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arXiv:2304.13474

The Quantum Measurement Spintronic Engine: Using Entanglement to Harvest Vacuum Fluctuations

Mathieu Lamblin, Martin Bowen

Published Apr 26, 2023• 0 citations
arXivHTMLPDF

Abstract

Quantum fluctuations, which result from the Heisenberg uncertainty principle, explain a number of physical observations, from the finite mass of elementary particles to the Lamb shift in hydrogen and the Casimir effect. The local violation of the conservation of energy raises the question of whether the energy of quantum fluctuations can sustain the cycle of a quantum engine. So far, a proposal has hinted that this is possible, but contains important caveats. In this Letter, we predict that quantum fluctuations can power an autonomous spintronic quantum information engine by converting entanglement energy into useful electrical work. Our two-stroke engine operates on two entangled spin quantum dots (QDs) that are connected in series with two fully spin-polarized baths. The ultrafast measurement stroke breaks the entanglement, thereby energizing the system on average. This energy is released into the leads as electrical current when the thermalizing stroke equilibrates the QDs with the electrode baths. Using a master equation approach, we analytically demonstrate the efficiency of the quantum fluctuation-driven engine, and we study the cycle numerically to gain insight into the relevant parameters to maximize power. Our results suggest that quantum fluctuations and the measurement back-action alone cannot explain prior experimental results. Measuring the spin dynamics of the engine's ferromagnetic electrodes should help determine its efficiency. This electronically driven feedback on quantum entanglement should also boost quantum chemistry, biology and cognition.

DOI
10.48550/arxiv.2304.13474

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Quantum fluctuations, which result from the Heisenberg uncertainty principle, explain a number of physical observations, from the finite mass of elementary particles to the Lamb shift in hydrogen and the Casimir effect. The local violation of the conservation of energy raises the question of whether the energy of quantum fluctuations can sustain the cycle of a quantum engine. So far, a proposal has hinted that this is possible, but contains important caveats. In this Letter, we predict that quantum fluctuations can power an autonomous spintronic quantum information engine by converting entanglement energy into useful electrical work. Our two-stroke engine operates on two entangled spin quantum dots (QDs) that are connected in series with two fully spin-polarized baths. The ultrafast measurement stroke breaks the entanglement, thereby energizing the system on average. This energy is released into the leads as electrical current when the thermalizing stroke equilibrates the QDs with the electrode baths. Using a master equation approach, we analytically demonstrate the efficiency of the quantum fluctuation-driven engine, and we study the cycle numerically to gain insight into the relevant parameters to maximize power. Our results suggest that quantum fluctuations and the measurement back-action alone cannot explain prior experimental results. Measuring the spin dynamics of the engine's ferromagnetic electrodes should help determine its efficiency. This electronically driven feedback on quantum entanglement should also boost quantum chemistry, biology and cognition.
Quantum information engines can advantageously convert information into work, usually through a feedback mechanism operated by a Maxwell demon. In principle, this opens prospects of autonomous machines that challenge the classical second law of thermodynamics. Yet prior research, which typically tests a given concept in isolation, usually makes strong assumptions on turning on/off internal interactions or the connection to the baths, which has fueled skepticism. Meanwhile, several recent experiments describe an autonomous spintronic engine that purportedly combines several concepts using inherent electronic interactions to harvest spin fluctuations and quantum correlations. So far, no full-fledged theory has described it. In this article, we address these several interdisciplinary shortcomings by presenting a theory for a solid-state, fully electronic spintronic quantum information engine that converts the energy of quantum coherence into useful electrical work thanks to quantum measurements. Our simple two-stroke engine operates on two correlated atomic, single-spin quantum dots (QDs) that are connected in series with two ferromagnetic electrodes. The ultrafast measurement stroke destroys the quantum coherence stored within the QDs and projects the system into a local high-energy separated state. The resulting energy is then released into the leads as electrical current when the partial thermalizing stroke restores quantum coherence. Using a master equation approach, we show that a robust steady-state current can flow between the electrodes despite the absence of a tunneling path and at thermal equilibrium. Our model proves the feasibility of harvesting quantum fluctuations by the measurement back-action through the on-site Coulomb interaction, and can reproduce experimental output power levels if bosons mediate this transport in the presence of an additional nonequilibrium resource. This can for instance be accomplished by the spin bias that is inherently generated by the ferromagnetic electrodes. Our work raises the prospect of measuring the ``spintronic temperature'' of the leads using magnetization dynamics experiments, while the model's underpinnings of built-in, materials-inherent measurements of quantum information can in principle be adapted to describe fundamental quantum processes in chemistry and biology.
We propose a many-body quantum engine powered by the energy difference between the entangled ground state of the interacting system and local separable states. Performing local energy measurements on an interacting many-body system can produce excited states from which work can be extracted via local feedback operations. These measurements reveal the quantum vacuum fluctuations of the global ground state in the local basis and provide the energy required to run the engine. The reset part of the engine cycle is particularly simple: The interacting many-body system is coupled to a cold bath and allowed to relax to its entangled ground state. We illustrate our proposal on two types of many-body systems: A chain of coupled qubits and coupled harmonic oscillator networks. These models faithfully represent fermionic and bosonic excitations, respectively. In both cases, analytical results for the work output (average value and standard deviation) and efficiency of the engine are derived. We prove the efficiency is controlled by the ``local entanglement gap,'' the energy difference between the many-body ground state and the lowest-energy eigenstate of the local Hamiltonian. In all the examples analyzed in this work, for a large number of coupled subsystems, the average work output scales linearly or faster and dominates over fluctuations, while the efficiency limits to a constant. In the qubit chain case, we highlight the impact of a quantum phase transition on the engine's performance as work and efficiency sharply increase at the critical point. In the case of a one-dimensional oscillator chain, we show the efficiency approaches unity as the number of coupled oscillators increases, even at finite work output.
The laws of thermodynamics allow work extraction from a single heat bath provided that the entropy decrease of the bath is compensated for by another part of the system. We propose a thermodynamic quantum engine that exploits this principle and consists of two electrons on a double quantum dot (QD). The engine is fueled by providing it with singlet spin states, where the electron spins on different QDs are maximally entangled, and its operation involves only changing the tunnel coupling between the QDs. Work can be extracted since the entropy of an entangled singlet is lower than that of a thermal (mixed) state, although they look identical when measuring on a single QD. We show that the engine is an optimal thermodynamic engine in the long-time limit. In addition, we include a microscopic description of the bath and analyze the engine's finite-time performance using experimentally relevant parameters.
Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, we derive the time-dependent state, the particle current, as well as the associated current correlation functions. Our findings establish a direct connection between coherence and internal current, elucidating the existence of a critical current that serves as an indicator for entanglement in the steady state. We then apply our results to investigate kinetic uncertainty relations (KURs) at finite times. We demonstrate that there is more than one possible definition for KURs at finite times. Although the two definitions agree in the steady-state regime, they lead to different parameter ranges for violating KUR at finite times.
In this paper, we consider fluctuations in a three-stroke cycle based on quantum measurement. In the first stroke, the engine is fueled by a nonselective quantum measurement; in the second stroke, an appropriate unitary operation is applied to extract work; and finally, the working medium is thermalized to complete the cycle. This protocol is analogous to charging, then discharging, and finally thermalizing a quantum battery. Using the Kirkwood-Dirac quasiprobability, we derive equations that provide insights into the fluctuations of heat and work, and thus into the charging and discharging processes. We then propose a quantum circuit to measure the cumulants of work and heat using a qubit ancilla. Afterward, we derive important upper and lower bounds on fluctuations in heat; this is thanks to the way we decompose heat fluctuations and the Kadison-Schwarz inequality. We also show, for the first time, that the imaginary part of the second cumulant of work equals the linear response of an average work (to be defined in the main text) or the quantum cross entropy. We further introduce an operator whose average defines the battery capacity and whose variance quantifies the corresponding fluctuations of the battery capacity. Our analytical results are illustrated and discussed through representative examples. We believe that our study will, on the one hand, be useful for understanding fluctuations in energy extracted from and injected into quantum batteries based on quantum measurements and, on the other hand, contribute to the foundations of quantum thermodynamics. More generally, our results can be applied beyond the three-stroke cycle considered here, especially to quantum batteries subject to environmental noise and decoherence.
We propose and analyze the theoretical model for a two-stroke quantum heat engine with one of the heat baths replaced by a non-selective quantum measurement. We show that the engine's invariant reference state depends on whether the cycle is monitored or unmonitored via diagnostic measurements to determine the engine's work output. We explore in detail the average work output and fluctuations of the proposed heat engine for the monitored and unmonitored cases. We also identify unitary work strokes for which the invariant states can support coherences in the energy basis leading to differing predictions for the average energy change during the unitary work strokes and the average work from the standard two-projective measurement approach.