Gan W.

In a previous paper,we propose quantum acoustical imaging based on the quantum effect of phonons entanglement. It reduces the resolution limit to sound wavelength divided by 2N where N is the number of phonons in the entanglement. Here the resolution is still limited by the wavelength. In this paper, we propose a new approach to quantum imaging. We realize that entanglement not only leads to the reduced resolution limit but also leads to tremendous increase in the sensitivity of the response of a certain parameter of the system. For instance, entanglement can lead to a tremendous improvement in quantum clock synchronization. In a quantum computer system, entanglement is exponentially sensitive to changes in the Hamiltonian of the simulated system. In our quantum acoustical system, we find that entanglement is exponentially sensitive to changes in the Hamiltonian of the simulated system. In this paper, we modify the Hamiltonian for phonon-phonon interaction by taking account of phonons entanglement. The Hamiltonian can be expressed in terms of the attenuation which shows the reduction in sound intensity during propagation. In a previous paper, we have shown that in quantum treatment, the attenuation varies inversely as the cube of the density of the propagation medium compared with classical treatment which shows that it is inversely proportional to the first order of the density of the medium. This in turns shows that the entanglement is exponentially sensitive to the changes in the density of the medium. We are in the process of designing the experimental quantum acoustical imaging which can show how to detect the effect of entanglement and capture it to display in the changes of the density of the propagation medium. If successful, this will show a breakthrough of resolution limit to be independent of sound wavelength.