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

Carlos Sánchez Muñoz (Clarendon Laboratory, University of Oxford)

12:00 03-06-2019

The presence of a strong symmetry guarantees the existence of several steady statesbelonging to different symmetry sectors. In this talk I discuss how, when the system isinitialized in a quantum superposition involving several of these sectors, each individualstochastic trajectory will randomly select a single one of them and remain there for the restof the evolution. Since a strong symmetry implies a conservation law for the symmetryoperator on the ensemble level, the selection of a single sector from an initial superpositionentails a breakdown of this conservation law at the level of individual realizations. Sincesuch a superposition is impossible in a classical, stochastic trajectory, this is a a purelyquantum effect with no classical analogue. Our results show that a system with a closedLiouvillian gap may exhibit, when monitored over a single run of an experiment, abehaviour completely opposite to the usual notion of dynamical phase coexistence andintermittency, typically considered hallmarks of a dissipative phase transition. We discussour results on a simple, realistic model of squeezed superradiance.

Seminar Room, Serrano 121 (CFMAC)

## Detecting order in optical lattice experiments

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

12:00 01-06-2019

The advent of quantum gases as quantum simulators of mesoscopicstrongly-correlated systems calls for the development of newexperimental and numerical methods to characterise quantum phases beyondwell-established order parameters suitable for systems in thethermodynamic limit.

In this talk I will present our analysis of two methods to detect phasesand phase transitions in the dipolar Bose-Hubbard model on finitetwo-dimensional lattices of sizes similar to those realised in opticallattice setups [1]. First, I will assess several observables in theirability to detect superfluidity and density-wave order in small latticesystems. Then, I will compare this approach with one based on applyingunsupervised machine-learning techniques to single-site-resolved densitymeasurements.

Time permitting, I will introduce a method to control dipole-dipoleinteractions by dressing molecular states with magnetic and microwavefields, and outline its potential application to implement a quantumgate 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, andJ. Mur-Petit, in preparation.

In this talk I will present our analysis of two methods to detect phasesand phase transitions in the dipolar Bose-Hubbard model on finitetwo-dimensional lattices of sizes similar to those realised in opticallattice setups [1]. First, I will assess several observables in theirability to detect superfluidity and density-wave order in small latticesystems. Then, I will compare this approach with one based on applyingunsupervised machine-learning techniques to single-site-resolved densitymeasurements.

Time permitting, I will introduce a method to control dipole-dipoleinteractions by dressing molecular states with magnetic and microwavefields, and outline its potential application to implement a quantumgate 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, andJ. Mur-Petit, in preparation.

Seminar Room, Serrano 121 (CFMAC)

## 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)

Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria)

11:30 15-03-2019

The possibility of levitating very small particles in controlled environments has brought fortha 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 mechanicalground 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 internaldynamics of levitated nanoparticles (NPs). In the first part, I will introduce our recent theoreticalmodel describing the cavity-assisted cooling of the COM temperature of a levitated NP via coherentscattering into an optical cavity [1]. This full quantum model extends on previous results by includingall relevant degrees of freedom and a detailed analysis of the decoherence mechanisms, and isbenchmarked 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 isattainable with state of the art experiments, indicating that such a milestone is likely to be reached inthe near future.In the second part of the talk, I will move on from external to internal dynamics, specificallyto the phenomenon of radiative thermalization in levitated NPs. I will argue why the extremeconfinement and isolation of the NP should make the usual quasi-equilibrium theoretical models failin high vacuum levitodynamics setups. Based on these arguments, I will introduce a theoretical toymodel of a NP which, on the one hand, allows to recover all its measurable thermal and opticalproperties and, on the other hand, is exactly solvable [3]. Such exact solution evidences that, accordingto our model, radiative thermalization in these systems is a largely out-of-equilibrium process, whereprevious models do indeed fail and where temperature cannot be defined. This is only one amongmany examples showing the new regimes of condensed matter and light-matter interaction arising inlevitodynamics 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