In the last decade, experimentalists have demonstrated their impressive ability to control mechanical modes within mesoscopic objects down to the quantum level: it is now possible to create mechanical Fock states, to entangle mechanical modes from distinct objects, and to store quantum information or transfer it from one quantum bit to another, among the many possibilities found in today's literature. Indeed, mechanics is quantum, very much like spins or electromagnetic degrees of freedom; and all of this is, in particular, referred to as a new engineering resource for quantum technologies. However, there is also much more beyond this utilitarian aspect: invoking the original discussions of Braginsky and Caves, where a quantum oscillator is thought of as a quantum detector for a classical field, namely, a gravitational wave, which is also a unique sensing capability for quantum fields. The subject of study is then the baths to which the mechanical mode is coupled to, let them be known or unknown in nature. This Perspective is about this new potentiality that addresses stochastic thermodynamics, potentially down to its quantum version, the search for a fundamental underlying (random) field postulated in recent theories that can be affiliated to the class of the wave-function collapse models, and more generally open questions of condensed matter like the actual nature of the elusive (and ubiquitous) two-level systems present within all mechanical objects. However, such research turns out to be much more demanding than the use of a few quantum mechanical modes: all the known baths have to be identified, experiments have to be conducted in-equilibrium, and the word “mechanics” needs to be justified by a real ability to move substantially the center-of-mass when a proper drive tone is applied to the system.
In the last decade, experimentalists have demonstrated their impressive ability to control mechanical modes within mesoscopic objects down to the quantum level: it is now possible to create mechanical Fock states, to entangle mechanical modes from distinct objects, and to store quantum information or transfer it from one quantum bit to another, among the many possibilities found in today's literature. Indeed, mechanics is quantum, very much like spins or electromagnetic degrees of freedom; and all of this is, in particular, referred to as a new engineering resource for quantum technologies. However, there is also much more beyond this utilitarian aspect: invoking the original discussions of Braginsky and Caves, where a quantum oscillator is thought of as a quantum detector for a classical field, namely, a gravitational wave, which is also a unique sensing capability for quantum fields. The subject of study is then the baths to which the mechanical mode is coupled to, let them be known or unknown in nature. This Perspective is about this new potentiality that addresses stochastic thermodynamics, potentially down to its quantum version, the search for a fundamental underlying (random) field postulated in recent theories that can be affiliated to the class of the wave-function collapse models, and more generally open questions of condensed matter like the actual nature of the elusive (and ubiquitous) two-level systems present within all mechanical objects. However, such research turns out to be much more demanding than the use of a few quantum mechanical modes: all the known baths have to be identified, experiments have to be conducted in-equilibrium, and the word “mechanics” needs to be justified by a real ability to move substantially the center-of-mass when a proper drive tone is applied to the system.
To understand in detail the relation between unitary quantum theory that describes our world at the microscopic scale and thermodynamics, which was long believed only to apply to macroscopic objects, is one of the most interesting and long-standing problems in physics. Recently, this problem has received renewed attention, in particular from the community of quantum information theory, but also from the field of statistical mechanics, inspired from stochastic thermodynamics. These results suggest that thermodynamics is also relevant for individual quantum systems, provided that they can be brought into contact with thermal baths. In this thesis, I use recently developed tools to provide new results both on fundamental questions, but also on questions which are of practical relevance for potential miniaturized thermal machines. In terms of fundamental questions, the results in this thesis contribute to understanding how the basic laws of thermodynamics and statistical mechanics can be understood directly from unitary quantum mechanics. In particular, I discuss and answer the following questions: i) How can we quantify the third law of thermodynamics using information theoretic methods? ii) How can we quantify the "thermodynamic value" of a state-transition in quantum systems? iii) How can we axiomatically characterize the non-equilibrium free energy and relative entropy? iv) How can we justify statistical ensembles from an operational perspective, without having to introduce either some probability measures or an information theoretic entropy measure? v) How can we understand the equilibration of closed quantum systems, how long does it take and how difficult is it to avoid? In the second part of the thesis I discuss in detail how experimental restrictions, which become important at the quantum scale, influence the ultimate thermodynamic bounds for thermal machines. In particular, the results in this thesis provide thermodynamic bounds on work-extraction and efficiencies of thermal machines in situations where 1.) an experimenter only has limited field strengths available, 2.) an experimenter cannot control the interactions between particles, but external fields arbitrarily well, and 3.) situations in which a small quantum system can only be strongly coupled to heat baths. These bounds are tight and I provide explicit examples illustrating the different behaviours. Finally, I come back to a classic problem in statistical physics: The emergence of spontaneous symmetry breaking. Here, I provide general and rigorous new results that show how symmetry-breaking stationary states emerge from fluctuations in order parameters in dissipative lattice models.
The building blocks of Nature, namely atoms and elementary particles, are described by quantum mechanics. This fundamental theory is the ground on which physicists have built their major mathematical models [1]. Today, the unique features of quantum objects have led to the advent of promising quantum technologies [2, 3]. However, the macroscopic world is manifestly classical, and the nature of the quantum-to-classical crossover remains one of the most challenging open question of Science to date. In this respect, moving objects play a specific role [4, 5]. Pioneering experiments over the last few years have begun exploring quantum behaviour of micron-sized mechanical systems, adapting laser cooling techniques developed in atomic physics to cool specific modes far below the temperature of their surroundings [6-11]. Here instead we describe a very different approach, passive cooling of a micromechanical system down to 500 microK, reducing the average number of quanta in the fundamental vibrational mode to just 0.3; the challenge being to be still able to detect the motion without disturbing the system noticeably. With such an approach higher harmonics and the surrounding environment are also cooled, leading to potentially much longer mechanical coherence times, and enabling experiments questioning mechanical wave-function collapse [12], potentially from the gravitational background [13, 14], and quantum thermodynamics [15]. Beyond the average behaviour, here we also report on the fluctuations of the fundamental vibrational mode of the device in-equilibrium with the cryostat. These reveal a surprisingly complex interplay with the local environment and allow characteristics of two distinct thermodynamic baths to be probed.
Levitodynamics, i.e., the levitation of objects of mesoscopic size has made huge progress in the last decade, giving rise to new experimental opportunities for instance in materials science, but also allowing to address questions of fundamental physics for the first time. It has become possible to cool a levitated particle of mesoscopic size down to its motional ground state and to observe its motion driven by quantum fluctuations. Such an experiment is ideally suited for an analysis within the stochastic mechanics approach to quantum mechanics, which allows for a dynamic description of individual particle paths. We show that within our approach we reproduce the findings of a recent experiment [Magrini et al., Nature 595-373-377 (2021)]. The phase space dynamics reported there based on a quantum optimal control using Kalman filtering can be understood using the concept of coherent states.
Abstract Heat and work in thermodynamics refer to the measurement of changes in energy content of external bodies (baths and agents). We discuss the implications of quantum mechanics on the possibility to measure work in the mesoscopic context. The agent is a quantum entity (say an oscillator) that is used to drive the system. An inherent limitation is related to back-reaction, leading to a classical-like restriction. We find that in order to resolve fingerprints of interference, an additional quantum uncertainty limitation should be taken into account in the design of the agent. This quantum limitation is fundamental, not merely noise-like blurring.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.