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Open Systems & Information Dynamics

Low-Frequency Noise Characterization in Charge-Based Coherent Nanodevices

G. Falci, Andrea Mastellone, Antonio D’Arrigo, Elisabetta Paladino

Published Aug 31, 2006• 5 citations
Publisher

Abstract

Low-frequency noise has been recognized as the main mechanism of decoherence in present-day solid state coherent nanodevices. Often low-frequency noise has a 1/f spectrum, thus the responsible degrees of freedom are almost static during the coherent time evolution of the device. Their effect is to reduce the amplitude of the measured signal by an effect analogous to in-homogeneous broadening in NMR. Here we present a way to characterize effects of adiabatic noise exploiting the tunability of nanodevices. The results apply in principle to many implementations of quantum bits, and are particularly suited for solid state devices. The accurate characterization of the physics of the noise sources represents the first step toward the design specific strategies to eliminate their effects.

DOI
10.1007/s11080-006-9002-6

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Low-frequency noise has been recognized as the main mechanism of decoherence in present-day solid state coherent nanodevices. Often low-frequency noise has a 1/f spectrum, thus the responsible degrees of freedom are almost static during the coherent time evolution of the device. Their effect is to reduce the amplitude of the measured signal by an effect analogous to in-homogeneous broadening in NMR. Here we present a way to characterize effects of adiabatic noise exploiting the tunability of nanodevices. The results apply in principle to many implementations of quantum bits, and are particularly suited for solid state devices. The accurate characterization of the physics of the noise sources represents the first step toward the design specific strategies to eliminate their effects.
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A high degree of quantum coherence is a crucial requirement for the implementation of quantum logic devices. Solid state nanodevices seem particularly promising from the point of view of integrability and flexibility in the design. However decoherence is a serious limitation, due to the presence of many types low energy excitations in the ``internal'' environment and of ``external'' sources due to the control circuitery. Here we study both kind of dephasing in a special implementation, the charge Josephson qubit, however many of our results are applicable to a large class of solid state qubits. This is the case of 1/f noise for which we introduce and study a model of an environment of bistable fluctuatiors. External sources of noise are analized in terms of a suitable harmonic oscillator environment and the explicit mapping on the spin boson model is presented. We perform a detailed investigation of various computation procedures (single shot measurements, repeated measurements) and discuss the problem of the information needed to characterize the effect of the environment. For a fluctuator environment with 1/f spectrum memory effects turn out to be important. Although in general information beyond the power spectrum is needed, in many situations this results in the knowledge of only one more microscopic parameter of the environment. This allows to determine which degrees of freedom of the environment are effective sources of decoherence in each different physical situation considered.
Recent experiments have demonstrated coherent phenomena in three-level systems based on superconducting nanocircuits. This opens the possibility to detect Stimulated Raman Adiabatic Passage (STIRAP) in artificial atoms. Low-fequency noise (often 1/f) is one of the main sources of decoherence in these systems, and we study its effect on the transfer efficiency. We propose a way to analyze low frequency fluctuations in terms of fictitious correlated fluctuations of external parameters. We discuss a specific implementation, namely the Quantronium setup of a Cooper-pair box, showing that optimizing the trade-off between efficient coupling and protection against noise may allow us to observe coherent population transfer in this nanodevice.
We study the effect of low-frequency noise in ac-driven two- or many-level coherent nanodevices. Fluctuations in the properties of the device are translated into equivalent fluctuations of the driving fields. The impact on Rabi oscillations can be modulated with the detuning and minimized at resonance. In three-level atoms slow noise produces qualitative changes for protocols as coherent population transfer. We propose a strategy allowing us to operate at parity symmetry points, where the device is well protected against noise, despite selection rules preventing direct couplings to external fields of involved transitions.
Decoherence is an essential mechanism that defines the boundary between classical and quantum behaviours, while imposing technological bounds for quantum devices. Little is known about quantum coherence of mechanical systems, as opposed to electromagnetic degrees of freedom. But decoherence can also be thought of in a purely classical context, as the loss of phase coherence in the classical phase space. Indeed the bridge between quantum and classical physics is under intense investigation, using, in particular, classical nanomechanical analogues of quantum phenomena. In the present work, by separating pure dephasing from dissipation, we quantitatively model the classical decoherence of a mechanical resonator: through the experimental control of frequency fluctuations, we engineer artificial dephasing. Building on the fruitful analogy introduced between spins/quantum bits and nanomechanical modes, we report on the methods available to define pure dephasing in these systems, while demonstrating the intrinsic almost-ideal properties of silicon nitride beams. These experimental and theoretical results, at the boundary between classical nanomechanics and quantum information fields, are prerequisite in the understanding of decoherence processes in mechanical devices, both classical and quantum. Introduction and background. Frequency noise in nano-mechanical systems (NEMS) is a topic intensely studied these last years, for both fundamental and practical reasons (references [ 13 – 23 ] of the paper): the frequency fluctuations can have an intrinsic origin linked to essential material properties, but they also limit the resolution of actual devices used as sensors. Recently, the Delft group proposed to analyze the effects of this noise on the dynamics of NEMS within a framework analogous to one of Nuclear Magnetic Resonance (NMR), or quantum bits (2014 Nat. Commun. 5 5819 ). Main results. Building on the analogy, in this paper we engineer frequency noise to study its impact on nano-resonators. We present a model experiment, with the full theory enabling the fit of data without free parameters. The effect of frequency noise is analogous to 'pure dephasing' in quantum bits, even though the device is a classical harmonic oscillator. As such, the analogy is very informative and interrogates the crossover between classical and quantum physics; it enters the class of 'classical analogues of quantum phenomena' studied in recent model nano-mechanical experiments (e.g. reference [ 10 ]). Wider implications. This is a broad topic that is of interest to many areas of science, far beyond NEMS and NMR. For the focused audience, we present the methods to quantitatively describe this 'classical pure dephasing' of NEMS, which can be used e.g. with carbon-based systems. As a conclusion, our results are a new tool for the understanding of classical decoherence in nano-resonators, and a pre-requisite for future experiments on quantum NEMS.