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arXiv:1910.11019 · Physical Review A

Pulse- and continuously driven many-body quantum dynamics of bosonic impurities in a Bose-Einstein condensate

K. Mukherjee, S. I. Mistakidis, Sonjoy Majumder, Peter Schmelcher

Published Feb 20, 2020• 13 citations
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Abstract

We unravel the periodically driven dynamics of two repulsively interacting bosonic impurities within a bosonic bath upon considering either the impact of a finite pulse or continuous shaking of the impurities harmonic trap. Following a pulse driving of initially miscible components, we reveal a variety of dynamical response regimes depending on the driving frequency. At resonant drivings, the impurities decouple from their host, while if exposed to a high-frequency driving, they remain trapped in the bosonic gas. For continuous shaking, we showcase that in the resonantly driven regime the impurities oscillate back and forth within and outside the bosonic medium. In all cases, the bosonic bath is perturbed performing a collective dipole motion. Referring to an immiscible initial state, we unveil that for moderate driving frequencies the impurities feature a dispersive behavior while for a high-frequency driving they oscillate around the edges of the Thomas-Fermi background. Energy transfer processes from the impurities to their environment are encountered, especially for large driving frequencies. Additionally, coherence losses develop in the course of the evolution with the impurities predominantly moving as a pair.

DOI
10.1103/physreva.101.023615

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We unravel the periodically driven dynamics of two repulsively interacting bosonic impurities within a bosonic bath upon considering either the impact of a finite pulse or continuous shaking of the impurities harmonic trap. Following a pulse driving of initially miscible components, we reveal a variety of dynamical response regimes depending on the driving frequency. At resonant drivings, the impurities decouple from their host, while if exposed to a high-frequency driving, they remain trapped in the bosonic gas. For continuous shaking, we showcase that in the resonantly driven regime the impurities oscillate back and forth within and outside the bosonic medium. In all cases, the bosonic bath is perturbed performing a collective dipole motion. Referring to an immiscible initial state, we unveil that for moderate driving frequencies the impurities feature a dispersive behavior while for a high-frequency driving they oscillate around the edges of the Thomas-Fermi background. Energy transfer processes from the impurities to their environment are encountered, especially for large driving frequencies. Additionally, coherence losses develop in the course of the evolution with the impurities predominantly moving as a pair.
We study the correlated dynamics of few interacting bosonic impurities immersed in a one-dimensional harmonically trapped bosonic environment. The mixture is exposed to a time-dependent impurity-medium interaction pulse moving it across the relevant phase-separation boundary. For modulation frequencies smaller than the trapping one, the system successively transits through the miscible and immiscible phases according to the driving of the impurity-medium interactions. For strong modulations, and driving from the miscible to the immiscible regime, a significant fraction of the impurities is expelled to the edges of the bath. They exhibit a strong localization behavior and tend to equilibrate. Following the reverse driving protocol, the impurities perform a breathing motion while featuring a two-body clustering and the bath is split into two incoherent parts. Interestingly, in both driving scenarios, dark-bright solitons are nucleated in the absence of correlations. A localization of the impurities around the trap center for weak impurity-impurity repulsions is revealed, which subsequently disperse into the bath for increasing interactions.
We unravel the many-body dynamics of a harmonically trapped impurity colliding with a bosonic medium confined in a double well upon quenching the initially displaced harmonic trap to the center of the double well.We reveal that the emerging correlation dynamics crucially depends on the impurity-medium interaction strength allowing for a classification into different dynamical response regimes.For strong attractive impurity-medium couplings the impurity is bound to the bosonic bath, while for intermediate attractions it undergoes an effective tunneling.In the case of weak attractive or repulsive couplings the impurity penetrates the bosonic bath and performs a dissipative oscillatory motion.Further increasing the impurity-bath repulsion results in the pinning of the impurity between the density peaks of the bosonic medium, a phenomenon that is associated with a strong impurity-medium entanglement.For strong repulsions, the impurity is totally reflected by the bosonic medium.To unravel the underlying microscopic excitation processes accompanying the dynamics, we employ an effective potential picture.We extend our results to the case of two bosonic impurities and demonstrate the existence of a qualitatively similar impurity dynamics.
Abstract We unravel the nonequilibrium correlated quantum quench dynamics of an impurity traveling through a harmonically confined Bose–Einstein condensate in one-dimension. For weak repulsive interspecies interactions the impurity oscillates within the bosonic gas. At strong repulsions and depending on its prequench position the impurity moves towards an edge of the bosonic medium and subsequently equilibrates. This equilibration being present independently of the initial velocity, the position and the mass of the impurity is inherently related to the generation of entanglement in the many-body system. Focusing on attractive interactions the impurity performs a damped oscillatory motion within the bosonic bath, a behavior that becomes more evident for stronger attractions. To elucidate our understanding of the dynamics an effective potential picture is constructed. The effective mass of the emergent quasiparticle is measured and found to be generically larger than the bare one, especially for strong attractions. In all cases, a transfer of energy from the impurity to the bosonic medium takes place. Finally, by averaging over a sample of simulated in situ single-shot images we expose how the single-particle density distributions and the two-body interspecies correlations can be probed.
We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a one-dimensional bosonic gas following an interspecies interaction quench. Monitoring the temporal evolution of the single-particle density of each species we reveal the existence of four distinct dynamical regimes. For weak interspecies repulsions both species either perform a breathing motion or the impurity density splits into two parts which interact and disperse within the bosonic cloud. Turning to strong interactions we observe the formation of dark-bright states within the mean-field approximation. However, the correlated dynamics shows that the fermionic density splits into two repelling density peaks which either travel toward the edges of the bosonic cloud where they equilibrate or they approach an almost steady state propagating robustly within the bosonic gas which forms density dips at the same location. For these strong interspecies interactions an energy transfer process from the impurities to their environment occurs at the many-body level, while a periodic energy exchange from the bright states (impurities) to the bosonic species is identified in the absence of correlations. Finally, inspecting the one-body coherence function for strong interactions enables us to draw conclusions on the spatial localization of the quench-induced fermionic density humps.
Quantum dynamics of impurities in a bath of bosons is a long-standing problem in solid-state, plasma, and atomic physics. Recent experimental and theoretical investigations with ultracold atoms have focused on this problem, studying atomic impurities immersed in an atomic Bose–Einstein condensate (BEC) and for various relative coupling strengths tuned by the Fano−Feshbach resonance technique. Here, we report extensive numerical simulations on a closely related problem: the collision between a bosonic impurity consisting of a few 41 K atoms and a BEC of 87 Rb atoms in a quasi one-dimensional configuration and under a weak harmonic axial confinement. For small values of the inter-species interaction strength (regardless of its sign), we find that the impurity, which starts from outside the BEC, simply causes the BEC cloud to oscillate back and forth, but the frequency of oscillation depends on the interaction strength. For intermediate couplings, after a few cycles of oscillation the impurity is captured by the BEC, and strongly changes its amplitude of oscillation. In the strong interaction regime, if the inter-species interaction is attractive, a local maximum (bright soliton) in the BEC density occurs where the impurity is trapped; if, instead, the inter-species interaction is repulsive, the impurity is not able to enter the BEC cloud and the reflection coefficient is close to one. However, if the initial displacement of the impurity is increased, the impurity is able to penetrate the cloud, leading to the appearance of a moving hole (dark soliton) in the BEC.
We consider impurity atoms embedded in a two-component Bose-Einstein condensate in a quasi-one dimensional regime. We study the effects of repulsive coupling between the impurities and Bose species on the equilibrium of the system for both miscible and immiscible mixtures by numerically solving the underlying coupled Gross-Pitaevskii equations. Our results reveal that the presence of impurities may lead to a miscible-immiscible phase transition due to the interaction of the impurities and the two condensates. Within the realm of the Bogoliubov-de Gennes equations we calculate the quantum fluctuations due to the different types of interactions. The breathing modes and the time evolution of harmonically trapped impurities in both homogeneous and inhomogeneous binary condensates are deeply discussed in the miscible case using variational and numerical means. We show in particular that the self-trapping, the miscibility and the inhomogeneity of the trapped Bose mixture may strongly modify the low-lying excitations and the dynamical properties of impurities. The presence of phonons in the homogeneous Bose mixture gives rise to the damping of breathing oscillations of impurities width.