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Register a new userQuantum-heat fluctuation relations in $3$-level systems under projective measurements
علاقات التقلبات الحرارية الكمونية في الأنظمة المستوى $3$ تحت القياسات المشروعية
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تدرسنا إحصاءات الانزلاقات الطاقية في نظام كمي ثلاثي المستويات الذي يتحمل سلسلة من القياسات الكمية المشروعة. نحن نتحقق من أن المساواة الجارزينسكي الكمية تحقق كما هو متوقع إذا تم تلبية الشرط الأولي الحراري. هذا الشرط يتلبى بسهولة للنظم المستويين، بينما هو عادة غير صحيح للنظم $N$ المستوية، مع $N > 2$. متركزين على النظم الثلاثية المستوية، نناقش وجود عامل مقياس طاقة فريد $beta_{rm eff}$ الذي يلعب دوراً رسمياً لدرجة حرارة معكوسة في المساواة الجارزينسكي الكمية. لهذا الغرض، ندخل تهيئة مناسبة للحالة الأولية بالنسبة إلى جزء حراري وجزء غير حراري. نحدد قيمة $beta_{rm eff}$ لعدد كبير من القياسات وندرس تبعيتها على الحالة الأولية. يمكن التحقق من توقعاتنا على الأحداثيات الكمية.
We study the statistics of energy fluctuations in a three-level quantum system subject to a sequence of projective quantum measurements. We check that, as expected, the quantum Jarzynski equality holds provided that the initial state is thermal. The latter condition is trivially satisfied for two-level systems, while this is generally no longer true for $N$-level systems, with $N > 2$. Focusing on three-level systems, we discuss the occurrence of a unique energy scale factor $beta_{rm eff}$ that formally plays the role of an effective inverse temperature in the Jarzynski equality. To this aim, we introduce a suitable parametrization of the initial state in terms of a thermal and a non-thermal component. We determine the value of $beta_{rm eff}$ for a large number of measurements and study its dependence on the initial state. Our predictions could be checked experimentally in quantum optics.
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We derive a general scheme to obtain quantum fluctuation relations for dynamical observables in open quantum systems. For concreteness we consider Markovian non-unitary dynamics that is unraveled in terms of quantum jump trajectories, and exploit techniques from the theory of large deviations like the tilted ensemble and the Doob transform. Our results here generalise to open quantum systems fluctuation relations previously obtained for classical Markovian systems, and add to the vast literature on fluctuation relations in the quantum domain, but without resorting to the standard two-point measurement scheme. We illustrate our findings with three examples in order to highlight and discuss the main features of our general result.
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In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and Wojcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at different generalized temperatures. Second, we extend the connections between heat exchange and Renyi divergences to quantum systems with very general initial conditions.These relations are applicable for quantum systems with conserved quantities and are universally valid for quantum systems in the integrable and chaotic regimes.
In Newtonian mechanics, any closed-system dynamics of a composite system in a microstate will leave all its individual subsystems in distinct microstates, however this fails dramatically in quantum mechanics due to the existence of quantum entanglement. Here we introduce the notion of a `coherent work process, and show that it is the direct extension of a work process in classical mechanics into quantum theory. This leads to the notion of `decomposable and `non-decomposable quantum coherence and gives a new perspective on recent results in the theory of asymmetry as well as early analysis in the theory of classical random variables. Within the context of recent fluctuation relations, originally framed in terms of quantum channels, we show that coherent work processes play the same role as their classical counterparts, and so provide a simple physical primitive for quantum coherence in such systems. We also introduce a pure state effective potential as a tool with which to analyze the coherent component of these fluctuation relations, and which leads to a notion of temperature-dependent mean coherence, provides connections with multi-partite entanglement, and gives a hierarchy of quantum corrections to the classical Crooks relation in powers of inverse temperature.
The non-equilibrium dynamics of quantum many-body systems is one of the most fascinating problems in physics. Open questions range from how they relax to equilibrium to how to extract useful work from them. A critical point lies in assessing whether a system has conserved quantities (or charges), as these can drastically influence its dynamics. Here we propose a general protocol to reveal the existence of charges based on a set of exact relations between out-of-equilibrium fluctuations and equilibrium properties of a quantum system. We apply these generalised quantum fluctuation relations to a driven quantum simulator, demonstrating their relevance to obtain unbiased temperature estimates from non-equilibrium measurements. Our findings will help guide research on the interplay of quantum and thermal fluctuations in quantum simulation, in studying the transition from integrability to chaos and in the design of new quantum devices.
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