Finite-time optimization of a quantum Szilard heat engine

We propose a finite-time quantum Szilard engine (QSE) with a spin-1/2 quantum particle as the working substance (WS) to accelerate the operation of information engines. We introduce a Maxwell's demon (MD) to probe the spin state within a finite measurement time <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>t</a:mi><a:mi mathvariant="normal">M</a:mi></a:msub></a:math> to capture the which-way information of the particle, quantified by the mutual information <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>I</c:mi><c:mo>(</c:mo><c:msub><c:mi>t</c:mi><c:mi>M</c:mi></c:msub><c:mo>)</c:mo></c:mrow></c:math> between WS and MD. We establish that the efficiency <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>η</d:mi></d:math> of QSE is bounded by <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>η</e:mi><e:mo>≤</e:mo><e:mn>1</e:mn><e:mo>−</e:mo><e:mrow><e:mo>(</e:mo><e:mn>1</e:mn><e:mo>−</e:mo><e:msub><e:mi>η</e:mi><e:mi>C</e:mi></e:msub><e:mo>)</e:mo></e:mrow><e:mi>ln</e:mi><e:mn>2</e:mn><e:mo>/</e:mo><e:mi>I</e:mi><e:mrow><e:mo>(</e:mo><e:msub><e:mi>t</e:mi><e:mi mathvariant="normal">M</e:mi></e:msub><e:mo>)</e:mo></e:mrow></e:mrow></e:math>, where <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>I</g:mi><g:mo>(</g:mo><g:msub><g:mi>t</g:mi><g:mi>M</g:mi></g:msub><g:mo>)</g:mo><g:mo>/</g:mo><g:mi>ln</g:mi><g:mn>2</g:mn></g:mrow></g:math> characterizes the ideality of quantum measurement, and approaches 1 for the Carnot efficiency reached under ideal measurement in quasistatic regime. We find that the output power of QSE scales as <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:msub><h:mi>P</h:mi><h:mi mathvariant="normal">O</h:mi></h:msub><h:mo>∝</h:mo><h:msubsup><h:mi>t</h:mi><h:mrow><h:mi>M</h:mi></h:mrow><h:mn>3</h:mn></h:msubsup></h:mrow></h:math> in the short-time regime and as <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:msub><j:mi>P</j:mi><j:mi mathvariant="normal">O</j:mi></j:msub><j:mo>∝</j:mo><j:msubsup><j:mi>t</j:mi><j:mrow><j:mi>M</j:mi></j:mrow><j:mrow><j:mo>−</j:mo><j:mn>1</j:mn></j:mrow></j:msubsup></j:mrow></j:math> in the long-time regime. Additionally, considering the energy cost for erasing the MD's memory required by Landauer's principle, there exists a threshold time that guarantees QSE to output positive work. Published by the American Physical Society 2024