Dipole fluctuation operator

A final interesting observation is the existence of a frequency scale, 3x10 see in Eq. (2-39). This is the frequency at which the electronic cloud around an atom fluctuates it is therefore the rate at which the spontaneous dipoles fluctuate. Since the electromagnetic field created by these dipoles propagates at the speed of light c = 3 x lO cm/sec, only a finite distance c/v 100 nm is traversed before the dipole has shifted. Since the dispersion interaction is only operative when these dipoles are correlated with each other, and this correlation is dismpted by the time lag between the fluctuation and the effect it produces a distance r away, the dispersion interaction actually falls off more steeply than r when molecules or surfaces become widely separated. This effect is called the retardation of the van der Waals force. The effective Hamaker constant is therefore distance dependent at separations greater than 5-10 nm or so. 

Trl(o — At — Tc, but a continuum in the energy domain. Under such conditions the FIR band shape of the absorption due to dipole-dipole coupling between the time-dependent vector of the FIR electric field and the time-dependent vector of the molecular dipole moment can be analyzed by a generalized fluctuation-dissipation theorem (Ref. 1, Eq. 3.E23), since the molecular dipole operator follows a GLE (Ref. 1, Eq. 3.F8) and off-diagonal elements of the density operator must be taken into account (Ref. 1, Eq. 3.E3). 

The two-photon correlations stored in the pure TPE state can be measured by detecting fluctuations of the fluorescence field emitted by the atomic system. Squeezing in the fluorescence field is proportional to the squeezing in the atomic dipole operators (squeezing in the atomic spins) which, on the other hand, can be found from the steady-state solutions for the density matrix elements. 

It has been established in a series of works that a transformation of the electric dipole interaction is valid for deriving the optical characteristics of molecular systems with a response dominated by two electronic states [68-70 73-77], This procedure relates to the employment of a fluctuation dipole operator [78,79] as given by... 

In the homogeneous metal, there are no real" charge fluctuations, just as in the Helium atom there is no real" dipole moment. Van der Waals attraction between two Helium atoms comes about as the result of the correlated quantum fluctuations of a virtual dipole moment induced in each atom by the other. Similarly, an attractive force comes about from correlated, virtual, charge fluctuations In the two planes. I eliminate H from the Hamiltonian to leading order in W. using the operator generalization of second-order perturbation theory for the energy levels. This yields ... 

If qubits are stored in hyperfine sublevels of the ground rovibrational electronic state the phase is relatively insensitive to local fluctuations of dc and ac electric fields, but more sensitive to magnetic field fluctuations, which should be minimized. The time scale of this minimization should be of the order of the coherence time of the trap. The states used to switch on the dipole-dipole interaction have to be long-lived to minimize decoherence from spontaneous emission. With gate operation times of <100 (jLsec and metastable excited state lifetimes of several hundred millisecond, decoherence due to spontaneous emission will be small. 

Since the transition dipole is a physical observable, it is evident that its value should be independent under symmetiy operations. In other words, die intramolecular change distribution and fluctuations are invariant with respect to symmetry operations. 

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