3-Wave Mixing Josephson Dipole Element (1702.00869v3)

Abstract: Parametric conversion and amplification based on three-wave mixing are powerful primitives for efficient quantum operations. For superconducting qubits, such operations can be realized with a quadrupole Josephson junction element, the Josephson Ring Modulator (JRM), which behaves as a loss-less three-wave mixer. However, combining multiple quadrupole elements is a difficult task so it would be advantageous to have a pure three-wave dipole element that could be tessellated for increased power handling and/or information throughput. Here, we present a dipole circuit element with third-order nonlinearity, which implements three-wave mixing. Experimental results for a non-degenerate amplifier based on the proposed pure third-order nonlinearity are reported.

3-Wave Mixing Josephson Dipole Element Analysis

The paper "3-Wave Mixing Josephson Dipole Element" presents the development and experimentation of a novel superconducting circuit element, the Superconducting Nonlinear Asymmetric Inductive eLement (SNAIL). This dipole configuration introduces $\varphi^3$ nonlinearity for three-wave mixing applications, circumventing the inherent Kerr nonlinearity (characteristic $\varphi^4$ terms) related to traditional Josephson junction interactions which often result in undesired frequency shifts.

The paper begins by addressing the disadvantages of conventional Josephson Ring Modulator (JRM) elements, which, despite being effective three-wave mixers, are cumbersome to integrate in modular architectures due to their quadrupolar nature. This paper proposes a dipolar substitute—the SNAIL—featuring a single-loop configuration. Its primary innovation lies in enabling effective three-wave mixing interactions through a minimal $\varphi^3$ nonlinearity while effectively nullifying fourth-order Kerr nonlinearity. Achieving this performance in a dipole assembly allows easier tessellation for enhanced power handling and throughput.

Technical Implementation and Experiments

The SNAIL is engineered from a loop with three large Josephson junctions and one smaller junction, generating the necessary nonlinearity when threaded by a specific DC magnetic flux. The authors optimally tuned the SNAIL's parameters, numerically determining conditions where $c_3 \neq 0$ and $c_4 = 0$, leading to the desired cubic interaction with suppressed Kerr terms. This arrangement was verified experimentally by integrating SNAIL into a non-degenerate parametric amplifier.

The capabilities of the SNAIL were demonstrated in a non-degenerate amplifier setup, replicating a design similar to the JRM but improved by its dipolar characteristics. Experimental evidence showed successful three-wave mixing using a high-frequency pump, indicative of effective $\varphi^3$ nonlinearity.

Results and Observations

The SNAIL-based amplifier showed reflection gain adjustments and demonstrated noise characteristics on par with existing quantum-limited amplifiers, notably maintaining the stable enhancement of gain with increased pump power while exhibiting minimal Kerr-induced frequency shifts.

Theoretical and Practical Implications

Theoretical implications include the potential for broad applications of SNAIL in scalable quantum devices necessitating modular structures. Its dipole configuration offers immense flexibility for architects of quantum circuit designs, especially in scenarios demanding robust coupling schemes without detrimental Kerr nonlinearity. Practically, there lies a significant advantage in scalability, where SNAILs could be arrayed similar to traditional SQUIDs, potentially benefiting high-bandwidth and dynamic range applications.

Future Developments

Future research could focus on characterizing the noise performance of SNAIL in diversified quantum setups and explore its integration into complex quantum circuits where cross-Kerr effects are mitigated. Further work might involve experimental validation of SNAIL’s potential in tunable coupling scenarios between superconducting qubits or cavities.

The paper's contributions notably streamline integrating parametric processes in quantum computing and communications, highlighting possibilities for improved modularity and enhanced functional capabilities in quantum circuits.