Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 60; Flight Crew Total 3300; Flight Crew Type 500
Aircraft Equipment Problem Critical
Flight Crew Overcame Equipment Problem; Flight Crew Took Evasive Action
Aircraft
We departed with zero passengers in VMC. I was the pilot flying (PF). We climbed to our cruising altitude of 41;000 feet with about three ATC level offs on the way up. About one minute after level off we experienced a rapid loss of cabin pressurization. We both noticed the change of pressure first in our ears which drew our attention to the pressurization controller.  I saw the cabin rate climbing through 2;000 fpm; as it approached 5;000 fpm I called to put the oxygen masks on (Pilot Monitoring said he saw the rate get to 7000+ fpm). By the time I had my mask on and secured the Master Warning along with the Cab Alt annunciator had illuminated. At this time I executed an emergency descent per the Flight Safety memory items. Due to hand flying the airplane I did not put my headset back on so I did not hear any of the radio communications between PM and ATC. PM did verify that we were an emergency aircraft and that we were continuing the descent. To my understanding; the PM did not declare an emergency but said we were in an 'emergency descent'. I did perform cross checks with PM throughout the descent; checking for any physical signs of hypoxia or adverse effects of the depressurization.  We leveled off at 11;000 feet per ATC instructions at which time we removed our masks and completed the emergency checklist.  We decided; as a crew; that continuing to [destination] was the nearest practical airport to land at. At that point we requested to fly direct at 10;000 feet and completed the flight without issue.  Approaching 24 hours since the incident I have not felt any physiological effects of the depressurization.
The ATC controllers were extremely helpful and accommodating and the requests they had for information were appropriate and did not interfere with the management of the situation from the cockpit. Once we got back and shut down; we as a crew declined any further flying that day. This turned out to be a very good decision as a couple of hours after the completion of the flight the adrenaline wore off and extreme fatigue set in which only abated after a night's rest. Had we been on a flight at this time; reaction times and decision making would have definitely been compromised.
CE560XL flight crew reported executing an emergency descent after loss of cabin pressure at FL410.