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Squeezing is a crucial resource for quantum information processing and quantum sensing. In levitated nanomechanics, squeezed states of motion can be generated via temporal control of the trapping frequency of a massive particle. However, the amount of achievable squeezing typically suffers from detrimental environmental effects. We analyze the performance of a scheme that, by embedding careful time-control of trapping potentials and fully accounting for the most relevant sources of noise -- including measurement backaction -- achieves significant levels of mechanical squeezing. The feasibility of our proposal, which is close to experimental state-of-the-art, makes it a valuable tool for quantum state engineering., Comment: 12 pages, 4 figures, comments are welcome! Quantum Sci. Technol (2024)

We report on an experiment achieving the dynamical generation of non-Gaussian states of motion of a levitated optomechanical system. We access intrinsic Duffing-like nonlinearities by thermal squeezing of an oscillator's state of motion by rapidly switching the frequency of its trap. We characterize the experimental non-Gaussian state versus expectations from simulations and give prospects for the emergence of genuine nonclassical features.

Non-equilibrium thermodynamics can provide strong advantages when compared to more standard equilibrium situations. Here, we present a general framework to study its application to concrete problems, which is valid also beyond the assumption of a Gaussian dynamics. We consider two different problems: 1) the dynamics of a levitated nanoparticle undergoing the transition from an harmonic to a double-well potential; 2) the transfer of a quantum state across a double-well potential through classical and quantum protocols. In both cases, we assume that the system undergoes to decoherence and thermalisation. In case 1), we construct a numerical approach to the problem and study the non-equilibrium thermodynamics of the system. In case 2), we introduce a new figure of merit to quantify the efficiency of a state-transfer protocol and apply it to quantum and classical versions of such protocols.

Manipulating quantum systems undergoing non-Gaussian dynamics in a fast and accurate manner is becoming fundamental to many quantum applications. Here, we focus on classical and quantum protocols transferring a state across a double-well potential. The classical protocols are achieved by deforming the potential, while the quantum ones are assisted by a counter-diabatic driving. We show that quantum protocols perform more quickly and accurately. Finally, we design a figure of merit for the performance of the transfer protocols -- namely, the protocol grading -- that depends only on fundamental physical quantities, and which accounts for the quantum speed limit, the fidelity and the thermodynamic of the process. We test the protocol grading with classical and quantum protocols, and show that quantum protocols have higher protocol grading than the classical ones.

Many advanced quantum techniques feature non-Gaussian dynamics, and the ability to manipulate the system in that domain is the next-stage in many experiments. One example of meaningful non-Gaussian dynamics is that of a double-well potential. Here we study the dynamics of a levitated nanoparticle undergoing the transition from an harmonic potential to a double-well in a realistic setting, subjecting to both thermalisation and localisation. We characterise the dynamics of the nanoparticle from a thermodynamic point-of-view, investigating the dynamics with the Wehrl entropy production and its rates. Furthermore, we investigate coupling regimes where the the quantum effect and thermal effect are of the same magnitude, and look at suitable squeezing of the initial state that provides the maximum coherence. The effects and the competitions of the unitary and the dissipative parts onto the system are demonstrated. We quantify the requirements to relate our results to a bonafide experiment with the presence of the environment, and discuss the experimental interpretations of our results in the end., Comment: 12 pages, 6 figures. Comments are welcome

Adiabatic evolution is considered to be the ideal situation for most thermodynamic cycles, as it allows for the achievement of maximum efficiency. However, no power output is produced in light of the infinite amount of time required to perform a transformation. Such issue can be overcome through Shortcuts-To-Adiabaticity (STA) protocols, which allows a dynamics to mimic its adiabatic counterpart, but in a finite time. Transitionless quantum driving (TQD) is one form of STA. We develop and study the effects of TQD on a single-qubit system subjected to a changing magnetic field and a general two-qubit Heisenberg model with a time-dependent interaction strength. We establish a quantitative relation between the work produced across the dynamics and the entropy production resulting from the evolution at hand, focusing on the role played by the initial states of the work medium. We identify the states that extremize performance under the TQD protocol. The thermodynamic implications of STA are discussed in the end., Comment: 9 pages, 10 figures. Comments are welcome!