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      Experimental Observation of Lee-Yang Zeros

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          Abstract

          Lee-Yang zeros are points on the complex plane of physical parameters where the partition function of a system vanishes and hence the free energy diverges. Lee-Yang zeros are ubiquitous in many-body systems and fully characterize their thermodynamics. Notwithstanding their fundamental importance, Lee-Yang zeros have never been observed in experiments, due to the intrinsic difficulty that they would occur only at complex values of physical parameters, which are generally regarded as unphysical. Here we report the first observation of Lee-Yang zeros, by measuring quantum coherence of a probe spin coupled to an Ising-type spin bath. The quantum evolution of the probe spin introduces a complex phase factor and therefore effectively realizes an imaginary magnetic field. From the measured Lee-Yang zeros, we reconstructed the free energy of the spin bath and determined its phase transition temperature. This experiment opens up new opportunities of studying thermodynamics in the complex plane.

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          Most cited references 34

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          Statistical Theory of Equations of State and Phase Transitions. II. Lattice Gas and Ising Model

           T D Lee,  C. N. Yang (1952)
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            Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation

             C. N. Yang,  T D Lee (1952)
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              Equilibrium information from nonequilibrium measurements in an experimental test of Jarzynski's equality.

              Recent advances in statistical mechanical theory can be used to solve a fundamental problem in experimental thermodynamics. In 1997, Jarzynski proved an equality relating the irreversible work to the equilibrium free energy difference, DeltaG. This remarkable theoretical result states that it is possible to obtain equilibrium thermodynamic parameters from processes carried out arbitrarily far from equilibrium. We test Jarzynski's equality by mechanically stretching a single molecule of RNA reversibly and irreversibly between two conformations. Application of this equality to the irreversible work trajectories recovers the DeltaG profile of the stretching process to within k(B)T/2 (half the thermal energy) of its best independent estimate, the mean work of reversible stretching. The implementation and test of Jarzynski's equality provides the first example of its use as a bridge between the statistical mechanics of equilibrium and nonequilibrium systems. This work also extends the thermodynamic analysis of single molecule manipulation data beyond the context of equilibrium experiments.
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                Author and article information

                Journal
                PRLTAO
                Physical Review Letters
                Phys. Rev. Lett.
                American Physical Society (APS)
                0031-9007
                1079-7114
                January 2015
                January 5 2015
                : 114
                : 1
                Article
                10.1103/PhysRevLett.114.010601
                25615455
                © 2015

                http://link.aps.org/licenses/aps-default-license

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