Robustness, decoherence, and scaling of AC-drive-controlled atom movement and entanglement on an optical superlattice: the untested performance envelope of the Zhang–Yang (2019) protocol

In 2019 Zhang and Yang proposed a scheme in which a sinusoidal driving force, applied to bosonic atoms in an optical superlattice, coherently suppresses tunneling on chosen bonds (coherent destruction of tunneling) so that single atoms can be routed site by site and pairs of atoms entangled via an effective superexchange interaction. The scheme was established only through numerical simulations in the ideal high-frequency, perfectly isolated, few-particle regime. What remains open is the quantitative performance envelope of this protocol: fidelity loss and decoherence rates under realistic noise, finite temperature, and ramp imperfections; robustness to departures from the strict high-frequency limit and to errors in the drive amplitude and frequency; and the trade-off between interaction strength, gate speed, and the validity of the second-order superexchange reduction. Extension to higher-dimensional lattices and many particles, and benchmarking beyond the specific simulated points, remain optional outlook beyond the source's demonstrated scope. No prior work addresses any part of this envelope.

Background

Ultracold neutral atoms can be trapped in the standing waves of interfering laser beams, forming a periodic potential called an optical lattice; superimposing two standing waves of commensurate wavelength produces an optical superlattice, whose unit cell contains several inequivalent sites and bond lengths. At low filling, the dynamics of interacting bosons in such a lattice are described by the single-band Bose–Hubbard model, in which atoms hop between neighboring sites with amplitude $J$ and two atoms on the same site repel with energy $U$ . Zhang and Yang (2019) studied this model supplemented by a spatially linear, sinusoidally time-dependent force $K\sin(\omega t)\sum_i x_i n_i$ , where $n_i$ counts atoms at site $i$ at position $x_i$ . When the drive frequency $\omega$ greatly exceeds $J$ (the high-frequency approximation of Floquet theory — the study of systems driven periodically in time, for which a stroboscopic effective Hamiltonian governs the averaged dynamics), the averaged hopping on a bond of length $x$ becomes $J_{\mathrm{eff}}(x)=J\,\mathcal{J}_0(Kx/\omega)$ , with $\mathcal{J}_0$ the zeroth-order Bessel function of the first kind. At zeros of $\mathcal{J}_0$ the tunneling is coherently suppressed — the phenomenon of coherent destruction of tunneling (CDT), first identified by Grossmann, Dittrich, Jung, and Hänggi (1991). Because a superlattice has inequivalent bond lengths $x_1$ and $x_2$ , one can choose the drive amplitude $K$ so that $\mathcal{J}_0(Kx_1/\omega)=0$ while $\mathcal{J}_0(Kx_2/\omega)\neq0$ : tunneling is then switched off on one class of bonds and survives on the other, and alternating the amplitude between two such values on consecutive half-periods moves an atom by exactly one site per cycle, with a variant of the timing splitting a pair of atoms. When two atoms occupy neighboring sites, virtual tunneling processes (valid to second order in $J_{\mathrm{eff}}/U$ , in direct analogy with magnetic superexchange) generate an effective spin Hamiltonian with coupling $J_H=4J_{\mathrm{eff}}^2/U$ , which entangles the pair; the entanglement is quantified by the concurrence (a standard measure taking the value 1 for a maximally entangled pair of two-level systems) and, for three atoms, by the three-tangle (the analogous measure of genuine three-party entanglement, normalized to 1 for the maximally entangled three-qubit state). The authors verified the routing and entangling protocols by exact numerical simulations on lattices of up to 60 sites, at drive frequency $\omega=32J$ and interactions $U=4J$ and $U=32J$ , finding near-unit concurrences at the predicted gate times. Predecessor work by the same group (Zheng and Yang 2015, 2016, 2017) established the driven-lattice control of correlated pairs that culminated in this scheme, and Creffield (2007) had earlier used periodic driving and CDT to manipulate qubits in static double wells; general Floquet machinery (high-frequency expansions, heating analyses; Bukov, D'Alessio, and Polkovnikov 2015; Eckardt 2017) supplies the tools but contains no treatment of this amplitude-modulated superlattice protocol. The demonstrations, however, all live in the ideal regime: perfectly isolated system, strict $\omega\gg J$ , exact drive parameters, few particles, one dimension.

Problem Statement

Determine the experimentally viable performance envelope of the AC-drive-controlled routing and entanglement protocol of Zhang and Yang (2019) for bosons on an optical superlattice — that is, quantify whether and where the protocol still works once the idealizations of the original simulations are removed. The objective is a quantitative feasibility assessment of this specific protocol within the scope demonstrated by the source — an optical superlattice with inequivalent bond lengths and few particles — covering: the fidelity loss and decoherence rates of the routing and entangling gates under realistic conditions, namely noise, finite temperature, and imperfect switching ramps of the drive; the robustness of the coherent-destruction-of-tunneling conditions (the zeros of $\mathcal{J}_0(Kx/\omega)$ ) to departures from the strict high-frequency limit $\omega\gg J$ and to inaccuracies in the drive amplitude $K$ and frequency $\omega$ , with the resulting corrections to $J_{\mathrm{eff}}$ and to the gate operation; and the trade-off between interaction strength $U$ , gate speed (the entangling time scales as $1/J_H=U/(4J_{\mathrm{eff}}^2)$ ), and the validity of the second-order perturbative reduction to the effective superexchange Hamiltonian — in particular whether the large- $U$ regime such as $U=32J$ remains inside that validity. These three facets each remove one idealization of the same protocol. Extension to higher-dimensional lattices or many particles (routing scalability, cross-talk, measurement overhead) and systematic benchmarking beyond the specific simulated cases (e.g., $\omega=32J$ with $U=4J$ or $U=32J$ ) are optional outlook beyond the source's demonstrated scope, not part of the objective; 'scaling' in the title refers to the gate-time versus interaction trade-off identified above, not to this many-particle or higher-dimensional scalability.

References

Jia-Chong Zhang and Shi-Jie Yang, 'Controllable movement and entanglement of atoms on an optical lattice', Journal of Physics B: Atomic, Molecular and Optical Physics 52, 215302 (2019), DOI 10.1088/1361-6455/ab4021, https://doi.org/10.1088/1361-6455/ab4021
F. Grossmann, T. Dittrich, P. Jung, and P. Hänggi, 'Coherent destruction of tunneling', Physical Review Letters 67, 516 (1991), DOI 10.1103/PhysRevLett.67.516, https://doi.org/10.1103/PhysRevLett.67.516
C. E. Creffield, 'Quantum Control and Entanglement using Periodic Driving Fields', Physical Review Letters 99, 110501 (2007), DOI 10.1103/PhysRevLett.99.110501, https://doi.org/10.1103/PhysRevLett.99.110501
Yi Zheng and Shi-Jie Yang, 'Controlling migration of a pair of correlated particles by doubly modulated fields', New Journal of Physics 18, 013005 (published online December 2015; volume year 2016), DOI 10.1088/1367-2630/18/1/013005, https://doi.org/10.1088/1367-2630/18/1/013005
Yi Zheng and Shi-Jie Yang, 'Producing directed migration with correlated atoms in a tilted ac-driven lattice', Physical Review A 93, 063609 (2016), DOI 10.1103/PhysRevA.93.063609, https://doi.org/10.1103/PhysRevA.93.063609
Yi Zheng and Shi-Jie Yang, 'Controlling correlated particles and generating entanglement in an ac-driving lattice', The European Physical Journal Special Topics 226, 2843 (2017), DOI 10.1140/epjst/e2016-60371-8, https://doi.org/10.1140/epjst/e2016-60371-8
Marin Bukov, Luca D'Alessio, and Anatoli Polkovnikov, 'Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to Floquet engineering', Advances in Physics 64, 139 (2015), DOI 10.1080/00018732.2015.1055918, https://doi.org/10.1080/00018732.2015.1055918
André Eckardt, 'Colloquium: Atomic quantum gases in periodically driven optical lattices', Reviews of Modern Physics 89, 011004 (2017), DOI 10.1103/RevModPhys.89.011004, https://doi.org/10.1103/RevModPhys.89.011004