Second harmonic generation in $\rm N@C_{60}$ and $\rm P@C_{60}$

The successful implantation of nitrogen and phosphorus into $\rm C_{60}$ opens many new applications. For instance, both $\rm N@C_{60}$ and $\rm P@C_{60}$ are ideal candidates for quantum computing. In this paper, we show that $\rm N@C_{60}$ and $\rm P@C_{60}$ can be used to generate the second harmonic generation. If N and P are at the center of the buckyball, the signal is zero, but if they are off the center, the signal comes out. Therefore, the oscillation of N and P atoms will generate a 0-1-0-1 bit, when detected along the incident light direction. If this signal is sent to another $\rm N@C_{60}$ and $\rm P@C_{60}$, they can control the sequence of bits. The intensity sensitively depends on the laser energy and polarization. This process can be useful for quantum control by $\rm N@C_{60}$ and $\rm P@C_{60}$ themselves. All the results are obtained using the first-principles method.