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arXiv:2106.12909 · Physical Review A

Unitary p -wave Fermi gas in one dimension

Hiroyuki Tajima, Shoichiro Tsutsui, Takahiro M. Doi, Kei Iida

Published Aug 23, 2021• 13 citations
arXivHTMLPDF

Abstract

We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the $p$-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is, $p$-wave scattering length and effective range. At the unitarity limit where the $p$-wave scattering length diverges and the effective range is reduced to zero without conflicting with the causality bound, the system obeys universal thermodynamics as observed in a unitary Fermi gas with contact $s$-wave interaction in three dimensions. It is in contrast to a Fermi gas with the $p$-wave resonance in three dimensions in which the effective range is inevitably finite. We present the universal equation of state in this unitary $p$-wave Fermi gas within the many-body $T$-matrix approach as well as the virial expansion method. Moreover, we examine the single-particle spectral function in the high-density regime where the virial expansion is no longer valid. On the basis of the Hartree-like self-energy shift at the divergent scattering length, we conjecture that the equivalence of the Bertsch parameter across spatial dimensions holds even for a one-dimensional unitary $p$-wave Fermi gas.

DOI
10.1103/physreva.104.023319

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We elucidate universal many-body properties of a one-dimensional, two-component ultracold Fermi gas near the ppp-wave Feshbach resonance. The low-energy scattering in this system can be characterized by two parameters, that is, ppp-wave scattering length and effective range. At the unitarity limit where the ppp-wave scattering length diverges and the effective range is reduced to zero without conflicting with the causality bound, the system obeys universal thermodynamics as observed in a unitary Fermi gas with contact sss-wave interaction in three dimensions. It is in contrast to a Fermi gas with the ppp-wave resonance in three dimensions in which the effective range is inevitably finite. We present the universal equation of state in this unitary ppp-wave Fermi gas within the many-body TTT-matrix approach as well as the virial expansion method. Moreover, we examine the single-particle spectral function in the high-density regime where the virial expansion is no longer valid. On the basis of the Hartree-like self-energy shift at the divergent scattering length, we conjecture that the equivalence of the Bertsch parameter across spatial dimensions holds even for a one-dimensional unitary ppp-wave Fermi gas.
Abstract We revisit the properties of the two-component Fermi gas with short-range interactions in three dimensions, in the limit where the s -wave scattering length diverges. Such a unitary Fermi gas possesses universal thermodynamic and dynamical observables that are independent of any interaction length scale. Focusing on trapped systems of N fermions, where N ≤ 10 , we investigate how well we can determine the zero-temperature behavior of the many-body system from published few-body data on the ground-state energy and the contact. For the unpolarized case, we find that the Bertsch parameters extracted from trapped few-body systems all lie within 15% of the established value. Furthermore, the few-body values for the contact are well within the range of values determined in the literature for the many-body system. In the limit of large spin polarization, we obtain a similar accuracy for the polaron energy, and we estimate the polaron’s effective mass from the dependence of its energy on N . We also compute an upper bound for the squared wave-function overlap between the unitary Fermi system and the non-interacting ground state, both for the trapped and uniform cases. This allows us to prove that the trapped unpolarized ground state at unitarity has zero overlap with its non-interacting counterpart in the many-body limit N → ∞ .
We study the universal relations and normal-phase thermodynamics of a two-component ultracold Fermi gas with coexisting sss- and ppp-wave interactions. Due to the orthogonality of two-body wave functions of different scattering channels, the universal thermodynamic relations of the system appear to be direct summations of contributions from each partial-wave scattering channel. These universal relations are dictated by a set of contacts, which can be associated with either sss- or ppp-wave interactions. Interestingly, due to the interplay of sss- and ppp-wave interactions on the many-body level, the contacts, and hence all the relevant thermodynamic quantities, behave differently from those with only sss- or ppp-wave interactions. These are manifest in our numerical calculations based on second-order virial expansions for 40K^{40}\mathrm{K}40K atoms under typical experimental parameters. A particularly interesting finding is that, due to the coexistence of sss- and ppp-wave scatterings, the interaction energy of the repulsive branch features abrupt changes across the ppp-wave resonances. Our results can be readily checked experimentally for 40K^{40}\mathrm{K}40K atoms near the 198Gp198\phantom{\rule{0.28em}{0ex}}\mathrm{G}\phantom{\rule{4pt}{0ex}}p198Gp-wave Feshbach resonance, where multiple partial-wave scatterings naturally coexist.
Universality is a crucial concept in modern physics, which allows us to describe phenomena without referring to microscopic details of systems.The unitary Fermi gas is a prime example, where universal relations among physical observables and a universal equation of state have been developed and studied in detail.In this thesis, we extend these notions beyond the paradigm of the unitary Fermi gas and investigate universal effects of few-body correlations in resonantly interacting ultracold atomic gases.In particular, we discuss (i) universal relations in a spinless Fermi gas with an anisotropic p-wave resonance and (ii) universality of the few-body spectra and the ground-state properties of an impurity-boson system.Firstly, we investigate the universal relations in a spinless Fermi gas with an anisotropic p-wave resonance.We show that the high-momentum distribution and the short-range density-density correlation have characteristic power laws, whose coefficients define the p-wave contact tensor.We derive the adiabatic sweep theorem, which relates the p-wave contact tensor to the total energy.We also discuss the experimental scheme to measure the p-wave contact tensor and test our results.Secondly, we examine the ground states and lower excited states of an impurity resonantly interacting with one, two, and three non-interacting bosons.We calculate the energy spectra of this few-body system with two different models.The overall scale of length depends on the models.However, we find that once we fix the three-body parameter, which is a critical scattering length of the ground-state Efimov trimer, the few-body spectrum is independent of a specific choice of the models.This finding is corroborated by comparing our numerical results with the one obtained by Ardila and Giorgini [Phys.Rev. A 92, 033612 (2015)].Thirdly, we investigate the case in which the mass of an impurity is infinite.In this limit, we show that the model of a Feshbach resonance can be mapped to a bosonic extension of Anderson's single impurity model, which can be used to analytically solve the three-body problem.We find that the ground-state energy with a Feshbach resonance is drastically different from that in a potential-interaction system, and that the former approaches the latter logarithmically as the unitarity limit is taken.We argue This thesis would not have been possible without the help and support of many people.I would like to express my gratitude to my supervisor, Professor Masahito Ueda, for his guidance and sincere encouragement over the period of my PhD program.He was a great teacher; he taught me a lot of things, from the way of a good scientist to a key to happy married life.I would also like to thank my secondary supervisors, Professor Tetsuo Hatsuda and Professor Junji Yumoto, for valuable advice on my study, and sometimes on job hunting.They also organized meetings where I could learn studies of other students.Much of the work in this thesis started during my stay at Quantum Matter group in Monash University, where I greatly benefited from fruitful collaboration with the group members.I am deeply grateful to Professor Meera M. Parish
The contact is an important concept that characterizes the universal properties of a strongly interacting quantum gas. It appears in both thermodynamic (energy, pressure, etc.) and dynamic quantities (radio-frequency and Bragg spectroscopies, etc.) of the system. Very recently, the concept of contact was extended to higher partial waves; in particular, the ppp-wave contacts have been experimentally probed in recent experiments. So far, discussions on ppp-wave contacts have been limited to three dimensions. In this paper, we generalize the ppp-wave contacts to two dimensions and derive a series of universal relations, including the adiabatic relations, high-momentum distribution, virial theorem, and pressure relation. At the high-temperature and low-density limit, we calculate the ppp-wave contacts explicitly using virial expansion. A formula which directly connects the shift of the breathing-mode frequency and the ppp-wave contacts is given in a harmonically trapped system. Finally, we also derive the relationships between interaction parameters in three- and two-dimensional Fermi gases and discuss possible experimental realization of a two-dimensional Fermi gas with ppp-wave interactions.
Thermodynamic properties of a Fermi system close to the unitarity limit, where the 2-body scattering length a approaches +/-infinity, are studied in the high temperature Boltzmann regime. For dilute systems the virial expansion coefficients in the Boltzmann regime are expected, from general arguments, to be universal. A model independent finite temperature T calculation of the third virial coefficient b3(T) is presented. At the unitarity limit, b3infinity approximately 1.11 is a universal number. The energy density up to the third virial expansion is derived. These calculations are of interest in dilute neutron matter and could be tested in current atomic experiments on dilute Fermi gases near the Feshbach resonance.
Unitary Fermi gases, where the scattering length is large compared to the interparticle spacing, can have universal properties, which are independent of the details of the interparticle interactions when the range of the scattering potential is negligible. We prepare an optically trapped, unitary Fermi gas of 6Li, tuned just above the center of a broad Feshbach resonance. In agreement with the universal hypothesis, we observe that this strongly interacting many-body system obeys the virial theorem for an ideal gas over a wide range of temperatures. Based on this result, we suggest a simple volume thermometry method for unitary gases. We also show that the observed breathing mode frequency, which is close to the unitary hydrodynamic value over a wide range of temperature, is consistent with a universal hydrodynamic gas with nearly isentropic dynamics.