Lossless Kerr-phase gate in a quantum-well system via tunneling interference effect for weak fields

We examine a lossless Kerr-phase gate in a semiconductor quantum-well system via the tunneling interference effect for weak fields. We show that there exists a magic detuning for the signal field, at which the absorption or amplification for the probe field can be eliminated by increasing the tunneling interference effect. Simultaneously, the probe field will acquire a $-\pi$ phase shift at the exit of the medium. We demonstrate with numerical simulations that a lossless Kerr-phase gate is achieved, which may result in many applications in information science and telecommunication.

Figure 1

The geometry of 100 periods of asymmetric double quantum wells and the configuration of the light field. Each asymmetric double quantum well consists of a narrow well and a wide well separated by a small tunneling barrier. $|1\rangle$ and $|4\rangle$ are localized hole states of the valence band. $|2\rangle$ and $|3\rangle$ are delocalized bonding and antibonding states, which are coupled by a thin tunneling barrier. $E_{s\left(p\right)}$ is the electric field of the signal (probe) field with the angular frequency ${\omega }_{s\left(p\right)}$. ${\mathrm{\Delta }}_j(j=2–4)$ are the detunings of state $|j\rangle$.

Figure 2

Contour plots of the absorption coefficient $\alpha$ of the signal field: (a) as a function of detuning $\delta$ and energy splitting $\mathrm{\Delta }$; (b) as a function of detuning $\delta$ and the parameter $\eta$. Bright areas correspond to large absorption, dark to low absorption. Other system parameters are given in the text.

Figure 3

Contour plots of the third-order gain or loss coefficient ${\alpha }_{\mathrm{NL}}$ (a) and the cross-phase modulation ${\varphi }_{\mathrm{XPM}}$ (b) of the probe field as functions of the detuning $\delta$ and the parameter $\eta$. The equal-altitude lines (zero for ${\alpha }_{\mathrm{NL}}$ and $-\pi$ for ${\varphi }_{\mathrm{XPM}}$) guide the selection of a magic detuning ${\delta }_{\mathrm{magic}}$ (the horizontal dashed line). The vertical line indicates that $\eta \approx 0.7$ is required to achieve the Kerr-phase-gate operation. Here, we choose $\mathrm{\Delta }=6.5$ meV and ${\mathrm{\Omega }}_{21}={\mathrm{\Omega }}_{31}=0.35$ meV. Other system parameters are given in the text.

Figure 4

The layout of the experimental setup (a) and plots of $I_p(z,\delta )$ as functions of $\delta$ and the normalized propagation distance $z/L$. The dashed line indicates a magic signal-field detuning with which a lossless Kerr-phase-gate operation can be achieved. Left plot: The signal field is turned off, $I_{\mathrm{in}}=1$ and $I_{\mathrm{out}}=1$ at the exit of the medium $z/L=1$ (b). Right plot: The signal field is turned on, $I_{\mathrm{in}}=1$ and $I_{\mathrm{out}}=0$ at the exit of the medium $z/L=1$ (c). Mach-Zehnder interferometers, controlled by PZT, are used to observe the nonlinear phase shift for the probe field.