Radio frequency coherence,

Next we proceed to develop the theory o resonance fluorescence experiments using the ensemble density matrix to describe the system of atoms. The important concepts of optical and radio-frequency coherence and of the interference of atomic states are discussed in detail. As an illustration of this theory general expressions describing the Hanle effect experiments are obtained. These are evaluated in detail for the frequently employed example of atoms whose angular momentum quantum numbers in the ground and excited levels are J =0 and Jg=l respectively. Finally resonance fluorescence experiments using pulsed or modulated excitation are described. 

Quantum mechanically the modulation of the fluorescent light is associated with the radio frequency coherence of the excited state density matrix. In a standard Brossel-Bitter double-resonance experiment Tt-polarized light excites the atoms initially to the m=0 state of the excited level. Fig. 16.13(b), and then interaction with the r.f. magnetic field transforms each atom into a coherent superposition of the m=0, l states. The relative phases of the probability amplitudes of these states are fixed by the phase of the r.f. field and are the same for every atom of the sample. Thus the r.f. field is able to generate substantial hertzian coherence in the excited state density matrix. The fluorescent light emitted in the direction of B is then a coherent... 

Figure 7.2 Schematic representation of coherent oscillations between states 0) and 1) of a qubit. For an electron spin placed in a dc magnetic field, oscillations can be induced via the application of an external radio frequency (rf) pulse resonant with the Zeeman energy. The amplitude 8 of the...

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... 

Fig. 5 Radio frequency pulse sequences for measurements of Sj and Si in DSQ-REDOR experiments. The MAS period rR is 100 ps. XY represents a train of 15N n pulses with XY-16 phase patterns [98]. TPPM represents two-pulse phase modulation [99]. In these experiments, M = Nt 4, N2+ N3 = 48, and N2 is incremented from 0 to 48 to produce effective dephasing times from 0 to 9.6 ms. Signals arising from intraresidue 15N-13C DSQ coherence (Si) are selected by standard phase cycling. Signal decay due to the pulse imperfection of 15N pulses is estimated by S2. Decay due to the intermolecular 15N-I3C dipole-dipole couplings is calculated as Si(N2)/S2(N2). The phase cycling scheme can be found in the original figure and caption. (Figure and caption adapted from [45])...

Exploitation of the TROSY effect is rather straightforward. In contrast to 15N-HSQC (Heteronuclear Single Quantum Coherence) or standard triple-resonance experiments based on 15N-HSQC, no radio frequency pulses or composite pulse decoupling should be applied on amide protons when HN spin is not in the transverse plane. Likewise the 15N decoupling should be... 

Figure 4. Schematic explanation of T] and T2 relaxation phenomena. The equilibrium macroscopic magnetization vector, MCi is tipped away from the direction of the magnetic field (z-axis) by application of a radio frequency field. After the rf field is removed, it continues to rotate in x y -plane about the z -axis. Two relaxation processes occur recovery of the magnetization Mz (component along the z-axis) to equilibrium value M and decay of Mxy (magnetization in the x y -plane) to zero due to the loss of phase coherence.

The next big advance towards higher precision was the 1997 phase-coherent measurement of the frequency gap with an optical frequency interval divider chain [27]. The 2.1 THz gap was no longer measured by counting cavity fringes, but divided down to the radio frequency domain by a phase-locked chain of five optical frequency interval dividers [56] (see Fig. 5). The accuracy of this approach was limited by the secondary frequency standard to 3.4 parts in 1013, exceeding the accuracy of the best previous measurements by almost two orders of magnitude. 

So we see that spectral broadening of the comb [29,30] is achieved by imposing a large frequency chirp on each of the pulses. Provided that the coupling efficiency into the fiber is stable, the periodicity of the pulse train is maintained. The discussion of section 3 is thus equally valid if the electric field E(t) as measured for example at the fiber output facet instead of the laser output coupler. As described below we have used a frequency comb widened to more than 45 THz by a conventional single mode fiber to perform the first phase coherent vacuum UV to radio frequency comparison in our Garching laboratory [16,31], In recent experiments we have confirmed that the fiber does not affect the mode spacing constancy within our experimental uncertainty of a few parts in 1018 [13]. 

All the powerful methods of magnetic resonance, from solid-state nuclear magnetic resonance (NMR) to medical magnetic resonance imaging, depend on measuring the time evolution of a spin system following the application of one or more radio frequency pulses. In the visible and ultraviolet, ultrafast optical pulse sequences have been used for many years to measure both population dynamics and coherence phenomena. At low... 

In 1993, the first ultrafast vibrational echo experiments on condensed matter systems were performed using a free electron laser as the source of temporally short, tunable infrared pulses (11). Recently, the development of Ti sapphire laser-based optical parametric amplifier (OPA) systems has made it possible to produce the necessary pulses to perform vibrational echoes using a tabletop experimental system (12,13). The development and application of ultrafast, IR vibrational echoes and other IR coherent pulse sequences are providing a new approach to the study of the mechanical states of molecules in complex molecular systems such as liquids, glasses, and proteins (14-20). While the spin echo, the photon echo, and the vibrational echo are, in many respects, the same type of experiment, the term vibrational echo is used to distinguish IR experiments on vibrations from radio frequency experiments on spins or vis/UV experiments on electronic states. In this chapter, recent vibrational echo experiments on liquids, glasses, and proteins will be described. 

The pulse methods rely on selective irradiation of a particular resonance line with a radio frequency (rf) and observation of the resulting effects in the rest of the spectrum. Among commonly employed methods are 2D correlated spectroscopy (COSY), 2D spin-echo correlated spectroscopy (SECSY), 2D nuclear Overhauser and exchange spectroscopy (NOESY), 2D J-resolved spectroscopy (2D-J), and relayed coherence-transfer spectroscopy (RELAYED-COSY) (Wutrich, 1986). 

SateUite Transition MAS (SATRAS or STMAS), developed by Gan in 2000 [25], is an alternative approach to MQMAS for the acquisihon of high-resolution NMR spectra of quadrupolar nuclei. The principal advantage of SATRAS over MQMAS is that it is not dependent upon an efficient transfer of multiple-quantum coherences. like MQMAS, SATRAS is a 2D experiment performed under MAS conditions. The technique involves exciting the sateUite transitions in the spin manifold of quadmpolar nuclei using short radio frequency (rf) pulses. The second-order... 

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