Thermal relaxation and dephasing

In addition to relaxation and dephasing, the coupling to the thermal bath may shift the position of energy levels. In (7b) it is assumed that the energy differences etc. already include this shift. 

Quantum-state decay to a continuum or changes in its population via coupling to a thermal bath is known as amplitude noise (AN). It characterizes decoherence processes in many quantum systems, for example, spontaneous emission of photons by excited atoms [35], vibrational and collisional relaxation of trapped ions [36] and the relaxation of current-biased Josephson junctions [37], Another source of decoherence in the same systems is proper dephasing or phase noise (PN) [38], which does not affect the populations of quantum states but randomizes their energies or phases. 

The proposed mechanism is thermal excitation of the Rh-C stretch mode causes the CO-stretching mode transition frequency to shift a small amount, Am, as shown in Fig. 7A. During the time period in which the Rh-C mode is excited, the initially prepared CO superposition state pre-cesses at a higher frequency, as indicated by the dashed arrow in Fig. 7A. Thus, a phase error develops. For a small Am and a short r, the phase error is on the order of rAm < 1. In the slow-exchange, weak coupling limit, the pure dephasing contribution to the linewidth from repeated excitation and relaxation of the low-frequency mode is (51,52) ... 

If at time zero, after the field has been switched off, the system is found in a state with nonvanishing coherences, oy (z 7), Eqs (18.43b,c) tell us that these coherences decay with the dephasing rate constant k. k was shown in turn to consist of two parts (cf. Eq. (10.176) The lifetime contribution to the decay rate of Oy is the sum of half the population relaxation rates out of states z and j, in the present case for 012 and <721 this is (l/2)( 2 i + 1 2)- Another contribution that we called pure dephasing is of the form (again from (10.176)) Zi 2C(0)(K — 22) - system operator that couples to the thermal bath so that — V22... 

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