  When a metal is subjected to strong magnetic field B nearly all measurable
quantities exhibit oscillations periodic in 1/B. Such quantum oscillations
represent a canonical probe of the defining aspect of a metal, its Fermi
surface (FS). In this study we establish a new mechanism for quantum
oscillations which requires only finite segments of a FS to exist. Oscillations
periodic in 1/B occur if the FS segments are terminated by a pairing gap. Our
results reconcile the recent breakthrough experiments showing quantum
oscillations in a cuprate superconductor YBCO, with a well-established result
of many angle resolved photoemission (ARPES) studies which consistently
indicate "Fermi arcs" -- truncated segments of a Fermi surface -- in the normal
state of the cuprates.
