Detailed Fluctuation Relation for Arbitrary Measurement and Feedback Schemes

Fluctuation relations are powerful equalities that hold far from equilibrium. However, the standard approach to include measurement and feedback schemes may become inapplicable in certain situations, including continuous measurements, precise measurements of continuous variables, and feedback induced irreversibility. Here we overcome these shortcomings by providing a recipe for producing detailed fluctuation relations. Based on this recipe, we derive a fluctuation relation which holds for arbitrary measurement and feedback control. The key insight is that fluctuations inferable from the measurement outcomes may be suppressed by post-selection. Our detailed fluctuation relation results in a stringent and experimentally accessible inequality on the extractable work, which is saturated when the full entropy production is inferable from the data.Comment: Published version. The first author was previously known as Patrick P. Hofe

Probabilistically Violating the First Law of Thermodynamics in a Quantum Heat Engine

Fluctuations of thermodynamic observables, such as heat and work, contain relevant information on the underlying physical process. These fluctuations are however not taken into account in the traditional laws of thermodynamics. While the second law is extended to fluctuating systems by the celebrated fluctuation theorems, the first law is generally believed to hold even in the presence of fluctuations. Here we show that in the presence of quantum fluctuations, also the first law of thermodynamics may break down. This happens because quantum mechanics imposes constraints on the knowledge of heat and work. To illustrate our results, we provide a detailed case-study of work and heat fluctuations in a quantum heat engine based on a circuit QED architecture. We find probabilistic violations of the first law and show that they are closely connected to quantum signatures related to negative quasi-probabilities. Our results imply that in the presence of quantum fluctuations, the first law of thermodynamics may not be applicable to individual experimental runs

Full counting statistics of the photocurrent through a double quantum dot embedded in a driven microwave resonator

Detection of single, itinerant microwave photons is an important functionality for emerging quantum technology applications as well as of fundamental interest in quantum thermodynamics experiments on heat transport. In a recent experiment [W. Khan et al., Nat. Commun. 12, 5130 (2021)], it was demonstrated that a double quantum dot (DQD) coupled to a microwave resonator can act as an efficient and continuous photodetector by converting an incoming stream of photons to an electrical photocurrent. In the experiment, average photon and electron flows were analyzed. Here we theoretically investigate, in the same system, the fluctuations of the photocurrent through the DQD for a coherent microwave drive of the resonator. We consider both the low frequency full counting statistics as well as the finite-frequency noise (FFN) of the photocurrent. Numerical results and analytical expressions in limiting cases are complemented by a mean-field approach neglecting dot-resonator correlations, providing a compelling and physically transparent picture of the photocurrent statistics. We find that for ideal, unity efficiency detection, the fluctuations of the charge current reproduce the Poisson statistics of the incoming photons, while the statistics for non-ideal detection is sub-Poissonian. Moreover, the FFN provides information of the system parameter dependence of detector short-time properties. Our results give novel insight into microwave photon-electron interactions in hybrid dot-resonator systems and provide guidance for further experiments on continuous detection of single microwave photons.Comment: 16 pages, 4 figure

Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir

In nano-scale systems coupled to finite-size reservoirs, the reservoir temperature may fluctuate due to heat exchange between the system and the reservoirs. To date, a stochastic thermodynamic analysis of heat, work and entropy production in such systems is however missing. Here we fill this gap by analyzing a single-level quantum dot tunnel coupled to a finite-size electronic reservoir. The system dynamics is described by a Markovian master equation, depending on the fluctuating temperature of the reservoir. Based on a fluctuation theorem, we identify the appropriate entropy production that results in a thermodynamically consistent statistical description. We illustrate our results by analyzing the work production for a finite-size reservoir Szilard engine

Efficient and Continuous Microwave Photodetection in Hybrid Cavity-Semiconductor Nanowire Double Quantum Dot Diodes

Single photon detectors are key for time-correlated photon counting applications [1] and enable a host of emerging optical quantum information technologies [2]. So far, the leading approach for continuous and efficient single-photon detection in the optical domain has been based on semiconductor photodiodes [3]. However, there is a paucity of efficient and continuous single-photon detectors in the microwave regime, because photon energies are four to five orders of magnitude lower therein and conventional photodiodes do not have that sensitivity. Here we tackle this gap and demonstrate how itinerant microwave photons can be efficiently and continuously converted to electrical current in a high-quality, semiconducting nanowire double quantum dot that is resonantly coupled to a cavity. In particular, in our detection scheme, an absorbed photon gives rise to a single electron tunneling event through the double dot, with a conversion efficiency reaching 6 %. Our results pave the way for photodiodes with single-shot microwave photon detection, at the theoretically predicted unit efficiency [4]

Information-to-work conversion in single molecule experiments: from discrete to continuous feedback

We theoretically investigate the extractable work in single molecule unfolding-folding experiments with applied feedback. Using a simple two-state model, we obtain a description of the full work distribution, from discrete to continuous feedback. The effect of the feedback is captured by a detailed fluctuation theorem, accounting for the information aquired. We find analytical expressions for the average work extraction as well as an experimentally measurable bound thereof, which becomes tight in the continuous feedback limit. We further determine the parameters for maximal power, or rate of work extraction. While our two-state model only depends on a single, effective transition rate, we find quantitative agreement with Monte Carlo simulations of DNA hairpin unfolding-folding dynamics.Comment: 5 pages, 4 figures, 5 pages of supplementary informatio

Quantum Fokker-Planck Master Equation for Continuous Feedback Control

Measurement and feedback control are essential features of quantum science, with applications ranging from quantum technology protocols to information-to-work conversion in quantum thermodynamics. Theoretical descriptions of feedback control are typically given in terms of stochastic equations requiring numerical solutions, or are limited to linear feedback protocols. Here we present a formalism for continuous quantum measurement and feedback, both linear and nonlinear. Our main result is a quantum Fokker-Planck master equation describing the joint dynamics of a quantum system and a detector with finite bandwidth. For fast measurements, we derive a Markovian master equation for the system alone, amenable to analytical treatment. We illustrate our formalism by investigating two basic information engines, one quantum and one classical

Microwave power harvesting using resonator-coupled double quantum dot photodiode

We demonstrate a microwave power-to-electrical energy conversion in a resonator-coupled double quantum dot system. The system operated as a photodiode, converts individual microwave photons to electrons tunneling through the double dot, resulting in an electrical current flowing against the applied voltage bias at input powers down to 1 femto-watt level. The device attains a maximum power harvesting efficiency of 2%, with the photon-to-electron conversion efficiency reaching 12%. We analyze the device operation in both the linear and non-linear microwave power response regimes and compare the results to theoretical predictions, finding good agreement.Comment: 5 pages, 3 figure