Efficient method to measure n-time correlation functions

J. S. Pedernales^a, R. Di Candia^a, I. L Egusquiza^b, J. Casanova^a, and E. Solano^a,c

^aDepartment of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain

^bDepartment of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain

^cIKERBASQUE, Basque Foundation for Science, Alameda Urquijo 36, 48011 Bilbao, Spain

Ranging from the linear response theory to quantum field theories, time correlation functions are omnipresent in physics and are considered a key magnitude for a complete description of nature. The measurement of time correlation functions of classical observables does not represent an especially difficult task, as it is just the product of the outcomes of two measurements performed at two different times. However, time correlations of quantum mechanical observables happen to be a demanding magnitude to extract. This is because a measurement at time t1 causes the collapse of the wave function, perturbing the outcome of any further measurement. In this talk we will present a method that provides efficient access to n-time correlation functions using an ancillary qubit [1]. We will also discuss a possible implementation of the method in trapped ions [2] and its applicability in the framework of the linear response theory, where one can measure magnitudes as the electric or magnetic susceptibilities in terms of time correlation functions. Finally, we will talk about the suitability of our method to the measurement of Leggett-Garg inequalities, a.k.a. temporal Bell inequalities, where the time correlation functions are used to unwrap the quantum character of nature.

[1] J. S. Pedernales, R. Di Candia, I. L. Egusquiza, J. Casanova, and E. Solano, arXiv:1401.2430

[2] J. S. Pedernales, J. Casanova, J. Home, and E. Solano, in preparation