Decoherence phase

The previous sections focused on the case of isolated atoms or molecules, where coherence is fully maintained on relevant time scales, corresponding to molecular beam experiments. Here we proceed to extend the discussion to dense environments, where both population decay and pure dephasing [77] arise from interaction of a subsystem with a dissipative environment. Our interest is in the information content of the channel phase. It is relevant to note, however, that whereas the controllability of isolated molecules is both remarkable [24, 25, 27] and well understood [26], much less is known about the controllability of systems where dissipation is significant [78]. Although this question is not the thrust of the present chapter, this section bears implications to the problem of coherent control in the presence of dissipation, inasmuch as the channel phase serves as a sensitive measure of the extent of decoherence. 

Thus in the zero dephasing case, 8s reduces to the Breit-Wigner phase of the intermediate state resonance, elaborated on in the previous sections. In the dissipative environment, it is sensitive also to decay and decoherence mechanisms, as illustrated later. 

It is interesting to note (see Eqs. (59)—(61)) that pure decoherence introduces dependence of the channel phase on the final state energies. This dependence can be utilized to obtain new insights into the resonance properties, as illustrated in Fig. 16. Here we explore the photon energy dependence of 8/ for final state... 

Abstract. We review the recent development of quantum dynamics for nonequilibrium phase transitions. To describe the detailed dynamical processes of nonequilibrium phase transitions, the Liouville-von Neumann method is applied to quenched second order phase transitions. Domain growth and topological defect formation is discussed in the second order phase transitions. Thermofield dynamics is extended to nonequilibrium phase transitions. Finally, we discuss the physical implications of nonequilibrium processes such as decoherence of order parameter and thermalization. 

Before the phase transition (t < 0), the measures for decoherence and classical correlation are exactly found... 

Therefore, we conclude that the long wavelength mode neither decoheres nor is classically correlated before the phase transition. However, after the phase transitions, the unstable long wavelength mode becomes classical, gaining both quantum decoherence and classical correlation. Thus an order parameter appears from long wavelength modes (S.P. Kim et.al., 2000 2002 2001). 

The results presented Irom vibrational relaxation calculations show that the method is numerically very feasible and that the short time approximatiorrs are welljustified as long as the energy difference between the initial and final quantum states is not too small. It is also found that the crossover from the early time quantiun regime to the rate constant regime can be due to either phase decoherence or due to the loss of correlation in the coupling between the states, or to a combination of these factors. The methodology described in Section n.C has been formulated to account for both of these mechanisms. 

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. 

We first survey in Section 4.2 the Kurizki-Shapiro-Brumer scheme [5-7] of phase-coherent photocurrent control and focus on its robustness to decoherence, relaxation, and quantum (Langevin) noise induced by the environment. We then... 

While the formalism of DD is quite different from the formalism presented here, it can be easily incorporated into the general framework of universal dynamical decoherence control by introducing impulsive PM. Let the phase of the modulation function periodically jump by an amount 4> at times r, 2t,. .. Such modulation can be achieved by a train of identical, equidistant, narrow pulses of nonres-onant radiation, which produce pulsed AC-Stark shifts of co. When (/> = tt, this modulation corresponds to DD pulses. 

Our analysis of multiple, field-driven qubits that are coupled to partly correlated or independent baths or undergo locally varying random dephasing allows one to come up with an optimal choice between global and local control, based on the observation that the maximal suppression of decoherence is not necessarily the best one. Instead, we demand an optimal phase relation between different but synchronous local modulations of each particle. The merits of local versus global modulations have been shown to be essentially twofold ... 

This coupling means that there is no population decay to the bath and the decoherence is only via the phase. In other pioneering works [39-41], off-diagonal coupling to a Lorentzian bath was considered within the RWA. The Hamiltonians in all of these works should be contrasted with the more general Hamiltonians (4.18), which account for both dephasing and decay into arbitrary baths, without the RWA. 

The realization of SPODS via PL, that is, impulsive excitation and discrete temporal phase variations, benefits from high peak intensities inherent to short laser pulses. In view of multistate excitation scenarios, this enables highly efficient population transfer to the target states (see Section 6.3.3). Furthermore, PL can be implemented on very short timescales, which is desirable in order to outperform rapid intramolecular energy redistribution or decoherence processes. On the other hand, since PL is an impulsive scenario, it is sensitive to pulse parameters such as detuning and intensity [44]. A robust realization of SPODS is achieved by the use of adiabatic techniques. The underlying physical mechanism will be discussed next. 

Assume that a noninteracting nanosystem is coupled weakly to a thermal bath (in addition to the leads). The effect of the thermal bath is to break phase coherence of the electron inside the system during some time Tph, called decoherence or phase-breaking time. rph is an important time-scale in the theory, it should be compared with the so-called tunneling time - the characteristic time for the electron to go from the nanosystem to the lead, which can be estimated as an inverse level-width function / 1. So that the criteria of sequential tunneling is... 

The master equation evolves the classical degrees of freedom on single adiabatic surfaces with instantaneous hops between them. Each single (fictitious) trajectory represents an ensemble of trajectories corresponding to different environment initial conditions. This choice of different environment coordinates for a given initial subsystem coordinate will result in different trajectories on the mean surface the average over this collection of classical evolution segments results in decoherence. Consequently, this master equation in full phase space provides a description in terms of fictitious trajectories, each of which accounts for decoherence. When the approximations that lead to the master equation are valid, this provides a useful simulation tool since no oscillatory phase factors appear in the trajectory evolution. 

We have presented some of the most recent developments in the computation and modeling of quantum phenomena in condensed phased systems in terms of the quantum-classical Liouville equation. In this approach we consider situations where the dynamics of the environment can be treated as if it were almost classical. This description introduces certain non-classical features into the dynamics, such as classical evolution on the mean of two adiabatic surfaces. Decoherence is naturally incorporated into the description of the dynamics. Although the theory involves several levels of approximation, QCL dynamics performs extremely well when compared to exact quantum calculations for some important benchmark tests such as the spin-boson system. Consequently, QCL dynamics is an accurate theory to explore the dynamics of many quantum condensed phase systems. 

The pump induced transient polarisation of the medium modifies the polarisation state of a time delayed probe pulse. Phenomenologically, this process can be regarded as a transient pump induced linear or circular birefringence, also called the Specular Optical Kerr Effect (SOKE) and the Specular Inverse Faraday Effect (SIFE) [18], These are cubic non-linear effects and are predicted to exist from symmetry arguments. Both effects consist of coherent and incoherent parts. For the coherent part, the pump drives the coherent electron-hole pair that affects the probe polarisation. The effect depends upon the probe phase relative to that of the electron-hole pair, and hence, that of the pump. For the incoherent part of the SIFE and the SOKE, the relative pump-probe phase is not important, since the probe pulse polarisation is modified by the pump induced sample polarisation that survives after the decoherence of the electron-hole pair. 

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