Work, heat and entropy production along quantum trajectories

Quantum open systems evolve according to completely positive, trace preserving maps acting on the density operator, which can equivalently be unraveled in term of so-called quantum trajectories. These stochastic sequences of pure states correspond to the actual dynamics of the quantum system during single realizations of an experiment in which the system's environment is monitored. In this chapter, we present an extension of stochastic thermodynamics to the case of open quantum systems, which builds on the analogy between the quantum trajectories and the trajectories in phase space of classical stochastic thermodynamics. We analyze entropy production, work and heat exchanges at the trajectory level, identifying genuinely quantum contributions due to decoherence induced by the environment. We present three examples: the thermalization of a quantum system, the fluorescence of a driven qubit and the continuous monitoring of a qubit's observable.Comment: Book chapter in 'Thermodynamics in the quantum regime - Recent Progress and Outlook

Probing the state of a mechanical oscillator with an ultra-strongly coupled quantum emitter

We study the dynamics of a mechanical resonator parametrically coupled to a driven dissipative quantum emitter in the ultra-strong coupling regime. We show that this regime is fully compatible with a semi-classical treatment, and we derive master equations for the emitter and the resonator. We show that the fluctuations of the driven emitter's population induce the non-symmetrical scattering of the mechanical quadratures. At long timescales, such scattering back-acts on the emitter, which eventually decouples from the driving light. This optical noise at the quantum limit is observable with state of the art hybrid devices.Comment: 6 pages, 3 figures. Comments are welcom

The role of quantum measurement in stochastic thermodynamics

This article sets up a new formalism to investigate stochastic thermodynamics in the quantum regime, where stochasticity and irreversibility primarily come from quantum measurement. In the absence of any bath, we define a purely quantum component to heat exchange, that corresponds to energy fluctuations caused by measurement back-action. Energetic and entropic signatures of measurement induced irreversibility are then investigated for canonical experiments of quantum optics, and the energetic cost of counter-acting decoherence is characterized on a simple state-stabilizing protocol. By placing quantum measurement in a central position, our formalism contributes to bridge a gap between experimental quantum optics and quantum thermodynamics

Reversible work extraction in a hybrid opto-mechanical system

With the progress of nano-technology, thermodynamics also has to be scaled down, calling for specific protocols to extract and measure work. Usually, such protocols involve the action of an external, classical field (the battery) of infinite energy, that controls the energy levels of a small quantum system (the calorific fluid). Here we suggest a realistic device to reversibly extract work in a battery of finite energy : a hybrid optomechanical system. Such devices consist in an optically active two-level quantum system interacting strongly with a nano-mechanical oscillator that provides and stores mechanical work, playing the role of the battery. We identify protocols where the battery exchanges large, measurable amounts of work with the quantum emitter without getting entangled with it. When the quantum emitter is coupled to a thermal bath, we show that thermodynamic reversibility is attainable with state-of-the-art devices, paving the road towards the realization of a full cycle of information-to-energy conversion at the single bit level.Comment: 10 pages, 3 figure

An autonomous quantum machine to measure the thermodynamic arrow of time

According to the Second Law of thermodynamics, the evolution of physical systems has a preferred direction, that is characterized by some positive entropy production. Here we propose a direct way to measure the stochastic entropy produced while driving a quantum open system out of thermal equilibrium. The driving work is provided by a quantum battery, the system and the battery forming an autonomous machine. We show that the battery's energy fluctuations equal work fluctuations and check Jarzynski's equality. Since these energy fluctuations are measurable, the battery behaves as an embedded quantum work meter and the machine verifies a generalized fluctuation theorem involving the information encoded in the battery. Our proposal can be implemented with state-of-the-art opto-mechanical systems. It paves the way towards the experimental demonstration of fluctuation theorems in quantum open systems.Comment: 9 pages, 5 figure