We consider a Fermi gas with short-range attractive interactions that is confined along one direction by a tight harmonic potential. For this quasi-two-dimensional (quasi-2D) Fermi gas, we compute the pressure equation of state, radiofrequency spectrum, and the superfluid critical temperature ${T}_{c}$ using a mean-field theory that accounts for all the energy levels of the harmonic confinement. Our calculation for ${T}_{c}$ provides a natural generalization of the Thouless criterion to the quasi-2D geometry, and it correctly reduces to the 3D expression derived from the local density approximation in the limit where the confinement frequency ${\ensuremath{\omega}}_{z}\ensuremath{\rightarrow}0$. Furthermore, our results suggest that ${T}_{c}$ can be enhanced by relaxing the confinement and perturbing away from the 2D limit.We consider a Fermi gas with short-range attractive interactions that is confined along one direction by a tight harmonic potential. For this quasi-two-dimensional (quasi-2D) Fermi gas, we compute the pressure equation of state, radiofrequency spectrum, and the superfluid critical temperature ${T}_{c}$ using a mean-field theory that accounts for all the energy levels of the harmonic confinement. Our calculation for ${T}_{c}$ provides a natural generalization of the Thouless criterion to the quasi-2D geometry, and it correctly reduces to the 3D expression derived from the local density approximation in the limit where the confinement frequency ${\ensuremath{\omega}}_{z}\ensuremath{\rightarrow}0$. Furthermore, our results suggest that ${T}_{c}$ can be enhanced by relaxing the confinement and perturbing away from the 2D limit.

arXiv:1408.0476Physical Review BDec 1, 201419 citations

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

Chingyun Cheng, Jayampathi Kangara, Ilya Arakelyan +1 more

We smoothly tune the dimensionality of pancake-shaped $^{6}\mathrm{Li}$ Fermi gas clouds from quasi-two-dimensional to two-dimensional (2D) to measure radio-frequency spectra and cloud profiles in both regimes. In the quasi-2D case, where ${E}_{F}/h{\ensuremath{\nu}}_{z}\ensuremath{\simeq}1$, with ${E}_{F}$ the Fermi energy and $h{\ensuremath{\nu}}_{z}$ the harmonic oscillator energy in the tightly confined direction, we confirm that the radio-frequency spectra strongly disagree with 2D mean-field theory. Then we tune to the 2D regime, ${E}_{F}<<h{\ensuremath{\nu}}_{z}$, where the measured radio-frequency spectra are in very good agreement with 2D mean-field theory. Nevertheless, the measured cloud profiles strongly disagree, confirming predictions that a beyond mean-field approach is required throughout the 2D to quasi-2D crossover.We smoothly tune the dimensionality of pancake-shaped $^{6}\mathrm{Li}$ Fermi gas clouds from quasi-two-dimensional to two-dimensional (2D) to measure radio-frequency spectra and cloud profiles in both regimes. In the quasi-2D case, where ${E}_{F}/h{\ensuremath{\nu}}_{z}\ensuremath{\simeq}1$, with ${E}_{F}$ the Fermi energy and $h{\ensuremath{\nu}}_{z}$ the harmonic oscillator energy in the tightly confined direction, we confirm that the radio-frequency spectra strongly disagree with 2D mean-field theory. Then we tune to the 2D regime, ${E}_{F}<<h{\ensuremath{\nu}}_{z}$, where the measured radio-frequency spectra are in very good agreement with 2D mean-field theory. Nevertheless, the measured cloud profiles strongly disagree, confirming predictions that a beyond mean-field approach is required throughout the 2D to quasi-2D crossover.

arXiv:1604.06063Physical Review ASep 30, 201626 citations

{T}_{c}

using a mean-field theory that accounts for all the energy levels of the harmonic confinement. Our calculation for

{T}_{c}

provides a natural generalization of the Thouless criterion to the quasi-2D geometry, and it correctly reduces to the 3D expression derived from the local density approximation in the limit where the confinement frequency ${\ensuremath{\omega}}_{z}\ensuremath{\rightarrow}0$. Furthermore, our results suggest that

{T}_{c}

can be enhanced by relaxing the confinement and perturbing away from the 2D limit.

We smoothly tune the dimensionality of pancake-shaped

^{6}\mathrm{Li}

Fermi gas clouds from quasi-two-dimensional to two-dimensional (2D) to measure radio-frequency spectra and cloud profiles in both regimes. In the quasi-2D case, where ${E}_{F}/h{\ensuremath{\nu}}_{z}\ensuremath{\simeq}1$, with

{E}_{F}

the Fermi energy and $h{\ensuremath{\nu}}_{z}$ the harmonic oscillator energy in the tightly confined direction, we confirm that the radio-frequency spectra strongly disagree with 2D mean-field theory. Then we tune to the 2D regime, ${E}_{F}<<h{\ensuremath{\nu}}_{z}$, where the measured radio-frequency spectra are in very good agreement with 2D mean-field theory. Nevertheless, the measured cloud profiles strongly disagree, confirming predictions that a beyond mean-field approach is required throughout the 2D to quasi-2D crossover.