Rabi microwave

If we transform the problem to a frame rotating with the microwave field, it is static and cannot induce transitions. The transformation to the rotating frame, often used to describe two level magnetic resonance experiments, is discussed by Salwen37 and Rabi et al.3H. 

Having examined the n - - 2)s — (n, 3) transitions as resonances we are now able to explain the apparently random fields required to drive the (n -b 3)s — (n, 3) transitions by a microwave field alone. Observation of the transition has two requirements, the levels must be resonant and the Rabi frequency must be adequate. Analyzing the data of Fig. 7 show that the Rabi frequency is adequate if = 0.7 (Ec - s, ) for all the states. In the absence of a static field the resonance condition is met when the AC Stark shift of the (n -b 3)s state brings it into resonance, which is random. Typically, the two conditions are only met simultaneously for a random microwave field amplitude larger than the anticrossing field, but for the 19s state in a 9.2789 GHz field the resonance condition is met for the 27 photon transition at E = 515 V/cm, 0.9 c> leading to the small resonant peak in the signal [18]. 

The earliest measurements, shown in Fig. 6, had large enough field inhomogeneities to make accurate measurements of Rabi frequencies impossible. However, with some refinements Gatzke et al. [25] were able to measure the Rabi frequencies directly. With a pulsed dye laser they excited the K atoms from the 4p state to the 21s state in microwave and static fields at the static fields of the m photon 21s- (19, 3) resonances. At these resonances the energy eigenstates li+ and vj/- are the linear superpositions vj/j. = l (i9,3i), and the... 

Fig. 9. Four photon Rabi oscillations between the K 21s and 19,3 states at 9.1 GHz for microwave amplitudes of 34, 42, and 45 V/cm (from [25])...

Fig. 10. K 21s -19,3 Rabi frequencies for 1,2, and 4 photon 9.1 GHz resonances as a function of the microwave fieid amplitude (from [25])...

The microwave detected MODR scheme closely resembles pulsed nuclear magnetic resonance (Hahn, 1950), optical coherent transients by Stark switching (Brewer and Shoemaker, 1971) and laser frequency switching (Brewer and Genack, 1976). The on-resonance microwave radiation field, ojq = ( 2 — Ei)/H, creates an oscillating bulk electric dipole polarization (off-diagonal element of the density matrix, pi2(t)). The oscillation is at u>o u>r, where ojr is the (Mj-dependent) Rabi frequency,... 

The problem of transit-time broadening was recognized many years ago in electric or magnetic resonance spectroscopy in molecular beams [1253]. In these Rabi experiments [1254], the natural linewidth of the radio frequency or microwave transitions is extremely small because the spontaneous transition probability is, according to Vol. 1, (2.22), proportional to co. The spectral widths of the microwave or RF lines are therefore determined mainly by the transit time AT = d/v of molecules with the mean velocity v through the interaction zone in the C field (Fig. 5.10a) with length d. 

Without a thermal radiation field in the resonantly tuned cavity, the populations N n,T) and N(n — I, T) of the Rydberg levels should be a periodic function of the transit time T = djv, with a period Tr that corresponds to the Rabi oscillation period. The incoherent thermal radiation field causes induced emission and absorption with statistically distributed phases. This leads to a damping of the Rabi oscillation (Fig. 9.75b). This effect can be proved experimentally if the atoms pass a velocity selector before they enter the resonator, which allows a continuous variation of the velocity and therefore of the transit time T = d/v. n Fig. 9.76 the schematic drawing of the experimental setup with microwave resonator, atom source and detector is shown. 

In order to induce strong dipole-dipole coupling we introduce a microwave field (x, t)ef with a frequency cof and Rabi-frequency tuned near resonance with the N = 0 N = I transition. The effective Hamiltonian acting on the lowest-energy states is obtained in second-order perturbation theory as... 

The Rabi technique of radio frequency or microwave spectroscopy in atomic or molecular beams [10.14-10.17] has made outstanding contributions to the accurate determination of ground state parameters, such as the hfs splittings in atoms and molecules, small Coriolis splitting in rotating and vibrating molecules, or the narrow rotational structures of weakly bound van der Waals complexes [10.18]. Its basic principle is illustrated in Fig. 10.9. A collimated beam of molecules with a permanent dipole moment is deflected in a static... 

Figure 9 Three-level atoms with dipole transitions 1,2>- 3) in the Lambda configuration. The dipole forbidden transition between two metastable states 1> and 2) are coupled to each other via microwave transition (a), or Raman transition (b), or two-photon transition (c) with effective half Rabi frequency Qo Another optical field is resonantly coupled to the dipole transition 2)- 3> with half Rabi frequency Qi. The two cavity fields 012 are amplified from Rabi sidebands on the dipole transition 1)- 3>.

Figure 13 A quantum-beat laser scheme with coherent drive. Qnantnm-beat is created by using a microwave field to couple the two closely spaced states 11) and 2). Atoms are pnmped incoherently from the ground state 0) to the excited states 1, 2) with rate A. Atomic coherence is created by coupling an external field to the 2)- 3> with half Rabi frequency Q. Atoms emit photons into two lasing modes (ai,2) on the 1,2)- 3> transitions.

In addition to the Rabi-type experiments, a second important method of modem microwave spectroscopy was introduced in the 1930s. Gases confined in closed resonance cells were investigated by measuring the absorption of a propagating microwave field as a function of its frequency (see Figure 4). Since no pumping mechanism or other state selection was... 

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