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Register a new userSemiclassical Description of Wavepacket Revival
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We test the ability of semiclassical theory to describe quantitatively the revival of quantum wavepackets --a long time phenomena-- in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are considered: time-dependent WKB and Van Vleck propagation. We show that both approaches describe with impressive accuracy the autocorrelation function and wavefunction up to times longer than the revival time. Moreover, in the Van Vleck approach, we can show analytically that the range of agreement extends to arbitrary long times.
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Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit resonance island chain structures with accurately controlled sizes and positions of the islands. Using complex classical trajectories that evolve along suitably defined paths in the complex time domain, we construct a semiclassical theory of the resonance-assisted tunneling process. This semiclassical approach yields a compact analytical expression for tunneling-induced level splittings which is found to be in very good agreement with the exact splittings obtained through numerical diagonalisation.
The Heisenberg spin ladder is studied in the semiclassical limit, via a mapping to the nonlinear $sigma$ model. Different treatments are needed if the inter-chain coupling $K$ is small, intermediate or large. For intermediate coupling a single nonlinear $sigma$ model is used for the ladder. Its predicts a spin gap for all nonzero values of $K$ if the sum $s+tilde s$ of the spins of the two chains is an integer, and no gap otherwise. For small $K$, a better treatment proceeds by coupling two nonlinear sigma models, one for each chain. For integer $s=tilde s$, the saddle-point approximation predicts a sharp drop in the gap as $K$ increases from zero. A Monte-Carlo simulation of a spin 1 ladder is presented which supports the analytical results.
Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum revival, i.e., periodic recurrence in the time evolution, can be restored almost completely by coupling the distorted system to an external field obtained from quantum optimal control theory. We demonstrate the procedure with wave-packet calculations in both one- and two-dimensional quantum wells, and analyze the required physical characteristics of the control field. Our results generally show that the inherent dynamics of a quantum system can be idealized at an extremely low cost.
Bohmian mechanics was designed to give rise to predictions identical to those derived by standard quantum mechanics, while invoking a specific interpretation of it - one which allows the classical notion of a particle to be maintained alongside a guiding wave. For this, the Bohmian model makes use of a unique quantum potential which governs the trajectory of the particle. In this work we show that this interpretation of quantum theory naturally leads to the derivation of interesting new phenomena. Specifically, we demonstrate how the fundamental Casimir-Polder force, by which atoms are attracted to a surface, may be temporarily suppressed by utilizing a specially designed quantum potential. We show that when harnessing the quantum potential via a suitable atomic wavepacket engineering, the absorption by the surface can be dramatically reduced. This is proven both analytically and numerically. Finally, an experimental scheme is proposed for achieving the required shape for the atomic wavepacket. All these may enable new insights into Bohmian mechanics as well as new applications to metrology and sensing.
A long-lived quantum memory was developed based on light-compensated cold $^{87}$Rb atoms in a dipole trap. The lifetime of the quantum memory was improved by 40 folds, from 0.67 ms to 28 ms with the help of a compensation laser beam. Oscillations of the memory efficiency due to the transverse mode breathing of the singly-excited spin wave have been clearly observed and clarified with a Monte-Carlo simulation procedure. With detailed analysis of the decoherence processes of the spin wave in cold atomic ensembles, this experiment provides a benchmark for the further development of high-quality quantum memories.
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