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arXiv:2101.05991 · Physical Review A

Matter-wave fractional revivals in a ring waveguide

Jayanta Bera, Suranjana Ghosh, Luca Salasnich, Utpal Roy

Published Dec 21, 2020• 13 citations
arXivHTMLPDF

Abstract

We report fractional revival phenomena in an ultracold matter wave inside a ring waveguide. The specific fractional revival times are precisely identified and corresponding spatial density patterns are depicted. Thorough analyses of the autocorrelation function and quantum carpet provide clear evidence of their occurrence. The exhibited theoretical model is in exact conformity of our numerical results. We also investigate the stability of the condensate and a variation of revival time with the diameter of the ring.

DOI
10.1103/physreva.102.063323

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•Jan 1, 2012•0 citations
We report fractional revival phenomena in an ultracold matter wave inside a ring waveguide. The specific fractional revival times are precisely identified and corresponding spatial density patterns are depicted. Thorough analyses of the autocorrelation function and quantum carpet provide clear evidence of their occurrence. The exhibited theoretical model is in exact conformity of our numerical results. We also investigate the stability of the condensate and a variation of revival time with the diameter of the ring.
Wave packet revivals and fractional revivals are hallmark quantum interference phenomena that arise in systems with nonlinear energy spectra, and their signatures in expectation values of observables have been studied extensively in earlier work. In this article, we build on these studies and extend the analysis in two important directions. First, we investigate fractional revival dynamics in angular momentum observables, deriving explicit expressions for the time evolution of their moments and demonstrating that higher-order angular momentum moments provide clear and selective signatures of fractional revivals. Second, we examine classical analogs of quantum revival phenomena and elucidate structural similarities between quantum fractional revivals and recurrence behavior in representative classical systems. Using the Kerr-type nonlinear Hamiltonian as a paradigmatic model, we analyze the autocorrelation function, moment dynamics, and phase-space structures, supported by visualizations such as quantum carpets. Our results broaden the range of experimentally accessible diagnostics of fractional revivals and provide a unified perspective on revival phenomena across quantum and classical dynamical systems.
Abstract Position-dependent-mass systems are of great importance in many physical situations, such as the transport of charge carriers in semiconductors with non-uniform composition and in the theory of many-body interactions in condensed matter. Here we investigate, numerically and analytically, the phenomenon of fractional revivals in such systems, which is a generic characteristic manifested by the wave-packet evolution in bounded Hamiltonian systems. Identifying the fractional revivals using specific probes is an important task in the theory of quantum measurement and sensing. We numerically simulate the temporal evolution of probability density and information entropy density, which manifest self-similarly recurring interference patterns, namely, quantum carpets. Our numerical results show that the quantum carpets not only serve as an effective probe for recognizing the fractional revivals of various order but they efficiently describe the effect of spatially-varying mass on the structure of fractional revivals, which is manifested as a symmetry breaking in their designs.
We propose a quantum-enhanced matter-wave interferometry protocol based on fractional-revival dynamics of a Bose-Einstein condensate in a ring, combined with a controlled interaction quench. Using the Truncated Wigner Approximation, we show that nonlinear evolution to the quarter revival generates modest spin squeezing of −2.03±0.28  -2.03\pm0.28\;−2.03±0.28dB, which subsequently degrades under further nonlinear evolution. In contrast, starting from a non-interacting condensate, a controlled interaction quench applied after the initial quarter-revival beam-splitter operation generates substantially stronger spin squeezing of −14.57±0.27  -14.57\pm0.27\;−14.57±0.27dB. We further show that phase control at t=3Tr/8t=3T_r/8t=3Tr​/8 rotates the squeezed quadrature onto the phase-sensitive direction J^y\hat{J}_yJ^y​, producing a phase-squeezed state at t=Tr/2t=T_r/2t=Tr​/2. The subsequent quarter-revival evolution converts this phase-squeezed state into a number-squeezed state, enabling population-difference readout. The resulting sequence provides a route to quantum-enhanced interferometry using the intrinsic fractional-revival dynamics of a ring together with controlled interaction and phase operations.
We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in reconstructing the initial state of the wave packet when its coherent structure is short-lived and decays before it is fully revived. Our calculations are based on the model example of fractional revivals in a Rydberg wave packet of circular states. We end by providing an analytical investigation which fully agrees with our numerical observations on the utility of time-frequency analysis in the study of wave packet fractional revivals.
The idea of wave packet, that clarified many conceptual difficulties, has more recently been revisited to address interferometric and dynamical issues.Present work focuses on the spatio-temporal dynamics of the quantum wave packets in the Fermi-Ulam Accelerator Model.The specific system considered here is a one-dimensional box under periodic oscillations at one boundary. Such a seemingly simple system can be mapped to non-trivial problems like BEC trapped in an oscillating cavity or dynamics of atomic wave packet in different potential in presence or absence of gravitational field.The system is shown to display rich dynamical features including transitions from regular to stochastic and further to chaotic domain in classical phase space. We have obtained the approximated eigen-value solutions of the problem through time dependent Schrodinger’s equation under rescaling transformations that effectively replace moving boundary with a static one. Consequently the running time becomes a nonlinear function of the continuously changing boundary.Based on these solutions, revivals or the resurrection of the original wave packet, in the driven and un-driven Fermi-Ulam model are presented. Such revivals correspond to the constructive interference whereas the wave packet’s collapse owes to destructive interference. Furthermore, interplay of constructive and destructive interferences also readily mimics the fractional revivals.It is further demonstrated that initial position and momentum play a highly crucial role in the emergent revival and fractional revival patterns.It is shown that the symmetries exhibited by such structures in un-driven systems are usually lost under driven conditions and the revival/fractional revival times can only be predicted through a transcendental equation whose solution mainly depends on the strength of the external driving force.In present thesis we have proposed a comprehensive mathematical technique to calculate these hitherto unpredictable times.In addition, a graphical method is also suggested to observe these asymmetric revival/fractional revival times.This apparent asymmetry, do display an overall periodicity over a comparatively long span covering many times of revivals.It is found that whenever the ratio between the period of wall oscillation and quantum revival time `α/β' is a rational number then the revivals time shows a periodicity after β number of revival times over α wall oscillation. Standard tools of autocorrelation and quantum carpets, a consequence of quantum interference, have been employed for visual manifestation of these revivals.These carpets amply demonstrate the explicit asymmetric shifting of revival times for the driven case.These micro changes exhibited in quantum carpet morphologies consequently yield amended phase velocities associated with the canals and ridges in the driven framework.Furthermore, to grasp the quantum phase space dynamics in its entirety, we have also utilized the more sophisticated techniques of the Wigner function and information entropy.It is demonstrated mathematically that revivals not apparent via autocorrelation become prominent in the Wigner phase space description along with the appearance of smooth mini wave packets in the fractional revivals.These interference patterns emerge due to the state vector formed through the linear combination of Gaussians with different positions and momenta having pure Gaussian as well as oscillatory terms. Moreover, the information entropy, like the Wigner function also predicts the revivals when and where they happen.Thus a rich pattern of fractional revivals, including some altogether new ones, are observed through this tool in both driven and un-driven situations.Finally we have elucidated various scenarios including cold atoms in magneto-optical traps where such a system can be experimentally realized along with the suggestions for future work in this specific domain