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arXiv:1709.03279 · Physical Review A

Superfluid Fermi atomic gas as a quantum simulator for the study of the neutron-star equation of state in the low-density region

Pieter van Wyk, Hiroyuki Tajima, Daisuke Inotani, Akira Ohnishi A, Yoji Ohashi

Published Jan 3, 2018• 46 citations
arXivHTMLPDF

Abstract

We propose a theoretical idea to use an ultracold Fermi gas as a quantum simulator for the study of the low-density region of a neutron-star interior. Our idea is different from the standard quantum simulator that heads for perfect replication of another system, such as the Hubbard model discussed in high-${T}_{\mathrm{c}}$ cuprates. Instead, we use the similarity between two systems and theoretically make up for the difference between them. That is, (1) we first show that the strong-coupling theory developed by Nozi\`eres and Schmitt--Rink (NSR) can quantitatively explain the recent experiment on the equation of state (EoS) in a $^{6}\mathrm{Li}$ superfluid Fermi gas in the BCS (Bardeen--Cooper--Schrieffer) unitary limit far below the superfluid phase-transition temperature ${T}_{\mathrm{c}}$. This region is considered to be very similar to the low-density region (crust regime) of a neutron star (where a nearly unitary $s$-wave neutron superfluid is expected). (2) We then theoretically compensate the difference that, while the effective range ${r}_{\mathrm{eff}}$ is negligibly small in a superfluid $^{6}\mathrm{Li}$ Fermi gas, it cannot be ignored (${r}_{\mathrm{eff}}=2.7$ fm) in a neutron star, by extending the NSR theory to include effects of ${r}_{\mathrm{eff}}$. The calculated EoS when ${r}_{\mathrm{eff}}=2.7$ fm is shown to agree well with the previous neutron-star EoS in the low-density region predicted in nuclear physics. Our idea indicates that an ultracold atomic gas may more flexibly be used as a quantum simulator for the study of other complicated quantum many-body systems, when we use not only the experimental high tunability, but also the recent theoretical development in this field. Since it is difficult to directly observe a neutron-star interior, our idea would provide a useful approach to the exploration for this mysterious astronomical object.

DOI
10.1103/physreva.97.013601

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We propose a theoretical idea to use an ultracold Fermi gas as a quantum simulator for the study of the low-density region of a neutron-star interior. Our idea is different from the standard quantum simulator that heads for perfect replication of another system, such as the Hubbard model discussed in high-Tc{T}_{\mathrm{c}}Tc​ cuprates. Instead, we use the similarity between two systems and theoretically make up for the difference between them. That is, (1) we first show that the strong-coupling theory developed by Nozi`eres and Schmitt--Rink (NSR) can quantitatively explain the recent experiment on the equation of state (EoS) in a 6Li^{6}\mathrm{Li}6Li superfluid Fermi gas in the BCS (Bardeen--Cooper--Schrieffer) unitary limit far below the superfluid phase-transition temperature Tc{T}_{\mathrm{c}}Tc​. This region is considered to be very similar to the low-density region (crust regime) of a neutron star (where a nearly unitary sss-wave neutron superfluid is expected). (2) We then theoretically compensate the difference that, while the effective range reff{r}_{\mathrm{eff}}reff​ is negligibly small in a superfluid 6Li^{6}\mathrm{Li}6Li Fermi gas, it cannot be ignored (reff=2.7{r}_{\mathrm{eff}}=2.7reff​=2.7 fm) in a neutron star, by extending the NSR theory to include effects of reff{r}_{\mathrm{eff}}reff​. The calculated EoS when reff=2.7{r}_{\mathrm{eff}}=2.7reff​=2.7 fm is shown to agree well with the previous neutron-star EoS in the low-density region predicted in nuclear physics. Our idea indicates that an ultracold atomic gas may more flexibly be used as a quantum simulator for the study of other complicated quantum many-body systems, when we use not only the experimental high tunability, but also the recent theoretical development in this field. Since it is difficult to directly observe a neutron-star interior, our idea would provide a useful approach to the exploration for this mysterious astronomical object.
Ultracold dilute atomic gases can be considered as model systems to address some pending problem in Many-Body physics that occur in condensed matter systems, nuclear physics, and astrophysics. We have developed a general method to probe with high precision the thermodynamics of locally homogeneous ultracold Bose and Fermi gases. This method allows stringent tests of recent many-body theories. For attractive spin 1/2 fermions with tunable interaction (6Li), we will show that the gas thermodynamic properties can continuously change from those of weakly interacting Cooper pairs described by BardeenCooper-Schrieffer theory to those of strongly bound molecules undergoing Bose-Einstein condensation. First, we focus on the finite-temperature Equation of State (EoS) of the unpolarized unitary gas. Surprisingly, the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid phase transition. A detailed comparison with theories including Monte-Carlo calculations has revealed some surprises and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids are quantitatively measured for the first time. Despite orders of magnitude difference in density and temperature, our equation of state can be used to describe low density neutron matter such as the outer shell of neutron stars.
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We will present recent experimental work on the thermodynamics of strongly interacting Fermi gases. We have developed a general method to probe with high precision the Equation of State (EoS) of locally homogeneous ultracold gases. This allows stringent tests of recent many-body theories. First, we focus on the finite-temperature EoS of the unpolarized unitary gas. Precise thermometry is provided by adding to the Fermi gas of 6Li a trace of bosonic 7Li. We show that the low-temperature properties of the strongly interacting normal phase are well described by Fermi liquid theory and we localize the superfluid transition. Second, we address the zero-temperature EoS of the spin-polarized system in the BEC-BCS crossover. Surprisingly, despite strong interactions, the polarized phase behaves as a mixture of two ideal gases: a Fermi gas of majority atoms and a non-interacting gas of dressed quasi-particles, the Fermi polarons. We also obtain the equation of state of the superfluid state as a function of interaction strength, that we compare to Monte Carlo simulations and to the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids.
The quantum many-body problem is at the heart of some of the most formidable open problems in modern physics, such as high-Tc_cc​ superconductivity or the behaviour of neutron stars. Ultracold atomic systems can now be used to simulate model Hamiltonians of condensed matter or nuclear physics, in very well-controlled environnement. In this thesis, we have developed a general method to probe the thermodynamics of homogeneous quantum systems using trapped atomic gases. These measurements are directly compared to the predictions of theories of the quantum many-body problem. We have applied this technique to the spin-1/21/21/2 Fermi gas and the Bose with short-range interactions. Using fermionic 6^66Li, we explored a part of the wide parameter space by changing the interaction strength, the spin-population imbalance or the temperature of the gas. This system exhibits remarkably rich physics, such as normal/superfluid phase transitions (that can be of thermal or quantum character) or a Fermi liquid-type behaviour of the normal phase. We have also used this method to probe a Bose gas of 7^77Li atoms close to a Feshbach resonance. We have measured the Equation of State of the Bose gas as a function of interactions at very low temperature. For the first time, we measured quantitatively the Lee-Huang-Yang beyond mean-field correction to the ground-state energy of the system, first predicted in 1957. We compared the experimental results to Quantum Monte-Carlo calculations. We have extended this study using out-of-equilibrium measurements of the Bose gas in the strongly interacting regime, which gives a first hint on the properties of the hypothetical unitary Bose gas.
The internal structure of neutron stars and the physical properties of nuclei depend on the equation of state (EOS) of neutron matter. Dilute neutron matter is a quantum system of spin-1/2 Fermi particles interacting via s-wave scattering. Although a nuclear system and an ultracold atomic system have length scales and energy scales that differ by several orders of magnitude, both systems follow a common universal EOS considering their nondimensional universal interaction parameters. In this study, we determine the EOS of neutron matter in the dilute region, where the influence of the s-wave scattering length is dominant but that of the effective range is small, by utilizing a quantum simulator of ultracold 6Li atoms with Feshbach resonance.
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