A. Marx

Circuit quantum electrodynamics in the ultrastrong-coupling regime

T. Niemczyk, F. Deppe, 2 H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, 7 A. Marx, and R. Gross 2 Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany∗ Physik-Department, Technische Universität München, D-85748 Garching, Germany Instituto de F́ısica Fundamental, CSIC, Serrano 113-bis, 28006 Madrid, Spain Instituto de Ciencia de Materiales de Aragón y Departamento de F́ısica de la Materia Condensada, CSIC-Universidad de Zaragoza, E-50012 Zaragoza, Spain. Institut für Physik, Universität Augsburg, Universitätsstraße 1, D-86135 Augsburg, Germany Departamento de Qúımica F́ısica, Universidad del Páıs Vasco Euskal Herriko Unibertsitatea, Apdo. 644, 48080 Bilbao, Spain IKERBASQUE, Basque Foundation for Science, Alameda Urquijo 36, 48011 Bilbao, Spain (Dated: December 24, 2010)

High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids.

We report the observation of strong coupling between the exchange-coupled spins in a gallium-doped yttrium iron garnet and a superconducting coplanar microwave resonator made from Nb. The measured coupling rate of 450 MHz is proportional to the square root of the number of exchange-coupled spins and well exceeds the loss rate of 50 MHz of the spin system. This demonstrates that exchange-coupled systems are suitable for cavity quantum electrodynamics experiments, while allowing high integration densities due to their spin densities of the order of one Bohr magneton per atom. Our results furthermore show, that experiments with multiple exchange-coupled spin systems interacting via a single resonator are within reach.

Two-photon probe of the Jaynes–Cummings model and controlled symmetry breaking in circuit QED

Superconducting qubits behave as artificial two-level atoms and are used to investigate fundamental quantum phenomena. In this context, the study of multi-photon excitations occupies a central role. Moreover, coupling superconducting qubits to on-chip microwave resonators has given rise to the field of circuit QED. In contrast to quantum-optical cavity QED, circuit QED offers the tunability inherent to solid-state circuits. In this work, we report on the observation of key signatures of a two-photon driven Jaynes-Cummings model, which unveils the upconversion dynamics of a superconducting flux qubit coupled to an on-chip resonator. Our experiment and theoretical analysis show clear evidence for the coexistence of one- and two-photon driven level anticrossings of the qubit-resonator system. This results from the symmetry breaking of the system Hamiltonian, when parity becomes a not well-defined property. Our study provides deep insight into the interplay of multiphoton processes and symmetries in a qubit-resonator system.

Slowing, advancing and switching of microwave signals using circuit nanoelectromechanics

Microwave superconducting coplanar waveguide resonators are crucial elements in sensitive astrophysical detectors [1] 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 [14–17] has been explored to realize hybrid systems with extended functionality. Here, we couple a superconducting coplanar waveguide resonator to a nano-mechanical oscillator, and demonstrate all-microwave field controlled slowing, advancing and switching of microwave signals. This is enabled by utilizing electromechanically induced transparency [4, 5, 20], an effect analogous to electromagnetically induced transparency (EIT) in atomic physics [21]. The exquisite temporal control gained over this phenomenon provides a route towards realizing advanced protocols for storage of both classical and quantum microwave signals [22–24], extending the toolbox of quantum control techniques of the microwave field.

Two-resonator circuit quantum electrodynamics : A superconducting quantum switch

We introduce a systematic formalism for two-resonator circuit QED, where two on-chip microwave resonators are simultaneously coupled to one superconducting qubit. Within this framework, we demonstrate that the qubit can function as a quantum switch between the two resonators, which are assumed to be originally independent. In this three-circuit network, the qubit mediates a geometric second-order circuit interaction between the otherwise decoupled resonators. In the dispersive regime, it also gives rise to a dynamic second-order perturbative interaction. The geometric and dynamic coupling strengths can be tuned to be equal, thus permitting to switch on and off the interaction between the two resonators via a qubit population inversion or a shifting of the qubit operation point. We also show that our quantum switch represents a flexible architecture for the manipulation and generation of nonclassical microwave field states as well as the creation of controlled multipartite entanglement in circuit QED. In addition, we clarify the role played by the geometric interaction, which constitutes a fundamental property characteristic of superconducting quantum circuits without counterpart in quantum-optical systems. We develop a detailed theory of the geometric second-order coupling by means of circuit transformations for superconducting charge and flux qubits. Furthermore, we show the robustness of the quantum switch operation with respect to decoherence mechanisms. Finally, we propose a realistic design for a two-resonator circuit QED setup based on a flux qubit and estimate all the related parameters. In this manner, we show that this setup can be used to implement a superconducting quantum switch with available technology.

Two-photon probe of the Jaynes-Cummings model and symmetry breaking in circuit QED

Superconducting qubits behave as artificial two-level atoms and are used to investigate fundamental quantum phenomena. In this context, the study of multi-photon excitations occupies a central role. Moreover, coupling superconducting qubits to on-chip microwave resonators has given rise to the field of circuit QED. In contrast to quantum-optical cavity QED, circuit QED offers the tunability inherent to solid-state circuits. In this work, we report on the observation of key signatures of a two-photon driven Jaynes-Cummings model, which unveils the upconversion dynamics of a superconducting flux qubit coupled to an on-chip resonator. Our experiment and theoretical analysis show clear evidence for the coexistence of one- and two-photon driven level anticrossings of the qubit-resonator system. This results from the symmetry breaking of the system Hamiltonian, when parity becomes a not well-defined property. Our study provides deep insight into the interplay of multiphoton processes and symmetries in a qubit-resonator system.

Path Entanglement of Continuous-Variable Quantum Microwaves

Path entanglement constitutes an essential resource in quantum information and communication protocols. Here, we demonstrate frequency-degenerate entanglement between continuous-variable quantum microwaves propagating along two spatially separated paths. We combine a squeezed and a vacuum state using a microwave beam splitter. Via correlation measurements, we detect and quantify the path entanglement contained in the beam splitter output state. Our experiments open the avenue to quantum teleportation, quantum communication, or quantum radar with continuous variables at microwave frequencies.

Tunable coupling engineering between superconducting resonators: From sidebands to effective gauge fields

In this work we show that a tunable coupling between microwave resonators can be engineered by means of simple Josephson junctions circuits, such as dc and rf superconducting quantum interference devices. We show that by controlling the time dependence of the coupling it is possible to switch on and off and modulate the cross-talk and boost the interaction towards the ultrastrong regime, as well as to engineer red and blue sideband couplings, nonlinear photon hopping, and classical gauge fields. We discuss how these dynamically tunable superconducting circuits enable key applications in the fields of all-optical quantum computing, continuousvariable quantum information, and quantum simulation—all within the reach of the state of the art in circuit-QED experiments.

Dual-path state reconstruction scheme for propagating quantum microwaves and detector noise tomography.

Quantum state reconstruction of weak propagating microwaves to date requires the use of linear amplifiers. We introduce a theory which, even in the presence of significant amplifier noise, allows one to use these devices for measuring all quadrature moments of propagating quantum microwaves based on cross correlations from a dual-path amplification setup. Simultaneously, the detector noise properties are determined, allowing for tomography. We demonstrate the feasibility of our novel concept by proof-of-principle experiments with classical mixtures of weak coherent microwaves.

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 17.5% 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 approximation. In contrast to earlier experiments, the high coupling strength is achieved without making use of an additional inductance provided by a Josephson junction.