Quantum weak measurement has attracted much interest recently [J. Dressel et al., Rev. Mod. Phys. 86, 307 (2014)] because it could amplify some weak signals and provide a technique to observe nonclassical phenomena. Here, we apply this technique to s
tudy the interaction between the free atoms and the vacuum in a cavity. Due to the gradient field in the vacuum cavity, the external orbital motions and the internal electronic states of atoms can be weakly coupled via the atom-field electric-dipole interaction. We show that, within the properly postselected internal states, the weak atom-vacuum interaction could generate a large change to the external motions of atoms due to the postselection-induced weak values.
We propose an approach to nondestructively detect $N$ qubits by measuring the transmissions of a dispersively-coupled cavity. By taking into account all the cavity-qubits quantum correlations (i.e., beyond the usual coarse-grained/mean-field approxim
ations), it is revealed that for an unknown normalized $N$-qubit state $|psi_N>=sum_{k=0}^{2^N-1}beta_k|k>_N$, each detected peak in the cavity transmitted spectra marks one of the basis states $|k>_N$ and the relative height of such a peak is related to the corresponding superposed-probability $|beta_k|^2$. Our results are able to unambiguously account for the intriguing multi-peak structures of the spectra observed in a very recent circuit-quantum-electrodynamics experiment [Phys. Rev. A {bf 81}, 062325 (2010)] with two superconducting qubits.
