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arXiv:1509.07829 · Physical Review A

Quantum entanglement and drifting generated by an ac field resonant with frequency-doubled Bloch oscillations of correlated particles

Wandearley S. Dias, F. A. B. F. de Moura, M. L. Lyra

Published Feb 16, 2016• 6 citations
arXivHTMLPDF

Abstract

We study the dynamics of initially localized and uncorrelated two-particle quantum wave packets evolving in a one-dimensional discrete lattice. In particular, we show that the particles become strongly entangled when directed by a harmonic ac field which is resonant with frequency-doubled Bloch oscillations promoted by a static dc field. Some degree of entanglement is also achieved when the ac field is resonant with the single-particle Bloch oscillations. However, in this case, entanglement is strongly limited by the survival of anticorrelated unbounded states. We further show that the drift velocity of the correlated-particle wave-packet centroid depends on the phase of the ac field. This dependence is similar to the semiclassical prediction for single-particle motion. The drift velocity vanishes in the limit of uncorrelated particles, as well as for Fock-like initial states, which have a null expectation value of the kinetic operator. We reveal that the interparticle interaction influences unbounded- and bounded-state components differently. This leads to a nontrivial nonmonotonic dependence of the drift velocity on the interaction strength.

DOI
10.1103/physreva.93.023623

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The coherent dynamics of two strongly interacting electrons hopping on a one-dimensional lattice and driven by combined dc-ac fields is theoretically investigated in the framework of the Hubbard model. It is shown that, under appropriate forcing conditions in the strong-field regime, super-Bloch oscillations (SBOs) can be observed for the bound particle state, but not for unpaired electrons that remain frozen in the lattice. As compared to single-particle SBOs, SBOs of correlated particles are generally quasiperiodic.
We investigate the influence of the on-site Hubbard interaction UUU on the eigenstates and dynamics of two electrons restricted to move in a linear chain with long-range correlated disorder. We solve the time-dependent Schr\"odinger equation to follow the time evolution of an initially localized Gaussian two-electron wave packet. In the regime of strongly correlated disorder, for which one-electron extended eigenstates emerge near the band center, the electron-electron coupling promotes the trapping of a finite portion of the wave packet. In the presence of a uniform electric field, the wave packet develops complex Bloch oscillations. The power spectrum of the centroid's velocity trace shows a splitting near the typical semiclassical Bloch frequency, as well as a frequency doubling phenomenon for intermediate couplings which is related to the bounded states components that are present in the wave packet. Finally, we show that localized and extended two-electron eigenstates coexist near the band center with the level spacing distribution showing a universal Poissonian form irrespective to the Hubbard coupling.
The effect of an additional high frequency alternating field on the Bloch-Zener oscillation of a quantum particle is investigated theoretically. The effective magnitude of the band gap is reduced by the ac field, and even collapsed to zero by appropriately tuning the amplitude and the frequency of the oscillation. This results in the enhancement of the Zener tunneling with dramatic changes of the Bloch-Zener oscillation. The temporal behavior of the wave packet is clarified as due to the interplay of the Landau-Zener interference in the repeated level crossings with two different time scales, namely, the period of the Bloch oscillation, and the period of the high frequency ac field.
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One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence of pure and correlated dephasing environments. We study the dynamics of entanglement while varying the interaction strength between the two qubits, their relative frequencies, and their coupling strength to the environment starting from different initial states of practical interest. The impact of the asymmetry of the two qubits, reflected in their different frequencies and coupling strengths to the environment, varies significantly depending on the initial state of the system and its degree of anisotropy. For an initial disentangled, or a Werner, state, as the difference between the frequencies increases, the entanglement decay rate increases, with more persistence at the higher degrees of anisotropy in the former state. However, for an initial anti-correlated Bell state, the entanglement decays more rapidly in the symmetric case compared with the asymmetric one. The difference in the coupling strengths of the two qubits to the pure (uncorrelated) dephasing environment leads to higher entanglement decay in the different initial state cases, though the rate varies depending on the degree of anisotropy and the initial state. Interestingly, the correlated dephasing environment, within a certain range, was found to enhance the entanglement dynamics starting from certain initial states, such as the disentangled, anti-correlated Bell, and Werner, whereas it exhibits a decaying effect in other cases such as the initial correlated Bell state.