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arXiv:2109.00696 · Physical Review X

Observation of the Quantum Boomerang Effect

Roshan Sajjad, Jeremy L. Tanlimco, Hèctor Mas, Alec Cao, Eber Nolasco-Martinez, Ethan Q. Simmons, Flávio L. N. Santos, Patrizia Vignolo, Tommaso Macrì, David Weld

Published Feb 23, 2022• 30 citations
arXivHTMLPDF

Abstract

A particle in an Anderson-localized system, if launched in any direction, should, on average, return to its starting point and stay there.Despite the central role played by Anderson localization in the modern understanding of condensed matter, this "quantum boomerang" effect, an essential feature of the localized state, was only recently theoretically predicted.We report the experimental observation of the quantum boomerang effect.Using a degenerate gas and a phase-shifted pair of optical lattices, we not only confirm the predicted dependence of the boomerang effect on Floquet gauge but also elucidate the crucial role of initial-state symmetries.Highlighting the key role of localization, we observe that as stochastic kicking destroys dynamical localization, the quantum boomerang effect also disappears.Measured dynamics are in agreement with numerical models and with predictions of an analytical theory we present which clarifies the connection between time-reversal symmetry and boomerang dynamics.These results showcase a unique experimental probe of the underlying quantum nature of Anderson localized matter.

DOI
10.1103/physrevx.12.011035

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A particle in an Anderson-localized system, if launched in any direction, should, on average, return to its starting point and stay there.Despite the central role played by Anderson localization in the modern understanding of condensed matter, this "quantum boomerang" effect, an essential feature of the localized state, was only recently theoretically predicted.We report the experimental observation of the quantum boomerang effect.Using a degenerate gas and a phase-shifted pair of optical lattices, we not only confirm the predicted dependence of the boomerang effect on Floquet gauge but also elucidate the crucial role of initial-state symmetries.Highlighting the key role of localization, we observe that as stochastic kicking destroys dynamical localization, the quantum boomerang effect also disappears.Measured dynamics are in agreement with numerical models and with predictions of an analytical theory we present which clarifies the connection between time-reversal symmetry and boomerang dynamics.These results showcase a unique experimental probe of the underlying quantum nature of Anderson localized matter.
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The quantum boomerang effect (QBE) is a unique dynamical signature of Anderson localization, characterized by a launched wavepacket that initially drifts but ultimately returns to its initial position due to fundamental quantum interference. In this work, we theoretically establish and quantitatively characterize the QBE in a time-crystalline structure using a periodically driven quantum particle in a one-dimensional potential well. By constructing maximally localized Floquet-Wannier states and introducing temporal disorder, we rigorously map the continuous Floquet dynamics onto a discrete disordered tight-binding lattice. By positioning a detector at a fixed spatial coordinate, we monitor the temporal evolution of the wavepacket, to extract the mean temporal center of mass of the probability density in a time-crystalline structure. This mean temporal center of mass exhibits an initial ballistic expansion, followed by a pronounced U-turn, and ultimately returns to its initial temporal position after long-time evolution. These results confirm the existence of the complete QBE in the time domain. They also demonstrate that non-trivial dynamics can be explored within time-crystalline systems, even though these structures already possess an inherent temporal periodicity.
In this thesis, we theoretically and numerically investigate the quantum boomerang effect - i.e. the return of a wave packet launched with a nonzero velocity to its initial position - in ultra-cold disordered atomic gases. We address three main problems. We study the effect of the time-reversal symmetry breaking on the existence of the quantum boomerang phenomenon. We show that time-reversal symmetry is not a necessary condition for the presence of the quantum boomerang. Next, we investigate the impact of interactions on the quantum boomerang effect, using the mean-field approximation. The interactions lead to partial destruction of the boomerang effect. Within the framework of the Gross-Pitaevskii equation, we identify a universal parameter that describes the observed destruction of the particle's return to the origin. Finally, we numerically study the effect of interactions using a quasi-exact approach. To this end, we study weakly interacting bosons, the Tonks-Girardeau gas, and strongly interacting bosons, which map to weakly interacting fermions. We find that weakly interacting bosons exhibit stronger destruction of the boomerang effect than in the case of the mean-field approach, thus that quantum fluctuations play a major role. Results for the Tonks-Girardeau gas show the existence of the full quantum boomerang phenomenon. Moreover, the results for strongly interacting bosons, where the boomerang is also only partial, provide evidence that the destruction of the quantum boomerang effect does not depend on the details of the interactions between particles.
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Abstract Quantum interference can terminate energy growth in a continually kicked system, via a single-particle ergodicity-breaking mechanism known as dynamical localization. The effect of many-body interactions on dynamically localized states, while important to a fundamental understanding of quantum decoherence, has remained unexplored despite a quarter-century of experimental studies. We report the experimental realization of a tunably-interacting kicked quantum rotor ensemble using a Bose-Einstein condensate in a pulsed optical lattice. We observe signatures of a prethermal localized plateau, followed for interacting samples by interaction-induced anomalous diffusion with an exponent near one half. Echo-type time reversal experiments establish the role of interactions in destroying reversibility. These results quantitatively elucidate the dynamical transition to many-body quantum chaos, advance our understanding of quantum anomalous diffusion, and delimit some possibilities for protecting quantum information in interacting driven systems.