Counting statistics of non-Markovian quantum stochastic processes

Tomas Novotny

Charles University in Prague, Department of Condensed Matter Physics, Prague, Czech Republic

We present a recursive method for calculating zero-frequency current cumulants of very high or- ders for quantum stochastic processes described by non-Markovian generalized master equations (GME) [1,2]. Within the same framework, the finite-frequency noise can also be evaluated. As a specific example, we consider charge transport through two coherently coupled Coulomb blockade quantum dots embedded in a dissipative environ- ment. For high orders, the cumulants show surpri- sing oscillations as functions of the level detuning.

Using mathematical properties of derivatives in the complex plane [3] we show that these oscillations are in fact universal and are expected to occur as functions of almost any parameter in a wide class of stochastic processes [4]. We present the first experimental evidence of universal oscillations in electron transport through a single quantum dot [4].

[1] C. Flindt, T. Novotný, A. Braggio, M. Sassetti, and A.-P. Jauho, Phys. Rev. Lett. 100, 150601 (2008)
[2] C. Flindt, T. Novotný, A. Braggio, and A.-P. Jauho, in preparation (2008)
[3] M. V. Berry, Proc. R. Soc. A 461, 1735 (2005)
[4] C. Flindt, C. Fricke, F. Hohls, T. Novotný, K. Netočný, T. Brandes, and R. J. Haug, submitted (2008)