Rabi oscillation

In equation (Cl.4.14) the saturation parameter essentially defines a criterion to compare the time required for stimulated and spontaneous processes. If I then spontaneous coupling of the atom to the vacuum modes of the field is fast compared to the stimulated Rabi coupling and the field is considered weak. If s" 1 then the Rabi oscillation is fast compared to spontaneous emission and the field is said to be strong. Setting s equal to unity defines the saturation condition... 

Figure C 1.5.10. Nonnalized fluorescence intensity correlation function for a single terrylene molecule in p-terjDhenyl at 2 K. The solid line is tire tlieoretical curve. Regions of deviation from tire long-time value of unity due to photon antibunching (the finite lifetime of tire excited singlet state), Rabi oscillations (absorjDtion-stimulated emission cycles driven by tire laser field) and photon bunching (dark periods caused by intersystem crossing to tire triplet state) are indicated. Reproduced witli pennission from Plakhotnik et al [66], adapted from [118].

A different sequence of electromagnetic pulses can be used to directly monitor Rabi oscillations between the two spin qubit basis states (Figure 7.7). As expected,... 

Figure 7.7 (a) Rabi oscillations of the mag netic moments of Er(lll) ions diluted in a single crystal of CaW04, measured under a magnetic field fiQH = 0.522T applied along the c crystallographic axis and at T = 3.5 K. 

The discretized adiabatic procedure, and its analog with STIRAP, is but one possibility for achieving broadband response of an optical device. An alternative, which we discuss, relies on the analogy between the Jones vector description of an optical beam and the two-state time-dependent Schrodinger equation (TDSE). This equation has two commonly used solutions. One is rapid adiabatic passage (RAP), produced by swept detuning (a chirp), and the other is Rabi oscillations, specifically a pi pulse. The RAP has theoretical connection with STIRAP, but the pi pulses have no such connections. We describe application of a procedure that has been used to extend the traditional pi pulses to broadband excitation. This can accomplish the present goal of PAP, under complementary conditions. 

Traditional polarization-altering devices act with constant cp and hence with a constant Y, lying in the 1,2 plane. This produces oscillations of the Stokes vector - the analog of Rabi oscillations - in which S moves regularly away from the equatorial plane and the polarization periodically becomes elliptical. 

Figures 6a-c show the population dynamics encountered in a three-level system (see Fig. 4) interacting resonantly with two Fourier-transform-limited laser pulses with three different delay times between the two pulses. The calculation was done assuming that the chosen Rabi frequencies fulfill the relation > 1/pulse duration) in all three cases. This relation ensures that the typical time for a Rabi oscillation of the population in an isolated two-level system is shorter than the pulse duration. Ionization from level 2 was introduced as a fast laser intensity-dependent decay of level 2 [6, 60], and resonant laser frequencies were assumed.

Hamiltonian (6), the operator Gln = (— I )bi b " (equation (5)) highly nonlinear in the phonon-1 appears mediated by phonons 2. It introduces multiple electron oscillations between the split levels mediated by continuous virtual absorption and emission of the phonons 1. The effect is analogous to Rabi oscillations in quantum optics due to photons [9]. Let us note that Rabi oscillations assist both the interlevel onsite and intersite electron transitions mediated by the electron transfer T. 

In two-level models with phonon assisted tunneling, there appears coupling of both phonon modes mediated by Rabi oscillations. Therefore, also the interlevel... 

To summarize this section, we have presented a new technique for studying radiation absorption in the molecular system Vi5 constituting a first step towards the observation of Rabi oscillations in molecular nanomagnets. The main results are the observation of relatively narrow resonant absorption lines that are dominated by hyperfine interaction. In order to observe Rabi oscillations in a magnetic system, an important requirement is a large AC field amplitude. 

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... 

The situation is quite different for a structured continuum. Consider Fig where the strong-pulse-induced transition to a narrow continuum (Ts = 50 bfi displayed. The results show behavior that is intermediate between a flat , 1 nuum and a discrete set of levels. We see that center-line , caE l — coj <5= 0, ( nuum levels display recurrences, or Rabi oscillations, similar, though not idet... 

If we apply a resonant external field to a two-level system, we can observe a Rabi oscillation. In such a case, the quantum state is well described by... 

This field is expected to be the optimal field that steers the quantum state (p,) at t = 0 to tpj) ait = T, and it also induces a CG Rabi oscillation beween 4>o(0)... 

We next examine when and how the analytic optimal field works for a random matrix system (256 x 256 GOE random matrix). Figure 9 demonstrates the coarse-grained Rabi oscillation induced by the analytic field, Eq. (45), with k = 3, where smooth oscillations of ((j)o(f) (t)(f))p and (Xo(0l4 (0)P observed. The initial and the target states are both Gaussian random vectors with 256 elements. This result shows that the field actually produces the CG Rabi oscillation in the random matrix system. 

Badii, R. and Meier, P.F. (1987). Comment on Chaotic Rabi oscillations under quasiperiodic perturbations , Phys. Rev. Lett. 58, 1045. 

Pomeau, Y., Dorizzi, B. and Grammaticos, B. (1986). Chaotic Rabi oscillations imder quasiperiodic perturbation, Phys. Rev. Lett. 56, 581-684. 

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])...

STRONG COUPLING OF LIGHT WITH ID QUANTUM DOT CHAIN FROM RABI OSCILLATIONS TO RABI WAVES... 

Rabi oscillations are periodical transitions of a two-state quantum system between its stationary states in the presence of an oscillatory driving field, see e.g. [1], Besides the fundamental interest, the effect of Rabi oscillations is promising for realization of binary logic and optical control in quantum informatics and quantum computing. 

The process of the excitation transition opens up new opportunities for controlling the dynamics of Rabi oscillations. For identification of control factors we need to know general solution of the system (2)-(3). It can be found by using the Fourier transform with respect to x and has the form... 

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