Medium Transport; Low Wing; 2 Turbojet Eng
Communication Breakdown; Situational Awareness; Training / Qualification
ATC Issue All Types; Deviation - Altitude Excursion From Assigned Altitude; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Requested ATC Assistance / Clarification
Human Factors; Airspace Structure; Procedure
Aircraft X enroute from the southeast. Shortly after check-in; the pilot requested direct to a waypoint direct EKO; which [was] about 10 miles east of EKO. I cleared him as requested; and confirmed that the pilot wanted to conduct a visual approach. A few minutes later; I cleared the pilot to descend to 14;000 ft; which the pilot read back. Soon after; I gave the pilot the airport's position and advised to 'report in sight for a visual approach.' The pilot did not read it back correctly. I still do not know exactly what he said; but it sounded wrong; so I repeated myself to the aircraft; 'Just want to confirm; report airport in sight for a visual approach.' This time; the pilot responded 'wilco.' At this point the aircraft was still well above the MIA (Minimum IFR Altitude); at around 16;000 ft; if I remember right. I went back to my scan; checking up on the rest of the sector. A short time later; Aircraft X came up on the radio asking to confirm that I cleared him for a visual approach but wanted him to report the airport in sight. At that moment his altitude indicated 13;400 ft; which [matched] the MIA where the plane was positioned. I immediately responded 'Negative; maintain one three thousand four hundred; report the airport in sight.' The next update to the aircraft's datablock showed 13;100 ft.; three hundred ft. below the MIA. The only thing I feel I could have done differently would have been to re-clear the aircraft to 14;000 ft after the bad readback.
[Report narrative contained no additional information.]
Salt Lake City Center Controller trainee and their instructor reported they did not notice an aircraft leave its assigned altitude and descend below the Minimum IFR Altitude.