 300 mT out-of-plane magnetic field. These findings make such resonators a compelling choice for circuit quantum electrodynamics experiments involving quantum systems with small electric dipole moments operated in finite magnetic fields.

Thermally pumped on-chip maser

We present a theoretical model of an on-chip three-level maser in a superconducting circuit based on a single artificial atom and pumped by a temperature gradient between thermal baths coupled to different interlevel transitions. We show that maser powers of the order of a few femtowatts, well exceeding the resolution of the sensitive bolometry, can be achieved with typical circuit parameters. We also demonstrate that population inversion in the artificial atom can be detected without measuring coherent radiation output of the maser. For that purpose, the system should operate as a three-terminal heat transport device. The hallmark of population inversion is the influx of heat power into the weakly coupled output terminal even though its temperature exceeds the temperatures of the two other terminals. The proposed method of on-chip conversion of heat into microwave radiation and control of energy-level populations by heating provide additional useful tools for circuit quantum electrodynamics experiments.

Inter-qubit interaction mediated by collective modes in a linear array of three-dimensional cavities

A design of LEGO-like construction set that allows assembling of different linear arrays of three-dimensional (3D) cavities and qubits for circuit quantum electrodynamics experiments has been developed. A study of electromagnetic properties of qubit-3D cavity arrays has been done by using high frequency structure simulator (HFSS). A technique for estimation of inter-qubit coupling strength between qubits embedded in different cavities of cavity array, which combines Hamiltonian description of the system with simple HFSS simulations, has been proposed. A good agreement between inter-qubit coupling strengths, which were obtained by using this technique and directly from simulation, demonstrates the suitability of the method for more complex qubit–cavity arrays where usage of finite-element electromagnetic simulators is limited.

Microwave dual-mode resonators for coherent spin-photon coupling

We implement superconducting Yttrium barium copper oxide planar resonators with two fundamental modes for circuit quantum electrodynamics experiments. We first demonstrate good tunability in the resonant microwave frequencies and in their interplay, as emerges from the dependence of the transmission spectra on the device geometry. We then investigate the magnetic coupling of the resonant modes with bulk samples of 2,2-diphenyl-1-picrylhydrazyl organic radical spins. The transmission spectroscopy performed at low temperature shows that the coherent spin-photon coupling regime with the spin ensembles can be achieved by each of the resonator modes. The analysis of the results within the framework of the input-output formalism and by means of entropic measures demonstrates coherent mixing of the degrees of freedom corresponding to two remote spin ensembles and, with a suitable choice of the geometry, the approaching of a regime with spin-induced mixing of the two photon modes.

Fabrication of Al air-bridge on coplanar waveguide**Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0301802) and the National Natural Science Foundation of China (Grant Nos. 11474152, 11274156, 11504165, and 61521001).

Superconducting coplanar waveguide (CPW) can be widely used as two-dimensional (2D) resonator, transmission line or feedline, providing an important component for superconducting quantum circuit which is a promising candidate for quantum information processing. Due to the discontinuities and asymmetries in the ground planes, CPW usually exhibits the spurious resonance, which is a common source of decoherence in circuit quantum electrodynamics experiments. To mitigate the spurious resonance, we fabricated superconducting aluminum air-bridges on Nb CPW. The fabricated air-bridges are approximately 3 μm high and up to 120 μm long. Compared with other methods, the fabrication procedures of our air-bridges are simpler, and the air-bridge can withstand strong ultrasound.

Qubit state tomography in a superconducting circuit via weak measurements

In this work we present a study on a new scheme for measuring the qubit state in a circuit quantum electrodynamics (QED) system, based on weak measurement and the concept of weak value. To be applicable under generic parameter conditions, our formulation and analysis are carried out for finite-strength weak measurement, and in particular beyond the bad-cavity and weak-response limits. The proposed study is accessible to present state-of-the-art circuit QED experiments.

3D microwave cavity with magnetic flux control and enhanced quality factor

Three-dimensional (3D) microwave cavities have been extensively used for coupling and interacting with superconducting quantum bits (qubits), providing a versatile platform for quantum control experiments and for realizing hybrid quantum systems. While having high quality factors (>106) superconducting cavities do not permit magnetic field control of qubits. In contrast, cavities made of normal metals are transparent to magnetic fields, but experience lower quality factors (∼104). We have created a hybrid cavity which is primarily composed of aluminium but also contains a small copper insert reaching the internal quality factor of ≃105, an order of magnitude improvement over all previously tested normal metal cavities. In order to demonstrate precise magnetic control, we performed spectroscopy of three superconducting qubits, where individual control of each qubit’s frequency was exerted with small external wire coils. An improvement in quality factor and magnetic field control makes this 3D hybrid cavity an attractive new element for circuit quantum electrodynamics experiments.

Ultrastrong coupling in two-resonator circuit QED

We report on ultrastrong coupling between a superconducting flux qubit and a resonant mode of a system comprised of two superconducting coplanar stripline resonators coupled galvanically to the qubit. With a coupling strength as high as 17% of the mode frequency, exceeding that of previous circuit quantum electrodynamics experiments, we observe a pronounced Bloch-Siegert shift. The spectroscopic response of our multimode system reveals a clear breakdown of the Jaynes-Cummings model. In contrast to earlier experiments, the high coupling strength is achieved without making use of an additional inductance provided by a Josephson junction.

Hybrid quantum circuit with implanted erbium ions

We report on hybrid circuit quantum electrodynamics experiments with focused ion beam implanted Er3+ ions in Y2SiO5 coupled to an array of superconducting lumped element microwave resonators. The Y2SiO5 crystal is divided into several areas with distinct erbium doping concentrations, each coupled to a separate resonator. The coupling strength is varied from 5 MHz to 18.7 MHz, while the linewidth ranges between 50 MHz and 130 MHz. We confirm the paramagnetic properties of the implanted spin ensemble by evaluating the temperature dependence of the coupling. The efficiency of the implantation process is analyzed and the results are compared to a bulk doped Er:Y2SiO5 sample. We demonstrate the integration of these engineered erbium spin ensembles with superconducting circuits.

Theory of the coplanar-waveguide Penning trap

A novel planar Penning trap is presented, which results from the projection of the well-known three-dimensional cylindrical trap onto the surface of a chip. The introduced trap is also a coplanar-waveguide cavity, similar to those used in circuit quantum electrodynamics experiments with superconducting two-level systems. It opens up the possibility of integrating a single trapped electron, or geonium atom, into quantum circuits. The trap is an elliptical Penning trap, with the magnetic field parallel to the chip's surface. A design procedure is described, which permits the compensation of electric anharmonicities up to sixth order. This should render possible the observation of a single trapped electron and the accurate measurement of its eigenfrequencies, a sine qua non requirement for a useful planar geonium technology.

A superconducting 180° hybrid ring coupler for circuit quantum electrodynamics

Superconducting circuit quantum electrodynamics experiments with propagating microwaves require devices acting as beam splitters. Using niobium thin films on silicon and sapphire substrates, we fabricated superconducting 180° microstrip hybrid ring couplers, acting as beam splitters with center frequencies of about 6 GHz. For the magnitude of the coupling and isolation, we find −3.5±0.5 dB and at least −15 dB, respectively, in a bandwidth of 2 GHz. We also investigate the effect of reflections at the superconductor-normal conductor contact by means of low temperature laser scanning microscopy. Our measurements show that our hybrid rings are well suited for on-chip applications in circuit quantum electrodynamics experiments.