Radio-frequency transition

Figure 11.42. Lower rotational levels of YbF X2E+, and the radio frequency transitions studied [83].

Except for N = 0, which has no spin-rotation interaction, Sauer, Wang and Hinds [83] measured the four radio frequency transitions indicated in figure 11.42 for N = 1 to 10 in the v = 0 level, and also obtained more limited data for v = 1. They also measured the lowest rotational transition at around 14.5 GHz, with hy-perfine splitting, as indicated in figure 11.42. An unusual feature observed by Sauer, Wang and Hinds [83] was a very strong dependence of the spin-rotation constant on the rotational quantum number N, which led them to express y by the power series expansion... 

Fig. 14. Energy levels of the free radical CN showing the observed optical and radio transition. The violet band is observed against Ophiuchi (Thaddeus and Clauser, 1966) and the radio frequency transitions are measured in the Orion nebula (Jefferts et al., 1970). In the interstellar optical spectra quadrupole hyperfine and spin-doubling structure are entirely unresolved and therefore the rotational levels can be approximated as though the electronic states were However, these splittings are partly resolved in the radio frequency region but we note that only one component of the spin doublet has been observed...

Radio-frequency transitions for Na F have been observed by Hollowell et al. (1 ). Infrared spectra of NaF have been analyzed by Snelson and Pitzer (IJ ), Ritchie and Lew (1 ), and Baikov... 

Chin, C. and Julienne, P.S., Radio-frequency transitions on weakly bound ultracold molecules, Phys. Rev. A, 71, 012713, 2005. 

An analysis of radio frequency transitions, occurring within individual rotational levels split by the Stark effect in external electric fields, yields fi = ( )0.30818 with an uncertainty of 0.01% [45]. 

If the primary excitation is performed, e.g., with tt light (Fig. 4.9) the magnetic sublevels of the D j2 state will be non-uniformly populated. The fluorescence in the different decay Imes will then also be linearly polarized. Radio-frequency transitions, that are induced in the primary state or in cascade states, will give rise to a depolarization and redistribution of the light that can be detected. Thus the properties of many P, D and F states can be investigated. Examples of ODR signals in excited S states, populated by stepwise excitation, were given in Fig. 7.11. 

The radio-frequency transitions observed provide valuable information about the interaction between the spin-oriented atoms and their surroundings, that is, about collisions with one another, with the buffer-gas atoms, and with the container walls. 

If energy of the proper frequency is supplied, a transition between these quantum states occurs with the absorption of an amount of energy equal to the separation of the states. The frequency of the absorbed radiation lies in the radio-frequency range and depends on the local magnetic field at the atom in question. 

Pulse A short burst of radio frequency used to bring about some nuclear spin transition. 

Single atomic ions confined in radio frequency traps and cooled by laser beams (Figure 7.4a) formed the basis for the first proposal of a CNOT quantum gate with an explicit physical system [14]. The first experimental realization of a CNOT quantum gate was in fact demonstrated on a system inspired by this scheme [37]. In this proposal, two internal electronic states of alkaline-earth or transition metal ions (e.g. Ba2+ or Yb3+) define the qubit basis. These states have excellent coherence properties, with T2 and T2 in the range of seconds [15]. Each qubit can be... 

Absorption of radiation in the radio-frequency, RF, region of the electromagnetic spectrum can be observed for those nuclei which are considered to spin about their own axes. The energy changes are associated with the orientation of the nuclear axis in space relative to an external applied magnetic field and are of the order of 0.1 J moH, 10-600 MHz (50 cm-30 m or 3 x 1(M to 2 x 10 2 cm1). This is considerably smaller than the energy changes associated with vibrational and electronic transitions (pp. 364, 378). 

Within its orbit, which has some of the characteristics of a molecular orbital because it is shared with electrons on the surrounding atoms, the electron has two possible spin multiplicity states. These have different energies, and because of the spin-multiplicity rule, when an (N-V) center emits a photon, the transition is allowed from one of these and forbidden from the other. Moreover, the electron can be flipped from one state to another by using low-energy radio-frequency irradiation. Irradiation with an appropriate laser wavelength will excite the electron and as it returns to the ground state will emit fluorescent radiation. The intensity of the emitted photon beam will depend upon the spin state, which can be changed at will by radio-frequency input. These color centers are under active exploration for use as components for the realization of quantum computers. 

The principle of the ENDOR method is illustrated in Fig. 1. It refers to the most simple spin system with an electron spin S = 1/2 and a nuclear spin I = 1/2 for which an isotropic hf interaction, aiso, is considered. In a steady state ENDOR experiment4, an EPR transition (A, D), called the observer, is partly saturated by microwave radiation of amplitude B while a driving rf field of amplitude B2, called the pump, induces nuclear transitions. At frequencies vj and v2, the rf field tends to equalize the populations within the ms-states. This alters the degree of saturation of the observer so that, in the display of the EPR signal height versus the radio frequency, two ENDOR lines at transition frequencies vj = aiso/2 - vn (A, B) and v2 = ais0/2 + v (C, D) will be observed (v = / NgnBo denotes the nuclear Zeeman frequency for a static field B0). 

The nuclear energy transitions that occur with the absorption of radio frequency light occur only in a strong magnetic field. 

Radio frequency wavelengths, because the energy required to cause the nuclear energy transitions in a magnetic field is on the order of radio frequency energy. 

Fig. 10.4 Experimental scheme for the 2D [ N. HJ-TROSY using single transition to single transition polarization transfer (box labeled ST2-PT). On the lines marked H and 15N, narrow and wide bars stand for nonselective 90° and 180° radio-frequency pulses, respectively. The delay t=2.7 ms (see text). The line marked PFG indicates the pulsed magnetic field gradients applied along the z-axis G, amplitude 30 G/cm, duration 1 ms G2, 40 G/cm, 1 ms G3, 40 G/cm, 1 ms ...

---