Deterministic generation of large Fock states in coupled optical-optomechanical cavities

The preparation of Fock states, as a fundamental problem in the research of quantum optics and quantum information, still faces challenges in achieving both unconditional preparation and large photon numbers. Here, we study the deterministic generation of large Fock states through the nonlinear interaction in coupled optical-optomechanical cavities. Under the condition that the mechanical frequency is twice the optical coupling strength, and much larger than the optomechanical coupling strength, there occurs a nonlinear interaction among two optical eigenmodes and the mechanical mode, i.e., a photon is annihilated, accompanied by the creation of another photon together with a phonon, and vice versa. It is analytically proved that, through this interaction, Fock states |n〉 and |1〉 will generate |n+1〉 at specific evolution times if the mechanical mode is initially on the ground state. In addition, numerical results show that Fock states |n〉 and |p〉 can also generate |n+p〉 with the fidelities larger than 94% (1<p≤n≤40). The proposed mechanism achieves deterministic generation of large Fock states, which can be applied to quantum metrology and quantum simulation.