Fano fluctuations in superconducting-nanowire single-photon detectors

A. G. Kozorezov, C. Lambert, F. Marsili, M. J. Stevens, V. B. Verma, J. P. Allmaras, M. D. Shaw, R. P. Mirin, and Sae Woo Nam

Phys. Rev. B 96, 054507 – Published 9 August 2017

Abstract

Because of their universal nature, Fano fluctuations are expected to influence the response of superconducting-nanowire single-photon detectors (SNSPDs). We predict that photon counting rate ( $P C R$ ) as a function of bias current ( $I_{B}$ ) in SNSPDs is described by an integral over a transverse coordinate-dependent complementary error function. Fano fluctuations in the amount of energy deposited into the electronic system contribute to the finite width of this error function $Δ I_{B}$ . The local response of an SNSPD can also affect this width: the location of the initial photon absorption site across the width of the wire can impact the probability of vortex-antivortex unbinding and vortex entry from the edges. In narrow-nanowire SNSPDs, the local responses are uniform, and Fano fluctuations dominate $Δ I_{B}$ . We demonstrate good agreement between theory and experiments for a series of bath temperatures and photon energies in narrow-wire WSi SNSPDs. In a wide-nanowire device, the strong local dependence will introduce a finite width to the $P C R$ curve, but with sharp cusps. We show how Fano fluctuations can smooth these features to produce theoretical curves that better match experimental data. We also show that the time-resolved hotspot relaxation curves predicted by Fano fluctuations match the previously measured Lorentzian shapes (except for their tails) over the entire range of bias currents investigated experimentally.

Received 9 February 2017
Revised 22 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.054507

Physics Subject Headings (PhySH)

Phonons Quasiparticles & collective excitations

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. G. Kozorezov¹, C. Lambert¹, F. Marsili², M. J. Stevens³, V. B. Verma³, J. P. Allmaras², M. D. Shaw², R. P. Mirin³, and Sae Woo Nam³

¹Department of Physics, Lancaster University, Lancaster, United Kingdom
²Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Dr., Pasadena, California 91109, USA
³National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 96, Iss. 5 — 1 August 2017

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Schematic picture of photoelectron-hole energy down-conversion cascade in a metal.
Reuse & Permissions
Figure 2
Calculated electron-electron $τ_{e e}^{- 1}$ , electron-phonon $τ_{e p}^{- 1}$ , and phonon-electron $τ_{p e}^{- 1}$ scattering rates vs excitation energy in WSi and NbN. Each rate is normalized to the characteristic time $τ_{0}$ of the corresponding material, and energy is shown in units of the material's critical temperature $T_{C}$ . Above the threshold energy $Ω_{1}$ (and below $E_{1}^{*}$ ), phonon emission dominates energy loss. Below $Ω_{1}$ , electron-electron scattering and phonon absorption dominate. The Debye energy $Ω_{D}$ is at the right edge of each plot, while the other thresholds $E_{1}$ and $E_{1}^{*}$ occur at much higher energies (not shown).
Reuse & Permissions
Figure 3
(a) Schematic predictions of $I_{det}$ vs transverse coordinate $y$ showing bell-shaped (upper solid curve) and w-shaped (lower solid curve) profiles. The dotted curves illustrate the variations expected at each position resulting from Fano fluctuations. The two sections with width $w / 2$ (or $w / 2 + δ w / 2$ if fluctuations are taken into account) form the part of the nanowire of total width $w (E, T_{b}, B)$ in expression (9), where vortex generation results in formation of a normal domain across the wire. (b) Predicted $P C R$ assuming a w-shaped $I_{det}$ profile in an ideal SNSPD without Fano fluctuations (black), along with the best-fit error function shape (red), and two shapes smeared by Fano fluctuations (blue and cyan) with variances differing by a factor 1.5. Curves of the same colors at the bottom show differences between each $P C R$ curve and the best-fit error function.
Reuse & Permissions
Figure 4
Normalized photon count rate ( $P C R$ ) for a WSi SNSPD operated in the single-photon detection regime for a series of (a) bath temperatures from 250 mK to 2 K with an increment 250 mK and (b) wavelengths $λ = 1200$ , 1350, 1450, 1550, and 1650 nm. Solid curves are theoretical simulations and solid circles are experimental results. Dashed lines indicate the slopes of the outer $P C R$ curves. All theoretical curves in (a) and (b) were fit simultaneously with only four fit parameters: $F_{eff} = 1.3$ , $\bar{χ} = 0.32$ , $τ_{0} = 5$ ns, and $I_{sw} / I_{dep} = 0.62$ .
Reuse & Permissions
Figure 5
Normalized click probability $P_{click}$ as a function of time delay $t_{D}$ for a series of bias currents. (a) Experimental data taken at a bath temperature of 0.25 K for photons of wavelength $λ = 1550$ nm. (b) Simulations. The entire set of theoretical curves was generated using the same set of fit parameters as in Fig. 4 except $I_{sw} / I_{dep} = 0.68$ .
Reuse & Permissions
Figure 6
Fitting $P C R$ vs $I_{B}$ for $λ = 1200$ , 1350, 1450, 1550, and 1650 nm by error functions.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics