We study how the decoherence of macroscopic objects originates intrinsically from the relativistic effect. With the degree of freedom of the center of mass (CM) characterizing the collective quantum state of a macroscopic object (MO), it is found that an MO consisting of N particles can decohere with a time scale of no more than N − 1 . Here, the special relativity can induce the coupling of the collective motion mode and the relative motion modes in an order of 1/ c 2 , which intrinsically results in the above minimum decoherence.
We consider a composite system consisting of coupled particles, and investigate decoherence due to coupling of the center-of-mass degree of freedom to the internal vibrational degrees of freedom. For a composite system of bound particles, we show that in general such a decoherence effect exists, and leads to suppression of interference between different paths of the center-of-mass. For the special case of harmonically-bound particles moving in an external potential, we show that the coupling between the center-of-mass and internal degrees of freedom takes the form of parametric driving of the vibrational degrees of freedom, and that nontrivial coupling depends on the second derivative of the external potential. We find a solution to this parametric driving problem in one dimension for a fixed center-of-mass trajectory. We also propose a measure of compositeness, which quantifies the extent to which such a composite system cannot be approximated as a single, indivisible particle. We perform numerical simulations for a simple interference experiment, consisting of two wave packets scattering off of a square well, and show a close connection between suppression of interference and entanglement between the center-of-mass and internal degrees of freedom, which depends on the initial state of the internal mode. We also calculate the measure of compositeness for this system.
The standard interpretation of the Stern-Gerlach experiment assumes that the atomic center-of-mass plays the role of "quantum apparatus" for the atomic spin. Following a recent, decoherence-based, model fitting with this interpretation, we investigate whether or not such model can be constructed. Our conclusions are somewhat surprising: only if the screen capturing the atoms in the experiment brings the information about the atomic-nucleus center-of-mass, one may construct the model desired. The nucleus
CM system is monitored by the nucleus "relative system (
R)". There appear the effective (the electrons-mediated) interaction between
CM and
R that is possibly responsible for decoherence. For larger atoms, the interaction scales as
Z2 (
Z is the "atomic number"), being totally independent on the atomic mass. The interaction selects the
CM-wave-packet states as the approximate pointer basis. Interestingly enough, the model stems nonoccurrence of decoherence due to the internal environment for the larger systems (such as the macromolecules and the macroscopic systems). Certainly, disproving this model (e.g. in an experiment) stems the active role of the screen, which becomes responsible for the "
CM + spin"-state "reduction" ("collapse"), i.e. for the irreversible retrieval of the classical information from the quantum world.
Environment induced decoherence entails the absence of quantum interference phenomena from the macroscopic world. The loss of coherence between superposed wave packets is a dynamical process the speed of which depends on the packet separation: The farther the packets are apart, the faster they decohere. The precise temporal course depends on the relative size of the time scales of decoherence and other processes taking place in the open system and its environment. We use the exactly solvable model of a harmonic oscillator coupled to a bath of harmonic oscillators to illustrate various decoherence scenarios: These range from exponential golden-rule decay for microscopic superpositions, system-specific decay for larger separations in a crossover regime, and finally the universal interaction-dominated decoherence for ever more macroscopic superpositions investigated in great generality in the accompanying Paper I [W. T. Strunz, F. Haake, and D. Braun, Phys. Rev. A
67, 022101 (2003)].