Hybrid Optomechanical Superconducting Qubit System: A Step Towards Large-Scale Quantum Error Correction

A team of researchers from the University of SouthEastern Norway and the University of Hamburg have proposed a hybrid optomechanical superconducting qubit system. This system, based on a nanoelectromechanical shuttle, allows for adjustable qubit-mechanical coupling, enabling tuning between linear and quadratic coupling in the mechanical degrees of freedom. The system could be a significant step towards implementing bosonic error correction with mechanical elements in large-scale superconducting circuits. The team also discussed a simple state-swapping protocol that uses this device as a quantum memory element, providing preliminary evidence of its potential.

What is a Hybrid Optomechanical Superconducting Qubit System?

A hybrid optomechanical superconducting qubit system is a proposed integrated nonlinear superconducting device based on a nanoelectromechanical shuttle. This system can be described as a qubit coupled to a bosonic mode. The topology of the circuit gives rise to an adjustable qubit-mechanical coupling, allowing the experimenter to tune between linear and quadratic coupling in the mechanical degrees of freedom. Due to its flexibility and potential scalability, the proposed setup represents an important step towards the implementation of bosonic error correction with mechanical elements in large-scale superconducting circuits.

The system is proposed by Juuso Manninen and Francesco Massel from the Department of Science and Industry Systems at the University of SouthEastern Norway, and Robert H Blick from the Center for Hybrid Nanostructures at the University of Hamburg and the Materials Science and Engineering department at the University of Wisconsin-Madison. The team provides preliminary evidence of this possibility by discussing a simple state-swapping protocol that uses this device as a quantum memory element.

How Does the Hybrid Optomechanical Superconducting Qubit System Work?

In recent years, optomechanical systems, both in the optical and in the microwave regime, have become one of the most prominent platforms for the investigation of quantum mechanical phenomena. They have allowed scientists to explore foundational aspects of quantum theory and have provided the test bed for future technological applications of quantum mechanics. Prominent results in the field include sideband and feedback cooling to the ground state, squeezing, and entanglement of mechanical resonators.

In most of the examples mentioned above, the optomechanical system consists of a mechanical resonator, such as a nanodrum, whose position is parametrically coupled to a photon cavity. One of the outstanding goals in these systems has been the realization of the so-called single-photon strong-coupling limit. In this regime, the parametric coupling energy between a single photon and the mechanical mode becomes comparable to the bare optical cavity linewidth and can therefore significantly alter the dynamics of the system.

What are the Applications of the Hybrid Optomechanical Superconducting Qubit System?

Another intriguing aspect of these systems is the possibility of realizing a quadratic coupling between the mechanical motion and the optical field. Its most prominent application is the detection of phonon-Fock states, even though two-photon cooling and squeezing both of the mechanical and the electromagnetic degrees of freedom have been predicted as well.

In the optical frequencies range, the quadratic coupling of an optical cavity with a mechanical mode has been realized in membrane-in-the-middle and ultracold gases setups. In the microwave regime, quadratic parametric coupling of a qubit to mechanical motion was recently realized with drumhead mechanical resonators coupled to superconducting circuits, exploiting the large mismatch of mechanical and qubit resonant frequency, where the generation of non-Gaussian number-squeezed states was demonstrated.

How is the Hybrid Optomechanical Superconducting Qubit System Designed?

In this work, the team extends the nonlinear circuit approaches mentioned above, integrating a mechanical shuttling element into the design of the superconducting circuit. The shuttling element consists of a portion of superconducting material that is free to perform mechanical oscillations between two superconducting electrodes.

Analogous shuttling devices were realized experimentally in normal (i.e., non-superconducting) circuits, demonstrating the ability of such devices to shuttle electrons along with the oscillatory mechanical motion. In addition, an analogous shuttling mechanism for Cooper pairs was theoretically investigated for superconducting circuits.

What are the Unique Features of the Hybrid Optomechanical Superconducting Qubit System?

More specifically, the team shows how in a lumped-element description, they are able to define a system constituted by a superconducting qubit exhibiting an intrinsic quadratic coupling to the mechanical motion in addition to a tunable linear one. The latter can be externally suppressed, leading to a dominant coupling that is quadratic in the mechanical degrees of freedom.

At the same time, the team shows that the tunability of the linear coupling term allows for a coherent state exchange between the qubit and the mechanical resonator. The device is constituted by a superconducting shuttle which is free to oscillate between two terminals. The terminals being gated to a voltage source through a gating capacitance. The addition of a shunting capacitance meant to ensure protection from charge fluctuations defines a transmon qubit-like device, the X2MON, exhibiting nontrivial properties as a function of the mechanical shuttle dynamics.