Interaction without interaction

Interaction without interaction is a quantum mechanical measurement effect, which implies that one physical quantity does not interact with the other physical quantity, when we measure the physical quantity, the other physical quantity will have an effect on the measured physical quantity.
In the measurement effect of interaction without interaction for entanglement dynamics, the two two-level atoms are coupled with a single-mode polarized cavity field, the atomic centers of mass classical harmonic vibrations are fully decoupled with the internal degrees of freedom including the energy levels of atoms and the cavity field. There is not the interaction between centers of mass motions and the internal degrees of freedom, we find that the entanglement concurrence between the two atoms depends on the harmonic vibrations of their respective centers of mass during a shorter measurement time interval delta t than the period T. The vibrant factor (delta t)^2/T^2 quantitatively describes the effects of the harmonic vibrations on the entanglement concurrence. If we measure the concurrence, we will obtain the period of the classical harmonic vibrations even extremely micro amplitude.
In the measurement effect of interaction without interaction for an atomic (ion) beam, the atomic (ion) beam collectively and harmonically vibrates perpendicular to the wave vector of the beam, there is not the interaction between the collective, transverse and harmonic vibration and the translational motion of the beam. However, the number of atoms of the translational motion depends on the collective and transverse vibration of the beam. The number of atoms reaching the atomic detector will have a vibrant factor i.e., (delta t)/T if the measurement time delta t is less than the period T. From the measurement effect the classical harmonic vibration’s period is evaluated even when the vibration is of extremely micro amplitude.
Surprisingly and interestingly the measurement effect for an atomic (ion) beam is actually a macroscopic quantum phenomenon, because the classical harmonic vibration and the process of registering the number of atoms by the atomic detector are both regarded as the macroscopic events. The measurement effect of interaction without interaction for an atomic (ion) beam is not only interesting in quantum measurement theory, but also potentially important in applications. The so-called vibrant factor (delta t)/T is independent of the amplitude and the initial phase, which implies that an atomic (ion) beam can be used to detect classical harmonic vibrations' periods induced by gravitational waves. We can verify this new measurement effect for an ion beam instead of an atomic beam with today’s techniques.

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