We study the coherent propagation of light whose dynamics is governed by the effective Schrödinger equation derived in a magneto-optically manipulated atomic ensemble with a four-level tripod configuration for electromagnetically induced transparency (EIT). The small transverse deflection of an optical beam, which is ultrasensitive to the EIT effect, could be drastically amplified via a weak measurement with an appropriate preselection and postselection of the polarization state. The physical mechanism is explained as the effect of wave-packet reshaping, which results in an enlarged group velocity in the transverse direction.

We investigate, within the weak measurement theory, the advantages of nonclassical pointer states over semiclassical ones for coherent, squeezed vacuum, and Schrödinger cat states. These states are utilized as pointer states for the system operator $\widehat{A}$ with property ${\widehat{A}}^2=\widehat{I}$, where $\widehat{I}$ represents the identity operator. We calculate the ratio between the signal-to-noise ratio of nonpostselected and postselected weak measurements. The latter is used to find the quantum Fisher information for the above pointer states. The average shifts for those pointer states with arbitrary interaction strength are investigated in detail. One key result is that we find the postselected weak measurement scheme for nonclassical pointer states to be superior to semiclassical ones. This can improve the precision of the measurement process.

We study the spectra of collective low excitations of two atomic ensembles which couple with a single-mode cavity field. When the left ensemble is driven with an external optical field, its corresponding response spectrum to the incident optical light shows an electromagnetically-induced-transparency\char21{}like (EIT-like) phenomenon when the layers are arranged in the sequence of node antinode but not in the sequence of antinode node. In the case of antinode-antinode sequence, the response spectrum shows an EIT-like phenomenon with two transparent windows. We also investigate the fluctuation spectra of the atomic collective excitation modes and show similar EIT-like phenomena.

State preparation via postselected weak measurements in a three-wave mixing process is studied. We assume the signal input mode is prepared in a vacuum state, coherent state, or squeezed vacuum state, while the idler input is prepared in a weak coherent state and passes the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of the idler beam's path, the signal output channel is prepared in a single-photon Fock state, single-photon-added coherent state, or single-photon-added squeezed vacuum state with very high fidelity, depending upon the input signal states and related controllable parameters. The properties of squeezing, signal amplification, second-order correlation, and the Wigner functions of the weak-measurement-based output states are also investigated. Our scheme promises to provide an alternate effective method for producing useful nonclassical states in quantum information processing.

Postselected von Neumann measurement characterized by postselection and weak value has been found to possess potential applications in quantum metrology and solved plenty of fundamental problems in quantum theory. As an application of this new measurement technique in quantum optics and quantum information processing, its effects on the features of single-mode radiation fields such as coherent state, squeezed vacuum state and Schrödinger cat sate are investigated by considering full-order effects of unitary evolution. The results show that the conditional probabilities of finding photons, second-order correlation functions, Q_m -factors and squeezing effects of those states after the postselected measurement is significantly changed are comparable with the corresponding initial pointer states.