We use continuous weak measurements of a driven superconducting qubit to experimentally study the information dynamics of a quantum Maxwell's demon. We show how information gained by a demon who can track single quantum trajectories of the qubit can be converted into work using quantum coherent feedback. We verify the validity of a quantum fluctuation theorem with feedback by utilizing information obtained along single trajectories. We demonstrate, in particular, that quantum backaction can lead to a loss of information in imperfect measurements. We furthermore probe the transition between information gain and loss by varying the initial purity of the qubit.

We consider continuously monitored quantum systems and introduce definitions of work and heat along individual quantum trajectories that are valid for coherent superposition of energy eigenstates. We use these quantities to extend the first and second laws of stochastic thermodynamics to the quantum domain. We illustrate our results with the case of a weakly measured driven two-level system and show how to distinguish between quantum work and heat contributions. We finally employ quantum feedback control to suppress detector backaction and determine the work statistics.PACS numbers: 03.65. Yz, Thermodynamics is, at its heart, a theory of work and heat. The first law is based on the realization that both quantities are two forms of energy and that their sum is conserved. At the same time, the fact that entropy, defined as the ratio of reversible heat and temperature, can only increase in an isolated system is an expression of the second law [1,2]. In classical thermodynamics, work is defined as the change of internal energy in an isolated system, W = ∆U , while heat is introduced as the difference, Q = ∆U − W , in a nonisolated system. Thermal isolation is thus crucial to distinguish W from Q. In the last decades, stochastic thermodynamics has successfully extended the definitions of work and heat to the level of single trajectories of microscopic systems [3]. In this regime, thermal fluctuations are no longer negligible and the laws of thermodynamics have to be adapted to fully include them. The second law has, for instance, been generalized in the form of fluctuation theorems that quantify the occurrence of negative entropy production [4]. A particular example is the Jarzynski equality, exp(−βW ) = exp(−β∆F ), that allows the determination of equilibrium free energy differences ∆F from the nonequilibrium work statistics in systems at initial inverse temperature β [5]. The laws of stochastic thermodynamics have been verified in a large number of different experiments, see Refs. [6,7] and the review [8].The current challenge is to extend the principles of thermodynamics to include quantum effects which are expected to dominate at smaller scales and colder temperatures. Some of the unsolved key issues concern the correct definition of quantum work and heat, means to distinguish between the two quantities owing to the blurring effect of quantum fluctuations, and the proper clarification of the role of quantum coherence. A variety of approaches have been suggested to tackle these problems [9][10][11][12][13][14][15][16][17][18][19][20], and quantum work statistics has been measured in isolated systems in two pioneering experiments using NMR [21] and trapped ions [22]. A new approach may emerge from the possibility of weakly monitoring quantum systems. Recently, individual quantum trajectories of a superconducting qubit in a microwave cavity have been observed using weak measurements [23,24]. These measurements only slightly disturb quantum systems owing to the weak coupling to the measuring device [25]. They hence a...

We use a near quantum limited detector to experimentally track individual quantum state trajectories of a driven qubit formed by the hybridization of a waveguide cavity and a transmon circuit. For each measured quantum coherent trajectory, we separately identify energy changes of the qubit as heat and work, and verify the first law of thermodynamics for an open quantum system. We further establish the consistency of these results by comparison with the master equation approach and the two-projective-measurement scheme, both for open and closed dynamics, with the help of a quantum feedback loop that compensates for the exchanged heat and effectively isolates the qubit. arXiv:1703.05885v3 [quant-ph]

Feedback control mechanisms are ubiquitous in science and technology, and play an essential role in regulating physical, biological and engineering systems. The standard second law of thermodynamics does not hold in the presence of measurement and feedback. Most studies so far have extended the second law for discrete, Markovian feedback protocols; however, non-Markovian feedback is omnipresent in processes where the control signal is applied with a non-negligible delay. Here, we experimentally investigate the thermodynamics of continuous, time-delayed feedback control using the motion of an optically levitated, underdamped microparticle. We test the validity of a generalized second law which bounds the energy extracted from the system, and study the breakdown of feedback cooling for very large time delays.

We propose an operational framework to study the non-equilibrium thermodynamics of a quantum system S that is coupled to a detector D whose state is continuously monitored, allowing to single out individual quantum trajectories of S. We focus on detailed fluctuation theorems and characterize the entropy production of the system. We establish fundamental differences with respect to the thermodynamics of unmonitored, unitarily evolved systems. We consider the paradigmatic example of circuit-QED, where superconducting qubits can be coupled to a continuously monitored resonator and show numerical simulations using state-of-the-art experimental parameters.