Periodic Reporting for period 1 - NEOVITA (Non-equilibrium optically levitated interacting nanoparticle arrays)
Periodo di rendicontazione: 2023-04-01 al 2025-03-31
This project aims at exploring the nonequilibrium and collective mechanical behaviour of an array of optically trapped nanoparticles (NP) by combining the nonreciprocal light induced interactions between two NPs with the optical control techniques of the atomic tweezer arrays. With these tools the goal is to upscale the experimental platform to multiparticle arrays and to study thermalization, and collective wave phenomena like Anderson localization and how these are affected by the dissipative nonreciprocal interactions. The four work packages (WP) of the project define the main research directions. The WP1 “More particles” consists in finding a way to simultaneously trap up to ten NPs, while maintaining the individual position readouts and the control of the two-body interactions. The WP2 “cavity assisted cooling” aims at placing the NP array into a cavity to cool NP motions via coherent scattering into the cavity mode. The WP3 “prethermalization and disorder” consists in exploring the nonequilibrium evolution of the array in different configurations to search for the prethermalization or the Anderson localization (and possibly the many-body-localization) in the array’s collective dynamics. Finally, the WP4 “manipulation of the non-reciprocal interactions” consists in exploring the full toolbox of the non-reciprocal light-induced interactions and applying the suitable parameters to realize a specific non-Hermitian potential that could suppress the phononic multiple scattering of the Anderson localized array and lead to the observation of the constant intensity waves (CIW).
Research activity during this project included experimental work on upgrading the existing setup, designing a new setup, data acquisition and its evaluation, theoretical modelling with numerical and analytical methods. Our first achievement is the extension of homodyne detection (interferometric method to read out particle positions), whose validity is restricted to small motional amplitudes, to arbitrarily large amplitudes via heterodyne detection with numerical phase reconstruction. This method, inspired from my former research, allowed us to probe the anti-reciprocal interaction, where the NPs drive each other’s motion into limit cycles with high motional amplitudes. Our second achievement was the exploration of the full non-Hermitian and nonlinear NP dynamics in this regime with the results that we reported in an article published in a peer reviewed journal. Our next achievement is the ability to tune the relative frequency difference between the optical tweezers. With this tool at hand, we were able to make the interparticle interactions time dependent and with additional implementation of feedback cooling of one of the particles, we could realize the nonequilibrium protocols where the interaction and cooling are suddenly switched on/off. Finally, special effort was devoted to upscaling the setup to more than two particles. In this direction we came up with the idea to build a new experiment where instead of NPs, we shall couple with light the flexural mechanical modes of the individual dielectric nanopillars on a fabricated nanopillar array. The advantage is that in difference to the nanoparticles, for which the laser plays the role of trap and mediator of interactions, the nanopillars do not require trapping which is very costly in terms of the laser power. Main achievement in this direction is the new collaboration with Prof. Eva Weig from the Technical University of Munich, who will supply us with the nanopillar samples.
The focus of the first experiment of this project was to measure the collective dynamics of two particles in the regime of anti-reciprocal interaction (one of the particles pushes the other one while the other one pulls the first one with the same strength). This experiment resulted in observation of the non-Hermitian dynamics of the NPs characterized by strong correlations in their motion resembling the chase-runaway dynamics. This, in turn, forces both NPs to oscillate at same frequency and at increased motional energies. This result is highly relevant for the WP4 since it allows to control the local amplification induced by non-Hermitian motion. When non-Hermitian gain overcame the motional damping rates, stable limit cycle trajectories emerged for both NPs, showing a transition into nonlinear dynamics, interpreted as mechanical lasing. The corresponding results were reported in an article published in the peer-reviewed Nature Physics journal.
Still with two NPs we then explored the time dependent interactions by precisely tuning the relative frequency difference between the optical tweezers, later called “optical detuning” (OD). The ability to tune this parameter conferred additional yet unexplored function to the Acousto-Optic Deflectors (AODs) already operating on our setup for producing and controlling the optical tweezers. This new function consists in switching on or off the interparticle coupling by making it on- or off-resonant via the optical detuning quasi-instantaneously compared to the mechanical time scales. Moreover, making sure that one of the NPs is electrically charged, we could cool down its motion via feedback cooling while leaving the other NP’s motion at (high) room temperature. Using this initial state, we measured the system’s nonequilibrium evolution once cooling and interaction were suddenly switched off and on, respectively. Importantly, once the interaction is switched on via the OD, it is not constant, but oscillating in time at the optical detuning frequency. Nevertheless, as mentioned above, the coupling between the NPs can be made resonant by either tuning the OD to the mechanical frequency difference (called difference frequency detuning, or DFD), or by tuning the OD to be equal to the sum of the mechanical oscillation frequencies (called sum frequency detuning, or SFD). In the first case the nature of coupling is the same as in the nondetuned case, while it becomes different different in the second case. For example, with reciprocal interaction, the DFD restores the energy exchange oscillations between the NPs, characteristic of the beamsplitter (also called state-swap) type coupling and non-Hermitian gain characteristic of the parametric amplification in case of the anti-reciprocal interaction. Interestingly, we observed that the SFD case transforms the reciprocal interaction into the parametric amplification type coupling while anti-reciprocal interaction gives rise to the state-swap type coupling. This experiment is currently at the final stage of the data evaluation and we expect to publish the results soon.
Despite the absence of experimental results with more than 2 NPs during this project, a realistic strategy was elaborated to upscale the experiment to a multiparticle tweezer array. For this we shall use the fabricated arrays of semiconductor nanopillars imprinted on a silicon substrate and couple them with laser light, the same way we have been doing with trapped NPs. A new collaboration with the group of Prof. Eva Weig from the Technical University of Munich has started and will provide us NP array samples and the expertise of their manipulation. This in turn will lead to the realization of objectives of the WP1 beyond the duration of the NEOVITA project.
Finally, it is worth noting that the WP2 “cavity assisted cooling” has not been elaborated during this project in order to avoid the overlap with my group colleague’s work, who was busy with the exploration of this direction on his setup during the same period. Significant progress that he could achieve will be easily transferrable within the group and implemented in the further research going beyond the NEOVITA project.
Still with two NPs we then explored the time dependent interactions by precisely tuning the relative frequency difference between the optical tweezers, later called “optical detuning” (OD). The ability to tune this parameter conferred additional yet unexplored function to the Acousto-Optic Deflectors (AODs) already operating on our setup for producing and controlling the optical tweezers. This new function consists in switching on or off the interparticle coupling by making it on- or off-resonant via the optical detuning quasi-instantaneously compared to the mechanical time scales. Moreover, making sure that one of the NPs is electrically charged, we could cool down its motion via feedback cooling while leaving the other NP’s motion at (high) room temperature. Using this initial state, we measured the system’s nonequilibrium evolution once cooling and interaction were suddenly switched off and on, respectively. Importantly, once the interaction is switched on via the OD, it is not constant, but oscillating in time at the optical detuning frequency. Nevertheless, as mentioned above, the coupling between the NPs can be made resonant by either tuning the OD to the mechanical frequency difference (called difference frequency detuning, or DFD), or by tuning the OD to be equal to the sum of the mechanical oscillation frequencies (called sum frequency detuning, or SFD). In the first case the nature of coupling is the same as in the nondetuned case, while it becomes different different in the second case. For example, with reciprocal interaction, the DFD restores the energy exchange oscillations between the NPs, characteristic of the beamsplitter (also called state-swap) type coupling and non-Hermitian gain characteristic of the parametric amplification in case of the anti-reciprocal interaction. Interestingly, we observed that the SFD case transforms the reciprocal interaction into the parametric amplification type coupling while anti-reciprocal interaction gives rise to the state-swap type coupling. This experiment is currently at the final stage of the data evaluation and we expect to publish the results soon.
Despite the absence of experimental results with more than 2 NPs during this project, a realistic strategy was elaborated to upscale the experiment to a multiparticle tweezer array. For this we shall use the fabricated arrays of semiconductor nanopillars imprinted on a silicon substrate and couple them with laser light, the same way we have been doing with trapped NPs. A new collaboration with the group of Prof. Eva Weig from the Technical University of Munich has started and will provide us NP array samples and the expertise of their manipulation. This in turn will lead to the realization of objectives of the WP1 beyond the duration of the NEOVITA project.
Finally, it is worth noting that the WP2 “cavity assisted cooling” has not been elaborated during this project in order to avoid the overlap with my group colleague’s work, who was busy with the exploration of this direction on his setup during the same period. Significant progress that he could achieve will be easily transferrable within the group and implemented in the further research going beyond the NEOVITA project.