Stochastic Thermodynamics of Nonlinear Quantum Systems

This award is being funded by the Condensed-Matter and Materials Theory program in the Division of Materials Research and by the Atomic, Molecular, and Optical Physics Theory program in the Division of Physics. Nontechnical summary

We are on the verge of a technological revolution. Over the last few years, computational hardware has become commercially available that promises to take full advantage of quantum supremacy. However, none of the available systems is readily useful for practical application, since the hardware is still prone to decoherence and the limitations of linear quantum mechanics.

The prevailing theory for studying effects of thermal noise in quantum systems is Quantum Thermodynamics. This emerging field has already delivered insights and results of practical consequence for the design of quantum computers. While most previous research has focused exclusively on linear systems, nonlinear quantum systems in photonic or ultracold atom gases exhibit unique and powerful capabilities for computing.

However, to design efficient quantum computers, one has to understand the thermodynamics of the underlying material, since writing as well as erasing comes at the expense of thermodynamic work (Landauer's principle). To date, the nonequilibrium thermodynamics of nonlinear systems has been understood only at a rudimentary level. Therefore, this project will extend the scope of stochastic thermodynamics to nonlinear quantum systems.

This project will help lay the groundwork for 21st-century information technology. By investigating the ultimate physical limits and tradeoffs of computation, it will help develop the theoretical foundation essential for constructing post-Moore's-Law computer architectures and contribute to future engineering and manufacturing of energy-efficient computer architectures.

To achieve these impacts, the project will involve graduate and undergraduate students in cutting-edge research, preparing the nation's next generation of scientists. Technical summary

Scientific efforts in classical as well as quantum stochastic thermodynamics have focused on the description of so-called information engines, which also have been realized experimentally. An information engine is a thermodynamic device that operates by processing information and can thus be considered the thermodynamic paradigm for any (quantum) computer.

The project will contribute to this dynamic field of research by generalizing the theory of quantum stochastic thermodynamics to nonlinear systems. This research is of topical interest, since to build a quantum computer in a nonlinear quantum system, one must understand the interplay of information and entropy production. To achieve this goal, the project will focus on three main topics: generalizing fundamental notions of work, heat, and entropy production at the nanoscale from linear to nonlinear quantum mechanics, studying the interplay of (quantum) information and (quantum) thermodynamics, and generalizing the quantum speed limit and its applications in order to identify optimal quantum processes with minimal dissipation or maximally fast information processing.

In particular, this project will aim at (i) the numerical study of the quantum speed limit, i.e., the maximal rate with which a quantum state can evolve under nonlinear dynamics; (ii) the development of a consistent framework for stochastic thermodynamics in nonlinear quantum systems, comprising the identification and study of entropy and information production, and the derivation of generalized fluctuation theorems; (iii) the theoretical study and design of minimal, yet self-contained, quantum information engines, which optimally exploit computational advantages arising from nonlinear dynamics; and (iv) the development of a conceptual framework and the design of experiments for quantum information engines in Bose-Einstein condensates.

The results could impact the design of quantum computers and the fundamental understanding of quantum nanotechnology. Moreover, this research will open new avenues for the understanding of time-dependent quantum-information-processing systems operating arbitrarily far from thermal equilibrium. Finally, the proposed research is also of basic theoretical interest, since the methodology, including quantum optics and quantum optimal control theory, provides conceptually simple models and tools to describe nano-devices subjected to both thermal and quantum fluctuations.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.