We examine the effects of intra-environmental coupling on decoherence by constructing a low temperature spin-spin-bath model of an atomic impurity in a Debye crystal. The impurity interacts with phonons of the crystal through Jahn-Teller vibronic coupling. Anharmonic intra-environmental vibrational coupling is incorporated through anti-ferromagnetic spin-spin interactions. The reduced density matrix of the central spin representing the impurity is calculated by dynamically integrating the full Schrödinger equation for the spin-spin-bath model for different thermally weighted eigenstates of the spin-bath. Exact numerical results show that increasing the intra-environmental coupling results in suppression of decoherence. This effect could play an important role in the construction of solid state quantum devices such as quantum computers. Intra-environmental coupling has customarily been neglected in theoretical models of subsystem-environment interaction. The popular spin-boson model [1,2], for example, assumes that the environment consists of a set of non-interacting harmonic oscillators linearly coupled to a central spin. The neglect of intra-environmental coupling is motivated more by mathematical convenience than by physical insight.One failing of such models is that intra-environmental energy transfer can only proceed by using the subsystem as an intermediate. In addition, it is well known that the statistical properties of the energy eigenfunctions and eigenspectra of strongly coupled (irregular) systems is qualitatively different from that of uncoupled (regular) systems. The Wigner functions of eigenvectors for irregular systems are almost uniform over the energetically allowed classical phase space [3]. Those of regular systems are more lumpy with energy localized in a subset of the available modes [4]. Similarly, irregular eigenspectra show level repulsion while regular spectra show level clustering [5]. These spectral signatures have important dynamical consequences [6]. For these reasons coupled environments may have decoherence properties which differ substantially from those predicted by uncoupled oscillator models.Proposed new technologies such as quantum computing [7], laser control of chemical reactions [8], and molecular electronics [9] all require a qualitative understanding of the effects of decoherence and dissipation for experimental implementation. Predictive theoretical studies for such systems would also greatly benefit from dynamical methods which accurately include the effects of intraenvironmental coupling and environmental memory effects.Unfortunately, exact theories such as the FeynmanVernon influence functional method [10] and the Nakajima-Zwanzig master equation [11] cannot be easily applied. Approximate theories such as the Redfield [12], completely-positive-dynamical-semigroup [13] and SRA [14] master equations need testing against exact results before they can be applied with confidence. Thus, exact numerical calculations for subsystems interacting with environments of a small num...
