LOng Range ENtanglement between charged levitated particles

Project Information

LOREN

Grant agreement ID: 101030987

DOI

10.3030/101030987

Project closed

EC signature date 19 April 2021

Start date 1 July 2021

End date 16 August 2023

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 186 167,04

EU contribution

€ 186 167,04

Coordinated by

UNIVERSITAT WIEN
Austria

Periodic Reporting for period 1 - LOREN (LOng Range ENtanglement between charged levitated particles)

Reporting period: 2021-07-01 to 2023-06-30

Summary of the context and overall objectives of the project

The quantum superposition principle and entanglement are fundamental microscopic features essential for advanced quantum technologies such as telecommunication and computing. Entangling macroscopic mechanical oscillators probes the boundary between quantum mechanics and classical physics. The entanglement generated by the long-range Coulomb interaction between large-mass systems is a pivotal step toward achieving gravitationally induced entanglement in future experiments. The experimental study of electromagnetic quantization and vacuum fluctuations, in the context of entanglement between macroscopic systems, is vital for testing core quantum principles like causality and complementarity at the macro scale. In this project, I address the problem of generation of quantum entanglement between two optically trapped large-mass (~10^8 amu) particles using Coulomb interaction. Generating entanglement between macroscopic systems is challenging, but I've broken it down into the following primary objectives: 1 – Optical trapping and precise control over the net charge of two closely located dielectric particles; 2 – Quantum ground state cooling of two sub-micron charged particles in separate optical traps; 3 – Protocol and verification of steady-state entanglement. Importantly LOREN offers a platform for exploring intersections between thermodynamics, information theory, and quantum physics, with potential applications in quantum technology, sensing, and metrology. This study aligns with the current research priorities of the EU society, emphasizing quantum metrology & sensing and fundamental quantum science.

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

To achieve quantum entanglement between strongly interacting particles, I designed and built a new experimental setup together with my team members. To define the parameter space in our experiment, we developed a quantum Langevin model featuring optimal control and active feedback based on continuous measurement. To achieve the high net charge necessary for strong interaction, we implemented several active and passive charging methods, including charging particles by creating plasma inside the vacuum chamber near optical traps or through directed ion flux onto the trapped particles and by modifying the particle surface chemically to achieve a high charge-to-mass ratio. By combining both active and passive charging methods, we successfully brought the experimentally accessible parameter space to the level necessary for quantum entanglement in the conditional state. To bring the normal modes of strongly interacting particles to the ground state of motion, we developed split homodyne detection with a high information collection efficiency of approximately 50%. This efficiency was achieved by using a custom-built trapping lens with an NA of 0.8 optimizing the design of the particle imaging system and mode-matching, and employing a custom-built balanced photodetector that provides up to 94% detection efficiency with an input power of 15mW. This was determined experimentally; the theoretical limit stands at 99%. We then developed an optimal protocol to cool both normal modes to the quantum ground state based on cold damping through a single pair of electrodes and laser parametric cooling addressing each particle individually. The protocol enables ground state preparation for both differential and common normal modes. Towards entanglement generation, we have made significant progress in developing an original protocol that brings our system into the entangled state within the experimental parameter set. Our approach is two-fold; it involves advanced quantum control based on a specifically optimized cost function of our time-dependent Kalman filter combined with modulation of the long-range interaction between particles. Numerical simulations demonstrate the entanglement of both conditional and unconditional states under realistic experimental conditions. Some of our findings related to motion control and Heisenberg-limited detection have been recently published in the manuscript: Reisenbauer et.al "Non-Hermitian dynamics and nonreciprocity of optically coupled nanoparticles," available at arXiv:2310.02610 (2023), https://doi.org/10.48550/arXiv.2310.02610.
In addition to the main course of the project, I developed some independent ideas towards the experimental realization of the vibrational Bose-Einstein condensate (BEC) and generation of optomechanical-type entanglement between collective vibrational and electronic light-matter states at room temperature. In particular, I propose a novel macro-coherent regime in molecular systems with strong vibronic coupling. In a recent manuscript: Shishkov et.al "Mapping polariton Bose--Einstein condensate onto vibrational degrees of freedom," arXiv:2309.08498 (2023), https://doi.org/10.48550/arXiv.2309.08498 we introduce an innovative methodology for vibrational amplification in a resonant blue-detuned configuration consistent with state-of-the-art experiments. Our research takes a step forward in the direction of vibrational BEC, offering potential advancements in cavity-controlled chemistry, as well as nonlinear and quantum optics.

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)

In our pursuit of quantum entanglement between interacting particles, we have designed and built a new experimental setup featuring Heisenberg-limited detection efficiency with independent control and motion readout for both optically trapped particles. We also developed an original quantum Langevin model to define the parameter space for the entanglement problem in both the steady state and the dynamical regime. By combining both active and passive particle charging methodologies, we achieved the experimental parameter space required for entanglement generation. We managed to trap mesoporous particles with a surface area two orders of magnitude larger and a few times less mass, resulting in almost an order of magnitude higher coupling strength. Our split homodyne interferometry achieves an impressive 50% total detection efficiency of motion, representing a significant advancement toward ground state cooling and entanglement generation. Furthermore, optimal protocols that we developed is a promising avenue for ground state preparation and entanglement generation. Expected future outcomes include realization of these protocols followed by experimental validation of the entanglement. Morevoer the project contributes to the field of cavity-controlled chemistry, nonlinear, and quantum optics with molecules, promising macroscopic quantum coherent phenomena immune against decoherence and disorder at room temperature. The socio-economic impact is substantial, as these innovations promote fundamental research, could drive technological advancements, foster international collaborations, and enhance educational initiatives in related fields.

Experimental setup to achieve entanglement (left) and schematic of vibrational amplification (right)