Entropy generation in nonlinear levitated optomechanics

Classic thermodynamic predicts that during a physical transformation, the entropy of the system either stays constant or increases due to heat production. Indeed, by looking at the entropy production we can understand if the process is going forward (the entropy increases) or backward (the entropy decreases) in time. When considering smaller systems, however, new phenomena like random fluctuation, non-linear interactions and quantum behaviour must be accounted for. Non equilibrium quantum thermodynamics is a new research topic that focuses on the production of irreversible entropy in these general small-scale systems. Here we use optically levitated nanoparticles in vacuum as an experimental platform to measure the entropy production in a controllable out of equilibrium nonlinear systems. This platform allows for a versatile tuning of the nonlinearity of a levitated oscillator and to operate under far-from-equilibrium conditions. We will investigate entropy production of non-Gaussian states in the classical scenario and then we will push the system to a regime where the quantum nature of the oscillator becomes relevant. This project will represent a cornerstone in validating non-equilibrium quantum thermodynamics and will shed light on the emergence of irreversibility, leading to the origin of an arrow of time.

Let's start by imagining a ball placed in a bowl. When set in motion, it sways back and forth in a rhythm we call harmonic motion-think of the steady swing of a pendulum. If we could create a vacuum-like environment around the ball, eliminating air disturbances, the oscillations would persist for much longer. Now, imagine cooling this system to extremely low temperatures. At this point, the swinging motion slows down and we enter the quantum realm. Here, energy changes occur in well-defined, precise steps known as 'phonons'. The ball begins to exhibit the characteristics of quantum objects, but fundamentally, it remains a harmonic oscillator. What happens if we modify the environment, though? What if we use a complex rollercoaster-like track instead of a simple bowl? The ball's motion will undoubtedly change, but how does it behave when we return it to the quantum state? Quantum theory suggests that the ball will start behaving more like a wave, exhibiting unique interference effects. In this research project, we set out to observe these intriguing behaviours for the first time using optically levitated nanoparticles. We designed an experiment where the rollercoaster-like track was simulated using optical manipulation. In this setup, we demonstrated how thermodynamic tasks, like memory erasure, can be enhanced by our ability of quickly manipulating the potential landscape. Next, we constructed a different setup to examine the effects of nonlinearities in the quantum realm. We outlined a scheme that would cool the particle to the ground state while making it experience a nonlinear potential. By leveraging thermodynamic properties, like entropy production, we developed a theoretical framework that measures the influence of these nonlinearities on the quantum dynamics of the system. This framework also estimates the effectiveness of different procedures to accomplish certain tasks (like transferring a particle from one side to another in a double-well potential), revealing that quantum strategies based on the tunnelling effect can lead to faster, less energy-consuming results. Our next steps involve applying these methods to the quantum setup to observe the effects of nonlinearities in quantum systems. Looking ahead, our next steps involve applying these methods to a quantum setup to observe the effects of nonlinearities within quantum systems. This is an exciting frontier in the field of quantum physics and optomechanics, and we look forward to sharing our further discoveries.