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Relaxation dynamics in closed quantum systems

Periodic Reporting for period 3 - DYNAMIQS (Relaxation dynamics in closed quantum systems)

Reporting period: 2019-05-01 to 2020-10-31

Statistical mechanics, a century-old theory, is probably one of the most powerful constructions of physics. It predicts that the equilibrium properties of any system composed of a large number of particles depend only on a handful of macroscopic parameters, no matter how the particles exactly interact with each other. From the viewpoint of classical physics, equilibration occurs because the microstate of the system uniformly explores the phase space over time — this is the long-known concept of ergodicity. But in quantum mechanics things are different: because quantum dynamics constrains the microstate to evolve along a periodic orbit in the Hilbert space, which is the quantum equivalent of the classical phase space. In the absence of classical ergodicity, what mechanism can then lead to the equilibration of an isolated quantum system? And how long will it take? Answering these questions is not only of fundamental interest. It will also help understand what limits the speed at which quantum information can be transported, or how fast one can change the state of a quantum system, with direct impact on future quantum technologies.

The concept of this project is to take advantage of the great versatility offered by ultra-cold atom systems to investigate the relaxation dynamics in regimes well beyond the boundaries of our current knowledge. We focus our attention on two-dimensional systems and systems with both short- and long-range interactions. Specifically, we will set the system out of equilibrium by a sudden change of the interaction parameter, a ‘quantum quench’, and characterise both the relaxation dynamics and the final state through the measurement of two-point correlation functions. The realisation of the project hinges on the construction of a new-generation quantum gas microscope experiment for Strontium gases enabling us to induce long-range interactions between the atoms. Beside the construction of this apparatus, our main scientific objectives are: (i) to confront the locality of the dynamics to a two-dimensional geometry, where most of the existing results have been obtained in a one-dimension geometry; (ii) to explore situations where quasiparticles are absent or short-lived, and see whether correlations still propagate in ballistic manner; (iii) to study the relaxation dynamics in the presence of long-range interactions, where counter-intuitive behaviours have been predicted, but not yet observed.
The first 30 months of the project have been devoted to the design and construction of the apparatus thanks to which we will produce the quantum gases and perform the experiments. This apparatus can be formally decomposed in five main parts.

I. A laser system for cooling the atoms from the oven temperature (between 500 and 600 degrees Celsius) to about 1 micro-Kelvin, that is a millionth of a degree above the absolute zero temperature. This laser system consists of seven diode lasers working at three different wavelengths: 403, 461 and 689 nanometres. It also includes two spectroscopy cells and a high-finesse reference optical cavity. This laser system is fully operational by now.

II. A vacuum system to isolate the Strontium gas. It is composed of several sections: an oven to produce a vapour a Strontium, a collimation stage to reduce the divergence of the atomic jet exiting the oven, a Zeeman slower to decrease the longitudinal velocity of the jet, a chamber for the magneto-optical trap, where the atoms from the jet are stopped, confined and cooled to about a 1 micro-Kelvin, and finally a 'science' chamber where the experiments will be performed and the microscope is located. The pressure in the last chamber must reach a challenging 10e-12 millibars to ensure a sufficient lifetime for the fragile quantum gas. This setup is almost complete by now.

III. A laser system for transporting the cold gas from the magneto-optical trap chamber to the science chamber and confining and precisely positioning the atoms underneath the microscope. This system involves no less than seven powerful laser beams, produced by two 50 W lasers at 1064 nanometres. Its design was a challenge because of many competing constraints, but the architecture we converged to is very promising. We are currently ordering all the optics necessary t shape the different laser beams.

IV. A fluorescence microscopy system capable of resolving individual atoms separated by half a micrometre. The challenge here consists in collecting enough light from individual atoms to raise the image above the noise level, and to achieve sub-micrometre resolution through a viewport. In order to solve these issues, we have devised an original illumination scheme using a single laser beam to both cool the atoms and make them fluoresce, and we have designed the optical system with a collimating lens placed inside the vacuum chamber, close to the gas. We have already validated the performance of this system on a test-bed.

V. A control software for programming and synchronizing with microsecond accuracy the numerous devices (lasers, RF signal generators, cameras) involved in an experimental cycle. Here we have largely benefited from the work of colleagues at the Max-Planck Institute for Quantum Optics, in Germany, who provided us with a software, which they recently developed for their own use. We have adapted it to our needs and also added a couple of new functionalities. We are now capable of running experiments in a fully automated way.
Our project goes beyond the state of the art in that:
(i) its innovative approach to the fluorescence microscopy imaging, which combines low-cost optics, efficient cooling and powerful, theory-based, digital processing of the images, shall relax the constraints that current methods impose on the optical resolution, the intensity level on the camera, and the depth of the pinning optical lattice;
(ii) it addresses the question of the relaxation dynamics in two-dimensional systems, without or short-or long-range interactions;
(iii) it explores regimes where the quasiparticles that are thought to drive the dynamics at the microscopic level are ill-defined, or even inexistent.

We expect our findings to clarify the status of the scenario according to which the relaxation dynamics of isolated quantum systems is essentially local and the propagation of correlations propagate is driven by that of quasiparticles. Does this scenario describe a universal behaviour? Does it apply to all systems (geometry, range of interaction)? Does it hold for all type of observables (local or non-local, few or many particles)? Our experimental observations will help find an answer to these fundamental questions and thereby improve our understanding of the out-of-equilibrium dynamics of isolated quantum systems well beyond linear response theory.