Three-level systems

In recent years, the three-level system of NDT experts certification, which corresponds to the EN 473, is being introduced m Ukraine The unified Rules of NDT Experts Certification will be introduced in the near future. This work is headed by the State Committee of Ukraine on Labour Safety), and with the aim of the most expedient transition to EN 473, the National Certification Committee of Ukraine on NDT was established by the initiative of US NDT TD. The Committee has the tasks of preparing the programs, procedures, questionnaires for carrying out the certification. It is a non-profit organisation which is in charge of the methodological issues of certification m the US NDT TD. 

Melinger J S and Albrecht A C 1986 Theory of time- and frequency-resolved resonance secondary radiation from a three-level system J. Chem. Phys. 84 1247-58... 

It was shown above that the normal two-level system (ground to excited state) will not produce lasing but that a three-level system (ground to excited state to second excited state) can enable lasing. Some laser systems utilize four- or even five-level systems, but all need at least one of the excited-state energy levels to have a relatively long lifetime to build up an inverted population. 

A dye molecule has one or more absorption bands in the visible region of the electromagnetic spectrum (approximately 350-700 nm). After absorbing photons, the electronically excited molecules transfer to a more stable (triplet) state, which eventually emits photons (fluoresces) at a longer wavelength (composing three-level system.) The delay allows an inverted population to build up. Sometimes there are more than three levels. For example, the europium complex (Figure 18.15) has a four-level system. 

In the three-level system of Figure 9.2(b) population inversion between levels 2 and 1 is achieved by pumping the 3-1 transition. The 3-2 process must be efficient and fast in order to build up the population of level 2 while that of level 1 is depleted. Lasing occurs in the 2-1 transition. 

Fig. 1. Pumping methods for lasers where is the pump light frequency and is the laser frequency, wavy lines represent radiationless transitions, and the dashed line collisions (a) optical pumping in three-level systems (b) optical pumping in four-level systems (c) pumping by electron impact and...

Fig. 1.12. The three-level system showing the creation of a Floquet ladder of states. Also shown is the weak one-photon coupling needed to make a transition to the Floquet ladder from the ground state. f i2 and Q-n are the Rabi frequencies between the states...

Teramobile, 112 Thomson scattering, 168, 179 Three-level system, 11 Three-step model, 65 Time-resolved second harmonic generation, 29 TOF spectroscopy, 5 Transient depletion field screening (TDFS), 28... 

Unlike the case of enhancement of yield of product in a chemical reaction, control of qubit state transfers in a quantum computer is useful only if the control does generate sensibly perfect fidelity of population transfer. Fortunately, a typical qubit has a spectrum of states that is much simpler than that of a polyatomic molecule, so that control protocols that focus attention on the dynamics of population transfer in two- and three-level systems are likely to capture the essential dynamics of population transfer in a real qubit system. A large fraction of the theoretical effort devoted to describing such transfers has been confined to those simple cases. To a certain extent, many of these studies are analogous to... 

S. Martfnez-Garaot, E. Torrontegui, X. Chen, and J. G. Muga Shortcuts to adiabaticity in three-level systems using Lie transforms. Phys. Rev. A, 89(5) 053408—053415(2014). 

W. Jakubetz. Limitations of STIRAP-like population transfer in extended systems the three-level system embedded in a web of background states. J. Chem. Phys., 137(22) 224312-224327(2012). 

J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann. Adiabatic population transfer in a three-level system driven by delayed laser pulses. Phys. Rev. A, 40(11) 6741-6744(1989). 

The photoabsorption of the probe pulse Cj (t) by the three-level system depicted in Figure 9.7 is now considered. The (channel-specific) photoabsorption probability from the ground state is given by Pi-(E), and the total photoabsorption of the cj pulse by Ai) ). 

An elementary treatment of a three-level system under pulsed excitation was given in Sec. II.C. Pollack treats the steady-state condition and the turn-off condition as well. These cases are quite interesting and deserve further discussion. Figure 51 shows the three-level system he analyzed. The quantities Ni(f), N2(f), and N3(f)are the electron-distribution functions (populations) and a9 b, and c represent the total transition probabilities per unit time. The boundary condition Nx + N2 + N = JV =constant is assumed. 

In order to insert a two-level factor in an orthogonal matrix to obtain a three-level system, the factor is formally transformed into a three-level one. Just assign one of the two already defined levels as the third level. This is the dummy-level technique. 

Tang et al. [20] have examined the population dynamics in a three-level system, and its representation in a surrogate two-level system, to test the scheme outlined above. In the model system considered state 3 is weakly coupled with states 1 and 2, so that population transfer between states 1 and 2 should dominate the dynamics, with only a small contribution from population transfer to and from state 3. The coupling of state 3 with states 1 and 2 was taken to be one-tenth of the coupling between states 1 and 2, that is, M)3 = M23 = Mn/10 = -1/10. Using the formalism sketched above, the exact system dynamics is governed by the coupled equations of motion for the three states,... 

Here p is the density matrix for all molecular states in the three-level system depicted in Fig. 4, and all incoherent relaxation terms caused, for example, by collisions, spontaneous emission, or decay in a (quasi)continuum are incorporated in the relaxation matrix rreiax. 

For a three-level system the Hamiltonian in the interaction picture //, in Rotating Wave Approximation is given in matrix representation by... 

Figures 6a-c show the population dynamics encountered in a three-level system (see Fig. 4) interacting resonantly with two Fourier-transform-limited laser pulses with three different delay times between the two pulses. The calculation was done assuming that the chosen Rabi frequencies fulfill the relation > 1/pulse duration) in all three cases. This relation ensures that the typical time for a Rabi oscillation of the population in an isolated two-level system is shorter than the pulse duration. Ionization from level 2 was introduced as a fast laser intensity-dependent decay of level 2 [6, 60], and resonant laser frequencies were assumed.

Figure 7. (a) Three-level system Calculated ion dip and fluorescence dip spectra with pump laser frequency tuned to resonance with the 2 1 transition. Ionization is treated as... 

We have presented a new technique for the investigation of intramolecular couplings in the electronic ground state 50. The new technique of CIS is based on the special population dynamics induced by the coherent excitation of a three-level system with two narrow-band Fourier-transform-limited laser pulses. It allows the investigation of high-lying intermolecular vibrational states in the electronic ground state of van der Waals complexes. These... 

I. Is it possible to observe a shift in coherent Raman scattering in the three-level system with A-type coupling We have done an experiment to obtain a femtosecond Raman gain spectrum in polydiacetylenes. The Raman spectrum is shifted to the red under increased pump (to i) intensity. By changing o>2> the amplification peak signal is to be shifted to lower frequency. If the optical Stark effect is observed, then, in principle, it should be possible to observe the effect of a high field on the coherent Raman spectrum (see Fig. 1). 

Consider now the resonance limit, when only a small number of eigenstates is involved. In this limit a true quantum beat spectrum is obtained. For simplicity of presentation we consider a three-level system in which the closely spaced coherently excited levels fa and fa decay into the ground state. The total number of photons counted is just... 

Finally, the equilibrium concentrations obtained in Eqs. 8.184 from the kinetic equations agree with those obtained using equilibrium statistical mechanics. In the three-level system in Fig. 8.25, the occupation probability for level 1 is... 

The LVC model further allows one to introduce coordinate transformations by which a set of relevant effective, or collective modes are extracted that act as generalized reaction coordinates for the dynamics. As shown in Refs. [54, 55,72], neg = nei(nei + l)/2 such coordinates can be defined for an electronic nei-state system, in such a way that the short time dynamics is completely described in terms of these effective coordinates. Thus, three effective modes are introduced for an electronic two-level system, six effective modes for a three-level system etc., for an arbitrary number of phonon modes that couple to the electronic subsystem according to the LVC Hamiltonian Eq. (7). In order to capture the dynamics on longer time scales, chains of such effective modes can be introduced [50,51,73]. These transformations, which are briefly summarized below, will be shown to yield a unique perspective on the excited-state dynamics of the extended systems under study. 

Population here either means the probability of a level to be occupied (for a single system) or the fraction of three-level systems that occupy the respective state (for a number N of systems). 

---