  Properties of superconducting nanowires set the performance level for
Superconducting Nanowire Single Photon Detectors (SNSPD). Reset time in
commonly employed large area SNSPDs,5-10ns,is known to be limited by the
nanowires kinetic inductance.On the other hand, reduction of the kinetic
inductance in small area (waveguide integrated) SNSPDs prevents biasing them
close to the critical current due to latching into a permanent resistive
state.In order to reduce the reset time in SNSPDs, superconducting nanowires
with both low kinetic inductance and fast electron energy relaxation are
required. In this paper, we report on narrow (15-100nm) and long (up to 120
$\mu$m) superconducting $MgB_{2}$ nanowires offering such combination of
properties.In 5 nm-thick $MgB_{2}$ films, grown using Hybrid Physical Chemical
Vapor Deposition, the electron relaxation time was 12ps, the critical
temperature was 32K, and the critical current density was 5x$10^{7}$ A/$cm^{2}$
(at 4.8K). Using microwave reflectometry, we measured a kinetic inductance of
Lk0(4.8K)=1.3-1.6 pH/sqr regardless of the nanowire width, which results in a
magnetic field penetration depth of 90 nm. These values are very close to those
in pristine $MgB_{2}$. For 120 $\mu$m long nanowires the response time was only
100ps, i.e. 1/80 of that in previously reported NbN nanowire photon detectors
of similar dimensions.
