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We present a general theoretical description of the extrinsic dephasing mechanism of spectral diffusion that dominates the decoherence dynamics in semiconductor quantum dots at low temperature. We discuss the limits of random telegraph and Gaussian stochastic noises and show that the combination of both approaches in the framework of the pre-Gaussian noise theory allows a quantitative interpretation of high-resolution experiments in single semiconductor quantum dots. We emphasize the generality and the versatility of our model where the inclusion of asymmetric jump processes appears as an essential extension for the understanding of semiconductor quantum dot physics.

Decoherence is one of the fundamental limitations in quantum information science, and the understanding and the control of its dynamics appears as a crucial issue for the development of quantum information devices. Various systems are being investigated in condensed matter physics because of their potential in terms of integrability and scalability, such as superconducting circuits [

At low temperature, the decoherence in QDs is mainly determined by the phenomenon of spectral diffusion. In fact, photoluminescence experiments in single QDs have revealed the extrinsic influence of the solid matrix that generates fluctuating electric fields and shifts the QD line through the quantum confined Stark effect. This so-called spectral diffusion phenomenon was interpreted as due to carriers randomly trapped in defects, impurities in the QD vicinity [

Our model is based on a Markov chain composed of an arbitrary number of

Frequency fluctuation of the QD emission line as a function of time in the presence of a single random telegraph.

In the presence of

According to the Wiener-Khintchine theorem, the optical spectrum is given by the Fourier transform of the electric field autocorrelation function which is proportional to the so-called relaxation function

By using (

The intensity spectrum in the presence of frequency fluctuation due to Markovian processes was addressed by Kubo in his seminal paper on the stochastic theory of lineshape where the general resolution of the Chapman-Kolmogorov equation was presented [

In the prospect of a more general theory that would catch the specific physics of semiconductor nanostructures, we have extended the former model to the case of asymmetric two-state jump processes and derived the expression of the relaxation function

If

Optical spectrum in the presence of a single random telegraph: the Fourier transform of the relaxation function

On the contrary, in the fast modulation limit or motional narrowing regime (

We now switch to the more realistic situation where a large number of random telegraphs contribute to the spectral diffusion of a QD line. For

In order to complete our generalization of the spectral diffusion theory and address the case of Gaussian stochastic processes with asymmetric jump events, we have derived the general expression of

Standard deviation

If

In the fast modulation limit

We will show now that the common configuration of Gaussian stochastic processes displays a rich and original phenomenology in the case of asymmetric jump processes

For symmetric jump processes, the frequency modulation amplitude is constant with a value given by

However, for asymmetric jump processes, the situation is totally different since the frequency modulation is no longer constant and strongly depends on the ratio

We illustrate the generality and the versatility of our model by several examples based on experimental data recorded by means of high-resolution Fourier-transform spectroscopy in single QDs.

We present measurements performed in self-assembled InAs/GaAs QDs grown by molecular beam epitaxy in the Stranski-Krastanow mode, and micro-photoluminescence measurements under nonresonant excitation are performed in the far field using the experimental setup described in [

We first present the experimental evidence for a random telegraph noise where the asymmetry of the jump processes is tuned with a dc-voltage. This effect is observed in the emission spectrum of a single QD embedded in a field-effect heterostructure as a pronounced beating in the Fourier transform measurements. The beating visibility varies as a function of the gate voltage applied to the device, thus showing the control of the doublet asymmetry with the internal electric field.

The sample consists of a single QD embedded in the field-effect structure depicted in Figure

Schematic sketch of the heterostructure (under reverse bias) displaying the conduction and valence band edges energy along the growth direction. The applied gate voltage

In Figure

(a), (b), (c): Interferogram contrast

In the framework of the pre-Gaussian noise theory, we take the product

In Figure

In the example above, the jump processes asymmetry is tailored by means of a dc-gate voltage that controls the fluctuation dynamics of a singular random telegraph. We discuss below another example where the jump processes asymmetry is modified by varying other external experimental parameters, but in the case of a Gaussian stochastic noise.

We present here the experimental evidence for a crossover from the fast to the slow modulation limits in the case of a Gaussian stochastic noise. We observe a smooth transition between a Lorentzian line-profile and a Gaussian one on increasing the incident power or the temperature for a QD in a simple heterostructure. We interpret the existence of motional narrowing at low incident power or low temperature as a striking manifestation of the asymmetry of the jump processes in semiconductor QDs.

The sample structure is simpler than in the previous case and it consists of a single QD layer embedded in GaAs so that no electric field is applied to the QD sample. In Figure

(a), (b), (c): Interferogram contrast

A quantitative interpretation of our measurements is achieved by comparing our experimental data with the convolution of

The asymmetry between the power dependences of

As explained above, the asymmetry of the capture and escape mechanisms is in fact the fundamental reason why motional narrowing strikingly occurs when decreasing the incident power or the temperature. If both processes had the same efficiency (

In this review, we have presented a general theoretical description of the extrinsic dephasing mechanism of spectral diffusion that dominates the QD decoherence at low temperature. We have discussed the limits of random telegraph and Gaussian stochastic noises and shown that the combination of both approaches in the framework of the pre-Gaussian noise theory allows a quantitative interpretation of high-resolution experiments in single semiconductor QDs. We emphasize the generality and the versatility of our model where the inclusion of asymmetric jump processes appears as an essential extension for the understanding of semiconductor QD physics, and hopefully, more generally, for quantum information devices based on solid-state nanostructures.