Fermi Polarons: from ultracold gases to 2D semiconductors – FermiPolar Workshop 07-18 Feb 2022

Oppong et al. PHYSICAL REVIEW LETTERS 122, 193604 (2019)
Spectral response of a spin-imbalanced Fermi gas across a orbital Feshbach resonance [Adapted from Oppong et al. Physical Review Letters 122, 193604 (2019)].
Smolenski et al. PHYSICAL REVIEW LETTERS 123, 097403 (2019)
Reflectance contrast spectra measured as a function of the gate voltage in a charge-tunable atomically thin valley semiconductor [Adapted from Smolenski et al., Physical Review Letters 123, 097403 (2019)].

Workshop Description

The goal of this workshop is to bring together researchers working on the “Fermi polaron” problem across two different fields: ultracold atom and semiconductor physics. In the semiconductor context, such physics underpins understanding how strong matter-light coupling may change charge transport or even induce superconductivity; in the atomic context they provide an ideal platform to understand how quasiparticles emerge in complex systems.

Even though the phenomenology of the Fermi polaron problem is common to both research fields, because the experimental realisations are very different, there has been so far a limited contact between researchers working in the two areas. A key objective of this workshop is to increase the communication between researchers in these fields, and to promote cross-fertilization between them.

This online workshop will extend over two weeks with around two to three hours of scheduled activities each day. This will include invited talks and discussions, poster sessions, and four panel discussion sessions on specific relevant topics. The format has been designed so as to maximise participation and informal discussion between participants. Seminars, panel and poster sessions will be in two different time blocks (9:00-11:00 UTC and 15:00-17:00 UTC) and will be recorded (available only to workshop attendees) so as to maximise the availability across multiple time zones.


  • Jonathan Keeling (University of St Andrews)
  • Jesper Levinsen (Monash University)
  • Francesca Maria Marchetti (Universidad Autónoma de Madrid & IFIMAC)
  • Meera Parish (Monash University)

Confirmed List of Invited Speakers

Numerical Methods for Trions and Fermi Gases


In the spirit of the workshop, I will present two separate stories about Fermi polaron type problems and associated numerical methods. First, I'll describe our work to simulate trions in low-dimensional semiconductors, such as TMDCs and halide perovskites. Specifically, I'll emphasize the simulation of time-resolved two-dimensional electronic spectroscopies, which provide insights into the relationship between trions and excitons in doped TMDCs. Second, I'll discuss the numerical simulation of spin-imbalanced attractive Fermi gases and argue that coupled-cluster theory is a promising but unexplored technique. The relationship to variational wavefunctions and simpler diagrammatic approaches, like the t-matrix approximation, will be discussed, as well as the numerical performance compared to quantum Monte Carlo.

Undamped Rabi Oscillations due to Polaron-like--emitter Hybrid States in Non-linear Photonic Wave Guide Coupled to Emitters


Structured wave guide that supports two-photon bound states, is investigated. Tuning the energy of the two emitters such that they are in resonance with the two photon bound state energy band, we identify parameter regimes where the system displays fractional populations and essentially undamped Rabi oscillations. The Rabi oscillations, which have no analog in the single-emitter dynamics, are attributed to the existence of a collective polaron like photonic state that is induced by the emitter-photon coupling. The full dynamics is reproduced by a two-state model, in which the polaron interacts with the state |e,e,vacuum> (two emitters in their excited state and empty wave guide) through a Rabi coupling frequency that depends on the emitter separation. Our work demonstrates that emitter-photon coupling can lead to an all-to-all momentum space interaction between two-photon bound states and tunable non-Markovian dynamics, opening up a new direction for emitter arrays coupled to a waveguide. Our theoretical findings apply to a number of experimental platforms and the predictions can be tested with state-of-the-art technology.

Strong photon interactions from weakly interacting particles


We investigate collisions between polaritons and discover a resonant process, which yields interactions that are orders of magnitude larger than the underlying interaction between their matter constituents. This remarkable effect is caused by the light dressing a dimer state formed by two metastable matter excitations so that its energy becomes resonant with the scattering polaritons. We systematically investigate how the resonance can be optimised by changing the parameters of the light coupling scheme so that the damping rate of the metastable dimer state is minimised. While our derivation is based on a concrete atomic setup, the resonance effect is quite general for systems hosting long-lived states dressed by light, and we discuss how it can also be realised in two-dimensional bilayer materials and in cuprous oxides.

Excited Excitons Dressed by Free Carriers in Monolayer WSe2


Following the rich field of atomic physics, an intriguing scenario in condensed matter is the coexistence of bound electron-hole pair states commonly known as excitons with the Fermi sea of free charge carriers. It leads to a number of fascinating phenomena including bound three-particle states known as charged excitons or trions, Fermi polarons, charged biexcitons, renormalization effects and screening, as well as the Mott-transition. Traditionally, the coupling of excitons to free carriers has been studied exclusively for the ground state. In contrast, the access to excited states was often limited either by weak Coulomb interaction or by the presence of disorder. Here, I will discuss experimental demonstration of excited states dressed by continuously tunable Fermi sea in a monolayer semiconductor. Conceptionally, these states are reminiscent of two-electron excitations of the negatively charged hydrogen ion. They are thus inherently subject to autoionization - a unique scattering pathway available for excited states in atomic systems. At sufficiently high carrier densities, however, accessible in the solid state platform, a complete transfer of the oscillator strength to the dressed states occurs. Under such conditions, these many-body complexes can also host transient populations and emit light as non-equilibrium, hot luminescence.

Electron-exciton Interactions in the Exciton-polaron Problem


Recently, it has been demonstrated that the absorption of moderately doped two-dimensional semiconductors can be described in terms of exciton-polarons. In this scenario, attractive and repulsive polaron branches are formed due to interactions between a photo-excited exciton and a Fermi sea of excess charge carriers. These interactions have previously been treated in a phenomenological manner. Here, we present a microscopic derivation of the electron-exciton interactions which utilizes a mixture of variational and perturbative approaches. We find that the interactions feature classical charge-dipole behaviour in the long-range limit and that they are only weakly modified for moderate doping. We apply our theory to the absorption properties and show that the dependence on doping is well captured by a model with a phenomenological contact potential.

1. D.K. Efimkin and A.H. MacDonald, Phys. Rev B 95, 035417 (2017).
2. D.K. Efimkin and A.H. MacDonald, Phys Rev. B 97, 235432 (2018).
3. D.K. Efimkin, E. K. Laird, J. Levinsen, M.M. Parish, A.H. MacDonald, Phys. Rev. B 103, 075417 (2021).

Trions vs. Fermi-polarons: Two Approaches to exciton in Fermi-sea Problem


Strong Coulomb interaction in two-dimensional semiconductors has opened broad prospects to study few- and many-body physics of electronic states. The scenario of an exciton, Coulomb bound electron-hole pair, interacting with a gas of resident electrons and holes is one of the fundamental problems in the field.

There are two theoretical approaches to exciton interaction with resident electrons. In a few-particle approach, one studies trions — bound three-particle states, consisting of two electrons and a hole or two holes and an electron. In a many-body approach, one considers Fermi-polarons that are correlated states of an exciton and a Fermi-sea.

We present the comparison of the two approaches and demonstrate that both trion and Fermi-polaron descriptions yield essentially the same results at sufficiently low resident charge carrier densities. We focus mainly on absorption and luminescence spectra, fine structure, and magnetooptics. We also briefly address the transport properties of excitons, trions, and Fermi-polarons.

A Diagrammatic Monte Carlo Study of The Resonant Fermi Polaron


The Fermi polaron is an exemplary system to study impurity problems, strongly imbalanced Fermi gases and quasiparticle properties. For strong interactions diagrammatic Monte Carlo provides a reliable tool to calculate various properties of the system quantitatively and from first principles. In my talk I will show how diagrammatic Monte Carlo, resummation techniques and numerical analytic continuation can be applied to obtain the spectral function of the resonant Fermi polaron, which can be measured in cold atoms experiments.

Exciton-polarons as Sensors of Strongly Correlated Electrons


Recent experiments have demonstrated that exciton-polarons can be used to probe strongly correlated states of electrons in 2D materials. Examples that will be discussed include Wigner crystals in monolayer semiconductors, fractional quantum Hall states in proximal graphene layers and correlated-Mott states of electrons in a moire superlattice.

Robust Quantum Coherence of Attractive Polarons in MoSe2 monolayers


Here, we study the emergence of attractive and repulsive polarons as the electron doping density in a MoSe2 monolayer increases. Using two-dimensional electronic coherent spectroscopy (2DECS), we discover that a red-shift in the energy of the attractive polaron (AP), suggesting that APs are more energetically favorable than the bound three-body trions. The red-shift continues to a critical doping density where a more pronounced blue-shift occurs. Surprisingly, quantum decoherence of APs (measured via the homogeneous linewidth) remains the same and only increases beyond the critical density. These experimental observations are well explained by a microscopic theory.

Stability and Breakdown of Fermi Polarons in a Strongly Interacting Fermi-Bose mixture


We investigate the properties of a strongly interacting imbalanced mixture of bosonic 41K impurities immersed in a Fermi sea of ultracold 6Li atoms. This enables us to explore the Fermi polaron scenario for large impurity concentrations including the case where they form a Bose-Einstein condensate. We find that the energy of the Fermi polarons formed in the thermal fraction of the impurity cloud remains rather insensitive to the impurity concentration, even as we approach equal densities for both species, in a manner consistent with Landau's quasiparticle theory. The condensed fraction of the bosonic 41K gas is much denser than its thermal component, leading to a break-down of the Fermi polaron description. Instead, we observe a new branch in the radio frequency spectrum with a small energy shift, which is consistent with the presence of Bose polarons formed by 6Li fermions inside the 41K condensate, indicating that we have realized Fermi and Bose polarons, two fundamentally different quasiparticles, in one cloud.

1. Isabella Fritsche, Cosetta Baroni, Erich Dobler, Emil Kirilov, Bo Huang, Rudolf Grimm, Georg M. Bruun, and Pietro Massignan Phys. Rev. A 103, 053314 (2021).

Thermalization of Eexciton-polaritons in 2D TMDCs - Role of Trions


We will discuss our recent work on trion assisted thermalization of exciton-polaritons in 2D transition metal dichalcogenides (TMDCs) embedded in a microcavity. The role of strain and potential traps will also be discussed.

Fermi Polarons in Multiorbital Two-dimensional Quantum Gases


In the last decade, ultracold atoms have emerged as a powerful platform to probe strongly interacting Fermi gases with short-range interactions in a well controlled environment. This has enabled the precise study of the Fermi polaron problem for variable impurity-medium interaction strength as well as different dimensionalities of the medium. While important experiments have recently also realized this quasiparticle in semiconductors, work in the field of ultracold atoms has been focused on alkali atoms and their magnetic Feshbach resonances. In contrast, alkaline-earth(-like) atoms, such as ytterbium, possess a more complex electronic structure with metastable excited states and interorbital interactions. These rich interactions give rise to a novel type of Feshbach resonance, which has been proposed for probing phenomena previously inaccessible to ultracold atoms.

In this talk, I will give an overview of the orbital Feshbach resonance in ytterbium and present our recent observation of Fermi polarons in two-dimensional quantum gases across this resonance. We produce and probe the quasiparticles by optically driving an ultra-narrow transition between the 1S0 ground and the metastable 3P0 excited state. In particular, we reveal an especially small decay rate of the repulsive polaron to lower-lying states in this two-dimensional system. Our findings and similar observations by another research group suggest a modified understanding of the quasiparticle lifetime in the repulsive branch. Finally, we discuss how recent developments in experimental techniques for ytterbium quantum gases pave the way for probing interesting extensions of the Fermi polaron problem.

Fermi Polarons: from cold atoms to electrons


I will present an overview of the Fermi polaron problem and I will discuss how its cold-atom realisation is related to excitons in doped semiconductors.

Excitons, Trions, and Polaritons in Optical Spectra of Two-Dimensional Materials


Transition metal dichalcogenide monolayers are direct bandgap semiconductors with the rich interplay of the valley and spin degrees of freedom. We quantify the role of strong Coulomb interaction, which leads to tightly bound excitons and trions, a quasiparticle composed of two electrons and a hole. We solve the three particle wavefunction for trions, an equation similar to the Bethe-Salpeter Equation for two-particle exciton wavefunction in the basis set of the model Hamiltonian for single particles. This talk will review our results for linear and nonlinear optical properties due to excitons, trions, and polaritons in two-dimensional quantum materials [1-5].

1. Y. V. Zhumagulov, A. Vagov, N. Y. Senkevich, D. R. Gulevich, and V. Perebeinos, Three-particle states and brightening of intervalley excitons in a doped MoS2 monolayer, Physical Review B 101, 245433 (2020).
2. Y. V. Zhumagulov, A. Vagov, D. R. Gulevich, P. E. Faria Junior, and V. Perebeinos, Trion induced photoluminescence of a doped MoS2 monolayer, The Journal of Chemical Physics 153, 044132 (2020).
3. Y. V. Zhumagulov, S. Chiavazzo, D. R. Gulevich, V. Perebeinos, I. A. Shelykh, and O. Kyriienko, Microscopic theory of exciton and trion polaritons in doped monolayers of transition metal dichalcogenides, arXiv:2107.06927 (2021).
4. Y. Zhumagulov, A. Vagov, N. Senkevich, D. Gulevich, and V. Perebeinos, Signatures of trions in the optical spectra of a doped MoS2 monolayer, arXiv:2002.08938 (2020).
5. V. D. Neverov, A. E. Lukyanov, Y. V. Zhumagulov, D. R. Gulevich, Andrey V. Krasavin, A. Vagov, and V. Perebeinos, Nonlinear spectroscopy of excitonic states in transition metal dichalcogenides, arXiv:2109.11633 (2021).

Exciton-Trion Superposition States and Fermi-Polarons in 2D Materials


Starting from first principles, the optical response of 2D materials can be cast into a set of coupled equations for fully connected 2-body and 4-body correlation functions whose solutions are exciton-trion superposition states which turn out to be identical to the Fermi-polaron solutions. We show that exchange-correlation energy favors 4-body bound trion states over conventional 3-body bound trion states. In 2D materials such as WSe2 and WS2 that have a complex conduction band structure, the exciton-trion superposition states become more involved since 4-body trions can come in many different flavors. Using our approach, we obtain radiative and non-radiative recombination rates for these superposition states, as well as relaxation rates between the higher and lower energy superposition states (with electron-hole pair excitation), and these rates agree well with experiments. Our experimental data on exciton-trion polaritons (or Fermi-polaron polaritons) in 2D materials also agrees well with the theory. We discuss unanswered questions related to Fermi-polarons in 2D materials at high doping densities. Dynamical screening and phase-space filling by free carriers at high doping densities can result in no virtual bound 4-body trion states and the Fermi-polaron solutions then describe a pure screening response. The similarities between the polaron problem and the well-studied Kondo problem are used to highlight the role played by multiple electron-hole pair excitations by excitons at high doping densities. Finally, unanswered questions related to polaron transport in current carrying 2D materials are discussed.

Smooth Polaron-Molecule Transition in a Degenerate Fermi Gas with Multiple Impurities


Understanding the behavior of a spin impurity strongly-interacting with a Fermi sea is a long-standing challenge in many-body physics. For short-range interactions and zero temperature, most theories predict a first-order phase transition between a polaronic ground state and a molecular one. We study this question with an ultracold Fermi gas [1]. Experimentally, the impurity problem poses a challenge: the signals from the minority atoms are inherently very weak. To overcome this difficulty, we have developed novel sensitive rf and Raman spectroscopic techniques, which are based on fluorescence detection. Raman spectroscopy allows us to isolate the quasiparticle contribution and extract the polaron energy [2-3]. As the interaction strength is increased, we observe a continuous variation of all observables, in particular a smooth reduction of the quasiparticle weight as it goes to zero beyond the transition point. Our observations are explained by a theoretical model where polaron and molecule quasiparticle states are thermally occupied according to their quantum statistics. At the experimental conditions, polaron states are hence populated even at interactions where the molecule is the ground state and vice versa. The emerging physical picture is thus that of a smooth transition between polarons and molecules and a coexistence of both in the region around the expected transition. A smooth transition happens even at zero temperature, while a true first-order transition occurs only in the single impurity limit.

1. G. Ness et. al., Phys. Rev. X 10, 041019 (2020).
2. C. Shkedrov, Y. Florshaim, G. Ness, A. Gandman, and Y. Sagi, PRL 121, 093402 (2018).
3. C. Shkedrov, G. Ness, Y. Florshaim, and Y. Sagi, PRA 101, 013609(2020).

Polaron Physics with Two-dimensional Materials and Ultracold Atoms


In this talk I will discuss how universality in complex quantum systems can be leveraged to connect the research areas of two-dimensional materials, ultracold atoms, and nanophotonics. The discussion will be particularly focussed on systems where strong coupling between particles in the few-body regime gives rise to new phenomena in the quantum many-body problem. We will argue that a striking example for the synergy of solid state and cold atom research is provided by recently discovered atomically thin two-dimensional semiconductors. The absence of strong dielectric screening in this new class of van-der Waals material leads to the existence of deeply bound excitons that remain robust bosonic quasiparticles even in the presence of substantial electron doping. Based on a quantum chemistry approach to exciton electron scattering we show how exciton-electron mixtures in these materials are remarkably similar to Bose-Fermi mixtures realized in ultracold atoms. By solving the quantum mechanical three-body problem of interacting charge carriers we obtain binding energies of excitons and trions that are in excellent agreement with quantum Monte Carlo predictions. From a calculation of the scattering phase shifts of electrons and excitons we derive an effective low-energy model of exciton electron scattering that can serve as an input to advanced many-body techniques and serves as a theoretical link between 2D semiconductor material and cold atoms. This opens the exciting perspective for the applied quantum simulation of two dimensional materials using the quantum optical tools available in cold atomic systems. We will present results on the study of emergent optical attractive and repulsive polaron resonances and discuss progress towards implementing tunable interactions in transition metal dichalcogenides akin to Feshbach resonances in ultracold atoms.

Giant Effective Zeeman Splitting in a Monolayer Semiconductor Realized by Spin-selective Strong Light-matter Coupling


Strong coupling between light and the fundamental excitations of a two-dimensional electron gas (2DEG) are of foundational importance both to pure physics and to the understanding and development of future photonic nanotechnologies. Here we study the relationship between spin polarization of a 2DEG in a monolayer semiconductor, MoSe2, and light-matter interactions modified by a zero-dimensional optical microcavity [1]. We find robust spin-susceptibility of the 2DEG to simultaneously enhance and suppress trion-polariton formation in opposite photon helicities. This leads to observation of a giant effective valley Zeeman splitting for trion-polaritons (g-factor >20), exceeding the purely trionic splitting by over five times. Going further, we observe robust effective optical non-linearity arising from the highly non linear behavior of the valley-specific strong light-matter coupling regime, and allowing all-optical tuning of the polaritonic Zeeman splitting from 4 to >10 meV. Our experiments lay the groundwork for engineering quantum-Hall-like phases with true unidirectionality in monolayer semiconductors, accompanied by giant effective photonic non-linearities rooted in many-body exciton-electron correlations.

1. T. P. Lyons, D. J. Gillard, C. Leblanc, J. Puebla, D. D. Solnyshkov, L. Klompmaker, I. A. Akimov, C. Louca, P. Muduli, A. Genco, M. Bayer, Y. Otani, G. Malpuech, A. I. Tartakovskii, arXiv:2109.05859 (2021).

Crystalline Correlation Emergent From a Smooth Crossover of Mass-imbalanced Fermi Polarons


In this talk, I will discuss the crystalline correlation emergent from the smooth crossover of mass-imbalanced Fermi polarons in two dimension. Here we have used a unified variational approach up to three particle hole excitations, which allows us to extract the dominant n-body correlations for n ranging from 2 (dimer), 3 (trimer) to 4 (tetramer). We find that in contrast to the equal-mass case, no phase transition exists for the mass-imbalanced Fermi polarons when the fermion-impurity mass ratio is beyond a critical value. Instead, the Fermi polaron undergoes a smooth polaron-trimer or polaron-trimer-tetramer crossover as increasing the fermion-impurity attraction, where the 3- or 4-body correlation gradually emerges and becomes dominant. Interestingly, these few-body correlations manifest themselves in the momentum-space crystallization, i.e., the particle-hole excitations of majority fermions tend to distribute with equal interval near the Fermi surface forming a stable diagonal or triangular structure. Such emergent crystallization can be detected through the density-density correlation of majority fermions. Our results shed light on the intriguing quantum phases in the mass-imbalanced Fermi-Fermi mixtures beyond the pairing superfluid paradigm.

Boiling a Fermi Liquid of Polarons


An impurity “swimming in the Fermi sea” forms the Fermi polaron, a dressed quasi-particle whose properties govern the thermodynamic and transport properties of spin-imbalanced Fermi mixtures. We have studied the thermal evolution of the Fermi polaron in the case of resonant, unitary interactions between the impurity and the bath, measuring the energy, lifetime and short-range correlations. At low temperatures, we observe a characteristic T2 dependence of the spectral width, as expected for a Fermi liquid. At high temperatures, the spectral width of impurity spectra decreases again towards the scattering rate of a classical, unitary Boltzmann gas. In the transition region between the quantum degenerate and classical regime, the spectral width attains its maximum, on the scale of the Fermi energy. A rather abrupt change in the spectral response as a function of temperature in this regime indicates the breakdown of the polaron.

Discussion Topics

Panel sessions invited panelists topics
Panel 1 M. Goldstein – D. Krizhanovskii – O. Kyriienko How might one distinguish between polaron/molecule/trion states? What do we know about polaron interactions and multipolaron complexes?
Panel 2 S. A. Crooker – A. H. MacDonald – D. Snoke What are the consequences of polarons for charge transport and signatures in magnetic fields?
Panel 3 T. Deilmann – M. Rohlfing – M. Semina What can we learn from more "exact" semiconductor calculations – what methods do we need to do them?
Panel 4 A. Bergschneider – F. Chevy  – J. Levinsen What quasiparticle properties – including thermodynamics – can we measure?


Seminars: 40m+20m

Day/Time 09:00 UTC 10:00 UTC 15:00 UTC 16:00 UTC
Monday 7 M. Parish R. Schmidt T. C. Berkelbach
Tuesday 8 A. İmamoğlu G. Bruun X. E. Li
Thursday 10 Y. Sagi Panel 1 V. Menon
Friday 11 A. Tartakovskii M. Zwierlein Panel 2
Monday 14 X. Cui D. Blume N. D. Oppong
Tuesday 15 M. Glazov A. Chernikov V. Perebeinos
Thursday 17 D. Efimkin O. Goulko Panel 3
Friday 18 P. Massignan Panel 4 F. Rana


In order to register for the FermiPolar Workshop, and to submit a poster, please sign up to the following form (the deadline for registration is midnight UTC between the 2nd/3rd February).


We acknowledge the projects 2DEnLight (MICINN) and NanoQuCo-CM (Proyecto Sinérgico CAM), and the Theory of Condensed Matter Department at UAM.

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