We consider a coupling element based on a symmetric superconducting quantum interference device (SQUID) and show that it mediates a two-photon interaction. This and other inductive interactions due to the SQUID can be switched off . We derive the system Hamiltonian for a coupled resonator and rf SQUID. The rf SQUID dwells in the vicinity of its metastable well holding a number of energy states and acts as an artificial atom. We discuss how the Josephson symmetry breaks owing to magnetic fields in the superconducting loops—both directly and via a nonzero superconducting phase difference over the rf SQUID. We assess that the two-photon coupling strength reaches 18 MHz which can exceed the single-photon capacitive interaction in the coupler.
We consider a coupling element based on a symmetric superconducting quantum interference device (SQUID) and show that it mediates a two-photon interaction. This and other inductive interactions due to the SQUID can be switched off . We derive the system Hamiltonian for a coupled resonator and rf SQUID. The rf SQUID dwells in the vicinity of its metastable well holding a number of energy states and acts as an artificial atom. We discuss how the Josephson symmetry breaks owing to magnetic fields in the superconducting loops—both directly and via a nonzero superconducting phase difference over the rf SQUID. We assess that the two-photon coupling strength reaches 18 MHz which can exceed the single-photon capacitive interaction in the coupler.
We study the interactions mediated by a symmetric superconducting quantum interference device (SQUID), their renormalizations, and the applicability of the anharmonic oscillator (bosonic) model for a coupled phase qubit. The latter dwells in its metastable well holding a number of anharmonic energy states. The coupling SQUID can switch between the single- and two-photon interactions in situ. We find that, in the bosonic two-photon regime, the cross-Kerr coupling never vanishes as it dresses due to asymmetry in the qubit potential and nonlinearity of the coupler. Our quantitative results also depend on the bosonic approximation. We approach determining its limits by finding the minimum number of coherent energy states required for a dressing. For that, we lay out diagrams of the dressing virtual processes that climb the qubit ladder as high as possible. Near the two-photon resonance with a coupled resonator, we systematically calculate other relevant renormalizations due to nonresonant interactions. We provide verifiable predictions for the coupling rates. Modified systems can be applied for two-photon detection and for quantum-nondemolition readout of a qubit with an asymmetrical potential.
Abstract We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency superconducting quantum interference devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the N × N × 2 overlapping metamaterial array, where we develop an understanding of the many ( 8 N 2 − 8 N + 3 ) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant responses of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10–30 GHz range on capacitively and inductively coupled rf SQUID metamaterials.
We propose a viable design of a microwave two-photon threshold detector. In essence, the considered scheme is an extension of the existing single-photon detector—a Josephson photomultiplier (JPM)—an absorbing microwave detector based on a capacitively shunted rf superconducting quantum interference device (SQUID). To implement a two-photon threshold detector, we utilize a dimer of resonators—two lumped-element resonators interacting via an asymmetric dc SQUID, with one of the resonators capacitively coupled to the JPM. By specific tuning of the resonator frequencies and the external flux through the dc SQUID coupler, we engineer a nonperturbative two-photon coupling between the resonators. This coupling results in the coherent conversion of a photon pair from one resonator into a single photon in another resonator, enabling selective response to quantum states with at least two photons. We also consider an extended coupler design that allows on-demand switching of two-photon coupling. In addition, we propose the modified JPM design to improve its performance. Our calculations demonstrate that, for realistic circuit parameters, we can achieve more than 99 % fidelity of photon pair detection in less than 50 ns. The considered scheme may serve as a building block for the implementation of efficient photon-number-resolving detectors in circuit QED architecture.
We use a flux-biased radio frequency superconducting quantum interference device (rf SQUID) with an embedded flux-biased direct current SQUID to generate strong resonant and nonresonant tunable interactions between a phase qubit and a lumped-element resonator. The rf SQUID creates a tunable magnetic susceptibility between the qubit and resonator providing resonant coupling strengths from zero to near the ultrastrong coupling regime. By modulating the magnetic susceptibility, nonresonant parametric coupling achieves rates >100 MHz. Nonlinearity of the magnetic susceptibility also leads to parametric coupling at the subharmonics of the qubit-resonator detuning.
We investigate a superconducting interference device (SQUID) with two asymmetric Josephson junctions coupled to a mechanical resonator embedded in the loop of the SQUID. We quantize this system in the case when the frequency of the mechanical resonator is much lower than the cavity frequency of the SQUID and in the case when they are comparable. In the first case, the radiation pressure and the cross-Kerr type interactions arise and are modified by the asymmetry. The cross-Kerr type coupling is the leading term at the extremum points where the radiation pressure is zero. In the second case, the main interaction is the single-photon beam splitter, which exists only at a finite asymmetry. Another interaction in this regime is of cross-Kerr type, which exists at all asymmetries, but is generally much weaker than the beam splitter interaction. Increasing magnetic field can substantially enhance the optomechanical couplings strength with a potential for the radiation pressure coupling to reach the single-photon strong coupling regime, even the ultrastrong coupling regime, in which the single-photon coupling rate exceeds the mechanical frequency.
Recently, we have proposed the half-Josephson laser (HJL): a device that combines lasing with superconducting leads, providing a locking between the optical phase and the superconducting phase difference between the leads. In this work, we propose and investigate two setups derived from a superconducting quantum interference device (SQUID), where two conventional Josephson junctions are replaced by two HJLs. In the first setup, the HJLs share the same resonant mode, while in the second setup two separate resonant modes of the two lasers are coupled optically. We dub the setup ``light-superconducting interference device'' (LSID). In both setups, we find the operating regimes similar to those of a single HJL. Importantly, the steady lasing field is significantly affected by the magnetic flux penetrating the SQUID loop, with respect to both amplitude and phase. This provides opportunities to tune or even quench the lasing by varying a small magnetic field. For the second setup, we find a parameter range where the evolution equation for the laser fields supports periodic cycles. The fields are thus modulated with the frequency of the cycle resulting in an emission spectrum consisting of a set of discrete modes. From this spectrum, two modes dominate in the limit of strong optical coupling. Therefore, the LSID can be also used to generate such modulated light.