Measurement of Quantum Noise in a Carbon Nanotube Quantum Dot in the Kondo Regime

The current emission noise of a carbon nanotube quantum dot in the Kondo regime is measured at frequencies $\nu$ of the order or higher than the frequency associated with the Kondo effect $k_B{T}_K/h$, with $T_K$ the Kondo temperature. The carbon nanotube is coupled via an on-chip resonant circuit to a quantum noise detector, a superconductor-insulator-superconductor junction. We find for $h\nu \approx k_B{T}_K$ a Kondo effect related singularity at a voltage bias $eV\approx h\nu$, and a strong reduction of this singularity for $h\nu \approx 3k_B{T}_K$, in good agreement with theory. Our experiment constitutes a new original tool for the investigation of the nonequilibrium dynamics of many-body phenomena in nanoscale devices.

Figure 1

(a) Sketch of the sample: a carbon nanotube (bottom electron microscope picture) is coupled to a superconductor-insulator-superconductor (SIS) junction (top electron microscope picture), used as a quantum detector, by a superconducting resonant circuit. This circuit is constituted by two transmission lines, placed close to one another, made of aluminum and terminated by on-chip Pd resistors. The SIS junction is fabricated by shadow angle evaporation. The carbon nanotube is CVD grown, connected with palladium contacts and side gated. (b) Lower curve: $I(V)$ of the detector in the subgap region. Upper curve: the real part of the impedance seen by the detector exhibits several resonances. (c) Differential conductance $dI/d{V}_S$ of the carbon nanotube as a function of voltage bias $V_S$ and gate voltage $V_G$. It exhibits a Kondo ridge for gate voltage between 3.05 and 3.20 V with an increase of conductance at zero bias.

Figure 2

(a) Derivative of the current noise and differential conductance of the CNT versus $V_S$ in the center of the Kondo ridge. Left axis: measured $d{S}_I/d{V}_S$ (in red) at 29.5 GHz as a function of bias voltage $V_S$. The black solid line corresponds to the calculated $d{S}_I/d{V}_S$ with a fitted decoherence rate incorporating both intrinsic and extrinsic decoherence (see text), while the dashed line is the theoretical prediction with the intrinsic decoherence rate. Right axis: Differential conductance $dI/d{V}_S$ of the CNT in units of $e^2/h$. (b) Same data at 78 GHz. Inset: measured conductance, symmetrized with respect to the bias voltage, in units of $e^2/h$. The black solid line corresponds to the FRG calculation of the conductance with the same fitted decoherence rate as the one used for the noise measurements. (c) Schematic picture of a quantum dot in the out-of-equilibrium Kondo regime together with the density of states for two distinct bias voltages. When the quantum dot is voltage biased, the Kondo resonance splits in two with a splitting given by the applied bias voltage. This leads to an increase of the emission at frequency $e{V}_S=h\nu$. The amplitude of the resonance peaks, and thus the emission noise at $e{V}_S=h\nu$, can be reduced by decoherence effects induced by the applied bias voltage.

Figure 3

$F(V_S)=[d{S}_I/d{V}_S]/[edI/d{V}_S(V_S-h\nu /e)]$ as a function of the bias voltage $V_S$ and the gate voltage $V_G$ at ${\nu }_1=29.5\mathrm{GHz}$ (a) and ${\nu }_3=78\mathrm{GHz}$ (b). $F(V_S)$ is arbitrarily fixed to zero for $e|V_S|<h\nu$. The gray curves on top of the color plot correspond to the bias voltage dependence of $F(V_S)$ at $V_G=3.12\mathrm{V}$ and $V_G=3.21\mathrm{V}$. The black arrow indicates a value of the $F(V_S)$ equal to 1. When the conductance is low, $F(V_S)$ is close to 1 while it is reduced in the highly conducting regions.