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arXiv:cond-mat/0506601 · Physical Review B

Quantum transitions induced by the third cumulant of current fluctuations

Teemu Ojanen, Tero Tapio Heikkilä

Published Jan 9, 2006• 8 citations
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Abstract

We investigate the transitions induced by non-Gaussian external fluctuations on a small quantum system. The rates for the transitions between the energy states are calculated using the real-time Keldysh formalism for the density matrix evolution. We detail the effects of the third cumulant of current fluctuations coupled to a quantum system with a discrete level spectrum and propose a setup for detecting the frequency-dependent third cumulant through the transitions it induces. We especially discuss a scheme where the fluctuations are coupled to a Josephson flux qubit.

DOI
10.1103/physrevb.73.020501

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We investigate the transitions induced by non-Gaussian external fluctuations on a small quantum system. The rates for the transitions between the energy states are calculated using the real-time Keldysh formalism for the density matrix evolution. We detail the effects of the third cumulant of current fluctuations coupled to a quantum system with a discrete level spectrum and propose a setup for detecting the frequency-dependent third cumulant through the transitions it induces. We especially discuss a scheme where the fluctuations are coupled to a Josephson flux qubit.
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Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyze experimental data and to optimize detection circuits.
We propose to probe the distribution of current fluctuations by means of the escape probability histogram of a Josephson junction (JJ), obtained using very short bias current pulses in the adiabatic regime, where the low-frequency component of the current fluctuations plays a crucial role. We analyze the effect of the third cumulant on the histogram in the small skewness limit, and address two concrete examples assuming realistic parameters for the JJ. In the first one we study the effects due to fluctuations produced by a tunnel junction, finding that the signature of higher cumulants can be detected by taking the derivative of the escape probability with respect to current. In such a realistic situation, though, the determination of the whole distribution of current fluctuations requires an amplification of the cumulants. As a second example we consider magnetic flux fluctuations acting on a SQUID produced by a random telegraph source of noise.
Quantum mechanics can strongly influence the noise properties of mesoscopic devices. To probe this effect we have measured the current fluctuations at high-frequency (5-90G Hz) using a superconductor-insulator-superconductor tunnel junction as an on-chip spectrum analyzer. By coupling this frequency-resolved noise detector to a quantum device we can measure the high-frequency, non-symmetrized noise as demonstrated for a Josephson junction. The same scheme has been used to detect the current fluctuations arising from coherent charge oscillations in a two-level system, a superconducting charge qubit. A narrow band peak was observed in the spectral noise density at the frequency of the coherent charge oscillations.
Non-Gaussian fluctuations of the electrical current can be detected with a Josephson junction placed on-chip with the noise source. We present preliminary measurements with an NIS junction as a noise source, and a Josephson junction in the thermal escape regime as a noise detector. It is shown that the Josephson junction detects not only the average noise, which manifests itself as an increased effective temperature, but also the noise asymmetry. A theoretical description of the thermal escape of a Josephson junction in presence of noise with a non-zero third cumulant is presented, together with numerical simulations when the noise source is a tunnel junction with Poisson noise. Comparison between experiment and theory is discussed.