Quantum beats ground state

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... 

For a description of the ground state magnetic quantum beats one might conveniently use the solution of Eq. (4.10) for multipole moments aPq-Assuming that the excitation takes place by a 6-pulse at time t = 0, one may write its solution for t > 0 in the form ... 

Fig. 4.19. Calculated signals of ground state quantum beats for u>j /7 = 10. Geometry as in Fig. 4.18(a).

Fig. 4.20. Experimental signals of ground state quantum beats in Kat E+.v" = 1, J" = 73) (a) field switched off, B = 0 (b) B = 0.816 T (c) differential signal with compensation of exponential decay (d) independence of (jJj .

Magnetic quantum beats in the transient process after pulsed depopulation of the ground state may be observed not only in fluorescence, but also in a more direct way, namely in absorption. In connection with what was discussed in Section 3.5, one must expect maximum sensitivity if the experiment is conducted according to the laser interrogated dichroism method see Fig. 3.17. To this end it is convenient to direct the external magnetic field B along the 2-axis as shown in Fig. 4.21 where the probe beam E-vector can be either in the xy plane (Em) or in the yz plane (Epr2). 

Auzinsh, M.P., Tamanis, M.Ya. and Ferber, R.S. (1985). Observation of quantum beats in the kinetics of the thermalization of diatomic molecules in the electronic ground state, JETP Lett., 42, 160-163. 

Auzinsh, M.P. (1990). Nonlinear phase resonance of quantum beats in the dimer ground state, Opt. Spectrosc. (USSR), 68, 750-752. 

Walther, Th., Bitto, H. and Huber, J.R. (1993). High-resolution quantum beat spectroscopy in the electronic ground state of a polyatomic molecule by IR-UV pump-probe method, Chem. Phys. 

As previously discussed, if two or more excited eigenstates can combine in absorption with a common ground-state level, then these eigenstates can be excited so as to form a coherent superposition state. The superposition state, in turn, can give rise to quantum beat-modulated fluorescence decays. All this, of course, lies at the heart of the theory of vibrational coherence effects. However, it also implies that the same experimental conditions under which vibrational coherence effects are observed should allow for the observation of rotational coherence effects. That is, since more than one rotational level in the manifold of an excited vibronic state can combine in absorption with a single ground-state ro-vibrational level, then in a picosecond-resolved fluorescence experiment rotational quantum beats should obtain. 

Fig. 12.1 la,b. Quantum-beat spectroscopy of atomic or molecular ground states measured by time-resolved polarization spectroscopy (a) experimental arrangement and (b) Zee-man quantum beat signal of the Na 3 Si/2 ground state recorded by a transient digitizer with a time resolution of 100 ns. (Single pump pulse, time scale 1 rs/div, magnetic field 1.63 X 10-4 T) [12.40]... 

The basic difference of stimulated quantum beats in emission or absorption is illustrated by Fig. 12.12. The V-type scheme of Fig. 12.12a creates coherences in the excited state that can be observed by stimulated emission. The A-type scheme of Fig. 12.12b, on the other hand, describes coherence in the ground state, which can be monitored by absorption [12.41]. 

Quantum-beat lasers are a particular form of correlated spontaneous emission lasers (CEL s) [43-49]. Quantum-beat is formed by creating coherence between near degenerate atomic states, either excited states or ground states. In particular, a beam of three-level atoms in Vee configuration emit photons into two modes. The atomic upper levels are initially prepared in a coherent superposition or are coupled by a coherent field [13-17]. The fluetuations of the relative phase and the relative amplitude drop to the vacuum levels. In addition to this, as a different form, correlated spontaneous emission can be formed by creating eoherenee between a pair of states between which lasing transitions occm. One such example is a two-photon CEL [13-17] with a beam of three-level atoms in cascade configuration. The top and bottom states are initially prepared in a coherent superposition state. It was predicted that the phase noise is reduced by 50% below the vacuum noise level. 

Figure 11 A quantum-beat laser scheme with dynamical noise reduction. Quantum-beat is created by using a microwave field to couple the two closely spaced states 1> and 2). Atoms are pumped incoherently from the ground state 0> to the top state 3) with rate A, emit photons into two lasing modes (ai 2) on the 11,2)- 3> transitions, and then return to the ground state at rate 72.

A quantum-beat laser with external coherent driving [67,78]. Shown in Fig. 13 is a pumping and coupling scheme. The atoms are pumped from the ground state 10 ) to the excited states (/=1,2) to provide necessary population for the laser gain. An external coherent field of circular frequency coq is applied to the 2 )- 3 ) transitions to create atomic coherence, by which the system can operate without population inversion. Atoms emit photons into the laser modes o of circular frequencies a 12. In the dynamics, the atoms recycle throngh the snccessive channels... 

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