Exploring nonclassical states of center-of-mass mechanical motion with superconducting magneto- and levitomechanics

Project Information

SuperMeQ

Grant agreement ID: 101080143

DOI

10.3030/101080143

EC signature date 18 August 2022

Start date 1 October 2022

End date 31 March 2027

Funded under

• Digital, Industry and Space

Total cost

€ 2 988 644,00

EU contribution

€ 2 988 644,00

Coordinated by

CHALMERS TEKNISKA HOGSKOLA AB
Sweden

Periodic Reporting for period 2 - SuperMeQ (Exploring nonclassical states of center-of-mass mechanical motion with superconducting magneto- and levitomechanics)

Reporting period: 2024-04-01 to 2025-09-30

Summary of the context and overall objectives of the project

Quantum technologies rely on the creation, manipulation, and read-out of nonclassical states. Any quantum advantage is hampered by the undesired, unavoidable and largely uncontrollable coupling to the environment, resulting in decoherence. Minimizing decoherence is a major driver of technology development in quantum technologies. Nonclassical states, however, must be generated first. To do so, a system of interest is coupled to another (quantum) system.

Mechanical resonators have been recently added to the quantum technology hardware toolbox. They open novel possibilities in quantum technologies, foremost in quantum sensing, as novel force and inertial sensing platforms, as well as in quantum networks in the form of quantum amplifiers, quantum memories, and quantum transducers. In addition, mechanical resonators are a leading system to test foundations of quantum physics in the form of massive quantum probes.

SuperMeQ addresses three basic science goals in quantum technologies, targeting to gain new insights into quantum control over the center-of-mass motion of mechanical resonators. The project is working on: (i) Pushing the limits of decoherence mechanisms of massive objects, (ii) Maximizing the vacuum coupling rate of the center-of-mass motion of a mechanical resonator to a quantum system, and (iii) Generating useful nonclassical states such as squeezed states or states with a negative Wigner function, which have direct relevance for quantum-enhanced force and inertial sensing.

Our project follows a unique approach by realizing two complementary experimental platforms that are tailored to our goals and that are mutually beneficial through parallel development: (a) magnetically levitated superconducting microparticles that access a mass regime spanning more than seven orders of magnitude between picogram and sub-milligram masses, and that are expected to exhibit ultra-low mechanical decoherence, and (b) integrated clamped magnetic or superconducting mechanical resonators that are expected to reach strong vacuum coupling rates.

Key in each of these approaches is that we couple both types of mechanical resonator inductively to superconducting quantum circuits, which allow for full quantum control over the center-of-mass degree of freedom of the mechanical resonators. Our project results will lead to a breakthrough in the development and growth of novel quantum sensing technologies and give new insights into foundational aspects of quantum physics.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

In the second period of the SuperMeQ project (M19 to M36) we focused on further developing the experimental platforms and on exploring ways for ground state cooling and nonclassical state generation.

In our levitation platforms, we focused on making levitation of microparticles more reliable by developing methods to reduce adhesion of microparticles resting on silicon surfaces. This allowed us to reduce the adhesion force by more than a factor of three, which increases the lift-off probability in levitation attempts drastically. We further developed a simple superconducting flip-chip method that allows for efficient flux transport between the pick-up loop in the particle trap and the flux-tunable cavity. We estimate that this method should allow us to achieve a magnetomechanical coupling rate of 0.1Hz which would be more than an order of magnitude larger than in our previous work (Phys. Rev. Applied 22, 014078 (2024)). We implemented a complementary read-out method that relies on using light. To this end, we realized optical read-out of levitated particle motion and achieved a read-out sensitivity of 1nm/√Hz. We discussed methods how to improve this sensitivity to be capable of measuring the ground state motional amplitude. Furthermore, we analyzed novel trap geometries relying on planar superconductors, shaping magnetic fields by a proper arrangement of suitable materials, or by exploiting nonlinear potentials. In particular, the latter approach provides a way forward to generate nonclassical states of levitated particle motion.

In our clamped platforms, we further analyzed the capabilities of using a Kerr nonlinear cavity for cooling of mechanical motion in a magnetomechanics. Importantly, we studied cooling in the regime of bistability, i.e. when the photon number in the cavity exceeds the critical photon number. We could verify our theory in an experiment, where a magnetic cantilever was coupled directly to a flux-tunable cavity. Crucially, we observed self-sustained oscillations in one of our nonlinear nanomagnetomechanical devices and developed a theoretical understanding of the observed phenomena. The observed behavior showed excellent agreement between theory and experiment. This work constitutes a potential path towards generating nonclassical states by exploiting the inherent nonlinearities provided the magnetomechanical coupling strength could be further increased. We estimate that we could achieve a coupling strength to cavity decay rate ratio of up to 0.2 in our future experiments in the clamped platforms, which would constitute a record in such systems.

In our experiments we routinely use passive cryogenic vibration isolation systems, which drastically reduce the undesired influence of external vibrations on the motion of the mechanical resonators.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

We achieved the following published results in the second period of SuperMeQ (M19-M36) that go beyond
the state-of-the-art:

We developed a simple superconducting flip-chip technology that allows one to transport superconducting currents between two chips that can be spaced by about 50 micrometers (Appl. Phys. Lett. 126, 022601 (2025)). This simple method can be used for any superconducting chip technology that requires galvanic contact between chips, without requiring sophisticated equipment for assembly.

We developed methods that reduce the adhesion between metallic microparticles and silicon surfaces (arXiv:2508.13887). These methods are relevant for any experiment that aims to minimize adhesion between microparticles and surfaces.

We implemented interferometric optical read-out of magnetically levitated superconducting microparticles (arXiv:2508.11731). This method will be further developed with the goal of achieving a measurement imprecession that allows for ground state cooling of the center-of-mass motion of the levitated microparticle.

We developed and applied a method to describe mechanical oscillations occurring in spectroscopic characterizations of magnetomechanical systems (arXiv:2510.01775). This method can be further developed to exploit the nonlinearity for generating nonclassical states.

We have deepened our understanding of magnetomechanical cooling using a Kerr-nonlinear cavity (Phys. Rev. A 111, 053505 (2025)) and applied it in an experiment that drives the cavity even in the bistable regime (Phys. Rev. Applied 23, 014082 (2025)).
We analyzed a simple method to levitate a magnetic dipole above a flat superconductor with a hole (Phys. Rev. B 111, 174530 (2025)). This constitutes an alternative levitation method, which could be relevant in sensing contexts, eg, in gravimetry.

The experimental platform of SuperMeQ.