Information Entropy, Fractional Revivals and Schrödinger Equation with Position-dependent Mass

Information entropy has played a key role in a wide range of disciplines, for instance, classical and quantum information processing, quantum computing, quantum dynamics and quantum metrology. Here, we develop an information theoretic formalism using Shannon entropy, to investigate the quantum dynamics of Hamiltonian systems with position-dependent mass. Such systems are of fundamental interest in many areas, for instance, condensed matter, mathematical physics and foundations of quantum mechanics. We explore the phenomenon of fractional revivals for the temporal evolution of wave-packet solutions of Schrödinger equation with position-dependent mass by studying, analytically and numerically, the time-development of Shannon information entropy in position and momentum spaces. It is shown by our numerical results that the effect of spatially varying mass on the fractional revivals can not be fully harnessed using conventional measures, for instance, autocorrelation function. However, based on our numerical analysis it is concluded that information entropy is not only more sensitive to identify the fractional revivals but it also better elucidates the effect of position-dependent mass on the structure of fractional revivals in the form of symmetry breaking.

Tailoring spin chain dynamics for fractional revivals

The production of quantum states required for use in quantum protocols & technologies is studied by developing the tools to re-engineer a perfect state transfer spin chain so that a separable input excitation is output over multiple sites. We concentrate in particular on cases where the excitation is superposed over a small subset of the qubits on the spin chain, known as fractional revivals, demonstrating that spin chains are capable of producing a far greater range of fractional revivals than previously known, at high speed. We also provide a numerical technique for generating chains that produce arbitrary single-excitation states, such as the W state.

Quantum unidirectional rotation directly imaged with molecules

A gas-phase molecular ensemble coherently excited to have an oriented rotational angular momentum has recently emerged as an appropriate microscopic system to illustrate quantum mechanical behavior directly linked to classical rotational motion, which has a definite direction. To realize an intuitive visualization of such a unidirectional molecular rotation, we report high-resolution direct imaging of direction-controlled rotational wave packets in nitrogen molecules. The rotational direction was regulated by a pair of time-delayed, polarization-skewed laser pulses, introducing the dynamic chirality to the system. The subsequent spatiotemporal propagation was tracked by a newly developed Coulomb explosion imaging setup. From the observed molecular movie, time-dependent detailed nodal structures, instantaneous alignment, angular dispersion, and fractional revivals of the wave packet are fully characterized while the ensemble keeps rotating in one direction. The present approach, providing an accurate view on unidirectional rotation in quantum regime, will guide more sophisticated molecular manipulations by utilizing its capability in capturing highly structured spatiotemporal evolution of molecular wave packets.