# Zenith Grant Awardee

## Jens Eisert

### Freie Universität Berlin

Co-Investigators

Jörg Schmiedmayer, Atominstitut Vienna; Marcus Huber, IQOQI Vienna

Project Title

Fueling quantum field machines with information

Project Summary

It has long been noted that thermodynamic notions and those of information are intricately intertwined: The forefathers of thermodynamics such as Boltzmann and Gibbs were driven in their work by deep insights on how the information available about a system alters its meaningful description, a picture later augmented by seminal work of Shannon on abstract information theory. Indeed, information is at the heart of any thermodynamic machine, determining whether energy is directed (work) or undirected (heat). The idea that thermodynamics ultimately emerges from a lack of certain information was corroborated by the famous thought experiments by Maxwell and Szilard that perplexed the scientific community by coming to paradoxical conclusions when making hypothetical assumptions on obtainable information.

We aim at a disruptive alteration of that picture. We set out to turn the connection between information and thermodynamics upside down, by exploring how information that can actually operationally be acquired can be harnessed to achieve control over quantum machines. We do so at hand of introducing and exploring a key vehicle constituting what we call a quantum field machine. Once realized, together with a portfolio of new theoretical and foundational techniques, we will delve into uncharted territory of the interplay of information and thermodynamics in complex quantum systems.

At the heart of our endeavor stands a proposed quantum field machine in the AtomChip of Jörg Schmiedmayer, theoretically driven by Jens Eisert and Marcus Huber. Instead of cogs and wheels, our device is made from collective excitations of thousands of atoms, that are best described by quantum fields. It could be viewed as one of the first genuine quantum thermal machines: antum mechanics is crucially required to capture its very functioning, and unlike machines involving a few particles, one cannot eiciently predict all its properties. A broad range of experimental measurement techniques allow deep insights into quantum properties of the information gained. This delicate information can be exploited to manipulate these quantum scale machines to literally use information as fuel. While classical machines are indierent to observation, quantum measurements intrinsically alter the machines. This galvanizes the challenge of identifying ways of minimally invasive measurements to acquire control. This ability, which we envision to experimentally demonstrate, conjures an intriguing question: If information is fuel, how much fuel is needed to gain information? Indeed, perfect knowledge of micro-states would enable a deterministic manipulation and even cooling to absolute zero, ruled out by the third law. Does this mean that the laws of thermodynamics have to be revised, or rather that perfect knowledge is as impossible as reaching zero temperature? We aim at unraveling the philosophical and mathematical underpinnings of information acquisition, proving from first principles that as certainty of knowledge increases, the thermodynamic cost of establishing it diverges. The quantum field machines will be the first testing ground where these ideas can be flexibly tested, connecting operational thermodynamic machines to fundamental challenges in the philosophy of science.

Technical Abstract

We propose no less, so we think, than the construction of the first genuine many-body quantum engine based on thermodynamic principles. It constitutes the vehicle of our comprehensive program of elucidating the role information plays as a notion of fuel in thermodynamics. It exhibits a complexity far transcending the few qubit regime, yet allows for flexible measurement schemes that enables a detailed study of how much fuel it takes to gain information, how that information is inevitably lost through thermalization and ultimately how information can be used as fuel. This anticipated device derives from ultra-cold atoms that in a tuneable fashion realize the full range from noninteracting to strongly correlated quantum fields. The key novel ingredient that brings this device to a new level are precisely programmable time-dependent potentials allowing to manipulate the quantum fields. In this way, operational primitives of compression, time evolution, spliing, merging, squeezing, and entangling can be implemented. antum mechanics is crucially required to capture its very functioning, and unlike machines involving a few degrees of freedom, one cannot eiciently predict all its properties. A broad range of experimental measurement techniques like single atom detection or high-order correlation measurements allow deep insights into quantum properties of the information gained. The functioning of this machine relies on thermalization dynamics and is intertwined with the long-standing puzzle of how thermalization and quantum mechanics can be precisely reconciled. This will allow us to investigate the next question: If we had more information, how could we use it to our benefit? Is information really a fuel for thermodynamic machines and how could we harness it? For a classical engine, knowing specific micro-states of some fuel particles will not allow any improvement of its eiciency – indeed, the very crucial part to this knowledge is also the ability to control systems at the level of the information one has about them. If apparent thermalization is accompanied with a loss of information, how can we, aer all, operationally exploit information? If the hypothetical Maxwell’s demon has implausibly much knowledge available leading to paradoxes, how much can practically accessible information available by an observer be teleologically exploited in thermalization control? Building upon ideas of harnessing information leads to the third core theme, asking about the thermodynamic cost of gaining knowledge. Indeed, the very fact that information can be used as fuel conjures the notion that it cannot be obtained freely. Here, we aim at unravelling the ultimate limits to obtaining knowledge, proving from first principles that as certainty of knowledge increases, the thermodynamic cost of establishing it diverges. The quantum field machines will be the first testing ground where these ideas can be flexibly tested, as the quality of information can be controlled by performing measurements of dierent levels of invasiveness by measuring only few atoms instead of the field and the obtainable information depends on the underlying emergent quantum field model, as well as the correlation functions one has experimental access to.

## QSpace Latest

Video: *IPI Talk – Dr. Emily Adlam: Are Entropy Bounds Epistemic?*

Entropy bounds have played an important role in the development of holography as an approach to quantum gravity. In this talk I will introduce the strong and covariant entropy bounds, and then discuss how the covariant bound should be interpreted. I will argue that there is a possible way of thinking about the covariant entropy bound which would suggest that it encodes an epistemic limitation rather than an objective count of the true number of degrees of freedom on a light-sheet; thus I will distinguish between ontological and epistemic interpretations of the covariant bound. I will consider the consequences that these interpretations might have for physics and discuss what each approach has to say about gravitational phenomena. My aim is not to advocate for either the ontological or epistemic approach in particular, but rather to articulate both possibilities clearly and explore some arguments for and against them.