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Bulletin of the American Physical Society

Non-equilibrium Charge Fluctuations as a Source of Inelastic Back-action in Quantum Point Contact Qubit Detectors

Carolyn Young, Aashish A. Clerk

Published Mar 17, 2009• 0 citations
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Charge detection at microsecond time-scales has far reaching consequences in both technology and in our understanding of electron dynamics in nanoscale devices such as quantum dots. Radio-frequency superconducting single electron transistors (RF-SET) and quantum point contacts (QPC) are ultra sensitive charge sensors operating near the quantum limit. The operation of RF-SETs outside the superconducting gap has been a topic of study; the sub-gap operation, especially in the presence of large quantum fluctuations of quasiparticles remains largely unexplored, both theoretically and experimentally. We have investigated the effects of quantum fluctuations of quasiparticles on the operation of RF-SETs for large values of the quasiparticle cotunneling parameter alpha = 8EJ/Ec, where EJ and Ec are the Josephson and charging energies. We find that, for alpha > 1, sub-gap RF-SET operation is still feasible despite quantum fluctuations that wash out quasiparticle tunneling thresholds. Such RF-SETs show linearity and signal-to-noise ratio superior to those obtained when quantum fluctuations are weak, while still demonstrating excellent charge sensitivity.\nWe have operated a QPC charge detector in a radio frequency mode that allows fast charge detection in a bandwidth of several megahertz. The noise limiting the sensitivity of the charge detector is not the noise of a secondary amplifier, but the non-equilibrium device noise of the QPC itself. The noise power averaged over a measurement bandwidth of about 10MHz around the carrier frequency is in agreement with the theory of photon-assisted shot noise. Frequency-resolved measurements, however show several significant discrepancies with the theoretical predictions. The measurement techniques developed can also be used to investigate the noise of other semiconductor nanostructures such as quantum dots in the Kondo regime.\nA study of the noise characteristics alone can not determine whether the device is operating at the quantum limit; a characterization of back action is also necessary. The inelastic current through a double quantum dot system (DQD) is sensitive to the spectral density of voltage fluctuations in its electromagnetic environment. Electrical transport studies on a DQD system electrostatically coupled to an SET shows qualitative evidence of back-action of SET. The design and fabrication of a few electron DQD device with integrated RF-SET and QPC charge sensors for the study of back action of the sensors and real-time electron dynamics in the DQD are also discussed.

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We study the dynamics of a charge qubit, consisting of a single electron in a double well potential, coupled to a point-contact (PC) electrometer using the quantum trajectories formalism. In contrast with previous work, our analysis is valid for arbitrary source-drain bias across the PC, but is restricted to the sub-Zeno limit. We find that the dynamics is strongly affected by inelastic tunnelling processes in the PC. These processes reduce the efficiency of the PC as a qubit readout device, and induce relaxation even when the source-drain bias is zero. We show that the sub-Zeno dynamics are divided into two regimes: low- and high-bias in which the PC current and current power spectra show markedly different behaviour. To further illustrate the division between the regimes and the inefficiency of the detector, we present simulated quantum trajectories of the conditional qubit and detector dynamics. We also describe how single shot measurements in an arbitrary basis may be achieved in the sub-Zeno regime.

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We perform real-time charge counting with a quantum point contact (QPC) for the last six electrons in a single quantum dot. At zero magnetic field, the charge-counting statistics show distinctive non-thermal-equilibrium effects for the even and odd electron numbers. A detailed study relates this difference to the excitation from the spin singlet state to triplet states driven by QPC back-action. At a finite magnetic field, spin excitations to different triplet states and Zeeman states are also observed. A master-equation model is developed to quantitatively characterize the back-action-driven spin excitation rate.

New Journal of Physics•Feb 13, 2013•4 citations
Charge detection at microsecond time-scales has far reaching consequences in both technology and in our understanding of electron dynamics in nanoscale devices such as quantum dots. Radio-frequency superconducting single electron transistors (RF-SET) and quantum point contacts (QPC) are ultra sensitive charge sensors operating near the quantum limit. The operation of RF-SETs outside the superconducting gap has been a topic of study; the sub-gap operation, especially in the presence of large quantum fluctuations of quasiparticles remains largely unexplored, both theoretically and experimentally. We have investigated the effects of quantum fluctuations of quasiparticles on the operation of RF-SETs for large values of the quasiparticle cotunneling parameter alpha = 8EJ/Ec, where EJ and Ec are the Josephson and charging energies. We find that, for alpha > 1, sub-gap RF-SET operation is still feasible despite quantum fluctuations that wash out quasiparticle tunneling thresholds. Such RF-SETs show linearity and signal-to-noise ratio superior to those obtained when quantum fluctuations are weak, while still demonstrating excellent charge sensitivity.\nWe have operated a QPC charge detector in a radio frequency mode that allows fast charge detection in a bandwidth of several megahertz. The noise limiting the sensitivity of the charge detector is not the noise of a secondary amplifier, but the non-equilibrium device noise of the QPC itself. The noise power averaged over a measurement bandwidth of about 10MHz around the carrier frequency is in agreement with the theory of photon-assisted shot noise. Frequency-resolved measurements, however show several significant discrepancies with the theoretical predictions. The measurement techniques developed can also be used to investigate the noise of other semiconductor nanostructures such as quantum dots in the Kondo regime.\nA study of the noise characteristics alone can not determine whether the device is operating at the quantum limit; a characterization of back action is also necessary. The inelastic current through a double quantum dot system (DQD) is sensitive to the spectral density of voltage fluctuations in its electromagnetic environment. Electrical transport studies on a DQD system electrostatically coupled to an SET shows qualitative evidence of back-action of SET. The design and fabrication of a few electron DQD device with integrated RF-SET and QPC charge sensors for the study of back action of the sensors and real-time electron dynamics in the DQD are also discussed.
We study the dynamics of a charge qubit, consisting of a single electron in a double well potential, coupled to a point-contact (PC) electrometer using the quantum trajectories formalism. In contrast with previous work, our analysis is valid for arbitrary source-drain bias across the PC, but is restricted to the sub-Zeno limit. We find that the dynamics is strongly affected by inelastic tunnelling processes in the PC. These processes reduce the efficiency of the PC as a qubit readout device, and induce relaxation even when the source-drain bias is zero. We show that the sub-Zeno dynamics are divided into two regimes: low- and high-bias in which the PC current and current power spectra show markedly different behaviour. To further illustrate the division between the regimes and the inefficiency of the detector, we present simulated quantum trajectories of the conditional qubit and detector dynamics. We also describe how single shot measurements in an arbitrary basis may be achieved in the sub-Zeno regime.
We perform real-time charge counting with a quantum point contact (QPC) for the last six electrons in a single quantum dot. At zero magnetic field, the charge-counting statistics show distinctive non-thermal-equilibrium effects for the even and odd electron numbers. A detailed study relates this difference to the excitation from the spin singlet state to triplet states driven by QPC back-action. At a finite magnetic field, spin excitations to different triplet states and Zeeman states are also observed. A master-equation model is developed to quantitatively characterize the back-action-driven spin excitation rate.