Continuous measurements of coherent quantum oscillations in two qubits

We develop a theory of coherent quantum oscillations in two, in general interacting, qubits measured continuously by a mesoscopic detector with arbitrary nonlinearity and discuss an example of SQUID magnetometer that can operate as such a detector. Calculated spectra of the detector output show that the detector nonlinearity should lead to mixing of the oscillations of the two qubits. For noninteracting qubits oscillating with frequencies ${\ensuremath{\Omega}}_{1}$ and ${\ensuremath{\Omega}}_{2}$, the mixing manifests itself as spectral peaks at the combination frequencies ${\ensuremath{\Omega}}_{1}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\Omega}}_{2}$. Additional nonlinearity introduced by the qubit-qubit interaction shifts all the frequencies. In particular, for identical qubits, the interaction splits coherent superposition of the single-qubit peaks at ${\ensuremath{\Omega}}_{1}={\ensuremath{\Omega}}_{2}$. Quantum mechanics of the measurement imposes limitations on the height of the spectral peaks.