Principle of the modulated double balanced amplifier setup. The setup measures the difference between the two input noise powers, with a ±1 factor given by the modulation.
(a) Direct amplification technique: the signal is amplified, filtered, and applied to the square law detector, measuring the sum of the noise temperature of the signal, the measurement load , and the noise temperature of the amplifier . Below is a schematic representation of the measured lock-in voltage as a function of time: the value of the lock-in voltage alternatively switches between and . The peak-peak amplitude of the detected square voltage is equal to . (b) Our setup detects and modulates the difference between the two input noises, and , that is . The lock-in voltage (schematic representation in the lower panel) is then centered on zero while its peak-peak amplitude is equal to . The standard deviation is however times larger in our setup.
(a) Schematic of the setup, as implemented in our Oxford Kelvinox 400 dilution refrigerator. (b) and (c) Pictures of the room-temperature parts of the setup.
(a) Phase difference between the two inner arms of the setup as a function of the frequency. The signals of the two arms are measured just before the second hybrid coupler. (b) Transmission between the input of the refrigerator and the two output arms of the setup (just before the square law detectors) for a positive ( + 1) and negative ( − 1) dc voltage on the modulator. The 1.5 GHz carrier is suppressed by more than 60 dB.
(a) 120–50 Ω transformer line: the coplanar waveguide is built on a TMM10 substrate for low-temperature performance. The width of the center conductor is 0.66 mm for the 50 Ω port, and 0.075 mm for the 120 Ω port. (b) and (c) Pictures of the 4-microwave ports sample holder. The 50 Ω lines and the transformer lines are encased in the four sides of the sample holder. (d) Zoom on the center part of the sample holder; the size of the sample is 2 mm × 2 mm. (e) Reflection on the 50 Ω port of the two transformer lines as a function of the frequency, measured in liquid nitrogen.
Operation of the setup. (a) stability of the setup for two nonconsecutive runs: measured noise (line) and temperature of the 1 K pot (circles) as a function of time. Noise data for both graphs are measured for the same reference gate voltage of the sample . The averaging time per point is 10 s for run A, and 20 s for run B; (b) datasets obtained after subtraction of noise at the reference gate voltage  for the first points of both runs (measured at different gate voltages). The dataset for run A presents a significantly larger standard deviation due to the shorter averaging time per point.
Average ac current and noise of a single electron source measured by our setup: (a) in-phase and out-of-phase parts of the average ac current emitted by the source at f = 1.5 GHz, as a function of the gate voltage Vg controlling the coupling between the dot and the electron gas. In this case, the signal () can easily be measured in less than a second. (b) Current autocorrelations measured with our setup as a function of Vg. The error bars demonstrate that our setup is well suited for precise measurements of noise spectral densities lower than .
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