  We present an ideal realization of the Tavis-Cummings model in the absence of
atom number and coupling fluctuations by embedding a discrete number of fully
controllable superconducting qubits at fixed positions into a transmission line
resonator. Measuring the vacuum Rabi mode splitting with one, two and three
qubits strongly coupled to the cavity field, we explore both bright and dark
dressed collective multi-qubit states and observe the discrete square root of N
scaling of the collective dipole coupling strength. Our experiments demonstrate
a novel approach to explore collective states, such as the W-state, in a fully
globally and locally controllable quantum system. Our scalable approach is
interesting for solid-state quantum information processing and for fundamental
multi-atom quantum optics experiments with fixed atom numbers.
