# Strongly Interacting Bose Polarons in Two-Dimensional Atomic Gases and Quantum Fluids of Polaritons

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## Abstract

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## 1. Introduction

## 2. The Polaron in a Two-Dimensional Atomic Bose–Einstein Condensate

#### 2.1. System

#### 2.2. Quasiparticle Properties

#### 2.3. Zero-Momentum Properties

## 3. The Polaron in a Bose–Einstein Condensate of Polaritons

#### 3.1. System

#### 3.2. Quasiparticle Properties

## 4. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Landau, L.; Pekar, S. Effective mass of a polaron. J. Exp. Theor. Phys.
**1948**, 18, 419–423. [Google Scholar] - Pekar, S. Theory of electromagnetic waves in a crystal with excitons. J. Phys. Chem. Solids
**1958**, 5, 11–22. [Google Scholar] [CrossRef] - Schirotzek, A.; Wu, C.H.; Sommer, A.; Zwierlein, M.W. Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms. Phys. Rev. Lett.
**2009**, 102, 230402. [Google Scholar] [CrossRef] - Kohstall, C.; Zaccanti, M.; Jag, M.; Trenkwalder, A.; Massignan, P.; Bruun, G.M.; Schreck, F.; Grimm, R. Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture. Nature
**2012**, 485, 615–618. [Google Scholar] [CrossRef] - Koschorreck, M.; Pertot, D.; Vogt, E.; Fröhlich, B.; Feld, M.; Köhl, M. Attractive and repulsive Fermi polarons in two dimensions. Nature
**2012**, 485, 619–622. [Google Scholar] [CrossRef] - Zhang, Y.; Ong, W.; Arakelyan, I.; Thomas, J. Polaron-to-polaron transitions in the radio-frequency spectrum of a quasi-two-dimensional Fermi gas. Phys. Rev. Lett.
**2012**, 108, 235302. [Google Scholar] [CrossRef] - Cetina, M.; Jag, M.; Lous, R.S.; Walraven, J.T.; Grimm, R.; Christensen, R.S.; Bruun, G.M. Decoherence of impurities in a fermi sea of ultracold atoms. Phys. Rev. Lett.
**2015**, 115, 135302. [Google Scholar] [CrossRef] - Massignan, P.; Zaccanti, M.; Bruun, G.M. Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases. Rep. Prog. Phys.
**2014**, 77, 034401. [Google Scholar] [CrossRef] - Levinsen, J.; Parish, M.M. Strongly interacting two-dimensional Fermi gases. Annu. Rev. Cold Atoms Mol.
**2015**, 3, 1–75. [Google Scholar] - Cetina, M.; Jag, M.; Lous, R.S.; Fritsche, I.; Walraven, J.T.; Grimm, R.; Levinsen, J.; Parish, M.M.; Schmidt, R.; Knap, M.; et al. Ultrafast many-body interferometry of impurities coupled to a Fermi sea. Science
**2016**, 354, 96–99. [Google Scholar] [CrossRef] - Scazza, F.; Valtolina, G.; Massignan, P.; Recati, A.; Amico, A.; Burchianti, A.; Fort, C.; Inguscio, M.; Zaccanti, M.; Roati, G. Repulsive Fermi polarons in a resonant mixture of ultracold Li 6 atoms. Phys. Rev. Lett.
**2017**, 118, 083602. [Google Scholar] [CrossRef] - Adlong, H.S.; Liu, W.E.; Scazza, F.; Zaccanti, M.; Oppong, N.D.; Fölling, S.; Parish, M.M.; Levinsen, J. Quasiparticle lifetime of the repulsive Fermi polaron. Phys. Rev. Lett.
**2020**, 125, 133401. [Google Scholar] [CrossRef] - Fritsche, I.; Baroni, C.; Dobler, E.; Kirilov, E.; Huang, B.; Grimm, R.; Bruun, G.M.; Massignan, P. Stability and breakdown of Fermi polarons in a strongly interacting Fermi–Bose mixture. Phys. Rev. A
**2021**, 103, 053314. [Google Scholar] [CrossRef] - Scazza, F.; Zaccanti, M.; Massignan, P.; Parish, M.M.; Levinsen, J. Repulsive Fermi and Bose Polarons in Quantum Gases. Atoms
**2022**, 10, 55. [Google Scholar] [CrossRef] - Hu, M.G.; Van de Graaff, M.J.; Kedar, D.; Corson, J.P.; Cornell, E.A.; Jin, D.S. Bose polarons in the strongly interacting regime. Phys. Rev. Lett.
**2016**, 117, 055301. [Google Scholar] [CrossRef] - Jørgensen, N.B.; Wacker, L.; Skalmstang, K.T.; Parish, M.M.; Levinsen, J.; Christensen, R.S.; Bruun, G.M.; Arlt, J.J. Observation of attractive and repulsive polarons in a Bose–Einstein condensate. Phys. Rev. Lett.
**2016**, 117, 055302. [Google Scholar] [CrossRef] - Ardila, L.P.; Jørgensen, N.; Pohl, T.; Giorgini, S.; Bruun, G.; Arlt, J. Analyzing a Bose polaron across resonant interactions. Phys. Rev. A
**2019**, 99, 063607. [Google Scholar] [CrossRef] - Skou, M.G.; Skov, T.G.; Jørgensen, N.B.; Nielsen, K.K.; Camacho-Guardian, A.; Pohl, T.; Bruun, G.M.; Arlt, J.J. Non-equilibrium quantum dynamics and formation of the Bose polaron. Nat. Phys.
**2021**, 17, 731–735. [Google Scholar] [CrossRef] - Yan, Z.Z.; Ni, Y.; Robens, C.; Zwierlein, M.W. Bose polarons near quantum criticality. Science
**2020**, 368, 190–194. [Google Scholar] [CrossRef] - Li, W.; Sarma, S.D. Variational study of polarons in Bose–Einstein condensates. Phys. Rev. A
**2014**, 90, 013618. [Google Scholar] [CrossRef] - Christensen, R.S.; Levinsen, J.; Bruun, G.M. Quasiparticle Properties of a Mobile Impurity in a Bose–Einstein Condensate. Phys. Rev. Lett.
**2015**, 115, 160401. [Google Scholar] [CrossRef] [PubMed] - Shchadilova, Y.E.; Schmidt, R.; Grusdt, F.; Demler, E. Quantum Dynamics of Ultracold Bose Polarons. Phys. Rev. Lett.
**2016**, 117, 113002. [Google Scholar] [CrossRef] [PubMed] - Levinsen, J.; Parish, M.M.; Christensen, R.S.; Arlt, J.J.; Bruun, G.M. Finite-temperature behavior of the Bose polaron. Phys. Rev. A
**2017**, 96, 063622. [Google Scholar] [CrossRef] - Guenther, N.E.; Massignan, P.; Lewenstein, M.; Bruun, G.M. Bose polarons at finite temperature and strong coupling. Phys. Rev. Lett.
**2018**, 120, 050405. [Google Scholar] [CrossRef] [PubMed] - Rath, S.P.; Schmidt, R. Field-theoretical study of the Bose polaron. Phys. Rev. A
**2013**, 88, 053632. [Google Scholar] [CrossRef] - Field, B.; Levinsen, J.; Parish, M.M. Fate of the Bose polaron at finite temperature. Phys. Rev. A
**2020**, 101, 013623. [Google Scholar] [CrossRef] - Ardila, L.P.; Giorgini, S. Impurity in a Bose–Einstein condensate: Study of the attractive and repulsive branch using quantum Monte Carlo methods. Phys. Rev. A
**2015**, 92, 033612. [Google Scholar] [CrossRef] - Grusdt, F.; Seetharam, K.; Shchadilova, Y.; Demler, E. Strong-coupling Bose polarons out of equilibrium: Dynamical renormalization-group approach. Phys. Rev. A
**2018**, 97, 033612. [Google Scholar] [CrossRef] - Drescher, M.; Salmhofer, M.; Enss, T. Theory of a resonantly interacting impurity in a Bose–Einstein condensate. Phys. Rev. Res.
**2020**, 2, 032011. [Google Scholar] [CrossRef] - Massignan, P.; Yegovtsev, N.; Gurarie, V. Universal Aspects of a Strongly Interacting Impurity in a Dilute Bose Condensate. Phys. Rev. Lett.
**2021**, 126, 123403. [Google Scholar] [CrossRef] - Guenther, N.E.; Schmidt, R.; Bruun, G.M.; Gurarie, V.; Massignan, P. Mobile impurity in a Bose–Einstein condensate and the orthogonality catastrophe. Phys. Rev. A
**2021**, 103, 013317. [Google Scholar] [CrossRef] - Christianen, A.; Cirac, J.I.; Schmidt, R. Chemistry of a Light Impurity in a Bose–Einstein Condensate. Phys. Rev. Lett.
**2022**, 128, 183401. [Google Scholar] [CrossRef] [PubMed] - Christianen, A.; Cirac, J.I.; Schmidt, R. Bose polaron and the Efimov effect: A Gaussian-state approach. Phys. Rev. A
**2022**, 105, 053302. [Google Scholar] [CrossRef] - Yegovtsev, N.; Massignan, P.; Gurarie, V. Strongly interacting impurities in a dilute Bose condensate. Phys. Rev. A
**2022**, 106, 033305. [Google Scholar] [CrossRef] - Naidon, P. Two Impurities in a Bose–Einstein Condensate: From Yukawa to Efimov Attracted Polarons. J. Phys. Soc. Jpn.
**2018**, 87, 043002. [Google Scholar] [CrossRef] - Dehkharghani, A.S.; Volosniev, A.G.; Zinner, N.T. Coalescence of Two Impurities in a Trapped One-dimensional Bose Gas. Phys. Rev. Lett.
**2018**, 121, 080405. [Google Scholar] [CrossRef] - Camacho-Guardian, A.; Peña Ardila, L.A.; Pohl, T.; Bruun, G.M. Bipolarons in a Bose–Einstein Condensate. Phys. Rev. Lett.
**2018**, 121, 013401. [Google Scholar] [CrossRef] - Camacho-Guardian, A.; Bruun, G.M. Landau Effective Interaction between Quasiparticles in a Bose–Einstein Condensate. Phys. Rev. X
**2018**, 8, 031042. [Google Scholar] [CrossRef] - Huber, D.; Hammer, H.W.; Volosniev, A.G. In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas. Phys. Rev. Res.
**2019**, 1, 033177. [Google Scholar] [CrossRef] - Deng, F.L.; Shi, T.; Yi, S. Effective interactions between two impurities in quasi-two-dimensional dipolar Bose–Einstein condensates. Commun. Theor. Phys.
**2020**, 72, 075501. [Google Scholar] [CrossRef] - Mukherjee, K.; Mistakidis, S.I.; Majumder, S.; Schmelcher, P. Induced interactions and quench dynamics of bosonic impurities immersed in a Fermi sea. Phys. Rev. A
**2020**, 102, 053317. [Google Scholar] [CrossRef] - Mistakidis, S.I.; Koutentakis, G.M.; Katsimiga, G.C.; Busch, T.; Schmelcher, P. Many-body quantum dynamics and induced correlations of Bose polarons. New J. Phys.
**2020**, 22, 043007. [Google Scholar] [CrossRef] - Will, M.; Astrakharchik, G.E.; Fleischhauer, M. Polaron Interactions and Bipolarons in One-Dimensional Bose Gases in the Strong Coupling Regime. Phys. Rev. Lett.
**2021**, 127, 103401. [Google Scholar] [CrossRef] - Keiler, K.; Mistakidis, S.I.; Schmelcher, P. Polarons and their induced interactions in highly imbalanced triple mixtures. Phys. Rev. A
**2021**, 104, L031301. [Google Scholar] [CrossRef] - Theel, F.; Mistakidis, S.I.; Keiler, K.; Schmelcher, P. Counterflow dynamics of two correlated impurities immersed in a bosonic gas. Phys. Rev. A
**2022**, 105, 053314. [Google Scholar] [CrossRef] - Ardila, L.A.P. Ultra-Dilute Gas of Polarons in a Bose–Einstein Condensate. Atoms
**2022**, 10, 29. [Google Scholar] [CrossRef] - Ardila, L.A.P.; Pohl, T. Ground-state properties of dipolar Bose polarons. J. Phys. B At. Mol. Opt. Phys.
**2018**, 52, 015004. [Google Scholar] [CrossRef] - Astrakharchik, G.E.; Ardila, L.A.P.; Schmidt, R.; Jachymski, K.; Negretti, A. Ionic polaron in a Bose–Einstein condensate. Commun. Phys.
**2021**, 4, 94. [Google Scholar] [CrossRef] - Christensen, E.R.; Camacho-Guardian, A.; Bruun, G.M. Charged Polarons and Molecules in a Bose–Einstein Condensate. Phys. Rev. Lett.
**2021**, 126, 243001. [Google Scholar] [CrossRef] - Ding, S.; Drewsen, M.; Arlt, J.J.; Bruun, G.M. Mediated interactions between ions in quantum degenerate gases. arXiv
**2022**, arXiv:2203.02768. [Google Scholar] [CrossRef] - Astrakharchik, G.E.; Peña Ardila, L.A.; Jachymski, K.; Negretti, A. Charged impurities in a Bose–Einstein condensate: Many-body bound states and induced interactions. arXiv
**2022**, arXiv:2206.03476. [Google Scholar] - Ardila, L.A.P. Monte Carlo methods for impurity physics in ultracold Bose quantum gases. Nat. Rev. Phys.
**2022**, 4, 214. [Google Scholar] [CrossRef] - Hopfield, J.J. Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals. Phys. Rev.
**1958**, 112, 1555–1567. [Google Scholar] [CrossRef] - Amo, A.; Lefrère, J.; Pigeon, S.; Adrados, C.; Ciuti, C.; Carusotto, I.; Houdré, R.; Giacobino, E.; Bramati, A. Superfluidity of polaritons in semiconductor microcavities. Nat. Phys.
**2009**, 5, 805–810. [Google Scholar] [CrossRef] - Deng, H.; Haug, H.; Yamamoto, Y. Exciton-polariton Bose–Einstein condensation. Rev. Mod. Phys.
**2010**, 82, 1489–1537. [Google Scholar] [CrossRef] - Daskalakis, K.S.; Maier, S.A.; Murray, R.; Kéna-Cohen, S. Nonlinear interactions in an organic polariton condensate. Nat. Mater.
**2014**, 13, 271–278. [Google Scholar] [CrossRef] - Lagoudakis, K.G.; Wouters, M.; Richard, M.; Baas, A.; Carusotto, I.; André, R.; Dang, L.S.; Deveaud-Plédran, B. Quantized vortices in an exciton–polariton condensate. Nat. Phys.
**2008**, 4, 706–710. [Google Scholar] [CrossRef] - Sanvitto, D.; Marchetti, F.M.; Szymańska, M.H.; Tosi, G.; Baudisch, M.; Laussy, F.P.; Krizhanovskii, D.N.; Skolnick, M.S.; Marrucci, L.; Lemaître, A.; et al. Persistent currents and quantized vortices in a polariton superfluid. Nat. Phys.
**2010**, 6, 527–533. [Google Scholar] [CrossRef] - Rubo, Y.G. Half Vortices in Exciton Polariton Condensates. Phys. Rev. Lett.
**2007**, 99, 106401. [Google Scholar] [CrossRef] - Lagoudakis, K.G.; Ostatnický, T.; Kavokin, A.V.; Rubo, Y.G.; André, R.; Deveaud-Plédran, B. Observation of Half-Quantum Vortices in an Exciton-Polariton Condensate. Science
**2009**, 326, 974–976. [Google Scholar] [CrossRef] - Takemura, N.; Trebaol, S.; Wouters, M.; Portella-Oberli, M.T.; Deveaud, B. Polaritonic Feshbach resonance. Nat. Phys.
**2014**, 10, 500–504. [Google Scholar] [CrossRef] - Wasak, T.; Schmidt, R.; Piazza, F. Quantum-Zeno Fermi polaron in the strong dissipation limit. Phys. Rev. Res.
**2021**, 3, 013086. [Google Scholar] [CrossRef] - Tan, L.B.; Cotlet, O.; Bergschneider, A.; Schmidt, R.; Back, P.; Shimazaki, Y.; Kroner, M.; İmamoğlu, A.M.C. Interacting Polaron-Polaritons. Phys. Rev. X
**2020**, 10, 021011. [Google Scholar] [CrossRef] - Bastarrachea-Magnani, M.A.; Camacho-Guardian, A.; Bruun, G.M. Attractive and Repulsive Exciton-Polariton Interactions Mediated by an Electron Gas. Phys. Rev. Lett.
**2021**, 126, 127405. [Google Scholar] [CrossRef] - Bastarrachea-Magnani, M.A.; Thomsen, J.; Camacho-Guardian, A.; Bruun, G.M. Polaritons in an Electron Gas Quasiparticles and Landau Effective Interactions. Atoms
**2021**, 9, 81. [Google Scholar] [CrossRef] - Muir, J.B.; Levinsen, J.; Earl, S.K.; Conway, M.A.; Cole, J.H.; Wurdack, M.; Mishra, R.; David, J.; Estrecho, E.; Lu, Y.; et al. Exciton-polaron interactions in monolayer WS _2. arXiv
**2022**, arXiv:2206.12007. [Google Scholar] - Sidler, M.; Back, P.; Cotlet, O.; Srivastava, A.; Fink, T.; Kroner, M.; Demler, E.; Imamoglu, A. Fermi polaron-polaritons in charge-tunable atomically thin semiconductors. Nat. Phys.
**2017**, 13, 255–261. [Google Scholar] [CrossRef] - Efimkin, D.K.; MacDonald, A.H. Exciton-polarons in doped semiconductors in a strong magnetic field. Phys. Rev. B
**2018**, 97, 235432. [Google Scholar] [CrossRef] - Efimkin, D.K.; MacDonald, A.H. Many-body theory of trion absorption features in two-dimensional semiconductors. Phys. Rev. B
**2017**, 95, 035417. [Google Scholar] [CrossRef] - Efimkin, D.K.; Laird, E.K.; Levinsen, J.; Parish, M.M.; MacDonald, A.H. Electron-exciton interactions in the exciton-polaron problem. Phys. Rev. B
**2021**, 103, 075417. [Google Scholar] [CrossRef] - Goldstein, T.; Wu, Y.C.; Chen, S.Y.; Taniguchi, T.; Watanabe, K.; Varga, K.; Yan, J. Ground and excited state exciton polarons in monolayer MoSe2. J. Chem. Phys.
**2020**, 153, 071101. [Google Scholar] [CrossRef] [PubMed] - Ravets, S.; Knüppel, P.; Faelt, S.; Cotlet, O.; Kroner, M.; Wegscheider, W.; Imamoglu, A. Polaron polaritons in the integer and fractional quantum Hall regimes. Phys. Rev. Lett.
**2018**, 120, 057401. [Google Scholar] [CrossRef] [PubMed] - Cotlet, O.; Wild, D.S.; Lukin, M.D.; Imamoglu, A. Rotons in optical excitation spectra of monolayer semiconductors. Phys. Rev. B
**2020**, 101, 205409. [Google Scholar] [CrossRef] - Imamoglu, A.; Cotlet, O.; Schmidt, R. Exciton–polarons in two-dimensional semiconductors and the Tavis–Cummings model. Comptes Rendus. Phys.
**2021**, 22, 1–8. [Google Scholar] [CrossRef] - Cotleţ, O.; Pientka, F.; Schmidt, R.; Zarand, G.; Demler, E.; Imamoglu, A. Transport of neutral optical excitations using electric fields. Phys. Rev. X
**2019**, 9, 041019. [Google Scholar] [CrossRef] - Rana, F.; Koksal, O.; Manolatou, C. Many-body theory of the optical conductivity of excitons and trions in two-dimensional materials. Phys. Rev. B
**2020**, 102, 085304. [Google Scholar] [CrossRef] - Pimenov, D.; von Delft, J.; Glazman, L.; Goldstein, M. Fermi-edge exciton-polaritons in doped semiconductor microcavities with finite hole mass. Phys. Rev. B
**2017**, 96, 155310. [Google Scholar] [CrossRef] - Shahnazaryan, V.; Kozin, V.; Shelykh, I.; Iorsh, I.; Kyriienko, O. Tunable optical nonlinearity for transition metal dichalcogenide polaritons dressed by a Fermi sea. Phys. Rev. B
**2020**, 102, 115310. [Google Scholar] [CrossRef] - Grusdt, F.; Fleischhauer, M. Tunable Polarons of Slow-Light Polaritons in a Two-Dimensional Bose–Einstein Condensate. Phys. Rev. Lett.
**2016**, 116, 053602. [Google Scholar] [CrossRef] - Levinsen, J.; Marchetti, F.M.; Keeling, J.; Parish, M.M. Spectroscopic Signatures of Quantum Many-Body Correlations in Polariton Microcavities. Phys. Rev. Lett.
**2019**, 123, 266401. [Google Scholar] [CrossRef] - Navadeh-Toupchi, M.; Takemura, N.; Anderson, M.D.; Oberli, D.Y.; Portella-Oberli, M.T. Polaritonic Cross Feshbach Resonance. Phys. Rev. Lett.
**2019**, 122, 047402. [Google Scholar] [CrossRef] [PubMed] - Bastarrachea-Magnani, M.A.; Camacho-Guardian, A.; Wouters, M.; Bruun, G.M. Strong interactions and biexcitons in a polariton mixture. Phys. Rev. B
**2019**, 100, 195301. [Google Scholar] [CrossRef] - Camacho-Guardian, A.; Nielsen, K.K.; Pohl, T.; Bruun, G.M. Polariton dynamics in strongly interacting quantum many-body systems. Phys. Rev. Res.
**2020**, 2, 023102. [Google Scholar] [CrossRef] - Camacho-Guardian, A.; Bastarrachea-Magnani, M.A.; Bruun, G.M. Mediated Interactions and Photon Bound States in an Exciton-Polariton Mixture. Phys. Rev. Lett.
**2021**, 126, 017401. [Google Scholar] [CrossRef] [PubMed] - Vashisht, A.; Richard, M.; Minguzzi, A. Bose polaron in a quantum fluid of light. SciPost Phys.
**2022**, 12, 008. [Google Scholar] [CrossRef] - Hryhorchak, O.; Panochko, G.; Pastukhov, V. Mean-field study of repulsive 2D and 3D Bose polarons. J. Phys. B At. Mol. Opt. Phys.
**2020**, 53, 205302. [Google Scholar] [CrossRef] - Casteels, W.; Tempere, J.; Devreese, J.T. Polaronic properties of an impurity in a Bose–Einstein condensate in reduced dimensions. Phys. Rev. A
**2012**, 86, 043614. [Google Scholar] [CrossRef] - Pastukhov, V. Polaron in dilute 2D Bose gas at low temperatures. J. Phys. B: At. Mol. Opt. Phys.
**2018**, 51, 155203. [Google Scholar] [CrossRef] - Ardila, L.A.P.n.; Astrakharchik, G.E.; Giorgini, S. Strong coupling Bose polarons in a two-dimensional gas. Phys. Rev. Res.
**2020**, 2, 023405. [Google Scholar] [CrossRef] - Ding, S.; Domínguez-Castro, G.A.; Julku, A.; Camacho-Guardian, A.; Bruun, G.M. Polarons and bipolarons in a two-dimensional square lattice. arXiv
**2022**, arXiv:2212.00890. [Google Scholar] - Shelykh, I.A.; Taylor, T.; Kavokin, A.V. Rotons in a Hybrid Bose–Fermi System. Phys. Rev. Lett.
**2010**, 105, 140402. [Google Scholar] [CrossRef] [PubMed] - Matuszewski, M.; Taylor, T.; Kavokin, A.V. Exciton Supersolidity in Hybrid Bose–Fermi Systems. Phys. Rev. Lett.
**2012**, 108, 060401. [Google Scholar] [CrossRef] - Laussy, F.P.; Kavokin, A.V.; Shelykh, I.A. Exciton-Polariton Mediated Superconductivity. Phys. Rev. Lett.
**2010**, 104, 106402. [Google Scholar] [CrossRef] [PubMed] - Cotleţ, O.; Zeytinoǧlu, S.; Sigrist, M.; Demler, E.; Imamoǧlu, A.m.c. Superconductivity and other collective phenomena in a hybrid Bose–Fermi mixture formed by a polariton condensate and an electron system in two dimensions. Phys. Rev. B
**2016**, 93, 054510. [Google Scholar] [CrossRef] - Julku, A.; Kinnunen, J.J.; Camacho-Guardian, A.; Bruun, G.M. Light-induced topological superconductivity in transition metal dichalcogenide monolayers. arXiv
**2022**, arXiv:2204.12229. [Google Scholar] [CrossRef] - Chin, C.; Grimm, R.; Julienne, P.; Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys.
**2010**, 82, 1225–1286. [Google Scholar] [CrossRef] - Fetter, A.; Walecka, J. Quantum Theory of Many-Particle Systems; Dover Books on Physics Series; Dover Publications: Mineola, NY, USA, 1971. [Google Scholar]
- Sun, M.; Zhai, H.; Cui, X. Visualizing the Efimov Correlation in Bose Polarons. Phys. Rev. Lett.
**2017**, 119, 013401. [Google Scholar] [CrossRef] - Sun, M.; Cui, X. Enhancing the Efimov correlation in Bose polarons with large mass imbalance. Phys. Rev. A
**2017**, 96, 022707. [Google Scholar] [CrossRef] - Levinsen, J.; Ardila, L.A.P.n.; Yoshida, S.M.; Parish, M.M. Quantum Behavior of a Heavy Impurity Strongly Coupled to a Bose Gas. Phys. Rev. Lett.
**2021**, 127, 033401. [Google Scholar] [CrossRef] - Wouters, M. Resonant polariton-polariton scattering in semiconductor microcavities. Phys. Rev. B
**2007**, 76, 045319. [Google Scholar] [CrossRef] - Schaibley, J.R.; Yu, H.; Clark, G.; Rivera, P.; Ross, J.S.; Seyler, K.L.; Yao, W.; Xu, X. Valleytronics in 2D materials. Nat. Rev. Mater.
**2016**, 1, 1–15. [Google Scholar] [CrossRef] - Xu, X.; Yao, W.; Xiao, D.; Heinz, T.F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys.
**2014**, 10, 343–350. [Google Scholar] [CrossRef] - García Jomaso, Y.A.; Vargas, B.; Ley Dominguez, D.; Ordoñez-Romero, C.L.; Lara-García, H.A.; Camacho-Guardian, A.; Pirruccio, G. The Fate of the Upper Polariton: Breakdown of the Quasiparticle Picture in the Continuum. arXiv
**2022**, arXiv:2209.13698. [Google Scholar] - Carusotto, I.; Ciuti, C. Quantum fluids of light. Rev. Mod. Phys.
**2013**, 85, 299–366. [Google Scholar] [CrossRef] - Fujii, K.; Hongo, M.; Enss, T. Universal van der Waals force between heavy polarons in superfluids. arXiv
**2022**, arXiv:2206.01048. [Google Scholar] [CrossRef] [PubMed] - Nielsen, K.K.; Ardila, L.A.P.; Bruun, G.M.; Pohl, T. Critical slowdown of non-equilibrium polaron dynamics. New J. Phys.
**2019**, 21, 043014. [Google Scholar] [CrossRef] - Seetharam, K.; Shchadilova, Y.; Grusdt, F.; Zvonarev, M.B.; Demler, E. Dynamical Quantum Cherenkov Transition of Fast Impurities in Quantum Liquids. Phys. Rev. Lett.
**2021**, 127, 185302. [Google Scholar] [CrossRef] - Drescher, M.; Salmhofer, M.; Enss, T. Quench Dynamics of the Ideal Bose Polaron at Zero and Nonzero Temperatures. Phys. Rev. A
**2021**, 103, 033317. [Google Scholar] [CrossRef]

**Figure 1.**Spectral function ${A}_{T}(0,\omega )$ for $\alpha =2$ (red) and $\alpha =0.5$ (black). Spectral function ${A}_{T}(0,\omega )$ in logarithmic scale (inset). The main peak corresponds to the bound state, whereas a continuum of excitations appear for $\omega >0$.

**Figure 2.**(

**a**) Spectral function of a two-dimensional impurity at zero momentum as a function of $\omega $ and $\alpha $. The coherent excitations (quasiparticle) are situated at the narrow maxima of the spectral function (red regions), whereas the incoherent parts of the spectral function correspond to the white regions at positive energies. (

**b**) Spectral function for fixed $\alpha =2$ (red), $\alpha =0.5$ (black) and for $\alpha =-2$ (blue) and varying $\omega $.

**Figure 3.**Zero-momentum quasiparticle properties of the two-dimensional polaron: (

**a**) Energy ${E}_{\mathbf{k}=0}$, (

**b**) Quasiparticle residue ${Z}_{\mathbf{k}=0}$, (

**c**) Effective mass ${m}_{\mathbf{k}=0}^{*}/m$ and (

**d**) Damping rate of the polaron. The red lines correspond to the repulsive branch, whereas the black lines depict the attractive polaron. System parameters are as in Figure 1.

**Figure 4.**(

**Left**) Relevant band structure. Exciton–polaritons are created by the coupling between cavity photons with left circular polarization ↓ and excitons in valley $-K$. Itinerant electrons form a spin-polarized 2DEG in valley $+K$. (

**Right**) Bogoliubov spectrum of exciton–polaritons as a function of $k/{k}_{n}$ for $\mathsf{\Omega}/{E}_{n}=0.75$ and $\delta /{E}_{n}=0$ (solid red) and $\delta /{E}_{n}=-1$ (solid blue). The dashed lines represent the parabolic dispersion of the exciton shifted by ${\Delta}_{LP}=-(\delta -\sqrt{{\delta}^{2}+4\mathsf{\Omega}})/2$.

**Figure 5.**Spectral function for zero-momentum electrons as a function of the cavity detuning $\delta $ and $\omega $ for $\mathsf{\Omega}/{E}_{n}=0.75,$ a coupling strength given by the binding energy $\mathsf{\Omega}/|{\u03f5}_{B}|=1,$ and assuming non-interacting excitons ${g}_{xx}=0$.

**Figure 6.**Quasiparticle energy and residue for zero-momentum electrons in the polariton BEC. (

**a**) Energy of the attractive (black) and repulsive polaron (red). (

**b**) Residue for the attractive (black) and repulsive polaron (red). The system parameters are as in Figure 5.

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**MDPI and ACS Style**

Cárdenas-Castillo, L.F.; Camacho-Guardian, A.
Strongly Interacting Bose Polarons in Two-Dimensional Atomic Gases and Quantum Fluids of Polaritons. *Atoms* **2023**, *11*, 3.
https://doi.org/10.3390/atoms11010003

**AMA Style**

Cárdenas-Castillo LF, Camacho-Guardian A.
Strongly Interacting Bose Polarons in Two-Dimensional Atomic Gases and Quantum Fluids of Polaritons. *Atoms*. 2023; 11(1):3.
https://doi.org/10.3390/atoms11010003

**Chicago/Turabian Style**

Cárdenas-Castillo, Luis Fernando, and Arturo Camacho-Guardian.
2023. "Strongly Interacting Bose Polarons in Two-Dimensional Atomic Gases and Quantum Fluids of Polaritons" *Atoms* 11, no. 1: 3.
https://doi.org/10.3390/atoms11010003