Abstract
Recent studies using the quantum information theoretic approach to thermodynamics show that the presence of coherence in quantum systems generates corrections to classical fluctuation theorems. To explicate the physical origins and implications of such corrections, we here convert an abstract framework of an autonomous quantum Crooks relation into quantum Crooks equalities for well-known coherent, squeezed and cat states. We further provide a proposal for a concrete experimental scenario to test these equalities. Our scheme consists of the autonomous evolution of a trapped ion and uses a position dependent AC Stark shift.
Highlights
The emergent field of quantum thermodynamics seeks to extend the laws of thermodynamics and nonequilibrium statistical mechanics to quantum systems
While we focus on the tapered beam implementation to maintain a closer resemblance to the classical Crooks equality setup, it is possible, as discussed in Section 3.3, to detect the quantum deviation predicted by the Autonomous Quantum Crooks equality (AQC) using a level splitting that varies sinusoidally or linearly with position
The AQC is derived from a simple set of physical principles and in virtue of this the coherent, squeezed and cat state Crooks equalities are both natural and general
Summary
The emergent field of quantum thermodynamics seeks to extend the laws of thermodynamics and nonequilibrium statistical mechanics to quantum systems. For incoherent quantum systems, general criteria for state conversion [5], generalisations of the second laws [6], and limits to work extraction protocols [7] have been established. These results have been extended to coherent quantum states [8,9,10,11]. A separate line of enquiry has explored fluctuation theorems, which can be seen as generalisations of the second law of thermodynamics to non-equilibrium processes [15] They consider systems that are driven out of equilibrium and establish exact relations between the resultant thermal fluctuations [16]. In this way an effectively time-dependent Hamiltonian for the two level system can be realised
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