# Research

My research focuses on physical aspects of quantum computing and simulation. I enjoy working at the interface between abstract and applied research. Read on to learn more about four areas that particularly excite me.

## Complexity of quantum dynamics

From a physical perspective, a (noiseless) quantum computer is a quantum system evolving under a time-dependent Hamiltonian. The Hamiltonian obeys certain constraints, such as locality, according to the underlying laws of physics. Investigating the complexity of quantum dynamics for a family of physically realistic Hamiltonians can therefore give insight into the power of quantum computers.

This perspective is especially helpful in the context of analogue quantum simulation. To firmly establish a quantum advantage in quantum simulation, it is necessary to map out the regimes in which reproducing the output of a quantum simulator is classically intractable. Together with Álvaro Alhambra, I proved in a recent paper that at short times, many quantities can be computed in polynomial time on a classical computer. I am interested in extending these results to include noise, which may extend the duration for which classical simulation is feasible.

\(t < t^*\) | \(t = O(1)\) | \(t = \mathrm{polylog}(N)\) | \(t = \mathrm{poly}(N)\) | |
---|---|---|---|---|

local observable (additive error) |
P |
P |
? | BQP-complete |

Loschmidt echo (multiplicative error) |
P |
#P-hard | #P-hard | #P-hard |

Loschmidt echo (additive error) |
P |
? | ? | BQP-complete |

*t*. The bold

**P**indicates the polynomial-time algorithm described in a recent paper.

This project received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 101023276.

**DSW**and Álvaro M. Alhambra, “Classical simulation of short-time quantum dynamics,”*arXiv preprint*, arXiv:2210.11490 (2022).

## Adiabatic quantum algorithms

The solution of any quantum computation can be encoded in the ground state of a Hamiltonian. In adiabatic quantum algorithms, this state is prepared starting from the known ground state of a simpler Hamiltonian. The system parameters are then slowly changed until the target Hamiltonian is reached. In the ideal, noiseless case, adiabatic quantum computing is computationally equivalent to the conventional circuit model.

The computational power of adiabatic quantum computing is less clear in the presence of noise. Unlike in the circuit model, there is no known systematic and scalable way to correct errors. Adiabatic algorithms may nevertheless be a powerful tool in the near term owing to their small experimental overhead. Adiabatic evolution also offers a general strategy for constructing heuristic quantum algorithms, which can guide us in the search for new applications of quantum computers.

**DSW**, Dries Sels, Hannes Pichler, Cristian Zanoci, and Mikhail D. Lukin, “Quantum Sampling Algorithms, Phase Transitions, and Computational Complexity,”*Phys. Rev. A*, 104, 032602 (2021), arXiv:2109.03007**DSW**, Dries Sels, Hannes Pichler, Cristian Zanoci, and Mikhail D. Lukin, “Quantum Sampling Algorithms for Near-Term Devices,”*Phys. Rev. Lett.*, 127, 100504 (2021), arXiv:2005.14059.**DSW**, Sarang Gopalakrishnan, Michael Knap, Norman Y. Yao, and Mikhail D. Lukin, “Adiabatic Quantum Search in Open Systems,”*Phys. Rev. Lett.*, 117, 150501 (2016), arXiv:1606.01898.

## Collective phenomena in atom arrays

Ultracold atoms trapped in optical lattices are a leading platform for quantum simulation. The most commonly studied model in this context is the Hubbard model, in which the atoms can hop between different lattice sites and interact when they occupy the same site. I am interested in exploring the fate of such systems when some of the atoms are optically excited. The optical excitations are described by hard-core bosons with long-range hopping via resonant dipole–dipole interactions. The system is inherently dissipative as the excitations can decay through spontaneous emission.

The long-range coupling gives rise to a strong collective response. In joint work with Ephraim Shahmoon, I showed that the collective excitations in atom array lead to perfect reflection at certain resonant frequencies. I am exploring various extension of these results, including the quantum many-body response, topologically nontrivial effects, and the interplay between the optical excitaitons and the motion of the atoms.

- Taylor L. Patti,
**DSW**, Ephraim Shahmoon, Mikhail D. Lukin, and Susanne F. Yelin, “Controlling interactions between quantum emitters using atom arrays,”*Phys. Rev. Lett.*, 126, 223602 (2021), arXiv:2005.03495. - Ephraim Shahmoon,
**DSW**, Mikhail D. Lukin, and Susanne F. Yelin, “Cavity quantum optomechanics with an atom-array membrane,”*arXiv preprint*, arXiv:2006.01973 (2020). - Ephraim Shahmoon,
**DSW**, Mikhail D. Lukin, and Susanne F. Yelin, “Theory of cavity QED with 2D atomic arrays,”*arXiv preprint*, arXiv:2006.01972 (2020). - A. W. Glaetzle, K. Ender,
**DSW**, S. Choi, H. Pichler, M. D. Lukin, and P. Zoller, “Quantum Spin Lenses in Atomic Arrays,”*Phys. Rev. X*, 7, 031049 (2017), arXiv:1704.08837. - Ephraim Shahmoon,
**DSW**, Mikhail D. Lukin, and Susanne F. Yelin, “Cooperative resonances in light scattering from two-dimensional atomic arrays,”*Phys. Rev. Lett.*, 118, 113601 (2017), arXiv:1610.00138.

## (Quantum) optics with 2D semiconductors

Transition metal dichalcogenides (TMDs) are layered materials with a lattice structure similar to graphene. The monolayers of some of these materials, which can be exfoliated or grown directly, are semiconductors with a direct band gap in the optical or near-infrared regime. In clean samples, the optical response is dominated by delocalized excitons.

Excitons in TMDs can often be thought of as a continuum limit of the collective optical excitations in atom arrays described above. Following this analogy, TMDs reflect almost perfectly at the exciton resonance, as demonstrated in an experimental collaboration with the Park lab at Harvard (see figure and reference ). I am interested in developing approaches to control and probe the exciton dynamics by, for instance, designing stacks of TMDs with other layered materials and tailoring the dielectric environment.

*Theory papers*

- Ovidiu Cotlet*,
**DSW***, Mikhail D. Lukin, and Atac Imamoglu, “Rotons in optical excitation spectra of monolayer semiconductors,”*Phys. Rev. B*, 101, 205409 (2020), arXiv:1812.10494. - Johannes Knörzer, Martin J. A. Schuetz, Geza Giedke,
**DSW**, Kristiaan De Greve, Richard Schmidt, Mikhail D. Lukin, and J. Ignacio Cirac, “Wigner Crystals in Two-Dimensional Transition-Metal Dichalcogenides: Spin Physics and Readout,”*Phys. Rev. B*, 101, 125101 (2020), arXiv:1912.11089. **DSW**, Ephraim Shahmoon, Susanne F. Yelin, and Mikhail D. Lukin, “Quantum Nonlinear Optics in Atomically Thin Materials,”*Phys. Rev. Lett.*, 121, 123606 (2018), arXiv:1805.04805.

*Collaborations with experimental groups*

- T. I. Andersen, R. J. Gelly, G. Scuri, B. L. Dwyer,
**DSW**, R. Bekenstein, A. Sushko, J. Sung, Y. Zhou, A. A. Zibrov, X. Liu, A. Y. Joe, K. Watanabe, T. Taniguchi, S. F. Yelin, P. Kim, H. Park, M. D. Lukin, “Beam steering at the nanosecond time scale with an atomically thin reflector,”*Nat. Commun.*13, 3431 (2022), arXiv:2111.04781. - A. Y. Joe, L. A. Jauregui, K. Pistunova, A. M. Mier Valdivia, Z. Lu,
**DSW**, G. Scuri, K. De Greve, R. J. Gelly, Y. Zhou, J. Sung, A. Sushko, T. Taniguchi, K. Watanabe, D. Smirnov, M. D. Lukin, H. Park, P. Kim, “Electrically controlled emission from singlet and triplet exciton species in atomically thin light-emitting diodes,”*Phys. Rev. B*, 103, L161411 (2021), arXiv:2012.04022. - T. I. Andersen, G. Scuri, A. Sushko, K. De Greve, J. Sung, Y. Zhou,
**DSW**, R. J. Gelly, H. Heo, D. Bérubé, A. Y. Joe, L. A. Jauregui, K. Watanabe, T. Taniguchi, P. Kim, H. Park, M. D. Lukin, “Excitons in a reconstructed moiré potential in twisted WSe_{2}/WSe_{2}homobilayers,”*Nat. Mater.*, 20, 480 (2021), arXiv:1912.06955. - J. Sung, Y. Zhou, G. Scuri, V. Zólyomi, T. I. Andersen, H. Yoo,
**DSW**, A. Y. Joe, R. J. Gelly, H. Heo, S. J. Magorrian, D. Bérubé, A. M. Mier Valdivia T. Taniguchi, K. Watanabe, M. D. Lukin, P. Kim, V. I. Fal’ko, H. Park, “Broken mirror symmetry in excitonic response of reconstructed domains in twisted MoSe_{2}/MoSe_{2}bilayers,”*Nat. Nanotechnol.*, 15, 750 (2020), arXiv:2001.01157. - G. Scuri, T. I. Andersen, Y. Zhou,
**DSW**, J. Sung, R. J. Gelly, D. Bérubé, H. Heo, L. Shao, A. Y. Joe, A. Mier Valdivia, T. Taniguchi, K. Watanabe, M. Lončar, P. Kim, M. D. Lukin, H. Park, “Electrically tunable valley dynamics in twisted WSe_{2}/WSe_{2}bilayers,”*Phys. Rev. Lett.*124, 217403 (2020), arXiv:1912.11306. - Y. Zhou, G. Scuri, J. Sung, R. J. Gelly,
**DSW**, K. De Greve, A. Y. Joe, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, H. Park, “Controlling excitons in an atomically thin membrane with a mirror,”*Phys. Rev. Lett.*124, 027401 (2020), arXiv:1901.08500. - L. A. Jauregui, A. Y. Joe, K. Pistunova,
**DSW**, A. A. High, Y. Zhou, G. Scuri, K. De Greve, A. Sushko, C.-H. Yu, T. Taniguchi, K. Watanabe, D. J. Needleman, M. D. Lukin, H. Park, P. Kim, “Electrical control of interlayer exciton dynamics in atomically thin heterostructures,”*Science*366, 870 (2019), arXiv:1812.08691. - A. M. Dibos, Y. Zhou, L. A. Jauregui, G. Scuri,
**DSW**, A. A. High, T. Taniguchi, K. Watanabe, M. D. Lukin, P. Kim, H. Park, “Electrically tunable exciton–plasmon coupling in a WSe_{2}monolayer embedded in a plasmonic crystal cavity,”*Nano Lett.*19, 3543 (2019). - Giovanni Scuri, You Zhou, Alexander A. High,
**DSW**, Chi Shu, Kristiaan De Greve, Luis A. Jauregui, Takashi Taniguchi, Kenji Watanabe, Philip Kim, Mikhail D. Lukin, and Hongkun Park, “Large Excitonic Reflectivity of Monolayer MoSe_{2}Encapsulated in Hexagonal Boron Nitride,”*Phys. Rev. Lett.*, 120, 037402 (2018), arXiv:1705.07245. - You Zhou*, Giovanni Scuri*,
**DSW***, Alexander A. High, Alan Dibos, Luis A. Jauregui, Chi Shu, Kristiaan De Greve, Kateryna Pistunova, Andrew Y. Joe, Takashi Taniguchi, Kenji Watanabe, Philip Kim, Mikhail D. Lukin, and Hongkun Park, “Probing dark excitons in atomically thin semiconductors via near-field coupling to surface plasmon polaritons,”*Nature Nanotech.*, 12, 856 (2017), arXiv:1701.05938. - A. A. High, R. C. Devlin, A. Dibos, M. Polking,
**DSW**, J. Perczel, N. P. de Leon, M. D. Lukin, H. Park, “Visible-frequency hyperbolic metasurface,”*Nature*522, 192 (2015).