High-polarization limit of the quasi-two-dimensional Fermi gas

Levinsen, Jesper; Baur, Stefan K.

doi:10.1103/physreva.86.041602

Cited by 22 publications

(35 citation statements)

References 32 publications

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“…Experimentally, the 2D regime can be accomplished by means of a transverse trapping potential V (z) = 1 2 mω 2 z z 2 (here, ω z is the frequency and z is the transverse direction) that fulfills the condition k B T F ω z (T is the temperature and F is the Fermi energy of the FS). When excitations in the z dimension are possible, one reaches the so-called quasi-2D regime [12,13]. The purely 2D limit is reached for F / ω z → 0 and will be the subject of this paper.…”

Section: Introductionmentioning

confidence: 99%

Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions

2014

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We study the properties of the two-dimensional Fermi polaron model in which an impurity attractively interacts with a Fermi sea of particles in the zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which allows us to sample a Feynman diagrammatic series to very high order. The convergence properties of the series and the role of multiple particle-hole excitations are discussed. We study the polaron and molecule energy as a function of the coupling strength, revealing a transition from a polaron to a molecule in the ground state. We find a value for the critical interaction strength which complies with the experimentally measured one and predictions from variational methods. For all considered interaction strengths, the polaron Z factor from the full diagrammatic series almost coincides with the one-particle-hole result. We also formally link the DiagMC and the variational approaches for the polaron problem at hand.

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Section: Introductionmentioning

confidence: 99%

Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions

2014

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“…The two-body binding energy E B must be adjusted to reflect the quasi-two-dimensional nature of our model. It is the solution of the following equation 21 :…”

Section: Modelmentioning

confidence: 99%

Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi polarons

Kroiß

Pollet

2014

Phys. Rev. B

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We apply a diagrammatic Monte Carlo method to the problem of an impurity interacting resonantly with a homogeneous Fermi bath for a quasi-two-dimensional setup. Notwithstanding the series divergence, we can show numerically that the three particle-hole diagrammatic contributions are not contributing significantly to the final answer, thus demonstrating a nearly perfect destructive interference of contributions in subspaces with higher-order particle-hole lines. Consequently, for strong enough confinement in the third direction, the transition between the polaron and the molecule ground state is found to be in good agreement with the pure two-dimensional case and agrees very well with the one found by the wave-function approach in the two-particle-hole subspace.

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“…For the strong coupling region, η < 1, the experimental uncertainty increases dramatically and there seem to be non-universal systematic effects in the experimental realization that need to be corrected (see for example Ref. [34]). …”

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confidence: 99%

Ab initioLattice Results for Fermi Polarons in Two Dimensions

Bour¹,

Lee

Hammer

et al. 2015

Phys. Rev. Lett.

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We investigate the attractive Fermi polaron problem in two dimensions using non-perturbative Monte Carlo simulations. We introduce a new Monte Carlo algorithm called the impurity lattice Monte Carlo method. This algorithm samples the path integral in a computationally efficient manner and has only small sign oscillations for systems with a single impurity. As a benchmark of the method, we calculate the universal polaron energy in three dimensions in the scale-invariant unitarity limit and find agreement with published results. We then present the first fully non-perturbative calculations of the polaron energy in two dimensions and density correlations between the impurity and majority particles in the limit of zero range interactions. We find evidence for a smooth crossover transition from fermionic quasiparticle to molecular state as a function of interaction strength.PACS numbers: 67.85. Lm, 02.70.Ss, One of the most interesting and fundamental problems in quantum many-body physics is the polaron problem, where a mobile impurity interacts with a bath of particles. With the advent of trapped ultracold atomic gases, the polaron problem can now be realized for both bosonic and fermionic baths, and also in the universal limit where the range of the particle interactions are negligible [1]. In a fermionic medium, the impurity can undergo a transition and change its quantum statistics by binding fermions from the surrounding Fermi gas [2,3]. The impurity is dressed by fluctuations of the Fermi sea forming a quasiparticle or polaron state. But with increasing particle interaction strength, molecules will form by capturing one or even two particles from the Fermi sea, and this behavior has been shown to depend on the mass ratio of the two components of the Fermi gas for the 3D case [2][3][4][5][6][7][8][9][10]. In 1D, the exact analytical solution for equal masses shows that the polaron-molecule transition is a smooth crossover [11,12].In 2D the Fermi polaron properties have been studied using different theoretical and experimental approaches, and these have predicted various scenarios for the existence or absence of a polaron-molecule transition [13][14][15][16][17][18][19][20][21]. The Fermi polaron system has been studied using diagrammatic Monte Carlo (diag MC) [20,21]. The diag MC method uses a worm algorithm to stochastically sample Feynman diagrams to high orders in the coupling constant. In this work we introduce a non-perturbative ab initio approach called impurity lattice Monte Carlo (ILMC) [22] to investigate highlyimbalanced Fermi gases. Unlike diag MC, impurity lattice Monte Carlo directly samples the path integral and so is a fully non-perturbative calculation. We present calculations for the energy of the 2D polaron and density correlations between the impurity and majority particles as a function of interaction strength. Our results show evidence for a smooth crossover from polaron to molecule.Impurity lattice Monte Carlo method. The impurity lattice Monte Carlo method is a hybrid of two Monte Carlo al...

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High-polarization limit of the quasi-two-dimensional Fermi gas

Cited by 22 publications

References 32 publications

Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions

Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions

Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi polarons

Ab initioLattice Results for Fermi Polarons in Two Dimensions

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