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Applied Physics Letters

High frequency components of current fluctuations in semiconductor tunneling barriers

Xavier Oriols, Ferran Martı́n, Jordi Suñé

Published May 27, 2002• 14 citations
Publisher

Abstract

The power spectral density of current noise in phase-coherent semiconductor tunneling scenarios is studied in terms of Bohm trajectories associated to time-dependent wave packets. In particular, the influence of the particles reflected by the barrier on the noise spectrum is analyzed. An enhancement of the power spectral density of the current fluctuations is predicted for very high frequencies. The experimental measurement of this high frequency effect is discussed as a possible test of Bohm trajectories.

DOI
10.1063/1.1482136

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Physical review. B, Condensed matter•Jul 1, 1982•117 citations
The power spectral density of current noise in phase-coherent semiconductor tunneling scenarios is studied in terms of Bohm trajectories associated to time-dependent wave packets. In particular, the influence of the particles reflected by the barrier on the noise spectrum is analyzed. An enhancement of the power spectral density of the current fluctuations is predicted for very high frequencies. The experimental measurement of this high frequency effect is discussed as a possible test of Bohm trajectories.
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.
The electrical noise of mesoscopic devices can be strongly influenced by the quantum motion of electrons. To probe this effect, we have measured the current fluctuations at high frequency (5 to 90 gigahertz) 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, nonsymmetrized noise as demonstrated for a Josephson junction. The same scheme is used to detect the current fluctuations arising from coherent charge oscillations in a two-level system, a superconducting charge qubit. A narrow band peak is observed in the spectral noise density at the frequency of the coherent charge oscillations.
We present a theory for the frequency-dependent current fluctuations in superconducting quantum point contacts (SQPC) within the dc transport regime. This theory is valid for any barrier transparency between the tunnel and ballistic limits, yielding an analytical expression for the fluctuations spectrum in the subgap region. It is shown that the level of noise in a quasiballistic SQPC may have a huge increase in comparison with the case of a normal contact carrying the same average current. The effect of this high level of noise on the actual observability of the current-phase relation for a ballistic point contact is discussed in connection with recent experimental measurements.
We calculate the full-frequency spectral density of voltage fluctuations in a single-electron transistor (SET), used as an electrometer biased above the Coulomb threshold so that the current through the SET is carried by sequential tunneling events. We consider both a normal-state SET and a superconducting SET. The whole spectrum, from low-frequency telegraph noise to quantum noise at frequencies comparable to the SET charging energy ${(E}_{C}/\ensuremath{\Elzxh})$ to high-frequency Nyquist noise, is described. We take the energy exchange between the SET and the measured system into account using a real-time diagrammatic Keldysh technique. The voltage fluctuations determine the backaction of the SET on the measured system, and we specifically discuss the case of superconducting charge qubit read-out and measuring the so-called Coulomb staircase of a single Cooper-pair box.
Time-dependent wave packet resonant scattering for the double square barrier has been studied in terms of Bohm quantum trajectories. The high transmission probability for the wave packet with a resonant energy can be explained by the behavior of the quantum trajectories under the influence of the relatively slow formation of a node within the first barrier. This node splits the trajectories into reflected and transmitted components. During this stage, many particle trajectories pass through the double-barrier region and contribute to the transmitted part of the wave packet. Due to the transient nature of the nodes, trajectories in the reflected wave packet bunch together between the nodes for a finite period of time so that temporary structure (localization of particles and accompanying increase in the probability density) develops on small length scales. These calculations also show that the particles gain high momentum near the nodal points, and they reach a uniform momentum distribution after transmitting the barrier region. We have found that the presence of a node between the two barriers influences the different lifetimes of the quasi-bound states. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 206–213, 2001
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where I0{I}_{0}I0​ is the critical current, CCC is the junction capacitance, and Ls{L}_{s}Ls​ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the LsC{L}_{s}CLs​C resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.