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arXiv:1307.5390 · Physical Review A

Low-dimensional pairing fluctuations and pseudogapped photoemission spectrum in a trapped two-dimensional Fermi gas

Ryota Watanabe, Shunji Tsuchiya, Yoji Ohashi

Published Jul 29, 2013• 29 citations
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Abstract

We investigate strong-coupling properties of a trapped two-dimensional normal Fermi gas. Within the framework of a combined $T$-matrix theory with the local density approximation, we calculate the local density of states, as well as the photoemission spectrum, to see how two-dimensional pairing fluctuations affect these single-particle quantities. In the BCS (Bardeen-Cooper-Schrieffer)--BEC (Bose-Einstein condensation) crossover region, we show that the local density of states exhibits a dip structure in the trap center, which is more remarkable than the three-dimensional case. This pseudogap phenomenon is found to naturally lead to a double-peak structure in the photoemission spectrum. The peak-to-peak energy of the spectrum at $p=0$ agrees well with a recent experiment on a two-dimensional ${}^{40}\mathrm{K}$ Fermi gas [Feld et al., Nature 480, 75 (2011)]. Since pairing fluctuations are sensitive to the dimensionality of a system, our results would be useful for the study of many-body physics in the BCS-BEC crossover regime of a two-dimensional Fermi gas.

DOI
10.1103/physreva.88.013637

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We investigate strong-coupling properties of a trapped two-dimensional normal Fermi gas. Within the framework of a combined TTT-matrix theory with the local density approximation, we calculate the local density of states, as well as the photoemission spectrum, to see how two-dimensional pairing fluctuations affect these single-particle quantities. In the BCS (Bardeen-Cooper-Schrieffer)--BEC (Bose-Einstein condensation) crossover region, we show that the local density of states exhibits a dip structure in the trap center, which is more remarkable than the three-dimensional case. This pseudogap phenomenon is found to naturally lead to a double-peak structure in the photoemission spectrum. The peak-to-peak energy of the spectrum at p=0p=0p=0 agrees well with a recent experiment on a two-dimensional 40K{}^{40}\mathrm{K}40K Fermi gas [Feld et al., Nature 480, 75 (2011)]. Since pairing fluctuations are sensitive to the dimensionality of a system, our results would be useful for the study of many-body physics in the BCS-BEC crossover regime of a two-dimensional Fermi gas.
We theoretically investigate excitation properties in the pseudogap regime of a trapped Fermi gas. Using a combined TTT-matrix theory with the local density approximation, we calculate strong-coupling corrections to single-particle local density of states (LDOS), as well as the single-particle local spectral weight (LSW). Starting from the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, we clarify how the pseudogap structures in these quantities disappear with increasing the temperature. As in the case of a uniform Fermi gas, LDOS and LSW give different pseudogap temperatures T∗{T}^{*}T∗ and T∗∗{T}^{**}T∗∗ at which the pseudogap structures in these quantities completely disappear. Determining T∗{T}^{*}T∗ and T∗∗{T}^{**}T∗∗ over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, we identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also show that the so-called back-bending peak recently observed in the photoemission spectra by the JILA group may be explained as an effect of pseudogap phenomenon in the trap center. Since strong pairing fluctuations, spatial inhomogeneity, and finite temperatures are important keys in considering real cold Fermi gases, our results would be useful for clarifying normal-state properties of this strongly interacting Fermi system.
We investigate the photoemission-type spectrum in a cold Fermi gas which was recently measured by the JILA group [Stewart et al., Nature (London) 454, 744 (2008)]. This quantity gives us very useful information about single-particle properties in the BCS-BEC crossover. In this paper, including pairing fluctuations within a TTT-matrix theory, as well as effects of a harmonic trap within the local density approximation, we show that spatially inhomogeneous pairing fluctuations due to the trap potential are an important key to understanding the observed spectrum. In the crossover region, while strong pairing fluctuations lead to the so-called pseudogap phenomenon in the trap center, such strong-coupling effects are found to be weak around the edge of the gas. Our results including this effect are shown to agree well with the recent photoemission data of the JILA group.
We theoretically investigate the recent photoemission-type experiment on 40^{40}40K Fermi gases done by JILA group. Including pairing fluctuations within a strong-coupling TTT-matrix theory, as well as effects of a harmonic trap within the local density approximation, we calculate photoemission spectra in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that the energy resolution of the current photoemission experiment is enough to detect the pseudogap phenomenon. We also show how the pseudogap in single-particle excitations continuously changes into the superfluid gap, as one decreases the temperature below the superfluid phase transition temperature. Our results would be useful for the study of single-particle properties of ultracold Fermi gases in the BCS-BEC crossover.
We theoretically investigate single-particle excitations in the BCS-BEC-crossover regime of an ultracold Fermi gas. Including strong pairing fluctuations within a TTT-matrix approximation, as well as effects of a harmonic trap potential in the local-density approximation, we calculate the local photoemission spectrum in the normal state. Recently, the JILA group measured this quantity in a 40K^{40}\mathrm{K}40K Fermi gas in order to examine homogeneous single-particle properties of this system. Comparing our results with this experiment, we show that this attempt indeed succeeds under JILA's experimental condition. However, we also find that the current local photoemission spectroscopy still has room for improvement in order to examine the pseudogap phenomenon predicted in the BCS-BEC-crossover region. Since ultracold Fermi gases are always in a trap, our results would be useful in applying this system to various homogeneous Fermi systems as a quantum simulator.
We theoretically investigate the recent photoemission-type experiment on40K Fermi gases done by JILA group. Including pairing fluctuations within a strong-coupling T-matrix theory, as well as effects of a harmonic trap within the local density approximation, we calculate photoemission spectra in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that the energy resolution of the current photoemission experiment is enough to detect the pseudogap phenomenon. We also show how the pseudogap in single-particle excitations continuously changes into the superfluid gap, as one decreases the temperature below the superfluid phase transition temperature. Our results would be useful for the study of single-particle properties of ultracold Fermi gases in the BCS-BEC crossover.
We investigate strong pairing fluctuations and effects of a harmonic trap in the superfluid phase of an ultracold Fermi gas. Including amplitude and phase fluctuations of the inhomogeneous superfluid order parameter $\ensuremath{\Delta}(r)$ in a trap within a combined TTT-matrix theory with the local density approximation, we examine local properties of single-particle excitations and a thermodynamic quantity in the BCS-BEC crossover region. Below the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, we show that inhomogeneous pairing fluctuations lead to a shell structure of the gas cloud in which the spatial region where the ordinary BCS-type superfluid density of states appears surrounded by the region where the pseudogap associated with strong pairing fluctuations dominates single-particle excitations. The former spatial region enlarges to eventually cover the whole gas cloud far below Tc{T}_{\mathrm{c}}Tc​. We also examine how this shell structure affects the photoemission spectrum, as well as the local pressure. Since a cold Fermi gas is always trapped in a harmonic potential, our results would be useful for the study of strong-coupling superfluid physics, including this realistic situation.