Fermi gases in the two-dimensional to quasi-two-dimensional crossover

Cheng, Charles Ching-An; Kangara, Jayampathi; Arakelyan, Ilya; Thomas, J. E.

doi:10.1103/physreva.94.031606

Cited by 34 publications

(34 citation statements)

References 48 publications

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“…The 2D system is important, since some of the most interesting physical phenomena, such as high temperature superconductivity [21], Dirac fermions in graphene [22] and topological superconductors [23], nuclear "pasta" phases [24] in neutron stars are two-dimensional in nature. Quantum fluctuations are known to be enhanced in 2D, making it even more important to have quantitative results beyond mean-field approaches.Experiments are just beginning to measure properties in the 2D gas [8,11,13,25,26]. An array of calculations have been performed [16,[27][28][29][30][31], although much less is available in 2D compared to three-dimensional systems.…”

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confidence: 99%

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Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

et al. 2017

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Experiments with ultracold atoms provide a highly controllable laboratory setting with many unique opportunities for precision exploration of quantum many-body phenomena. The nature of such systems, with strong interaction and quantum entanglement, makes reliable theoretical calculations challenging. Especially difficult are excitation and dynamical properties, which are often the most directly relevant to experiment. We carry out exact numerical calculations, by Monte Carlo sampling of imaginary-time propagation of Slater determinants, to compute the pairing gap in the two-dimensional Fermi gas from first principles. Applying state-of-art analytic continuation techniques, we obtain the spectral function, and the density and spin structure factors providing unique tools to visualize the BEC-BCS crossover. These quantities will allow for a direct comparison with experiments.It is truly unusual when, starting from a microscopic Hamiltonian, theory can achieve an exact description of a strongly correlated fermionic system which, at the same time, can be realized in a laboratory with great precision and control. Experiments with ultracold atoms [1,2] have provided a possibility to realize such a scenario. The accuracy that can be reached in experiments with Fermi atomic gases and optical lattices is exceptional, thus offering a unique setting to explore highly correlated quantum fermion systems. In this paper, we demonstrate that, from the theoretical side, advances in computational methods now make it feasible to obtain numerically exact results for not only equilibrium properties, but also excited states. We compute the pairing gap, spectral functions and dynamical response functions in the two-dimensional Fermi gas across the range of interactions, which will allow direct comparisons with spectroscopy or scattering experiments. The dynamical properties provide a powerful tool to probe the behavior of the system and to visualize the crossover from a gas of molecules to a BCS superfluid.We study the Fermi gas with a zero-range attractive interaction, which has generated a great deal of research activity [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The interest of the system is very wide, ranging from condensed matter physics [6,16] to nuclear physics, with possible important applications also in the study of neutron stars [17,18]. This system describes experiments with a collection of atoms, for example 6 Li, which are cooled to degeneracy in an equal mixture of two hyperfine ground states, labeled | ↑ and | ↓ . Feshbach resonances allow the tuning of the interactions by varying an external magnetic field, making the system a unique laboratory to explore many-body physics [19,20]. Starting from a weakly interacting BCS regime, where the attraction between particles induces a pairing similar to the one observed in ordinary superconductors, a crossover is observed as the interaction strength is increased, leading to a BEC regime where the Cooper pairs are tightly bound such that the system behaves as a gas of...

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confidence: 99%

“…Experiments are just beginning to measure properties in the 2D gas [8,11,13,25,26]. An array of calculations have been performed [16,[27][28][29][30][31], although much less is available in 2D compared to three-dimensional systems.…”

mentioning

confidence: 99%

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

et al. 2017

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“…(36) and Eq. (37), are based on the limiting behaviour on each side of the crossover and they each contain 3 parameters that are determined by continuity restrictions. In an effort to include as much of the intermediate polynomial as possible and minimize the overall variance of our fit, we select the matching points as η = −0.25 and η = 2.5.…”

Section: Equation Of Statementioning

confidence: 99%

“…A rich area of study subject to ongoing investigation is that of low dimensionality [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38]. These dilute cold atomic gases have been trapped using anisotropic potentials, resulting in a quasi-2D pancake-shape gas cloud.…”

Section: Introductionmentioning

confidence: 99%

Fermions in Two Dimensions: Scattering and Many-Body Properties

et al. 2017

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Ultracold atomic Fermi gases in two-dimensions (2D) are an increasingly popular topic of research. The interaction strength between spin-up and spindown particles in two-component Fermi gases can be tuned in experiments, allowing for a strongly interacting regime where the gas properties are yet to be fully understood. We have probed this regime for 2D Fermi gases by performing T = 0 ab initio diffusion Monte Carlo (DMC) calculations. The many-body dynamics are largely dependent on the two-body interactions, therefore we start with an in-depth look at scattering theory in 2D. We show the partial-wave expansion and its relation to the scattering length and effective range. Then we discuss our numerical methods for determining these scattering parameters. We close out this discussion by illustrating the details of bound states in 2D. Transitioning to the many-body system, we use variationally optimized wave functions to calculate ground-state properties of the gas over a range of interaction strengths. We show results for the energy per particle and parametrize an equation of state. We then proceed to determine the chemical potential for the strongly interacting gas.

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“…An array of ground state properties in 2D have already been measured, both theoretically and experimentally [7,8,9,10,11,12,13,14,15,16], although much less is available in 2D compared to 3D systems. Exact calculations have been recently achieved using auxiliary-field quantum Monte Carlo (AFQMC) methodologies both for ground state properties [17] and excited states [18].…”

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confidence: 99%

Response Functions for the Two-Dimensional Ultracold Fermi Gas: Dynamical BCS Theory and Beyond

et al. 2017

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Response functions are central objects in physics. They provide crucial information about the behavior of physical systems, and they can be directly compared with scattering experiments involving particles like neutrons, or photons. Calculations of such functions starting from the many-body Hamiltonian of a physical system are challenging, and extremely valuable. In this paper we focus on the two-dimensional (2D) ultracold Fermi atomic gas which has been realized experimentally. We present an application of the dynamical BCS theory to obtain response functions for different regimes of interaction strengths in the 2D gas with zero-range attractive interaction. We also discuss auxiliary-field quantum Monte Carlo (AFQMC) methods for the calculation of imaginary-time correlations in these dilute Fermi gas systems. Illustrative results are given and comparisons are made between AFQMC and dynamical BCS theory results to assess the accuracy of the latter.

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Fermi gases in the two-dimensional to quasi-two-dimensional crossover

Cited by 34 publications

References 48 publications

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

Visualizing the BEC-BCS crossover in a two-dimensional Fermi gas: Pairing gaps and dynamical response functions from ab initio computations

Fermions in Two Dimensions: Scattering and Many-Body Properties

Response Functions for the Two-Dimensional Ultracold Fermi Gas: Dynamical BCS Theory and Beyond

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