Sensitivity to pulsars in the Galactic centre by this survey (continuous red line) and a hypothetical survey with ALMA at similar frequencies (dashed light blue line). The black dots represent the pseudo-luminosities for the known population of pulsars extrapolated to 120 GHz (see Sect. 3.4 for details), simulating a population of pulsars in the Galactic centre. The dots above each corresponding threshold line are pulsars that may theoretically be detected by the surveys. The sensitivity lines are calculated assuming a duty cycle for the minimum detectable flux density of δ = 0.1. We assumed a hyper-strong scattering towards the Galactic centre following the NE2001 model, s (Cordes & Lazio 2002) to consider a worst-case scenario. The effect of scattering is negligible (see text). The dominant interstellar effect is the uncorrected dispersion smearing for the IRAM 30m data, which is apparent at the very end of the short spin periods as a raising limit. The dispersion smearing effect is not affecting the ALMA limit because we consider that the ALMA data will enable the correction for dispersion. The red stars indicate the synthetic pulsar signals injected for the sensitivity tests. The three circles around the red stars with P ≃ 1.92, 55.22, and 141.87 ms mark the three pulsars orbiting black holes that were injected to test the sensitivity to highly accelerated pulsar systems. The orange diamond shows the average pseudo-luminosity of the Galactic centre magnetar PSR J1745−2900, and the blue triangle and green square mark the 120 GHz pseudo-luminosities of the Vela pulsar (PSR B0833−45) and PSR B0355+54, respectively.