This paper presents an experimental study of conditional phase shifts for quantum logic using a single atom strongly coupled to a high-finesse optical resonator. The researchers report the measurement of birefringence in a single atom and observe nonlinear phase shifts for intracavity photon numbers much less than one. They propose using these conditional phase shifts to implement quantum logic via a quantum-phase gate (QPG). The parameters of the "truth table" for the QPG are determined within a simple model of field transformation. The study highlights the challenges of experimental quantum computation, which requires strong coupling between quantum carriers of information ("qubits") in an environment with minimal dissipation. The authors demonstrate conditional dynamics at the single-photon level between two frequency-distinct fields in an optical resonator. They use the circular birefringence of an atom to rotate the polarization of a transmitted probe beam, with phase shifts conditioned on the intensity of a pump beam via a Kerr-type nonlinearity. They extract conditional phase shifts of approximately 16 degrees per intracavity photon. The researchers investigate a candidate quantum-phase gate (QPG) and extract relevant phase shifts for the "truth table" of the QPG. In their proposed implementation, "flying qubits" are single-photon pulses propagating in two frequency-offset channels, with internal states specified by σ± polarization. The experiment demonstrates the realization of a nonlinear optical susceptibility at the single-photon level and unambiguously shows the conditional dynamics necessary for implementing quantum logic. The authors also consider the practical application of their findings, noting that any laboratory quantum gate must exhibit coherence and produce entanglement between qubits. They propose measurement strategies for evaluating the potential of their system for performing quantum logic, emphasizing the importance of observing coherence and producing entanglement as necessary conditions for a candidate device to be considered a quantum gate. The study concludes that the measured conditional phase shifts hold great promise for implementing quantum logic with "flying qubits" encoded by the polarization of single-photon pulses. The results demonstrate the feasibility of quantum logic operations using cavity quantum electrodynamics (CQED) and highlight the potential for further advancements in quantum information processing.This paper presents an experimental study of conditional phase shifts for quantum logic using a single atom strongly coupled to a high-finesse optical resonator. The researchers report the measurement of birefringence in a single atom and observe nonlinear phase shifts for intracavity photon numbers much less than one. They propose using these conditional phase shifts to implement quantum logic via a quantum-phase gate (QPG). The parameters of the "truth table" for the QPG are determined within a simple model of field transformation. The study highlights the challenges of experimental quantum computation, which requires strong coupling between quantum carriers of information ("qubits") in an environment with minimal dissipation. The authors demonstrate conditional dynamics at the single-photon level between two frequency-distinct fields in an optical resonator. They use the circular birefringence of an atom to rotate the polarization of a transmitted probe beam, with phase shifts conditioned on the intensity of a pump beam via a Kerr-type nonlinearity. They extract conditional phase shifts of approximately 16 degrees per intracavity photon. The researchers investigate a candidate quantum-phase gate (QPG) and extract relevant phase shifts for the "truth table" of the QPG. In their proposed implementation, "flying qubits" are single-photon pulses propagating in two frequency-offset channels, with internal states specified by σ± polarization. The experiment demonstrates the realization of a nonlinear optical susceptibility at the single-photon level and unambiguously shows the conditional dynamics necessary for implementing quantum logic. The authors also consider the practical application of their findings, noting that any laboratory quantum gate must exhibit coherence and produce entanglement between qubits. They propose measurement strategies for evaluating the potential of their system for performing quantum logic, emphasizing the importance of observing coherence and producing entanglement as necessary conditions for a candidate device to be considered a quantum gate. The study concludes that the measured conditional phase shifts hold great promise for implementing quantum logic with "flying qubits" encoded by the polarization of single-photon pulses. The results demonstrate the feasibility of quantum logic operations using cavity quantum electrodynamics (CQED) and highlight the potential for further advancements in quantum information processing.