Figure 1

(a) Illustration of the experimental apparatus. Laser light is focused onto the sample and is homodyned with Rayleigh scattered light in the forward (backward) direction for dc (ac) sensing. (b) Single electric charge sensing with a vertically stacked quantum dot molecule. The top left panel is an illustration of the excited state configuration with 1 electron and 1 hole in the bottom quantum dot and no charge in the top quantum dot. The bottom left panel is an illustration of the excited state configuration with 1 electron and 1 hole in the bottom quantum dot and 1 electron in the top quantum dot. The right panel is the absorption spectrum corresponding to this excited state. (c) DT spectroscopy of the QD transition. The laser power equals the saturation power, and the QD gate voltage is modulated by a square wave with peak-to-peak amplitude of 100 mV.Reuse & Permissions

Figure 2

(a) Description of static electric-field (dc) sensing. A small sublinewidth voltage modulation is applied to the device to enable lock-in detection. The top panel illustrates 1 cycle of the lock-in detector when the laser (vertical red arrow) is tuned to the point of highest slope for the Lorentzian response, reporting a signal level $-s$. The lock-in output in this case is 0. The lower panel is 1 cycle of the lock-in detector, but here the laser is detuned from the highest slope point due to the presence of an applied electric field. The lock-in reports a nonzero voltage that reveals the magnitude and polarity of the applied electric field. (b) Description of transient electric-field (ac) sensing. The modulation frequency determines the measured frequency component of the local oscillating electric field. The top panel illustrates 1 cycle of the lock-in detector when the laser (vertical red arrow) is tuned to a point such that the lock-in reports a signal level $-2s$. The lower panel is 1 cycle of the lock-in detector in the presence of an applied transient electric field oscillating at the lock-in frequency. The lock-in reports an additional voltage that reveals the magnitude of this oscillating field.Reuse & Permissions

Figure 3

(a) Absorption spectrum of a single quantum dot (DT). Each data point is recorded for 8 s with 1-ms time resolution. (b) A log-log plot of the variation of measurement noise, quantified by the standard deviation, with measurement time constant. Each data point is determined by subdividing the measured time trace into a collection of equal size time bins, finding the mean of each time bin, and then finding the standard deviation of the collection of means. The open orange diamonds correspond to 0 frequency shift in (a), the open red squares to 0.25 frequency shift, and the open blue circles to 0.75 frequency shift. At the dc sensor operating point—0 frequency shift—the noise magnitude is largest. Inset: same noise data, but all curves are normalized to 1 at 10 ms time constant. The black line plots the inverse square root of the measurement time constant. For spectral locations away from the dc electrometer operating point [0 frequency shift in (a)], the noise exhibits the expected time constant dependence. When the laser is at the electrometer operating spectral region, the measured noise is colored as indicated by the departure of the data from the black line. (c) The laser power dependence of the measured sensitivity when the laser is resonant with the QD transition.Reuse & Permissions

Figure 4

(a) A DR spectrum of a single QD. Each data point is recorded for 8 s with 1-ms time resolution. (b) DR spectroscopy of the QD transition as the square wave modulation peak-to-peak voltage is varied. Inset: DR signal along the black dashed line. The vertical arrow identifies the square wave modulation peak-to-peak voltage of 2 mV used for the data presented in (c),(d). (c) A log-log plot of the variation of measurement noise, quantified by the standard deviation, with measurement time constant. The open orange diamonds correspond to the dc electrometer operating point presented in Fig. 3a. The point-up red (point-down blue) triangles correspond to ac noise when the ac electrometer is characterized at (away) from its operating point. Inset: normalized as in Fig. 3b. The black line plots the inverse square root of the measurement time constant. (d) Panel I: DR signal when the laser power is slightly above saturation, the peak-to-peak amplitude of the square wave modulation is 2 mV, and the amplitude of an additional sine wave applied to the QD gate is varied. Each point is determined from the mean of 8 s worth of data acquired with 0.5-ms time bins. The error bars correspond to 1 standard deviation for 1 s of averaging time. Panel II: numerical derivative of panel I. Panel III: sine wave peak-to-peak voltage amplitude dependence of the ac sensitivity. To calculate the sensitivity, the standard deviation of each time trace is evaluated by subdividing the full time trace into 80 ms bins, finding the average of each bin, and then evaluating the standard deviation of this collection of means.Reuse & Permissions