Encuesta de acceso a los servicios de salud:

This experiment was the first demonstration of a working charge qubit in a semiconductor device. Coherent oscillations have been shown and an upper bound for the dephasing time T2 = 1 ns has been given. The sample design has already been shown in Figure 1.4 (b). Here, the two states used as a qubit are the two states, where one excess electron occupies either the left (_|L_i) or the right (_|R_i) quantum dot. During the manipulation of the qubit, also the bonding and antibonding states are used. But since in this experiment the coupling between the two dots is assumed to be weak, the two localized states are used during initilization and measurement. With the gates in Figure 1.4 (b), one can tune the

energy levels in both dots, the coupling to the leads and the coupling between the dots. How the double quantum dot system is initialized, manipulated and measured can be seen in Figure 2.15.

Figure 2.15: From Ref. [53]: The left picture shows, how the qubit is initialized. Because the rate Γi is small, the excess electron will be localized in the left quantum dot. A large bias voltageVSD =Vp is applied to achieve this. In the middle picture, the bias voltage is pulsed to VSD = 0, such that the double quantum dot is in the Coulomb blockade regime and the electron is delocalized (in the bonding and antibonding states) between both dots. The right picture depicts the read-out of the double quantum dot qubit, namely the occupation of the right quantum dot is probed, since the coupling between the dots is small. The bias voltage is again VSD =Vp as during the initialization.

The initialization works with a large bias voltage VSD = Vp and a small coupling between the dots (represented by the tunneling rate Γi), such that the excess electron in the double quantum dot is always localized in the left dot. During the manipulation or the coherent oscillation, the system is brought to the Coulomb blockade regime. This can be achieved by pulsing the bias voltage to zero for a time duration tp. In the next step, the measurement, the bias voltage is again pulsed back to its original value VSD = Vp. And the electron can only tunnel out of the double quantum dot, if the excess electron happens to be on the right dot (also due to the small coupling between the two dots).

Doing this, Hayashi et al. found the following results, shown in Figures 2.16 and 2.17. Figure 2.16 (b) and (c) show the coherent oscillation of the occupation probability on the right quantum dot. The oscillations in Figure 2.16 (c) can be fitted with

np(tp)'A− 1 2Be

−Ttp_{2 cos (Ωt}

p)−Γitp, (2.31)

where A is an offset andB the amplitude of the oscillations for the resonant level α. The fitted parameters A _∼ 0.6 and B _∼ 0.3 are comparable to the ideal ones (A = 0.5 and B = 1). At energy offset ε1 = 0, one then finds for the oscillation frequency ₂Ω_π ∼2.3 GHz and for T2 ∼1 ns. Ω gives also rise to the coupling energy ∆.

In addition to these results, Hayashi et al. demonstrate, how the dephasing rate is related to the energy offset ε1, the coupling energy ∆ and the lattice temperature Tlat

Figure 2.16: From Ref. [53]: (a) Current profile as a function of the gate voltageVRon the right dot. Two resonant levels α and β lay in the bias window provided by Vp. (b) The average number np of pulse-induced tunneling electrons as a function of VR and the pulse periodtp. (c) np as a function of the pulse period alone at ε1 = 0. The data can nicely be fitted by Eq. (2.31), as depicted with the red lines. (d) Coupling energy ∆ as a function of the gate voltage VC between the two dots.

Figure 2.17: From Ref. [53]: (a) Dephasing rate T₂−1 as a function of the energy offset ε1. (b) Dephasing rateT₂−1 as a function of the coupling energy ∆. (c) Dephasing rateT₂−1 as a function of the lattice temperature Tlat.

(see Figure 2.17). These findings have also been discussed by the authors of Ref. [53]. They name three probably relevant decoherence mechanisms: background charge fluctua- tions [Figure 2.17 (a)], cotunneling [Figure 2.17 (b) and (c)] and electron-phonon coupling [Figure 2.17 (b) and (c)]. Unfortunately, from the plots in Figure 2.17, one cannot single

out one most important decoherence mechanism. In principle, all three mechanisms can and will contribute to the dephasing rate T₂−1. The formal expressions were simplified in Ref. [53], but for an estimation of the order of magnitude of the effects, it should be suf- ficient. The problem is that the mechanisms cannot be separated clearly from each other. Due to the large tunneling amplitude between the leads and the dots, e.g., cotunneling naturally plays an important role. Therefore one could probably increase the coherence time by using an indirect measurement technique and another initilization scheme. If the coupling to the leads is small, the cotunneling contribution is only a weak effect, as it will be discussed in Chapters 3 and 4 of this thesis. We will also discuss the influence of the electron-phonon interaction in Chapters 5 and 6. To analyse the influence of background charge fluctuations and to apply the methods of Falci et al. [109, 110], one would need more coherent oscillations and these ideally in a Ramsey fringe [111] experiment. A short introduction to 1/f noise and useful methods to treat it can be found in Chapter 9.