Synthetic Magnetic Fields with Interactions and Anyons

This project is funded by Croatian National Science Foundation (www.hrzz.hr).

Summary 

In this project we explore interacting ultracold atomic gases in synthetic magnetic (gauge) fields (SMGF), explore potential experimental
realizations and signatures of anyons (particles with fractional statistics interpolating between bosons and fermions), and analogous
photonic systems. Our team has expertise and experience of research in interacting ultracold atomic gases as well as in optics and photonics;
thus, the design of the project is perfectly suited for our team. The famous fractional quantum Hall (FQH) state emerges in a system of
interacting charged particles in a strong magnetic field, confined in two-dimensions (2D). The richness of FQH state motivates the quest for
novel topological states of matter in interacting bosonic systems. Ultracold atomic gases are ideal playground for a controlled preparation,
manipulation, and detection of quantum many-body states. To achieve topological states (such as the FQH state) in ultracold atomic gases, one
must create a SMGF wherein (neutral) atoms behave as electrons in a magnetic field. Most of the work on SMGF up-to-date was focused on single
particle effects, which provides great motivation for this project. The scientific effort is systematically organized in three workpackages (WP).
In WP1, synthetic gauge/magnetic fields in interacting bosonic systems, all interaction ranges and dimensionalities (1D-3D) are explored. The
objectives are to (i) discovering and exploring novel topological phases and states and (ii) to explore the boundaries and limitations of methods,
suggesting improvements and novel schemes. In WP2, anyons in ultracold atomic gases, the objectives are (i) to explore and propose potential
experimental realization of anyons using ultracold gases, and (ii) to propose and investigate the signatures of anions in these systems (e.g.,
by simulating time-of-flight experiments in 2D). In WP3, we connect our work to synthetic magnetic fields in photonics.

Team

1.      Prof. Hrvoje Buljan, Principal Investigator (PI), Department of Physics, Faculty of Science, University of Zagreb, Bijenička cesta 32, Zagreb, Croatia

2.      Prof. Dario Jukić, Faculty of Civil Engineering, University of Zagreb

3.      Prof. Karlo Lelas, Faculty of Textile Technology, University of Zagreb

4.      Tena Dubček (pHd student), Department of Physics, Faculty of Science

5.      Marija Todorić (pHd student), Department of Physics, Faculty of Science

Publications:

1.  T. Dubček, B. Klajn, R. Pezer, H. Buljan, D. Jukić, Quasimomentum distribution and expansion of an anyonic gas, Phys. Rev. A 97, 011601(R) (2018).

poveznica: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.011601

2. Quantum Hall Effect with composites of magnetic flux tubes and charged particles, M. Todorić, D. Jukić, D. Radić, M. Soljačić, H. Buljan, Phys. Rev. Lett.  120, 267201 (2018).

poveznica: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.267201

3. A. Hudomal, I. Vasić, H. Buljan, and W. Hofstetter, A. Balaž, Dynamics of weakly interacting bosons in optical lattices with flux, Phys. Rev. A 98, 053625 (2018).

poveznica: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.053625

4. Y. Yang, C. Peng, D. Zhu, H. Buljan, J.D. Joannopoulos, B. Zhen, M. Soljačić, Synthesis of non Abelian gauge fields in real space, Science 365, 1021 (2019)

poveznica: https://science.sciencemag.org/content/365/6457/1021/tab-article-info

5. F. Lunić, M. Todorić, B. Klajn, T. Dubček, D. Jukić, H. Buljan, Exact solutions of a model for synthetic anyons in noninteracting systems, Phys. Rev. B 101, 115139 (2020).

poveznica: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.101.115139

6. X. Liu, S. Xia, E. Jajtić, D. Song, D. Li, L. Tang, D. Leykam, J. Xu, H. Buljan, Z. Chen, Universal momentum-to-real space mapping of topological singularities, Nature Communications 11, 1586 (2020).

poveznica: https://www.nature.com/articles/s41467-020-15374-x

7. M. Todorić, B. Klajn, D. Jukić, H. Buljan, Berry phase for a Bose gas on a one-dimensional ring, submitted

poveznica: https://arxiv.org/abs/2003.02625

8. K. Lelas, O. Čelan, D. Prelogović, H. Buljan, D. Jukić, Modulation instability in a nonlinear Schrodinger equation with a synthetic magnetic field, submitted

poveznica: https://arxiv.org/abs/2003.12620

9. S. Xia, D. Jukić, N. Wang, D. Smirnova, L. Smirnov, L. Tang, D. Song, A. Szameit, D. Leykam, J. Xu, Z. Chen, and H. Buljan, Nonlinear coupling of light into a defect: the interplay of nonlinearity and topology, submitted

poveznica: https://arxiv.org/abs/2005.13848

In Croatian only:

Sažetak:

U ovom projektu istražujemo međudjelujuće ultrahladne atomske plinove u sintetičkim magnetskim (baždarnim) poljima (SMGF od eng. Synthetic
Magnetic/Gauge Field), moguće eksperimentalne realizacije anyona (čestica s necjelobrojnom statistikom koja interpolira između statistike za bozone
i fermione), te analogne fotoničke sustave. Naš tim ima višegodišnje iskustvo istraživanja međudjelujućih ultrahladnih atomskih plinova i
fotoničkih sustava, što se izvrsno uklapa u tematiku projekta. Čuveno necjelobrojno kvantno Hallovo (FQH) stanje pojavljuje se u sustavu
međudjelujućih nabijenih čestica u jakom magnetskom polju, zatočenim u dvije dimenzije (2D). Anyoni su dosad eksperimentalno realizirani kao
kvazičestice višečestičnih pobuđenja samo u tom sustavu. Bogatstvo FQH stanja motivira potragu za novim (topološkim) stanjima tvari u
međudjelujućim bozonskim sustavima. Ultrahladni atomski plinovi su idealan poligon za kontroliranu pripremu, manipulaciju i detekciju kvantnih
višečestičnih stanja. Kako bi ostvarili topološka stanja (analogna FQH stanju) u ultrahladnim atomskim plinovima, potrebno je stvoriti SMGF u
kojem će se (neutralni) atomi ponašati kao elektroni u magnetskom polju. Većina radova o SMGF dosad bila je fokusirana na jednočestične efekte, što
nas motivira za ovo istraživanje. Znanstveni dio projekta organiziran je u tri radna paketa (WP od eng. Work Package). U WP1 istražujemo SMGF u
međudjelujućim bozonskim sustavima, za sve raspone međudjelovanja i dimenzionalnosti (1D-3D). Ciljevi su dvostruki: (i) otkrivanje i
istraživanje novih topoloških faza i stanja. Na primjer, jako korelirana 1D osnovna i pobuđena stanja u diskretnim rešetkama s kompleksnim
parametrima preskoka (oponašaju SMGF), s idejom da nađemo 1D analogon FQH stanja i necjelobrojna pobuđenja. (ii) Istraživanje granica samih metoda,
sugerirajući poboljšanja i nove sheme. U WP2, anyoni u ultrahladnim atomskim plinovima, ciljevi su (i) istražiti i predložiti moguće
eksperimentalne realizacije anyona koristeći ultrahladne plinove, te (ii) predložiti i proučiti potpise anyona u tim sustavima (npr. simulirajući
time-of-flight eksperimente u 2D). U WP3, veza s optičkim sustavima, planiramo istražiti nove pojave u nelinearnim optičkim sustavima kroz
analogiju sa spomenutim međudjelujućim bozonskim sustavima. Uz našu stručnost u oba polja, izvršenjem ovog projekta možemo dati dodanu
vrijednost u oba područja. Primjerice, istraživanjem natjecanja između modulacijske nestabilnosti i stvaranja vrtloga u SMGF, te traženjem nove
vrste optičkog vlakna baziranog na SMGF. Konačno, zadnji radni paket (WP4) posvećen je upravljanju i diseminaciji.