zum Hauptkapitel Emerging Quantum Mechanics:
The coupling to the phonon is suppressed, because the D-wave eigenstate is spread
out over the environmental degrees of freedom. The environmental degrees of freedom
do not couple to the phonon directly, only indirectly via phonon <-> eigenstate
<-> environment. The coupling to the environmental degrees of freedom is very
small and entanglement between D-wave eigenstates and environmental states occurs
only on the energy shell. The broadening of the eigenvalues due to coupling
to the environment is much smaller than the energetic separation of the eigenvalues.
Therefore the coupling to the environment cannot induce transitions between
the eigenstates. In this way the D-wave system stays in an eigenstate, once it
is there. This is not only valid for the ground state (global minimum), but also
The found results can be interpreted in the usual decoherence picture: Due to entanglement
with the environment the non-diagonal matrix elements of the density matrix vanish
This does not contradict the short live time (50 nano seconds) of the Rabi oscillations
of a single qubit. In this case a magnetic flux is first applied, which makes the
two current directions energetically inequivalent. When the qubit is in its ground
state, a (resonant) microwave photon is injected such that ground state plus
photon is energetically degenerate with the first excited state (current in opposite
direction). The qubit then oscillates bewteen the two states (ground state
+ photon and excited state). These are the Rabi oscillations. At any time "collapses"
of the following kind are possible:
a) The photon escapes or is absorbed by the matter and the qubit remains in its ground
b) The current absorbs the photon and the qubit stays in the excited state. If these
two processes occur with equal probability and the read out of the qubit occurs
after the collapses, the measured switching probability will be 0.5. The measured
decay time of 50 nano seconds then just means that after this time the collapse
has already occurred with high probability. The coupling to the environment
has no influence on the Rabi oscillations, because the photon drives the qubit
to switch between different eigenstates and it provides the necessary energy. The
coupling to the environment might, however,
protect the Rabi oscillations from disturbances by phonons.
In the case a) the qubit cannot collapse, because it is already in the ground state
and it is not driven by a photon.
There remains the question why the coupling to the environment does not protect the
eigenstates from coupling to the photon. The answer is that the photon couples
to charge and charge is conserved. The charge will not vanish, if the eigenstates
entangle to the environment. Therefore, even when entangled to the environment,
the photon can still drive the current states between their two directions.