## New results in levitodynamics: a tale of two temperatures

Carlos González-Ballestero (Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria)

The possibility of levitating very small particles in controlled environments has brought forth a whole new field of research: levitodynamics. In the last few years, significant experimental advances have been reported, e.g. the achievement of stable levitation in ultra-high vacuum, and the levitation of particles of many different shapes and materials. One of the most sought goals of current levitodynamics experiments is the cooling of the center of mass (COM) motion to the mechanical ground state, as such a milestone would allow to access the quantum regime of an extremely isolated nanomechanical oscillator. Moreover, the extreme isolation and confinement of levitated particles suggests that the behavior of internal degrees of freedom in these systems (electrons, phonons, magnons…) might significantly differ from bulk matter or from less isolated nanoparticles. In my talk, I will present our results on both the external (COM) dynamics and the internal dynamics of levitated nanoparticles (NPs). In the first part, I will introduce our recent theoretical model describing the cavity-assisted cooling of the COM temperature of a levitated NP via coherent scattering into an optical cavity [1]. This full quantum model extends on previous results by including all relevant degrees of freedom and a detailed analysis of the decoherence mechanisms, and is benchmarked by quantitatively reproducing the recent experiments reporting, for the first time, three- dimensional cooling near the ground state [2]. I will further demonstrate how ground state cooling is attainable with state of the art experiments, indicating that such a milestone is likely to be reached in the near future. In the second part of the talk, I will move on from external to internal dynamics, specifically to the phenomenon of radiative thermalization in levitated NPs. I will argue why the extreme confinement and isolation of the NP should make the usual quasi-equilibrium theoretical models fail in high vacuum levitodynamics setups. Based on these arguments, I will introduce a theoretical toy model of a NP which, on the one hand, allows to recover all its measurable thermal and optical properties and, on the other hand, is exactly solvable [3]. Such exact solution evidences that, according to our model, radiative thermalization in these systems is a largely out-of-equilibrium process, where previous models do indeed fail and where temperature cannot be defined. This is only one among many examples showing the new regimes of condensed matter and light-matter interaction arising in levitodynamics experiments. [1] C. Gonzalez-Ballestero, P. Maurer, D. Windey, L. Novotny, R. Reimann, O. Romero-Isart, arXiv: 1902.01282 (2019) [2] Dominik Windey, C. Gonzalez-Ballestero, P. Maurer, L. Novotny, O. Romero-Isart, R. Reimann, arXiv: 1812.09176 (2018) [3] A. E. Rubio López, C. Gonzalez-Ballestero, and O. Romero-Isart, Phys. Rev.B 98, 155405 (2018)

Seminar Room, Serrano 113b

## Detecting order in optical lattice experiments

Jordi Mur-Petit (Clarendon Laboratory, University of Oxford)

The advent of quantum gases as quantum simulators of mesoscopic strongly-correlated systems calls for the development of new experimental and numerical methods to characterise quantum phases beyond well-established order parameters suitable for systems in the thermodynamic limit. In this talk I will present our analysis of two methods to detect phases and phase transitions in the dipolar Bose-Hubbard model on finite two-dimensional lattices of sizes similar to those realised in optical lattice setups [1]. First, I will assess several observables in their ability to detect superfluidity and density-wave order in small lattice systems. Then, I will compare this approach with one based on applying unsupervised machine-learning techniques to single-site-resolved density measurements. Time permitting, I will introduce a method to control dipole-dipole interactions by dressing molecular states with magnetic and microwave fields, and outline its potential application to implement a quantum gate between polar molecules [2]. [1] P. Rosson, M. Kiffner, J. Mur-Petit, and D. Jaksch, to be submitted. [2] M. Hughes, M. D. Frye, D. Jaksch, M. R. Tarbutt, J. M. Hutson, and J. Mur-Petit, in preparation.

Seminar Room, Serrano 121 (CFMAC)

## Symmetries and Conservation Laws in Quantum Trajectories: Dissipative Freezing

Carlos Sánchez Muñoz (Clarendon Laboratory, University of Oxford)

The presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. In this talk I discuss how, when the system is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the symmetry operator on the ensemble level, the selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Since such a superposition is impossible in a classical, stochastic trajectory, this is a a purely quantum effect with no classical analogue. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behaviour completely opposite to the usual notion of dynamical phase coexistence and intermittency, typically considered hallmarks of a dissipative phase transition. We discuss our results on a simple, realistic model of squeezed superradiance.

Seminar Room, Serrano 121 (CFMAC)