Scalable, noise-robust generation and certification of multipartite entanglement in optical lattices using only local interactions and lattice driving

Floquet-driven optical superlattices can route and entangle atoms using only the periodic drive: bond-selective coherent destruction of tunneling (CDT) moves selected atoms, and on-site interactions during a timed encounter entangle them. A 2019 study by Zhang and Yang demonstrated this route for one to three particles in one dimension (concurrence and three-tangle reaching unity) and gave an algebraic four-particle Bell-measurement/entanglement-swapping construction, but left the scheme's scalability, robustness, and noise behavior unanalyzed. The open problem is whether this drive-only route can be extended to a scalable, quantitatively noise-robust scheme for generating and certifying genuine multipartite entanglement: many-particle and higher-dimensional protocols with cross-talk and measurement-overhead analysis, a quantitative decoherence and fidelity budget under realistic noise, robustness beyond the strict high-frequency approximation and to drive-parameter inaccuracies, and a physical realization of the Bell-measurement/swapping step. These directions remain open.

Background

An optical lattice traps ultracold atoms in the standing-wave potential of interfering laser beams; superposing two standing waves with commensurate wavelengths produces an optical superlattice, a lattice whose alternating bonds have different lengths $x_1$ and $x_2$ . Atoms in such a lattice are described by a Bose–Hubbard model — hopping amplitude $J$ between neighboring sites plus an on-site interaction energy $U$ per doubly occupied site — and a sinusoidal driving field (experimentally, a periodic phase modulation of the lattice lasers) adds a term $K\sin(\omega t)\sum_i x_i n_i$ with drive amplitude $K$ and frequency $\omega$ . Periodic driving of a quantum system is described by Floquet theory, whose central object is the stroboscopic effective (Floquet) Hamiltonian; in the high-frequency approximation ( $\omega\gg J$ ), the drive renormalizes the hopping on each bond to $J_{\mathrm{eff}}(x)=J\,\mathcal{J}_0(Kx/\omega)$ , where $\mathcal{J}_0$ is the zeroth-order Bessel function of the first kind. Because $\mathcal{J}_0$ has zeros, tuning $Kx/\omega$ to a zero suppresses tunneling on that bond — coherent destruction of tunneling (CDT), also called dynamic localization, observed experimentally in driven optical lattices since 2007–2008. In a superlattice the two bond lengths respond differently to the same drive, so alternating the amplitude between values that null $\mathcal{J}_0(Kx_1/\omega)$ and $\mathcal{J}_0(Kx_2/\omega)$ switches which bond is open, allowing a particle to be routed deterministically one site per cycle or coherently split. When two distinguishable atoms are brought onto adjacent sites, virtual hopping processes in the large- $U$ regime produce an effective Heisenberg-like exchange at rate $J_H=4J_{\mathrm{eff}}^2/U$ (a superexchange-type scale), so holding the pair for $t_z=\pi/(2J_H)$ entangles them. Entanglement of a two-qubit state is measured by the concurrence $C=2|c_{00}c_{11}-c_{01}c_{10}|$ computed from the state's amplitudes; genuine tripartite entanglement of three qubits is measured by the three-tangle $\tau_3=4|d_1-2d_2+4d_3|$ , a polynomial invariant of the state coefficients that vanishes for states that are not genuinely tripartite entangled. A Bell-state measurement is a joint projection of two qubits onto the four maximally entangled Bell states; entanglement swapping uses such a measurement on one member of each of two Bell pairs to project the two remaining, possibly distant, qubits into an entangled state. Creffield (2007) first showed that periodic driving can generate directed motion and two-atom entanglement control in a lattice via CDT. Zhang and Yang (2019) then combined bond-selective CDT routing with collisional entanglement in a one-dimensional bipartite superlattice: single-particle directed motion and coherent splitting; two-atom entanglement with concurrence exactly 1 in a 10-site simulation ( $\omega=32J$ , $U=4J$ ); three-atom sequential mixing reaching three-tangle 1 in a 60-site simulation; and an algebraic decomposition showing that a Bell measurement on the central pair of a four-atom state implements entanglement swapping (parameters $U=32J$ , no time-dependent simulation). All demonstrations were few-particle, one-dimensional, and at specific idealized parameters, and the entanglement measures were computed after projecting onto two sites. The open questions the authors themselves posed concern whether this route scales and survives realistic imperfections.

Problem Statement

Establish whether entanglement generation using only local on-site interactions and periodic lattice driving in optical (super)lattices can be made scalable and quantitatively robust, by extending the CDT-routing-plus-collisional-entanglement protocols of Zhang and Yang (2019) — validated for at most three particles in one dimension at idealized parameters — to a scalable, quantitatively noise-robust scheme. The open directions of this program include: (i) protocols for many particles and higher-dimensional superlattices, with an analysis of routing cross-talk between simultaneously routed atoms and of the measurement overhead for certifying the resulting many-body entanglement; (ii) a quantitative decoherence and fidelity budget for the full protocol under realistic noise sources, including interaction-induced and drive-induced decoherence channels, finite temperature, and imperfect drive-amplitude switching and ramps; (iii) an analysis of the protocols' robustness to departures from the strict high-frequency approximation ( $\omega\gg J$ ) and to inaccuracies in the drive amplitude $K$ and frequency $\omega$ , including the trade-off among interaction strength $U$ , entangling time $t_z=\pi/(2J_H)$ with $J_H=4J_{\mathrm{eff}}^2/U$ , and the validity of the perturbative exchange reduction; and (iv) whether the Bell-state measurement and entanglement-swapping step that the source paper established only algebraically admits a physically realizable implementation by drive-only routing together with site-resolved measurement. The common objective uniting these directions is to generate and certify genuine multipartite entanglement in an optical lattice at particle numbers beyond the few-particle demonstrations, with quantified robustness to the drive and noise imperfections listed above. A rigorous no-go or obstruction result establishing that cross-talk between simultaneously routed atoms, decoherence channels, or drive-parameter sensitivity prevents such scaling also resolves the task. The directions (i)–(iv) define the scope of this objective, which includes the physical realization of the Bell-state measurement and entanglement swapping in (iv). A claimed scaling or quantitative-robustness result must be backed by explicit quantitative thresholds — a scaling trend in particle number (and in lattice dimensionality where direction (i) is claimed) rather than a single finite case just beyond the few-particle demonstrations, together with a stated fidelity or tolerable dephasing/noise level — and a rigorous no-go must rule out scaling at a level fixed independently of, and prior to, the proposed protocol.

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
C. E. Creffield, "Quantum control and entanglement using periodic driving fields", Physical Review Letters 99, 110501 (2007), DOI 10.1103/PhysRevLett.99.110501, arXiv:0704.1792, https://arxiv.org/abs/0704.1792
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 (preprint arXiv:1407.4803, https://arxiv.org/abs/1407.4803)
Ahmed Omran, Harry Levine, Alexander Keesling, Giulia Semeghini, Tout T. Wang, Sepehr Ebadi, Hannes Bernien, Alexander S. Zibrov, Hannes Pichler, Soonwon Choi, Jian Cui, Marco Rossignolo, Phila Rembold, Simone Montangero, Tommaso Calarco, Manuel Endres, Markus Greiner, Vladan Vuletić and Mikhail D. Lukin, "Generation and manipulation of Schrödinger cat states in Rydberg atom arrays", Science 365, 570 (2019), DOI 10.1126/science.aax9743, https://doi.org/10.1126/science.aax9743 (preprint arXiv:1905.05721, https://arxiv.org/abs/1905.05721)
Harry Levine, Alexander Keesling, Giulia Semeghini, Ahmed Omran, Tout T. Wang, Sepehr Ebadi, Hannes Bernien, Markus Greiner, Vladan Vuletić, Hannes Pichler and Mikhail D. Lukin, "Parallel implementation of high-fidelity multi-qubit gates with neutral atoms", Physical Review Letters 123, 170503 (2019), DOI 10.1103/PhysRevLett.123.170503, https://doi.org/10.1103/PhysRevLett.123.170503 (preprint arXiv:1908.06101, https://arxiv.org/abs/1908.06101)
T. M. Graham, Y. Song, J. Scott, C. Poole, L. Phuttitarn, K. Jooya, P. Eichler, X. Jiang, A. Marra, B. Grinkemeyer, M. Kwon, M. Ebert, J. Cherek, M. T. Lichtman, M. Gillette, J. Gilbert, D. Bowman, T. Ballance, C. Campbell, E. D. Dahl, O. Crawford, N. S. Blunt, B. Rogers, T. Noel and M. Saffman, "Demonstration of multi-qubit entanglement and algorithms on a programmable neutral atom quantum computer", arXiv:2112.14589 (2021), https://arxiv.org/abs/2112.14589; published in shortened form as "Multi-qubit entanglement and algorithms on a neutral-atom quantum computer", Nature 604, 457 (2022), DOI 10.1038/s41586-022-04603-6, https://doi.org/10.1038/s41586-022-04603-6
Dolev Bluvstein, Simon J. Evered, Alexandra A. Geim, Sophie H. Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, Marcin Kalinowski, Dominik Hangleiter, J. Pablo Bonilla Ataides, Nishad Maskara, Iris Cong, Xun Gao, Pedro Sales Rodriguez, Thomas Karolyshyn, Giulia Semeghini, Michael J. Gullans, Markus Greiner, Vladan Vuletic and Mikhail D. Lukin, "Logical quantum processor based on reconfigurable atom arrays", Nature 626, 58 (2024), DOI 10.1038/s41586-023-06927-3, https://doi.org/10.1038/s41586-023-06927-3 (preprint arXiv:2312.03982, https://arxiv.org/abs/2312.03982)