Kerr Enhancement Nonlinearity Induced By Quantum Tunneling In An Asymmetric Double-Well Potential

The third-order Kerr nonlinearity plays an important role in nonlinear optics, and it has tremendous and potential prospects for practical applications and other impacts. In the past few years, scientists have already, both theoretically and experimentally, investigated the third-order Kerr nonlinearity in the atomic system, and they have achieved giant Kerr nonlinearity without optical resonant absorption, which results from quantum coherence and interference. Yet, as far as I know, there appears to be few investigations of Kerr nonlinearity in semiconductor quantum well(SQW). From the practical application points of view, it has many attractions to extend the study of nonlinear optics into the semiconductor material, for SQW material has many inherent advantages.In the present Letter, we investigate an n-doped AlGaAs/GaAs asymmetric double quantum well(ADQW) with a continuum. The band structure is shown in Fig. 1, the ground subband of the shallow well and the first excited subband of the right deep well are coupled by tunneling, and two new subbands |2> and |3> are created. And tunneling to a continuum of energies takes place from subbands |2> and |3> through the thin barrier on the right. A probe field couples subband|1> to subbands |2> and |3>, which are themselves coupled to the common excited subband |4> via a pump field. In the absence of the pump beam, the probability amplitude for the absorption of a probe photon can be thought of as the superposition of two absorption paths, one via subbands |2> and one via subbands |3>, both decaying by tunneling to the same continuum, which reduced Fano-type destructive interference so as to cancel the probe absorption altogether. The intensity of Fano-type interference depends on the intensity of tunneling, which can be modified by changing the width of the tunneling barrier and by controlling the temperature. Since the split between subbands |2> and |3> is very small, the Fano-type interference is very similar to that of the spontaneously generated coherence(SGC). We adopt the similar analysis method to investigate the properties of the linear and nonlinear responses in this structure. And we find out that Kerr nonlinearity can be enhanced due to coherent resonant tunneling, while maintaining vanishing the linear and nonlinear absorptions by appropriately choosing the values of the detunings and the intensity of the pump field.In this paper, we firstly consider the influence of dephasing rates on the linear probe absorption spectra under the situation that the pump field is off. As observed in Fig. 2, the efficiency is reduced by a temperature increase which generally leads to larger dephasing rates. In order to induce larger effects of tunneling induced interference, we need to keep the temperature low to reduce the dephasing rates. Next, when the pump is on, form Fig.3, we can get that a third probe absorption peak appears whose height depends on the applied pumping field strength. From these results, we can see that our results coming from the equations of motion for density matrix are in accord with that of previous studies, which shows the rationality of our theories.Afterwards, we derived the relations among the pumping Rabi frequency, the pumping detuning and the probe detuning, satisfying the nonabsorptions(both the linear and nonlinear absorptions)conditions. As shown in Fig.4, under certain conditions, Kerr nonlinearity can be enhanced due to effects of coherent resonant tunneling, while companying with vanishing the linear and nonlinear absorptions by appropriately choosing the values of the detunings and the intensity of the pump field. And the coefficient of Kerr nonlinearity can be enhanced by keeping lower temperature to getting lower dephasing rates, which reduce in larger effects of coherent resonant tunneling.Finally, in Fig.5, we plot the representative profiles of the linear and nonlinear absorptions and the Kerr nonlinearity versus the probe detuning without the effects of coherent resonant tunneling. As expected, when there is no tunneling, the linear and nonlinear absorptions are always very large within the region where the Kerr nonlinearity is enhanced. Comparing with Fig. 4, it can be concluded that the enhanced Kerr nonlinearity with vanishing linear and nonlinear absorptions is a result of coupling reduced by coherent resonant tunneling.As, on the one hand, we can design the height and the width of the thin barriers to modulate the cross coupling intensity, and on the other hand, we can also do that by controlling the environment temperature, the pumping intensity and the pumping detuning. It makes the research more practical to achieve large Kerr nonlinearity without absorptions or with low level absorptions.