We theoretically study the thermodynamic properties of a strongly interacting Fermi gas at the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC), by applying a recently outlined strong-coupling theory that includes pair fluctuations beyond the commonly-used many-body $T$ -matrix or ladder approximation at the Gaussian level. The beyond Gaussian pair fluctuation (GPF) theory always respects the exact thermodynamic relations and recovers the Bogoliubov theory of molecules in the BEC limit with a nearly correct molecule-molecule scattering length. We show that the beyond-GPF theory predicts quantitatively accurate ground-state properties at the BEC-BCS crossover, in good agreement with the recent measurement by Horikoshi et al. in Phys. Rev. X 7, 041004 (2017). In the unitary limit with infinitely large $s$ -wave scattering length, the beyond-GPF theory predicts a reliable universal energy equation of state up to 0.6 $T_c$ , where $T_c$ is the superfluid transition temperature at unitarity. The theory predicts a Bertsch parameter $\xi \simeq 0.365$ at zero temperature, in good agreement with the latest quantum Monte Carlo result $\xi = 0.367(7)$ and the latest experimental measurement $\xi = 0.367(9)$ . We attribute the excellent and wide applicability of the beyond-GPF theory in the broken-symmetry phase at sufficiently low temperatures to the empirically useful partial re-summation of Feynman diagrams following a dimensional $\epsilon$ -expansion analysis near four dimensions ( $d=4-\epsilon$ ), which gives rise to accurate predictions at the second order $\mathcal{O}(\epsilon^2)$ . Our work indicates the possibility of further improving the strong-coupling theory of strongly interacting fermions based on the systematic inclusion of large-loop Feynman diagrams at higher orders $\mathcal{O}(\epsilon^n)$ with $n\ge 3$ .We theoretically study the thermodynamic properties of a strongly interacting Fermi gas at the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC), by applying a recently outlined strong-coupling theory that includes pair fluctuations beyond the commonly-used many-body $$T$$ -matrix or ladder approximation at the Gaussian level. The beyond Gaussian pair fluctuation (GPF) theory always respects the exact thermodynamic relations and recovers the Bogoliubov theory of molecules in the BEC limit with a nearly correct molecule-molecule scattering length. We show that the beyond-GPF theory predicts quantitatively accurate ground-state properties at the BEC-BCS crossover, in good agreement with the recent measurement by Horikoshi et al. in Phys. Rev. X 7, 041004 (2017). In the unitary limit with infinitely large $$s$$ -wave scattering length, the beyond-GPF theory predicts a reliable universal energy equation of state up to 0.6 $$T_c$$ , where $$T_c$$ is the superfluid transition temperature at unitarity. The theory predicts a Bertsch parameter $$\xi \simeq 0.365$$ at zero temperature, in good agreement with the latest quantum Monte Carlo result $$\xi = 0.367(7)$$ and the latest experimental measurement $$\xi = 0.367(9)$$ . We attribute the excellent and wide applicability of the beyond-GPF theory in the broken-symmetry phase at sufficiently low temperatures to the empirically useful partial re-summation of Feynman diagrams following a dimensional $$\epsilon$$ -expansion analysis near four dimensions ( $$d=4-\epsilon$$ ), which gives rise to accurate predictions at the second order $$\mathcal{O}(\epsilon^2)$$ . Our work indicates the possibility of further improving the strong-coupling theory of strongly interacting fermions based on the systematic inclusion of large-loop Feynman diagrams at higher orders $$\mathcal{O}(\epsilon^n)$$ with $$n\ge 3$$ .

arXiv:2201.04798AAPPS bulletinAug 25, 20262 citations

Foundations

Bruce Cameron Reed

Springer eBooksJan 1, 20220 citations

Beyond-mean-field phases of rotating dipolar condensates in the strongly correlated regime

Paolo Molignini

Rotating dipolar Bose-Einstein condensates exhibit rich physics due to the interplay of long-range interactions and rotation, leading to unconventional vortex structures and strongly correlated phases. While most studies rely on mean-field approaches, these fail to capture quantum correlations that become significant at high rotation speeds and strong interactions. In this study, we go beyond the mean-field description by employing a numerically exact multiconfigurational approach to study finite-sized dipolar condensates. We reveal novel vortex structures, rotating cluster states, and strong fragmentation effects, demonstrating that beyond-mean-field correlations remain prominent even in larger systems. By quantifying deviations from mean-field theory, we provide a predictive framework for analyzing experiments and exploring emergent quantum phases, with implications for both the fundamental theory of ultracold gases and the quantum simulation of correlated superfluid systems like in neutron stars.Rotating dipolar Bose-Einstein condensates exhibit rich physics due to the interplay of long-range interactions and rotation, leading to unconventional vortex structures and strongly correlated phases. While most studies rely on mean-field approaches, these fail to capture quantum correlations that become significant at high rotation speeds and strong interactions. In this study, we go beyond the mean-field description by employing a numerically exact multiconfigurational approach to study finite-sized dipolar condensates. We reveal novel vortex structures, rotating cluster states, and strong fragmentation effects, demonstrating that beyond-mean-field correlations remain prominent even in larger systems. By quantifying deviations from mean-field theory, we provide a predictive framework for analyzing experiments and exploring emergent quantum phases, with implications for both the fundamental theory of ultracold gases and the quantum simulation of correlated superfluid systems like in neutron stars.

arXiv:2503.04890Journal of Physics Condensed MatterOct 6, 20252 citations

Large mechanical squeezing beyond 3dB of hybrid atom-optomechanical systems in a highly unresolved sideband regime

Jian-Song Zhang, Aixi Chen

We propose a scheme for the generation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in the highly unresolved sideband (HURSB) regime where the decay rate of cavity is much larger than the frequency of the mechanical oscillator. The system is formed by two two-level atomic ensembles and an optomechanical system with cavity driven by two lasers with different amplitudes. In the HURSB regime, the squeezing of the movable mirror can not be larger than 3dB if no atomic ensemble or only one atomic ensemble is put into the optomechanical system. However, if two atomic ensembles are put into the optomechanical system, the strong mechanical squeezing beyond 3dB is achieved even in the HURSB regime. Our scheme paves the way toward the implementation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in experiments.We propose a scheme for the generation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in the highly unresolved sideband (HURSB) regime where the decay rate of cavity is much larger than the frequency of the mechanical oscillator. The system is formed by two two-level atomic ensembles and an optomechanical system with cavity driven by two lasers with different amplitudes. In the HURSB regime, the squeezing of the movable mirror can not be larger than 3dB if no atomic ensemble or only one atomic ensemble is put into the optomechanical system. However, if two atomic ensembles are put into the optomechanical system, the strong mechanical squeezing beyond 3dB is achieved even in the HURSB regime. Our scheme paves the way toward the implementation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in experiments.

arXiv:2004.08768Optics ExpressApr 10, 202022 citations

Beyond Understanding

Physics WorldApr 1, 20000 citations

T

-matrix or ladder approximation at the Gaussian level. The beyond Gaussian pair fluctuation (GPF) theory always respects the exact thermodynamic relations and recovers the Bogoliubov theory of molecules in the BEC limit with a nearly correct molecule-molecule scattering length. We show that the beyond-GPF theory predicts quantitatively accurate ground-state properties at the BEC-BCS crossover, in good agreement with the recent measurement by Horikoshi et al. in Phys. Rev. X 7, 041004 (2017). In the unitary limit with infinitely large

s

-wave scattering length, the beyond-GPF theory predicts a reliable universal energy equation of state up to 0.6

T_c

, where

T_c

is the superfluid transition temperature at unitarity. The theory predicts a Bertsch parameter

\xi \simeq 0.365

at zero temperature, in good agreement with the latest quantum Monte Carlo result

\xi = 0.367(7)

and the latest experimental measurement

\xi = 0.367(9)

. We attribute the excellent and wide applicability of the beyond-GPF theory in the broken-symmetry phase at sufficiently low temperatures to the empirically useful partial re-summation of Feynman diagrams following a dimensional

\epsilon

-expansion analysis near four dimensions (

d=4-\epsilon

), which gives rise to accurate predictions at the second order

\mathcal{O}(\epsilon^2)

. Our work indicates the possibility of further improving the strong-coupling theory of strongly interacting fermions based on the systematic inclusion of large-loop Feynman diagrams at higher orders

\mathcal{O}(\epsilon^n)

with

n\ge 3