Abstract
Practical implementations of quantum technology are limited by unavoidable effects of decoherence and dissipation. With achieved experimental control for individual atoms and photons, more complex platforms composed by several units can be assembled enabling distinctive forms of dissipation and decoherence, in independent heat baths or collectively into a common bath, with dramatic consequences for the preservation of quantum coherence. The cross-over between these two regimes has been widely attributed in the literature to the system units being farther apart than the bath’s correlation length. Starting from a microscopic model of a structured environment (a crystal) sensed by two bosonic probes, here we show the failure of such conceptual relation, and identify the exact physical mechanism underlying this cross-over, displaying a sharp contrast between dephasing and dissipative baths. Depending on the frequency of the system and, crucially, on its orientation with respect to the crystal axes, collective dissipation becomes possible for very large distances between probes, opening new avenues to deal with decoherence in phononic baths.
Highlights
Microscopic model to clarify and illustrate several details: a phonon bath in a crystal probed at different spatial locations
We address the cross-over from common bath (CB) to separate baths (SB) in detail, providing a physical ground for the description of intermediate regimes, and assessing the role played by geometric factors, spatial extension of the system-probe contact and bath correlations
Our model allows to clarify several issues including: a) why when increasing the system size in 1D environments[27,28,30,36] there is no asymptotic interpolation between CB and SB, but a periodic cross-over; b) why choosing an isotropic environmental dispersion relation will always lead to distance-decaying cross-damping, c) why anisotropic dispersion relations can lead to surprising effects like CB at large distances, showing d) that in general the correlation length is not related to the CB/SB transition
Summary
Microscopic model to clarify and illustrate several details: a phonon bath in a crystal probed at different spatial locations. We address the cross-over from CB to SB in detail, providing a physical ground for the description of intermediate regimes, and assessing the role played by geometric factors, spatial extension of the system-probe contact and bath correlations. Our model allows to clarify several issues including: a) why when increasing the system size in 1D environments[27,28,30,36] there is no asymptotic interpolation between CB and SB, but a periodic cross-over; b) why choosing an isotropic environmental dispersion relation will always lead to distance-decaying cross-damping, c) why anisotropic dispersion relations (like those in real crystals with symmetries) can lead to surprising effects like CB at large distances, showing d) that in general the correlation length is not related to the CB/SB transition. For clarity we introduce a particular model displaying all the phenomenology, and leave the discussion on the generality of these effects to the last section
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