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arXiv:1606.03318 · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

Organic molecule fluorescence as an experimental test-bed for quantum jumps in thermodynamics

Cormac Browne, Tristan Farrow, Oscar Dahlsten, Robert A. Taylor, Vlatko Vedral

Published Aug 1, 2017• 1 citation
arXivHTMLPDF

Abstract

We demonstrate with an experiment how molecules are a natural test bed for probing fundamental quantum thermodynamics. Single-molecule spectroscopy has undergone transformative change in the past decade with the advent of techniques permitting individual molecules to be distinguished and probed. We demonstrate that the quantum Jarzynski equality for heat is satisfied in this set-up by considering the time-resolved emission spectrum of organic molecules as arising from quantum jumps between states. This relates the heat dissipated into the environment to the free energy difference between the initial and final state. We demonstrate also how utilizing the quantum Jarzynski equality allows for the detection of energy shifts within a molecule, beyond the relative shift.

DOI
10.1098/rspa.2017.0099

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We demonstrate with an experiment how molecules are a natural test bed for probing fundamental quantum thermodynamics. Single-molecule spectroscopy has undergone transformative change in the past decade with the advent of techniques permitting individual molecules to be distinguished and probed. We demonstrate that the quantum Jarzynski equality for heat is satisfied in this set-up by considering the time-resolved emission spectrum of organic molecules as arising from quantum jumps between states. This relates the heat dissipated into the environment to the free energy difference between the initial and final state. We demonstrate also how utilizing the quantum Jarzynski equality allows for the detection of energy shifts within a molecule, beyond the relative shift.
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In open quantum systems, a clear distinction between work and heat is often challenging, and extending the quantum Jarzynski equality to systems evolving under general quantum channels beyond unitality remains an open problem in quantum thermodynamics. In this Letter, we introduce well-defined notions of guessed quantum heat and guessed quantum work, by exploiting the one-time measurement scheme, which only requires an initial energy measurement on the system alone. We derive a modified quantum Jarzynski equality and the principle of maximum work with respect to the guessed quantum work, which requires the knowledge of the system only. We further show the significance of guessed quantum heat and work by linking them to the problem of quantum hypothesis testing.
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Abstract Since the onset of the 1990s, the development of single-molecule spectroscopy has led to the discovery of various quantum optical signatures in organic single molecules. The single-photon nature of an organic chromophore is of particular importance because of its potential as a nonclassical photon source at room temperature for quantum information science and optical quantum computing. This condensed review focuses on the introduction of fundamental knowledge and basic experimental methods for single-photon sources and organic molecular photophysics and summarizes the research developments in this field, providing an understanding of quantum emission from organic single molecules.
The Jarzynski equality (JE), which connects the equilibrium free energy with nonequilibrium work statistics, plays a crucial role in quantum thermodynamics. Although practical quantum systems are usually multilevel systems, most tests of the JE were executed in two-level systems. A rigorous test of the JE by directly measuring the work distribution of a physical process in a high-dimensional quantum system remains elusive. Here, we report an experimental test of the JE in a single spin-1 system. We realized nondemolition projective measurement of this three-level system via cascading high-fidelity single-shot readouts and directly measured the work distribution utilizing the two-point measurement protocol. The validity of the JE was verified from the nonadiabatic to adiabatic zone and under different effective temperatures. Our work puts the JE on a solid experimental foundation and makes the nitrogen-vacancy (NV) center system a mature toolbox to perform advanced experiments of stochastic quantum thermodynamics.
Various theories that use the sudden jump model to explain the time dependence of the optical band of a single molecule in a fluctuating environment are analyzed. It is shown that the dynamic theory of the optical band, based on the Hamiltonian of the system, should necessarily include the initial conditions for the quantum system. We show how these initial conditions should be chosen for the dynamic theory to properly describe the quantum jumps of the optical band of a single molecule. Unlike stochastic theories based on the sudden jump model, the dynamic theory predicts several absorptances of a single molecule and directly connects the absorptance fluctuations with this fact. The theory is used to account for the time dependence of the broadening of experimentally measured lines of individual molecules.