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arXiv:1808.03890 · Physical Review A

Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions

Fang Qin

Published Nov 20, 2018• 7 citations
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Abstract

In a recent experiment [Peng et al., Phys. Rev. A 97, 012702 (2018)], it has been shown that the $p$-wave Feshbach resonance can be shifted toward the $s$-wave Feshbach resonance by a laser field. Based on this experiment, we study the universal relations and the normal-state properties in an ultracold Fermi gas with coexisting $s$- and $p$-wave interactions under optical control of a $p$-wave magnetic Feshbach resonance. Within the operator-product expansion, we derive the high-momentum tail of various observable quantities in terms of contacts. We find that the high-momentum tail becomes anisotropic. Adopting the quantum virial expansion, we calculate the normal-state contacts with and without a laser field for $^{40}\mathrm{K}$ atoms using typical experimental parameters. We show that the contacts are dependent on the laser dressing. We also reveal the interplay of laser dressing and different partial-wave interactions on various contacts. In particular, we demonstrate that the impact of the laser dressing in the $p$-wave channel can be probed by measuring the $s$-wave contacts, which is a direct manifestation of few-body effects on the many-body level. Our results can be readily checked experimentally.

DOI
10.1103/physreva.98.053621

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In a recent experiment [Peng et al., Phys. Rev. A 97, 012702 (2018)], it has been shown that the ppp-wave Feshbach resonance can be shifted toward the sss-wave Feshbach resonance by a laser field. Based on this experiment, we study the universal relations and the normal-state properties in an ultracold Fermi gas with coexisting sss- and ppp-wave interactions under optical control of a ppp-wave magnetic Feshbach resonance. Within the operator-product expansion, we derive the high-momentum tail of various observable quantities in terms of contacts. We find that the high-momentum tail becomes anisotropic. Adopting the quantum virial expansion, we calculate the normal-state contacts with and without a laser field for 40K^{40}\mathrm{K}40K atoms using typical experimental parameters. We show that the contacts are dependent on the laser dressing. We also reveal the interplay of laser dressing and different partial-wave interactions on various contacts. In particular, we demonstrate that the impact of the laser dressing in the ppp-wave channel can be probed by measuring the sss-wave contacts, which is a direct manifestation of few-body effects on the many-body level. Our results can be readily checked experimentally.
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.
In a recent proposal [Jie and Zhang, Phys. Rev. A 95, 060701(R) (2017)], it has been shown that center-of-mass-momentum-dependent two-body interactions can be generated and tuned by Raman coupling the closed-channel bound states in a magnetic Feshbach resonance. Here we investigate the universal relations in a three-dimensional Fermi gas near such a laser modulated sss-wave Feshbach resonance. Using the operator-product expansion approach, we find that to fully describe the high-momentum tail of the density distribution up to ${q}^{\ensuremath{-}6}$ (qqq is the relative momentum), four center-of-mass-momentum-dependent parameters are required, which we identify as contacts. These contacts appear in various universal relations connecting microscopic and thermodynamic properties. One contact is related to the variation of energy with respect to the inverse scattering length and determines the leading ${q}^{\ensuremath{-}4}$ tail of the high-momentum distribution. Another vector contact appears in the subleading ${q}^{\ensuremath{-}5}$ tail, which is related to the velocity of closed-channel molecules. The other two contacts emerge in the ${q}^{\ensuremath{-}6}$ tail and are respectively related to the variation of energy with respect to the range parameter and to the kinetic energy of closed-channel molecules. Particularly, we find that the ${q}^{\ensuremath{-}5}$ tail and part of the ${q}^{\ensuremath{-}6}$ tail of the momentum distribution show anisotropic features. We derive the universal relations and, as a concrete example, estimate the contacts for the zero-temperature superfluid ground state of the system using a mean-field approach.
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
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.
We investigate the properties of a spinless Fermi gas close to a p-wave interaction resonance. We show that the effects of interaction near a p-wave resonance are captured by two contacts, which are related to the variation of energy with the p-wave scattering volume v and with the effective range R in two adiabatic theorems. Exact pressure and virial relations are derived. We show how the two contacts determine the leading and subleading asymptotic behavior of the momentum distribution (∼1/k^{2} and ∼1/k^{4}) and how they can be measured experimentally by radio-frequency and photoassociation spectroscopies. Finally, we evaluate the two contacts at high temperature with a virial expansion.
We report a unique feature of magnetic-field Feshbach resonances in which atoms collide with nonzero orbital angular momentum. ppp-wave (l=1)(l=1)(l=1) Feshbach resonances are split into two components depending on the magnitude of the resonant state's projection of orbital angular momentum onto the field axis. This splitting is due to the magnetic dipole-dipole interaction between the atoms and it offers a means to tune anisotropic interactions of an ultracold gas of atoms. Furthermore this splitting in the ppp-wave Feshbach resonance has been experimentally observed and is reported. A parametrization of the ppp-wave resonance in terms of an effective-range expansion is given.