Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction

Mohammadsadegh Khazali

doi:10.22331/q-2022-03-03-664

Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction

Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck, Austria

Published:	2022-03-03, volume 6, page 664
Eprint:	arXiv:2101.11412v6
Doi:	https://doi.org/10.22331/q-2022-03-03-664
Citation:	Quantum 6, 664 (2022).

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Abstract

This article proposes the first discrete-time implementation of Rydberg quantum walk in multi-dimensional spatial space that could ideally simulate different classes of topological insulators. Using distance-selective exchange-interaction between Rydberg excited atoms in an atomic-array with dual lattice-constants, the new setup operates both coined and coin-less models of discrete-time quantum walk (DTQW). Here, complicated coupling tessellations are performed by global laser that exclusively excite the site at the anti-blockade region. The long-range interaction provides a new feature of designing different topologically ordered periodic boundary conditions. Limiting the Rydberg population to two excitations, coherent QW over hundreds of lattice sites and steps are achievable with the current technology. These features would improve the performance of this quantum machine in running the quantum search algorithm over topologically ordered databases as well as diversifying the range of topological insulators that could be simulated.

Featured image: Rydberg discrete-time quantum walk (DTQW) scheme. (a) Level scheme: The walker is an $nP$ Rydberg excitation. QW operates by exciting a neighboring lattice site to $nS$ Rydberg state featuring resonant exchange-interaction with the walker. (b) The exchange interaction $V$ forms a site-dependent level shift of $nS$ Rydberg state. Using two lattice constants and tuning the exciting laser's frequency only a desired site get in resonance with the laser and apply quantum walk. (c[d]) By adjusting the laser's detuning to the inter- [intra-] dimer interaction, the desired coupling tessellation $W_0$ [$W_1$] would be formed.

Popular summary

Topological insulators are a new class of quantum materials that insulate in the bulk but exhibit robust topologically protected current-carrying edge states. These materials are challenging to synthesize, and limited in topological phases accessible with solid-state materials. This has motivated the search for topological phases on the systems that simulate the same principles underlying topological insulators. Discrete-time quantum-walk (DTQW) has been proposed for making Floquet topological insulators. The topological properties of these systems are controlled via an external periodic drive rather than an external magnetic field. Topological edge states have been realized exclusively in photonic DTQW with limited sites and steps.

Atomic lattices are the pioneering quantum platform in terms of scalability. An ideal tool to perform complicated quantum operations in an atomic system is provided by the laser-excited Rydberg atoms. This paper proposes the implementation of multiple time-dependent connectivity tessellations in a 3D lattice of dimers that run coined and coinless DTQW. The scheme operates by a simple Rydberg population rotation scheme via a global laser, shining on the lattice. The desired operation is performed via distance-selective spin-exchange interaction between Rydberg atoms in a holographically designed lattice structure. Switching among different coupling tessellations is controlled by tuning the laser’s energy to form a resonant interaction exclusively between the targeted sites. The long-range interaction allows engineering the periodic boundary conditions resulting in DTQW over topological surfaces like torus and Mobius stripe.

Studying a wide range of decoherence sources, the proposed scheme preserves the coherence over hundreds of lattice sites and steps. This major improvement is obtained by suppressing the population of the short-lived Rydberg states to two atoms. Finally, based on the mentioned advances, the paper address different classes of Rydberg Floquet topological insulators with an experimental breakthrough on the scale that these quantum materials could be realized.

► BibTeX data

@article{Khazali2022discretetimequantum,
  doi = {10.22331/q-2022-03-03-664},
  url = {https://doi.org/10.22331/q-2022-03-03-664},
  title = {Discrete-{T}ime {Q}uantum-{W}alk & {F}loquet {T}opological {I}nsulators via {D}istance-{S}elective {R}ydberg-{I}nteraction},
  author = {Khazali, Mohammadsadegh},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {664},
  month = mar,
  year = {2022}
}

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[2] Ceren B. Dag and Aditi Mitra, "Floquet topological systems with flat bands: Edge modes, Berry curvature, and orbital magnetization", Physical Review B 105 24, 245136 (2022).

[3] Andrzej Grudka, Marcin Karczewski, Paweł Kurzyński, Jan Wójcik, and Antoni Wójcik, "Topological invariants in quantum walks", Physical Review A 107 3, 032201 (2023).

[4] Mohammadsadegh Khazali, "All-optical quantum information processing via a single-step Rydberg blockade gate", Optics Express 31 9, 13970 (2023).

[5] Ying Lei, Xi-Wang Luo, and Shaoliang Zhang, "Second-order topological insulator in periodically driven optical lattices", Optics Express 30 13, 24048 (2022).

[6] Aaron W. Young, William J. Eckner, Nathan Schine, Andrew M. Childs, and Adam M. Kaufman, "Tweezer-programmable 2D quantum walks in a Hubbard-regime lattice", Science 377 6608, 885 (2022).

[7] Alberto D. Verga, "Entanglement dynamics and phase transitions of the Floquet cluster spin chain", Physical Review B 107 8, 085116 (2023).

[8] R. Cardman and G. Raithel, "Hyperfine structure of nP1/2 Rydberg states in Rb85", Physical Review A 106 5, 052810 (2022).

[9] Hemlata Bhandari and P. Durganandini, "Long time dynamics of a single-particle extended quantum walk on a one-dimensional lattice with complex hoppings: a generalized hydrodynamic description", Quantum Information Processing 22 1, 43 (2023).

[10] Kai Li, Jiong-Hao Wang, Yan-Bin Yang, and Yong Xu, "Symmetry-Protected Topological Phases in a Rydberg Glass", Physical Review Letters 127 26, 263004 (2021).

[11] Mohammadsadegh Khazali, "Rydberg noisy dressing and applications in making soliton molecules and droplet quasicrystals", Physical Review Research 3 3, L032033 (2021).

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