Through the von Neumann interaction followed by post-selection, we can extract not only the eigenvalue of an observable of the measured system but also the weak value. In this post-selected von Neumann measurement, the initial pointer state of the measuring device is assumed to be a fundamental Gaussian wave function. By considering the optical implementation of the post-selected von Neumann measurement, higher-order Gaussian modes can be used. In this paper, we consider the Hermite-Gaussian (HG) and Laguerre-Gaussian (LG) modes as pointer states and calculate the average shift of the pointer states of the post-selected von Neumann measurement by assuming the system observable  with A Î2 = and A Â2 = for an arbitrary interaction strength, where Ir epresents the identity operator. Our results show that the HG and LG pointer states for a given coupling direction have advantages and disadvantages over the fundamental Gaussian mode in improving the signal-to-noise ratio. We expect that our general treatment of the weak values will be helpful for understanding the connection between weak-and strong-measurement regimes and may be used to propose new experimental setups with higher-order Gaussian beams to investigate further the applications of weak measurement in optical systems such as the optical vortex.

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 fourlevel tripod configuration for electromagnetically induced transparency (EIT). The small transverse deflection of an optical beam, which is ultra-sensitive 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 wavepacket reshaping, which results in an enlarged group velocity in the transverse direction.

We study the spectra of collective low excitations of two atomic ensembles coupled indirectly through 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-(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, which show similar EIT-like phenomena.

We investigate, within the weak measurement theory, the advantages of non-classical pointer states over semi-classical ones for coherent, squeezed vacuum, and Schröinger cat states. These states are utilized as pointer state for the system operator with property 2 =Î, whereÎ represents the identity operator. We calculate the ratio between the signal-to-noise ratio (SNR) of non-postselected 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 non-classical pointer states to be superior to semi-classical ones. This can improve the precision of measurement process.

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, Qm -factors and squeezing effects of those states after the postselected measurement is significantly changed are comparable with the corresponding initial pointer states.

In this study, we investigate the advantages of non-classical pointer states in the generalized modular value scheme. We consider a typical von Neumann measurement with a discrete quantum pointer, where the pointer is a projection operator onto one of the states of the basis of the pointer Hilbert space. We separately calculate the conditional probabilities, Q M factors, and signal-to-noise ratios of quadrature operators of coherent, coherent squeezed, and Schrödinger cat pointer states and find that the non-classical pointer states can increase the negativity of the field and precision of measurement compared with semi-classical states in generalized measurement problems characterized by the modular value.

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The linear driving for a single-mode optical field in a cavity can result from the external driving of classical field even when the coupling between the classical field and the cavity is weak. We revisit this well known effect with a microscopic model where a classical field is applied to a wall of the cavity to excite the atoms in the wall, and re-combination of the low excitations of the wall mediates a linear driving for the single-mode field inside the cavity. With such modeling about the indirect driving through the quantum excitations of the wall, we theoretically predict several non-linear optical effects for the strong coupling cases, such as photon anti-bunching and photon squeezing. In the sense, we propose the most simplified non-linear quantum photonics model. PACS numbers: 42.50Wk, 42.50Lc, 42.50.Pq