Rabi state and frequency

Note that this state is interpreted to represent a transition between < )o(0) IXo(O) or between cp ) and (pj). Since this is very similar to the usual Rabi state, Eq. (14), we call this state, Eq. (26), CG Rabi state and call the frequency, Eq. (24), CG Rabi frequency. ... 

We see that / (i, t) displays damped Rabi-type oscillations between the initial state and the final continuum states, where the damping is given by resonance decay rate TJ2h. Although the frequency of the Rabi oscillations is a function of the fieldib strength 0, the branching ratio between channels is independent of the laser para- 4... 

Because dipole moments can only connect states of opposite parity, we obtain that the Rabi frequencies for transition between different symmetry-broken states ) ) and I/ ) are given as... 

In their experiment, Rabi, Nafe, and Nelson used a beam of hydrogen atoms and measured the transition frequencies between the two hyperfine states. The measured values were as follows ... 

QED [17] where energy is coherently exchanged between the internal state and single-photon radiation field. The first blue sideband, at 8 = +co drives transitions between states 11, n) 11, n+l) with Rabi frequency 2 +i = gTi(n+l) . ... 

Here bexc = ( i %) is the column vector (hence the transpose sign) of amplitudes of the excited bound states, S2d = ( i,o n,o) is the vector of Rabi frequencies between the 0) state and the excited bound states, and ftp is its conjugate transpose. 

The atomic system imder consideration is shown in Fig. 1. Here a) is an upper excited state and 1, I and I (fj are three lower metastable states. The transition O c) is taken to be nearly resonant with a driving field with Rabi frequency Q = Qq sin ( ), where k = TcjX and X is the wavelength. A weak probe field with Rabi frequency e couples the states a) and... 

Rabi is the Rabi frequency which is determined by intrinsic atomic properties and by the intensity of the laser. By proper timing of the laser pulse any rotation between the two states ) and e) can be performed. For example, by choosing Rabi = 7t/2 transformation (6.8) is realized. As a sideremark we note that for microwave transitions Rabi oscillations can be induced by exposing the atom to a microwave field. 

The population in the upper state as a flinction of time is shown in figure A1.6.2. There are several important things to note. At early times, resonant and non-resonant excitation produce the same population in the upper state because, for short times, the population in the upper state is independent of the Rabi frequency ... 

Lanthanide ions offer several salient properties that make them especially attractive as qubit candidates (i) their magnetic states provide proper definitions of the qubit basis (ii) they show reasonably long coherence times (iii) important qubit parameters, such as the energy gap AE and the Rabi frequency 2R, can be chemically tuned by the design of the lanthanide co-ordination shell and (iv) the same molecular structure can be realized with many different lanthanide ions (e.g. with or without nuclear spin), thus providing further versatility for the design of spin qubits or hybrid spin registers. 

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...

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