Population trapping

The rate constant k3 for the population with the fastest decay rate was shown to be equal to the rate constant, k, for desorption from polymer in the rubbery state [148], and the rate constants ki for the set of n populations trapped in the glassy state (attained when a, becomes equal to oeg) are related one to another by ... 

In this section we will describe the application of these methods to some examples of population transfer by delayed bichromatic pulses in two- and three-level systems. Bichromatic effects with CW lasers in population trapping have been also investigated in Ref. 83. 

EIT is based on the phenomenon of coherent population trapping [Harris 1997 Scully 1997 Liu 2001], in which the application of two laser fields to a three-level A system creates the so-called "dark state", which is stable against absorption of both fields. Dark states are also found in several other... 

In the literature, the population trapping is often referred to as a consequence of a cancellation of spontaneous emission. However, the cancellation of spontaneous emission from an atomic state not always leads to the trapping of the population in this nondecaying state. We shall illustrate this by considering the process of spontaneous emission from a V-type atom composed of two excited states 1), 3) and the ground state 2). For simplicity, we assume that spontaneous emission occurs from the excited states to the ground state with the same decay rates T] = r2 = F, and the transition between the excited states is forbidden in the electric dipole approximation. The allowed transitions are represented by the dipole operators S = (Sf) = 1)(2 and = (S ) = 3)(2. In the absence of the driving held (f>i IF 0), the master... 

We can conclude that the cancellation of spontaneous emission not necessary leads to the population trapping. The population can be trapped in a nondecaying state only if the state is completely decoupled from any interactions. 

The equation of motion (115) allows us to analyze conditions for population trapping in the driven A system. In the steady state (p = 0) with p / 1 and Ac = 0 the population in the upper state p33 = 0. Thus the state 3) is not populated even though it is continuously driven by the laser. In this case the population is entirely trapped in the antisymmetric superposition of the ground states. This is the CPT effect. However, for p 1 and Ac = 0, the antisymmetric state decouples from the interactions, and then the steady-state population p33 is different from zero [46]. This shows that coherent population trapping is possible... 

In Fig. 14, we plot the correlation functions (146) and (147) computed from the equations of motion (96) for the case of degenerate transitions (A = 0) and two different values of p p = 0 corresponding to the case of perpendicular dipole moments, and p = 0.99 corresponds to almost parallel dipole moments. We have chosen p < 1 to avoid population trapping, which can appear for p = 1. The correlations show the characteristic photon antibunching effect [59] that g1-11 (x)... 

E. Arimondo, Coherent population trapping in laser spectroscopy. Progr. Opt. 35. p. 257 354,(1996). 

In this section we present a brief historical account of LICS without going into too many details, as our main concern is aspects of quantum interferences. LICS was initially suggested by Heller and Popov [4] and by Armstrong et al. [27], who termed the effect "pseudo-autoionization." Early theoretical investigations on LICS focused on coherent population trapping [28, 29], multichannel effects [30-33], and Raman-type transitions [2, 34 0]. 

The topics that mainly concern us in this review have to do with the connections between various coherent optical experiments and LICS. In the next section we discuss the relation between LICS and EIT, examples of which include experiments done in Rb [83,84] and Kr [85]. We then extend the discussion to EIT with structured continua [86, 87]. We proceed by reviewing the use of LICS in the control of population transfer processes [88] the control of PD [89] the production of photo-electrons [90-92] and as a means of steering population transfer processes [93]. We also discuss the connection between LICS and ultrafast methodologies [94] generalized STIRAP techniques [95-97] and coherent population trapping [69,93, 98-101]. 

Two-photon processes can also be modified using CC. It is possible to selectively inhibit or enhance two-photon absorption by phase modulation [166-168] and other interference techniques [169, 170]. It is also possible to use CC to induce population trapping and gain in V-type systems [171,172]. Furthermore, it has been realized that interference between one-photon and N-photon transitions results in FIT in atomic systems [173-175]. 

The first substantial 70% ionization suppression and population trapping in relation to LlCS has been observed in atomic helium [69, 101]. Earlier experiments on LlCS have observed dominantly ionization enhancement, with only a few percent recognizable ionization suppression [50-54,56,57,62,65]. The LlCS in the flat photo-ionization continuum of helium is a strong and spectrally sharp resonance showing both enhancement and diminished ionization. 

The LICS, produced by an idealized Continuous-Wave (CW) laser (steady amplitude and single-frequency laser), can differ substantially from the structure produced by a pulsed laser, since the AC Stark shifts produce time-dependent detunings relative to one- and two-photon resonance. The time-dependent pulse and frequency effects in population trapping in LICS have received attention in theoretical works [93]. Using numerical approaches, as well as approximate analytical solution, it was shown that the trapped population in realistic atomic systems can be sufficiently decreased, to the point when no population remains in the system, by the increase in laser energies. Furthermore, the use of properly chirped laser pulses not only helps to increase the trapped population but also makes the system more stable against increases in the pulse energy. 

Phase control of two-channel photo-ionization rates and coherent population trapping induced by four laser fields operating on an atomic system initially in its ground state 1), which proceeds via a pair of intermediate bound states, 2) and 3), to a manifold of structureless continua, has also... 

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