Dephasing and Relaxation

There are many factors that affect how incident light fields entangle the quantum states of the system.  As mentioned when optical nutation was introduced, the field strength and duration will effect the conversion process, but properties intrinsic to the system will also dictate the end product.  We briefly overview a source of conversion loss brought on by the system known as dephasing.

Optical Nutation requires that the oscillations of the coherences can remain synchronized with the exciting field. If synchronization is maintained, the system's emission is coherent. Different mechanisms, however, can cause this synchronization to drift and eventually be lost.  This process is known as dephasing and can usually be quantified by a extinction rate of a coherence between states a and b: $\Gamma_{ab}$. If the light field is turned off, coherent emission will decay exponentially at this dephasing rate.  This is known as free induction decay (FID).  All mechanisms combine to produce the overall dephasing rate.

  • Pure Dephasing
    This mechanism is always present because a quantum system of interest will never be completely isolated from its surrounding environment.  Interactions with the thermally fluctuating environment perturbs the light-polarization phase relationship of the quantum system.  Given enough time, the correlation of phase becomes completely randomized, and evolution of the quantum system's Rabi cycle ceases.  This pure dephasing time produces a hard time limit for which a light field can progress a system through the Rabi cycle.
  • Ensemble Dephasing
    This mechanism occurs when a spectroscopic technique measure many quantum systems at the same time.  This is often the case, as an individual quantum system is typically very small in both size and individual dipole strength.  In this mechanism, each quantum state is not entirely identical (i.e. each state has a slighly different energy), so that the actual intrinsic way in which each quantum system wants to interact with the field has variability.  Over the course of time, the synchronization of the net sample will be lost.  A key difference between this mechanism and pure dephasing is that this dephasing process is reversible:  since each quantum system remembers its intrinsic phase relationship, reversing the direction of phase propagation can bring all the phases back together.  This phenomenon is known as rephasing and is the basis for many spectroscopies such as photon echo and 3PEPS.
  • Quantum Beats
    Quantum beating is a similar phenomenon to ensemble dephasing.  Instead of fairly random different quantum states, the distribution of energies is highly ordered.  Consider the case in which only two discrete states exist in the ensemble.  If each state is simultaneously excited, their phases will gradually walk away from eachother, which results in interference just as before, but the phase will continue to walk until it becomes constructive again.  This beating phenomenon can occur when system energies are sufficiently discrete and when both states are excited simultaneously.  The beating pattern can be truncated if pure dephasing is not sufficiently slow to allow this interference.
  • Relaxation
    Just as the fluctuating environment perturbs the phase of a coherence, it also provides channels to perturb and reduce its amplitude.  This coupling dissipates the excited state of the wavefunction in a way that has no phase relationship.  This coupling affects both coherence amplitude and population amplitude, but dispite this fact is usually referred to as population relaxation.  Since populations lack temporal phase, this is the only mechanism listed that affect and attenuate populations.  Because populations are not susceptable to other mechanisms of decoherence, they persist longer (often much longer) than coherences.

Condensed phase dephasing rates for NMR are ~103 sec-1, vibrational states are ~1012 sec-1, and electronic states are ~1014 sec-1. Since the Rabi frequencies are usually much lower, the evolution of the states does not proceed very far into a Rabi period before dephasing occurs so absorption usually dominates in electronic spectroscopies.  This situation is quite different from NMR where the Rabi frequency exceeds the dephasing rate so that coherences can be isolated. Typically $|c_b|/|c_a| \ll 1$ when stimulating the transition $a \rightarrow b$ with optical and infrared light.