We have investigated the microwave response of a transmon qubit coupled directly to a transmission line. In a transmon qubit, owing to its weak anharmonicity, a single driving field may generate dressed states involving more than two bare states. We confirmed the formation of three-state dressed states by observing all of the six associated Rabi sidebands, which appear as either amplification or attenuation of the probe field. The experimental results are reproduced with good precision by a theoretical model incorporating the radiative coupling between the qubit and the microwave.PACS numbers: 42.50. Gy, 42.50.Ct, 85.25.Cp The optical response of two-level systems is a central research subject in the field of atomic, molecular and optical physics. When two-level systems are driven by a resonant field, the ground and excited states are mixed to form dressed states. For each unique transition between dressed states, two Rabi sidebands appear symmetrically about the transition frequency in the fluorescence power spectrum [1,2]. Driving transitions also populates the excited state. However, even in the strong-driving limit, a continuous field cannot induce population inversion, and therefore effects which rely on inversion, such as lasing, are generally thought to be forbidden in two-level systems. However, when an additional field, e.g., a probe field, is also applied to such a driven atom, the field is amplified when tuned to one of the Rabi sidebands, whereas it is attenuated when tuned to the other sideband. In other words, amplification (lasing) can take place without explicit population inversion in the bare-state basis [3][4][5][6][7], provided there is a mechanism for population inversion in the dressed-state basis.Many experiments analogous to those in optics are now being performed within the context of circuit quantum electrodynamics (QED), in which the optical fields and atoms of conventional QED are replaced with microwave fields and superconducting qubits, respectively [8,9]. An advantage of using superconducting qubits is their large transition dipole moments, which enable strong coupling to the microwave field [10]. Exploiting this strong coupling, lasing experiments become possible by using a single quantum emitter: Maser operation has been demonstrated by a single driven qubit-cavity system [11,12] and a driven qubit coupled directly to a transmission line [13], where population inversion takes place in the bare-state basis. Amplification due to dressed-state inversion has been reported recently in a qubit-cavity system [14], and lasing without inversion independent of basis has also been proposed theoretically [15]. Furthermore, the Autler-Townes effect and the electromagnetically induced transparency have been investigated by driving a higher transition of the qubit [16][17][18][19][20][21], and the quantum interference induced by longitudinal driving has been confirmed [22][23][24].Superconducting qubits are multilevel quantum systems having designed energy-level spacings. In transmon qubits,...