Gulfstream IV / G350 / G450
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Distraction; Human-Machine Interface; Situational Awareness
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Human Factors
Aircraft was cleared for the RNAV (GPS) RWY XXR at ZZZ. PF armed APP mode and commenced the approach. Passing ZZZZZ [fix]; PF was utilizing EVS (Enhanced Vision System) and HUD in an attempt to see runway lights. PF continued to focus on EVS and HUD when GROUND PROX illuminated almost the same time as a TERRAIN ALERT call from ZZZ Tower was received between ZZZZZ and ZZZZZ1. Aircraft was level at 1;100 feet; where it climbed to regain VPATH to continue approach. PF and PM both had vertical ground contact and were familiar with local terrain (ZZZ is aircraft's home base) and were comfortable reacquiring the VPATH and continuing approach.Suggest using EVS and HUD as secondary tool during. Verify APP has properly captured prior to shifting focus to EVS and HUD.
During RNAV XXR approach to ZZZ with approach close to minimums the Tower called low altitude alert almost simultaneously with Ground Prox warning.  The approach had been setup properly and I saw the PF arm approach mode when we were cleared to switch to tower.  I went heads down to change frequency and checked in with tower.  Shortly thereafter the Tower called a low altitude alert and ground proximity called terrain.  At that time I noticed that we were well below the vertical path but I could see the ground and almost immediately the tower on my right side which we were well clear of.  I told PF to level off and even climb a couple hundred feet.  We were able to rejoin the V Path about ZZZZZ1 on the approach and continued down to MDA where we were able to proceed visually when the runway was observed visually.  If we were not at our local airport with local knowledge of the terrain I am sure I would have called for a go around.I believe that the PF was focused inside the HUD on the EVS looking for runway lights and lost his instrument scan.  As the PM I also lost situational awareness.  Really have no idea how we ended up I believe in a pitch hold mode with the autopilot and no idea how it did not capture the V Path.
GIV flight crew reported descending too low on approach while looking for runway lights using an EVS and not scanning the instruments. Air traffic control issued a low altitude alert and the crew returned to clearance.