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We present how basic logic gates including nand, nor, and xor gates can be implemented counterfactually. The two inputs (Bob and Charlie) and the output (Alice) of the proposed counterfactual logic gate are not within the same station but rather separated in three different locations. We show that there is no need to prearrange entanglement for the gate, and, more importantly, there are no real physical particles traveling among Alice, Bob, and Charlie during the information processing. Bob and Charlie only need to independently control the blocking and unblocking of the transmission channels that connect them to Alice. In this way, they can completely determine the state of a real photon at Alice's end, thereby leading to implemention of a counterfactual logic gate. The functionality of a particular counterfactual logic gate is determined only by an appropriate design of Alice's optical device. Furthermore, by utilizing the proposed counterfactual logic gates, we demonstrate how to counterfactually prepare the Greenberger-Horne-Zeilinger state and W state with three remote quantum objects, which are in superposition states of blocking and unblocking the transmission channel.

We introduce a scheme to reconstruct the quantum state of a mechanical mirror in a hybrid optomechanical system. The scheme involves sending a beam of two-level atoms to interact with a quantized cavity field which is weakly coupled to the mechanical mirror. We show that the measured data of the excited-state probability of the atoms can be used directly to reconstruct the initial state of the mechanical mirror. If the mechanical mirror is initially a pure quantum state, we can reconstruct both the probability and the phase of the mechanical state. If it is initially a mixed state, we can reconstruct all the diagonal matrix elements and the first two diagonals above and below them.

We consider a three-level atomic medium and discuss how to control the Goos-H\"anchen (longitudinal) and Imbert-Fedorov (transverse) shifts for a circular polarized Gaussian beam via a pump field and a coherent driving field applied to the atomic medium. The susceptibility of the atomic medium can be adjusted by changing the driving and pump fields. Consequently, for a fixed driving field, by turning on and off the pump field the amplitude and the direction of the longitudinal and transverse shifts of such beam can be changed. We adopt stationary phase and beam simulation methods to derive our results.