Controlling frequency-domain Hong-Ou-Mandel interference via electromagnetically induced transparency

Hong-Ou-Mandel (HOM) interference is a compelling quantum phenomenon that demonstrates the nonclassical nature of single photons. In this study, we investigate an electromagnetically induced transparency-based double-$\mathrm{\ensuremath{\Lambda}}$ four-wave mixing system from the perspective of quantized light fields. The system can be used to realize efficient HOM interference in the frequency domain. By using the reduced density operator theory, we demonstrate that although the double-$\mathrm{\ensuremath{\Lambda}}$ medium does not exhibit phase-dependent properties for the closed-loop case of two incident single photons, frequency-domain HOM two-photon interference occurs. For experimentally achievable optical depth conditions, our theory indicates that this double-$\mathrm{\ensuremath{\Lambda}}$ scheme can perform high-fidelity Hadamard gate operations on frequency-encoded single-photon qubits, and thereby generate HOM two-photon NOON states with a fidelity greater than 0.99. Furthermore, we demonstrate that this scheme can be used to realize arbitrary single-qubit gates and two-qubit SWAP gates by simply controlling the laser detuning and phase, exhibiting its multifunctional properties and providing a different route to scalable optical quantum computing.