Rabi frequency

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 ... 

In equations (Cl. 4.4) and (Cl. 4.5) Acoj = cu - coj is the detuning of the optical field from the atomic transition frequency Q is the natural width of the atomic transition and m is tenned the Rabi frequency and reflects the... 

It is interesting to note that to actually implement a useful algorithm it is necessary to implement a certain number of quantum operations within the coherence time. Recently, we reported that it was possible to increase the number of coherent rotations by a factor of 10 by matching the Rabi frequency with the frequency of the proton in the polyoxometalate SIM GdW30. Under these conditions, it was possible to perform at least 80 such operations (Figure 2.14) [75]. 

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...

Because the Stokes pulse precedes but overlaps the pump pulse, initially Up and all population initially in field-free state 11) coincides with flo(0)- At the final time, ilp Q5 so all of the population in flo(0) projects onto the target state 6). Note that flo(0) has no projeetion on the intermediate field-free state 5 ). The Rabi frequencies of the Stokes and pump pulses that are required for efficient STIRAP-generated population transfer satisfy the condition [66]... 

Figure 3.7 Time dependences of the Rabi frequencies of the pump, Stokes, and CDFs. (From Ref. 67).

The hopping rate is a function of R and site numbers as noted above, it will play the role of the half Rabi frequency of the Stokes and pump fields in a STIRAP process with Vq = 0. Assuming T pp(m, t) 0 (0 (m, R(t)) 0) we divide Eq. (3.120)... 

We now show that the fast-forward protocol gives the same Rabi frequency as does the counter-diabatic protocol with... 

Figure 3.41 (a) The time dependences of the amplitudes of the half Rabi frequencies for... 

The Rabi frequencies Qp and appearing here parameterize the pulsed pump and Stokes field strengths, controlled by the experimenter. To write this as a torque equation... 

Figure 6.6 Two-state quantum system driven on resonance by an intense ultrashort (broadband) laser pulse. The power spectral density (PSD) is plotted on the left-hand side. The ground state 11) is assumed to have s-symmetry as indicated by the spherically symmetric spatial electron distribution on the right-hand side. The excited state 12) is ap-state allowing for electric dipole transitions. Both states are coupled by the dipole matrix element. The dipole coupling between the shaped laser field and the system is described by the Rabi frequency Qji (6 = f 2i mod(6Iti-...

Here we introduced the Rabi frequency Q21 (0 defined by the relation (t) =... 

Herein complex-valued envelope of the Rabi frequency (cf. Eq. (6.6)) and The static demning 5 = q - 2... 

For resonant excitation, 5 = 0, the splitting is determined only by the amplitude of the Rabi frequency, which is conveniently adjusted via the laser field amplitude. Finally, we obtain the population dynamics d t) = dJ(t)Y in the dressed state picture from the bare state amplitudes by the transformation d t) = V t)c t). 

Herein a is the rate of change of the lower dressed state energy i(t) (black dashed line in Figure 6.10c) evaluated at the inflection points at t = +15 fs, and the Rabi frequency H22 is evaluated at the crossing times. For symmetry reasons, the Landau-Zener probability is the same for both avoided crossings. Now the second requirement concerning the field amplitude is to tailor the Rabi frequency of the main pulse such that = 0.5. Then 50% of the population is transferred... 

The use of strong fields to drive the dynamics leads to somehow similar effects than those of ultrafast pulses. If the Rabi frequency or energy of the interaction is much larger than the energy spacing between adjacent vibrational states, a wave packet is formed during the laser action. The same laser can prepare and control the dynamics of the wave packet [2]. Both short time widths and large amplitudes can concur in the experiment. However, the precise manipulation of dynamic observables usually becomes more difficult as the duration of the pulses decreases. 

The dynamics of x(t) using intuitive sequences in APLIP is considerably different. It involves two intermediate steps at x(t) > x and x t) < x at initial and late times respectively, where the bond length is almost constant. The exact value of x(t) in these plateau regions is quite robust to the ratio of Rabi frequencies, but it can be controlled by the peak amplitude of the pulses. Therefore, the intuitive sequence provides a more robust scenario than the counterintuitive one for preparing the system at certain bond lengths. Additional control can be achieved by changing the time delays. 

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