Thermal liquid-gas phase transition in a quasi-one-dimensional dipolar Fermi gas

TL;DR

This work addresses the finite-temperature thermodynamics of a quasi-one-dimensional, single-component dipolar Fermi gas and demonstrates a thermal liquid-gas phase transition within the Hartree-Fock framework. By self-consistently computing the self-energy $\Sigma_k^{\rm HF}$ and the pressure $P$ from the grand potential, the authors map the phase diagram in the $P$-$n$ and $T$-$n$ planes, identifying a flashing point $T_f$ and a critical point $T_c$ that delimit the coexistence region and the spinodal instability. The results reveal how the self-bound liquid state forms at $T=0$ for sufficiently strong attraction (characterized by $\alpha\ell_{dd}/\ell_\perp \gtrsim 1.8$) and persist at finite temperature with clear similarities to nuclear-matter equations of state, including approximate linear relations between $T_c$ and $T_f$ and between $n_c$ and $n_f$, consistent with phenomenological models. The study highlights the importance of the density-dependent effective mass $m^*(n)$ in the thermal equation of state and suggests that this system can serve as an analog quantum simulator for nuclear matter and a testbed for beyond-mean-field theories.

Abstract

We theoretically investigate thermodynamic properties in a quasi-one-dimensional single-component dipolar Fermi gas at finite temperatures. The self-bound fermionic droplet can be achieved by exchange correlations with the long-range dipole-dipole interactions under the quasi-one-dimensional confinement, where the interaction can be tuned by tilting the dipoles along the system coordinate. Using the Hartree-Fock approximation, we show how the liquid-gas phase transition occurs in this system, and elucidate the finite-temperature phase structure consisting of the gas phase, liquid phase, their coexistence, and the spinodal phase. We also discuss its similarity with the liquid-gas phase transition in nuclear matter through the comparison with phenomenological models. Our results would be useful for an interdisciplinary understanding of self-bound fermionic matter as well as an analog quantum simulation of nuclear systems.

Figures (7)

• Figure 1: Zero-temperature energy per particle $E/N\omega_\perp$ in a quasi-one-dimensional dipolar Fermi gas at the gas parameter $\alpha \ell_{dd}/\ell_\perp=1.44$ and $\alpha\ell_{dd}/\ell_\perp=1.90$, obtained by the Hartree-Fock approximation PhysRevA.88.033611. The horizontal axis is the number density $n=N/L$ where $N$ and $L$ are the particle number and the system length. $\omega_\perp$ and $\ell_\perp$ are the transverse harmonic trap frequency and associated length scale, respectively. $\alpha$ is a dimensionless quantity for the dipolar angle. The dotted line shows the result of an ideal Fermi gas. While the case of $\alpha \ell_{dd}/\ell_\perp=1.44$ corresponds to the threshold for a two-body bound state and hence can be regarded as an analog of pure neutron matter (PNM), the case of $\alpha\ell_{dd}/\ell_\perp=1.90$ involving the two-body bound state may be analogous to symmetric neutron matter (SNM) with a local minimum of $E/N$.
• Figure 2: (a) Pressure $P$ and (b) energy per particle $E/N$ at several temperatures with $\alpha l_{dd}/l_\perp =1.9$. The black solid line represents the zero-temperature results. The blue and purple lines represent isotherms at critical temperature and flashing temperature in the panels (a) and (b). The two dashed lines with light blue and yellow colors in panel (a) represent the isotherms at $T/\omega_\perp = 0.02$ and $0.07$, respectively. Also, the red dotted horizontal line in panel (a) represents $P= 0$, which is tangent to the flashing temperature isotherm. In panel (b), the two horizontal dotted lines show $E/N\omega_\perp = T_\mathrm{c}/2\omega_\perp=0.0315$ and $E/N\omega_\perp = T_\mathrm{f}/2\omega_\perp = 0.0155$, respectively, showing that $E/N\omega_\perp = T/2\omega_\perp$ at the dilute limit. (c) Phase diagram with respect to pressure and particle density with $\alpha\ell_{dd}/\ell_\perp = 1.9$. The spinodal line satisfies $\partial P/\partial n=0$, and the coexistence curve corresponds to states with the same $T$, $P$, and $\mu$. The black dashed line represents EOS at zero temperature, which is the lower limit of pressure for finite temperature. (d) Temperature-density ($T-n$) phase diagram. The left and right regions with respect to the coexistence line represent the liquid phase and the gas phase, respectively.
• Figure 3: The free energy $F$ in the plane of $T/\omega_\perp$ and $n\ell_\perp$. One can find a convex anomaly, in which the convex is upward, inside the coexistence phase (below the coexistence line). For comparison, we also show the spinodal line.
• Figure 4: (a) The relationship between $T_\mathrm{c}$ and $T_\mathrm{f}$ and (b) that between $n_\mathrm{c}$ and $n_\mathrm{f}$ with different interaction strength $\alpha \ell_{dd}/\ell_\perp$ = 1.8, 1.9, 1.95, and 2.0 (from left to right). The blue dots show the numerical data of the Hartree-Fock approximation and the orange solid line shows the linear fit given by $T_\mathrm{c} = 1.53 T_\mathrm{f} +0.015\omega_\perp$ and $n_\mathrm{c}\ell_\perp = 0.67n_\mathrm{f}\ell_\perp + 0.048$. The green lines show the results of the Jaqaman model given by $T_\mathrm{c}/T_\mathrm{f} = 4/3.$ and $n_\mathrm{c}/n_\mathrm{f} = 2/3$, respectively.
• Figure 5: Scaling of thermal effect of pressure $P$. Here, $P_0$ represents the pressure at $T=0$. It can be seen that higher density ($n\ell_\perp = 0.3$ and $0.4$ in this case) exhibits a quadratic dependence on $T$ while the behavior at $n\ell_\perp = 0.2$ becomes linear as $T$ increases at higher temperature (where the chain-dotted line represents $\propto T$). The dash line represents the extended Kapusta model with density-dependent effective mass, where the $T$ dependence of the thermal pressure is quadratic.