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Inertial Sensing Based on Quantum-Enhanced Levitation Systems

Periodic Reporting for period 2 - IQLev (Inertial Sensing Based on Quantum-Enhanced Levitation Systems)

Reporting period: 2021-01-01 to 2023-06-30

The overarching goal of IQLev is to establish a new technological paradigm for high-performance inertial sensors (accelerometers and gyroscopes) based on optical, magnetic and electrostatic levitation of microscopic and mesoscopic systems and their control at the quantum level. By the end of the project we will have selected the most promising implementations and fields of application in the inertial sensing domain and will have established a sufficient level of maturity to lay the foundation of new future inertial sensors. Three major objectives will bring our levitation approach to quantum sensing to a technologically relevant level of maturity.

Objective 1: Demonstrate the exceptional potential of levitated systems for tailored inertial sensing.

Objective 2: Develop and experimentally test quantum protocols for sensing.

Objective 3: Combine developments into sensor platforms.

It is at the heart of IQLev to promote a connection between science and industry. The commercial aims of our quantum-enhanced levitated systems are applications in high-end inertial measurement units (IMUs) and inertial navigation systems (INSs), that is, applications that demand stabilities and sensitivities that are better than what is achievable with current technology. We expect a particularly large impact of this radically new inertial sensing technology in areas such as navigation, positioning and gravimetry/seismometry.
Within the IQLev project, we have been extending and perfecting levitated systems toolbox and demonstrating the potential of this technology for inertial sensing. Our most prominent achievements in optical, electrostatic and magnetic levitated sensors development include:

Hybrid optical-electrostatic on-chip accelerometer
Optically levitated nanoparticles are promising candidates for force and inertial sensing applications owing to their high level of isolation under UHV conditions and their relatively high mass. To integrate their acceleration sensing capabilities onto a compact and robust platform, we developed a hybrid chip combining optical and electrostatic trapping potentials. The developed platform allows today for the stable levitation of 415nm particles at 10-6 mbar, leading to an acceleration sensitivity of the order of 50 μ/√. Further immediate improvements related to pressure and particle size promise an additional order of magnitude improvement.

Magnetically levitated accelerometer
We have developed a platform for acceleration sensing that uses levitated superconductors in a magnetic field gradient and performs the read-out via superconducting quantum interference devices (SQUID). This platform has several advantages over optically levitated systems, including a higher mass of a levitated object, low intrinsic damping of the superconductor (Q ~ 26 mill), and cryogenic temperatures of 20 mK. These features enabled the quantification of the thermally limited inertial noise density to be 9 ⋅ 10^-12 /√.
Additional information regarding this platform is available at Hofer et al, to appear in Phys. Rev. Lett. (2023).

Optically levitated gyroscopes
We are working towards a gyroscope based on a spinning anisotropic nanoparticle trapped in optical tweezers. Thanks to extremely high rotational speeds achievable with optically levitated particles (reaching several GHz), this design will allow us to mitigate the sensitivity limitation arising from mass constraints in optical levitation. In order to develop the prototype gyroscope, we created new tools for controlling the rotational degrees of freedom of optically levitated objects. By using an optical beam with variable degree of polarization for levitation, we have demonstrated an “optical gimbal mount” (more details in Zielinska et al, Phys. Rev. Lett. 130, 203603, 2023). Additionally, our platform allows for controlling spinning motion of the nanodumbbell around both short and long axes of the particle. Our current operating parameters translate into thermal-limited gyroscope sensitivity (angular random walk) of 4 × 10 ^-6 rad/s/√Hz.

Towards quantum-enhanced inertial sensing
The IQLev consortium has experimentally shown that optically levitated systems are on the brink of entering the quantum regime (see Magrini et al, Nature 595, 373–377, 2021; Tebbenjohanns et al Nature 595, 378–382, 2021). In the future this will lead to new exciting opportunities for high-performance inertial sensing using quantum (e.g. squeezed) states of mechanical degrees of freedom. In order to guide experimental efforts, we have developed a theoretical formalism to further understand how the electromagnetic field interacts with levitated particles of arbitrary size in the quantum regime (see Maurer et al, arXiv:2106.07975 [quant-ph], 2021) . We are also building a theoretical toolbox to enable platform-independent modeling of quantum dynamics of largely squeezed quantum states and their optimization. We believe our theoretical advances are paving the way for smart quantum sensing techniques, particularly for based on hybrid optical-electrostatic levitation.

The IQLev consortium has dedicated a substantial effort to disseminating and promoting the results to scientific, industry, and lay audiences. The lay audiences were targeted through public events, publications, and social media. These channels allowed us to effectively communicate our research in a manner that is accessible and engaging to the general public. The dissemination of our work to professional audiences, (including academics and industry experts) is accomplished via publications (which are made available in an open-access repository) and our participation in conferences. In terms of exploitation, the expertise gained through IQLev to is of crucial importance for supporting additional research projects and as a foundation for fellowship applications. The consortium members are planning to continue advancing the technology created as part of this project.
The potential of quantum-enhanced levitated systems for sensing is based on two key ingredients: 1) the physical decoupling from the environment (levitation), and 2) the possibility quantum-enhanced operation. The IQLev consortium has pushed levitation technologies beyond the state of the art is technologies in many aspects. The key achievements include: ground state cooling of optically levitated to their ground state, increasing control over the motion of magnetically levitated objects and developing hybrid on-chip electrostatic/optical traps, to name a few.

Working closely with our industrial partner, the technology created within IQLev will eventually lead to the emergence of a competitive European industry for inertial sensing based on levitation. Indeed, we have identified future use cases for our sensors. For example, the future scientific space missions are in need for compact high-sensitivity inertial sensors in the low frequency regime. Moreover, the field of seismometry is in desperate need of such sensors which are sufficiently sensitive and noise-free for measurements and which are currently not available. In the long run our quantum-enhanced levitation systems can cover niche markets that require lightweight and compact IMUs, such as for navigation of drones in tunnels and mines, and stabilization of microsatellites.
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