• Frenkel-Kontorova model
• Rydberg-dressing
• thermalization
• quantum thermodynamics
• quantum engine
• quantum simulation
• cold atoms
• optical tweezers
• rubidum
• potassium
• Raman spectroscopy

The main topic of this thesis is the manipulation of single ultracold atoms, that have proven to be an excellent tool for quantum thermodinamics experiments and for the simulation of physical systems. This work fits into the Qmix experiment developed by the Quantum Gases research group at the School of Physics and Astronomy of the University of Birmingham. Qmix is an experiment devoted to the study of quantum thermodynamics in which single K-41 atoms are trapped in species-selective optical tweezers and immersed in a thermal bath of Rb-87 atoms. This experiment will enable the realisation of arbitrary quantum thermodynamic transformations that, combined in cycles, will implement quantum heat engines. Being able to control single atoms with optical tweezers is also useful to build quantum simulators. In my thesis I will discuss a proposal for the study of the Frenkel-Kontorova model (FKM) with this technology. The FKM consists of a chain of particles with long-range spring interactions, placed in a sinusoidal potential. Its distinguishing feature is the competition between the length scales of these two potentials.

The thesis is structured as follows. Chapter 1 provides an introduction to the topics addressed in the thesis and places this work in the current state of the art of research. Chapter 2 describes a compact setup for the Raman sideband spectroscopy of the K-41 atom. This setup will allow to measure the temperature of the single atom and assess the thermalization with the bath. In the first section of the chapter, I give a brief overview on the whole Qmix experiment. Then I present a numerical code that simulates Raman coupling by solving the quantum master equation, providing a tool for predicting the behaviour of the experiment and for fitting the data. Finally, I describe the experimental setup and present some characterisation measures.

In chapter 3, I present a Monte Carlo simulation of the thermalization of a single K-41 atom trapped in optical tweezers and immersed in a thermal bath of ultracold Rb-87 atoms. This code will inform the optimal procedure to reach the thermalization in the Qmix experiment. First, an expression for the transition rates between the trap levels for the single atom is derived. The simulation is then used to explore the dependence of the thermalization timescale on various parameters. A bath undergoing evaporative cooling is also simulated, providing a rather efficient way to sympathetically cool the single atom. Finally, losses due to three-body recombination are taken into account, demonstrating how they don’t substantially limit the efficiency of this sympathetic cooling process.

Chapter 4 describes a method for the experimental realization of the Frenkel-Kontorova model using an array of Rydberg-dressed atoms in an optical lattice. Since the original model uses a nonrealistic infinite range spring interaction potential, it's interesting to develop a fully controlled system where the effect of realistic interaction potentials can be tested. Rydberg-dressed atoms allow to control the range and the functional dependence of the interaction potentials. Two different interaction potentials are examined: a springlike potential whose phenomenology is very close to the original fkm, and a repulsive potential that exhibits some anomalous features. Numerically calculated phase diagrams for the ground states of such systems are reported.

Finally, in chapter 5, I summarize the results and draw out some considerations on future developments.