Physical mechanisms of timing jitter in photon detection by current-carrying superconducting nanowires

We studied timing jitter in the appearance of photon counts in meandering nanowires with different fractional amount of bends. Intrinsic timing jitter, which is the probability density function of the random time delay between photon absorption in current-carrying superconducting nanowire and appearance of the normal domain, reveals two different underlying physical mechanisms. In the deterministic regime, which is realized at large photon energies and large currents, jitter is controlled by position-dependent detection threshold in straight parts of meanders. It decreases with the increase in the current. At small photon energies, jitter increases and its current dependence disappears. In this probabilistic regime jitter is controlled by Poisson process in that magnetic vortices jump randomly across the wire in areas adjacent to the bends.

Figure 1

Images of the largest and the smallest (inset) meanders obtained with a scanning electron microscope. The size of the largest meander is $4\times 4\mu {\mathrm{m}}^2$; the length of straight wires between bends is 3.5 µm. The size of the smallest meander is $4\times 1\mu {\mathrm{m}}^2$; the length of straight wires between bends is 0.5 µm.

Figure 2

(a) Schematics of the setup for jitter measurements at 800 and 1560 nm. (b) Voltage transient recorded by the 50 GHz sampling oscilloscope. Points occurring within the rectangle window at the level $H$ are used to build statistical distribution of arrival times shown in the inset. Dotted lines show locations where the vertical distributions of sampling points were additionally measured. $\sigma U_{\mathrm{\Sigma }}, \sigma U_N$, and ${\sigma }_{\mathrm{syst}}$ denote corresponding standard deviations.

Figure 3

Artificial jitter ${\sigma }_{\mathrm{amp}}$ due to the difference in amplitudes of two pulses arriving at the same time.

Figure 4

(a) Histograms (PDFs) of the delay time for the meander $4\times 4\mu {\mathrm{m}}^2$ and $4\times 1\mu {\mathrm{m}}^2$ at currents $0.95I_{\mathrm{C}}$ (closed symbols) and for the meander $4\times 4\mu {\mathrm{m}}^2$ at the current $0.8I_{\mathrm{C}}$ (open symbols). Data were obtained at 4.2 K and the wavelength 800 nm. Horizontal dashed line marks the level where FWHM were defined. Solid lines show Gaussian fits to the left parts of histograms. Dashed line shows the best fit of the PDF for the smaller meander with Eq. (4). (b) Standard deviation in the intrinsic jitter as function of bias current for four studied meanders. The error bars denote cumulative uncertainties which arise from fitting PDFs with Eq. (4) and computing ${\sigma }_{\mathrm{int}}$ with Eq. (2). Lines are to guide the eyes.

Figure 5

(a) Histograms (PDFs) of the delay time at the current $0.95I_C$ for the meanders $4\times 4\mu {\mathrm{m}}^2$ (rhombs) and for the meander $4\times 1\mu {\mathrm{m}}^2$ (squares). Data were obtained at 4.2 K and the wavelength 1560 nm. Horizontal dashed line marks the level where FWHM were defined. Solid line shows Gaussian fit to the left parts of the histograms. Dashed line shows the best fit of the PDF with Eq. (4) for the meander $4\times 1\mu {\mathrm{m}}^2$. (b) Standard deviation in the intrinsic jitter as function of bias current for four studied meanders. The error bars denote cumulative uncertainties which arise from fitting PDFs with Eq. (4) and computing ${\sigma }_{\mathrm{int}}$ with Eq. (2). Lines are to guide the eyes.

Figure 6

Contributions to the local jitter from bends (triangles) and wires (circles) vs. relative current. Open and closed symbols correspond to wavelengths 1560 and 800 nm, respectively. Lines show best fits to experimental data obtained with Eq. (7) (solid line) and Eq. (6) (dashed line). The error bars denote the uncertainties of which result from solving system containing Eq. (5) for all four meanders.