Hong-Ou-Mandel (HOM) interference is a compelling quantum phenomenon that
demonstrates the nonclassical nature of single photons. Herein, we investigate
an electromagnetically induced transparency-based double-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-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-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 new route to scalable optical quantum computing.Comment: 10 pages, 5 figure