arXiv:2411.13086 · Physical Review A

Measurement of p -wave contacts in an ultracold Fermi gas of Li 6 atoms

Kenta Nagase, Soki Oshima, H. Takahashi, Takashi Mukaiyama

Published Jan 23, 2025• 2 citations

Abstract

Using radio-frequency (rf) spectroscopy, we measure the $p$-wave contacts in a Fermi gas of $^{6}\mathrm{Li}$ atoms near the $p$-wave Feshbach resonance. The rf spectrum exhibits clear asymptotic behavior, characterized by ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}^{\ensuremath{-}1/2}$ and ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}^{\ensuremath{-}3/2}$ dependencies. The magnetic-field dependence of the $p$-wave contacts agrees reasonably well with the virial expansion theory in a detuned magnetic-field range, validating the theory near half of the Fermi temperature. The $p$-wave contacts measured in this article constitute a second data set, complementing the data obtained from the $^{40}\mathrm{K}$ system and contributing valuable insights into $p$-wave interactions in ultracold Fermi gases.

DOI: 10.1103/physreva.111.013314

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Temperature Dependence of p -Wave Contacts in a Harmonically Trapped Fermi Gas

Kenta Nagase, Hikaru Takahashi, Soki Oshima +1 more

arXiv:2509.04738Physical Review LettersDec 2, 20253 citations

Universal Relations for a Fermi Gas Close to a p -Wave Interaction Resonance

Zhenhua Yu, Joseph H. Thywissen, Shizhong Zhang

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High-Sensitivity rf Spectroscopy of a Strongly Interacting Fermi Gas

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Radio-frequency spectroscopy of Li6 p -wave molecules: Towards photoemission spectroscopy of a p -wave superfluid

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

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Orbital-resolved three-body recombination across a p-wave Feshbach resonance in ultracold $^6$Li

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arXiv:2512.02479Dec 2, 20250 citations

arXiv:2411.13086 · Physical Review A

Measurement of p -wave contacts in an ultracold Fermi gas of Li 6 atoms

Kenta Nagase, Soki Oshima, H. Takahashi, Takashi Mukaiyama

Published Jan 23, 2025• 2 citations

arXiv HTML PDF

Abstract

Using radio-frequency (rf) spectroscopy, we measure the

p

-wave contacts in a Fermi gas of

^{6}\mathrm{Li}

atoms near the

p

-wave Feshbach resonance. The rf spectrum exhibits clear asymptotic behavior, characterized by

{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}^{\ensuremath{-}1/2}

and

{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}^{\ensuremath{-}3/2}

dependencies. The magnetic-field dependence of the

p

-wave contacts agrees reasonably well with the virial expansion theory in a detuned magnetic-field range, validating the theory near half of the Fermi temperature. The

p

-wave contacts measured in this article constitute a second data set, complementing the data obtained from the

^{40}\mathrm{K}

system and contributing valuable insights into

p

-wave interactions in ultracold Fermi gases.

DOI: 10.1103/physreva.111.013314

Related papers

Temperature Dependence of p -Wave Contacts in a Harmonically Trapped Fermi Gas

Kenta Nagase, Hikaru Takahashi, Soki Oshima +1 more

We study the dependence of the p-wave contact on the Fermi temperature T_{F} and reduced temperature T/T_{F} based on the number of closed-channel molecules. From the anisotropic pattern of dissociated molecules, we resolve the narrow m=0 and m=±1 dipolar splitting of the p-wave Feshbach resonance in ^{6}Li, enabling the independent determination of the contact for all three m components. For each component, we identify a near-resonant scaling with sqrt[T_{F}], indicating the contribution of the normalized effective range k_{F}R_{e}. In addition, we show that the peak contacts observed near resonance increase as T/T_{F} is lowered, a trend that is accurately captured by estimates based on the second-order virial expansion. Our results, together with estimates from the p-wave virial expansion, provide a route toward a complete understanding of the thermodynamics of resonantly enhanced p-wave Fermi gases.We study the dependence of the p-wave contact on the Fermi temperature T_{F} and reduced temperature T/T_{F} based on the number of closed-channel molecules. From the anisotropic pattern of dissociated molecules, we resolve the narrow m=0 and m=±1 dipolar splitting of the p-wave Feshbach resonance in ^{6}Li, enabling the independent determination of the contact for all three m components. For each component, we identify a near-resonant scaling with sqrt[T_{F}], indicating the contribution of the normalized effective range k_{F}R_{e}. In addition, we show that the peak contacts observed near resonance increase as T/T_{F} is lowered, a trend that is accurately captured by estimates based on the second-order virial expansion. Our results, together with estimates from the p-wave virial expansion, provide a route toward a complete understanding of the thermodynamics of resonantly enhanced p-wave Fermi gases.

arXiv:2509.04738Physical Review LettersDec 2, 20253 citations

Universal Relations for a Fermi Gas Close to a p -Wave Interaction Resonance

Zhenhua Yu, Joseph H. Thywissen, Shizhong Zhang

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 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.

arXiv:1505.02526Physical Review LettersSep 23, 201579 citations

High-Sensitivity rf Spectroscopy of a Strongly Interacting Fermi Gas

Constantine Shkedrov, Yanay Florshaim, Gal Ness +2 more

rf spectroscopy is one of the most powerful probing techniques in the field of ultracold gases. We report on a novel rf spectroscopy scheme with which we can detect very weak signals of only a few atoms. Using this method, we extended the experimentally accessible photon-energies range by an order of magnitude compared to previous studies. We directly verify a universal property of fermions with short-range interactions which is a power-law scaling of the rf spectrum tail all the way up to the interaction scale. We also determine, with high precision, the trap average contact parameter for different interaction strength. Finally, we employ our technique to precisely measure the binding energy of Feshbach molecules in an extended range of magnetic fields. These data are used to extract a new calibration of the Feshbach resonance between the two lowest energy levels of ^{40}K.rf spectroscopy is one of the most powerful probing techniques in the field of ultracold gases. We report on a novel rf spectroscopy scheme with which we can detect very weak signals of only a few atoms. Using this method, we extended the experimentally accessible photon-energies range by an order of magnitude compared to previous studies. We directly verify a universal property of fermions with short-range interactions which is a power-law scaling of the rf spectrum tail all the way up to the interaction scale. We also determine, with high precision, the trap average contact parameter for different interaction strength. Finally, we employ our technique to precisely measure the binding energy of Feshbach molecules in an extended range of magnetic fields. These data are used to extract a new calibration of the Feshbach resonance between the two lowest energy levels of ^{40}K.

arXiv:1803.01770Physical Review LettersAug 30, 201826 citations

Radio-frequency spectroscopy of Li6 p -wave molecules: Towards photoemission spectroscopy of a p -wave superfluid

R. A. W. Maier, C. Marzok, Claus Zimmermann +1 more

We study rf spectroscopy of a lithium gas with the goal to explore the possibilities for photoemission spectroscopy of a strongly interacting $p$ -wave Fermi gas. Radio-frequency spectra of quasibound $p$ -wave molecules and of free atoms in the vicinity of the $p$ -wave Feshbach resonance located at $159.15$ G are presented. The spectra are free of detrimental final-state effects. The observed relative magnetic-field shifts of the molecular and atomic resonances confirm earlier measurements realized with direct rf association. Furthermore, evidence of molecule production by adiabatically ramping the magnetic field is observed. Finally, we propose the use of a one-dimensional optical lattice to study anisotropic superfluid gaps as most direct proof of $p$ -wave superfluidity.We study rf spectroscopy of a lithium gas with the goal to explore the possibilities for photoemission spectroscopy of a strongly interacting $p$-wave Fermi gas. Radio-frequency spectra of quasibound $p$-wave molecules and of free atoms in the vicinity of the $p$-wave Feshbach resonance located at $159.15$ G are presented. The spectra are free of detrimental final-state effects. The observed relative magnetic-field shifts of the molecular and atomic resonances confirm earlier measurements realized with direct rf association. Furthermore, evidence of molecule production by adiabatically ramping the magnetic field is observed. Finally, we propose the use of a one-dimensional optical lattice to study anisotropic superfluid gaps as most direct proof of $p$-wave superfluidity.

arXiv:1003.2516Physical Review AJun 22, 201028 citations

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

Fang Qin

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.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.

arXiv:1808.03890Physical Review ANov 20, 20187 citations

Orbital-resolved three-body recombination across a p-wave Feshbach resonance in ultracold $^6$ LiOrbital-resolved three-body recombination across a p-wave Feshbach resonance in ultracold $^6$Li

Shaokun Liu, Z. P. Xu, Peng, Shuai +4 more

We report precision, orbital-resolved measurements of three-body recombination near the 159~G $p$ -wave Feshbach resonance in an ultracold gas of $^{6}$ Li atoms prepared in their lowest hyperfine state. Using a radio-frequency gated protocol that suppresses magnetic-field transients below the milligauss level, we resolve loss features associated with the $|m_\ell|=1$ and $m_\ell=0$ orbital projections. The measured three-body loss coefficient $L_3$ is well captured by a thermally averaged cascade-recombination model, enabling extraction of the resonance splitting $δB$ and effective-range parameter $k_e$ . At the lowest temperature, we obtain $δB = 7.6(3)$ ~mG and $k_e = 0.151(6)\,a_0^{-1}$ , both in quantitative agreement with coupled-channel theory. These results establish orbital-resolved three-body spectroscopy as a precision probe of $p$ -wave scattering and provide a benchmark for microscopic models of resonant few-body loss.We report precision, orbital-resolved measurements of three-body recombination near the 159~G $p$-wave Feshbach resonance in an ultracold gas of $^{6}$Li atoms prepared in their lowest hyperfine state. Using a radio-frequency gated protocol that suppresses magnetic-field transients below the milligauss level, we resolve loss features associated with the $|m_\ell|=1$ and $m_\ell=0$ orbital projections. The measured three-body loss coefficient $L_3$ is well captured by a thermally averaged cascade-recombination model, enabling extraction of the resonance splitting $δB$ and effective-range parameter $k_e$. At the lowest temperature, we obtain $δB = 7.6(3)$~mG and $k_e = 0.151(6)\,a_0^{-1}$, both in quantitative agreement with coupled-channel theory. These results establish orbital-resolved three-body spectroscopy as a precision probe of $p$-wave scattering and provide a benchmark for microscopic models of resonant few-body loss.

arXiv:2512.02479Dec 2, 20250 citations

Using radio-frequency (rf) spectroscopy, we measure the

p

-wave contacts in a Fermi gas of

^{6}\mathrm{Li}

atoms near the

p

-wave Feshbach resonance. The rf spectrum exhibits clear asymptotic behavior, characterized by

{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}^{\ensuremath{-}1/2}

and

{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}^{\ensuremath{-}3/2}

dependencies. The magnetic-field dependence of the

p

-wave contacts agrees reasonably well with the virial expansion theory in a detuned magnetic-field range, validating the theory near half of the Fermi temperature. The

p

-wave contacts measured in this article constitute a second data set, complementing the data obtained from the

^{40}\mathrm{K}

system and contributing valuable insights into

p

-wave interactions in ultracold Fermi gases.

We study rf spectroscopy of a lithium gas with the goal to explore the possibilities for photoemission spectroscopy of a strongly interacting

p

-wave Fermi gas. Radio-frequency spectra of quasibound

p

-wave molecules and of free atoms in the vicinity of the

p

-wave Feshbach resonance located at

159.15

G are presented. The spectra are free of detrimental final-state effects. The observed relative magnetic-field shifts of the molecular and atomic resonances confirm earlier measurements realized with direct rf association. Furthermore, evidence of molecule production by adiabatically ramping the magnetic field is observed. Finally, we propose the use of a one-dimensional optical lattice to study anisotropic superfluid gaps as most direct proof of

p

-wave superfluidity.

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.

Orbital-resolved three-body recombination across a p-wave Feshbach resonance in ultracold

^6

We report precision, orbital-resolved measurements of three-body recombination near the 159~G

p

-wave Feshbach resonance in an ultracold gas of

^{6}

Li atoms prepared in their lowest hyperfine state. Using a radio-frequency gated protocol that suppresses magnetic-field transients below the milligauss level, we resolve loss features associated with the

|m_\ell|=1

and

m_\ell=0

orbital projections. The measured three-body loss coefficient

L_3

is well captured by a thermally averaged cascade-recombination model, enabling extraction of the resonance splitting

δB

and effective-range parameter

k_e

. At the lowest temperature, we obtain

δB = 7.6(3)

~mG and

k_e = 0.151(6)\,a_0^{-1}

, both in quantitative agreement with coupled-channel theory. These results establish orbital-resolved three-body spectroscopy as a precision probe of

p

-wave scattering and provide a benchmark for microscopic models of resonant few-body loss.