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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.

The response of elastoplastic nanocomposites in contact with rigid indenter has a lot of importance in engineering applications such as material characterization, Young modulus, Poisson's ratio and strain hardening parameters. With the aim of presenting a predictive model for the loading and unloading response, the problem of contact between elastoplastic composites with stiff spherical indenter was simulated using 2D axisymmetric model implemented in ANSYS. Parametric studies were performed numerically to investigate effects of geometrical and material parameters on the behavior of nanocomposites. Based on the parametric study observation, a normalization procedure is presented to express the loading and unloading responses in a nondimensional form. Three equations were numerically derived by fitting the FE normalized data to predict the loading and unloading responses and the residual indentation depth after unloading for elastoplastic nanocomposite with wide range strain hardening exponent. The predictions of proposed equations were in excellent agreement with experimental results for Al-Al2O3 nanocomposites and also with other experiments available in the literature for nanocomposites and pure metals. Moreover, derived equations were exploited to predict the Rockwell hardness of nanocomposites.

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 two-level atom interacting with a quantized field in an optomechanical cavity and study the population inversion of the atom in this hybrid optomechanical system. Analytical solutions of the excited state population in the hybrid system are derived for various initial states of the cavity field and the mechanical mirror in the limit of weak single-photon coupling regime. Due to the mechanical mirror, the population inversion exhibits anomalous behavior, compared to the results predicted by the Jaynes–Cummings (JC) model. For an initial Fock state cavity field, we show that the atomic population inversion can undergo collapses and revivals induced by the mechanical mirror which is in a Fock state for the resonant atom-field interaction. When the cavity field is far-detuned from the atomic transition, the atom can couple to the mechanical mirror effectively via the JC interaction. In this case, the atomic population inversion can display either full Rabi oscillations or the collapse and revival behavior induced by a Fock state or a coherent state of the mechanical mirror, respectively. We also explore an experimentally more relevant situation when the mechanical mirror is initially in a mixed state. We derive an analytical expression of the excited state population via the unitary evolution for the density operator of the whole system. We find that the population inversion in this case exhibits slower collapse and smaller revival amplitude due to the initial mixture of the mechanical state. For an initial coherent state cavity field, we show that the predicted collapse regime in the original JC model can display nonzero oscillating values. Our analytical predications are further confirmed with numerical calculations in which the dissipation mechanism from the system is included.

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.