The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. To find solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N 2 × N 2 . When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a 15-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy levels.

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We demonstrate a high-efficiency optical modulator at ~1323 nm using the quantum Zeno effect in a ladder transition in a Rb vapor cell. The lower leg of the transitions represents the control beam while the upper leg of the transitions represents the signal beam. The cross-modulation of the signal beam transmission is observed as the control beam is intensity modulated, and is explained in terms of the quantum Zeno effect. We observe a modulation depth of near 100% at frequencies up to 1 MHz and demonstrate modulation at speeds up to 75 MHz, with a 3 dB bandwidth of about 5 MHz, limited by the homogeneous linewidth of the intermediate state. We also describe how much higher modulation speeds could be realized by using a buffer gas to broaden the transitions. We identify and explain the special conditions needed for optimizing the modulation efficiency. Numerical simulations of modulation at ~1 GHz are presented. The maximum modulation speed is found to scale with the pressure-broadened linewidth of the intermediate state, so that much higher speeds should be attainable.

We have demonstrated a heterogeneously integrated III-V-on-Silicon laser based on an ultra-large-angle super-compact grating (SCG). The SCG enables single-wavelength operation due to its high-spectral-resolution aberration-free design, enabling wavelength division multiplexing (WDM) applications in Electronic-Photonic Integrated Circuits (EPICs). The SCG based Si/III-V laser is realized by fabricating the SCG on silicon-on-insulator (SOI) substrate. Optical gain is provided by electrically pumped heterogeneous integrated III-V material on silicon. Single-wavelength lasing at 1550 nm with an output power of over 2 mW and a lasing threshold of around 150 mA were achieved.