Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

“Hard probes” of strongly-interacting atomic gases

Yusuke Nishida

Published Jun 18, 2012• 1 citation
OpenAlex

Abstract

We investigate properties of an energetic atom propagating through strongly interacting atomic gases. The operator product expansion is used to systematically compute a quasiparticle energy and its scattering rate both in a spin-1/2 Fermi gas and in a spinless Bose gas. Reasonable agreement with recent quantum Monte Carlo simulations even at a relatively small momentum k/kF > 1.5 indicates that our large-momentum expansions are valid in a wide range of momentum. We also study a differential scattering rate when a probe atom is shot into atomic gases. Because the number density and current density of the target atomic gas contribute to the forward scattering only, its contact density (measure of short-range pair correlation) gives the leading contribution to the backward scattering. Therefore, such an experiment can be used to measure the contact density and thus provides a new local probe of strongly interacting atomic gases.

Related papers

Probing strongly interacting atomic gases with energetic atoms

Yusuke Nishida

We investigate properties of an energetic atom propagating through strongly interacting atomic gases. The operator product expansion is used to systematically compute a quasiparticle energy and its scattering rate both in a spin-1/2 Fermi gas and in a spinless Bose gas. Reasonable agreement with recent quantum Monte Carlo simulations even at a relatively small momentum $k/{k}_{\mathrm{F}}\ensuremath{\gtrsim}1.5$ indicates that our large-momentum expansions are valid in a wide range of momentum. We also study a differential scattering rate when a probe atom is shot into atomic gases. Because the number density and current density of the target atomic gas contribute to the forward scattering only, its contact density (measure of short-range pair correlation) gives the leading contribution to the backward scattering. Therefore, such an experiment can be used to measure the contact density and thus provides a new local probe of strongly interacting atomic gases.

arXiv:1110.5926•Physical Review A•May 29, 2012•30 citations

Exact Relations for a Strongly Interacting Fermi Gas from the Operator Product Expansion

Eric Braaten, Lucas Platter

The momentum distribution in a Fermi gas with two spin states and a large scattering length has a tail that falls off like 1/k4 at large momentum k, as pointed out by Tan. He used novel methods to derive exact relations between the coefficient of the tail in the momentum distribution and various other properties of the system. We present simple derivations of these relations using the operator product expansion for quantum fields. We identify the coefficient as the integral over space of the expectation value of a local operator that measures the density of pairs.

arXiv:0803.1125•Physical Review Letters•May 21, 2008•298 citations

Momentum-resolved spectroscopy of a Fermi liquid

Elmer V. H. Doggen, J. J. Kinnunen

We consider a recent momentum-resolved radio-frequency spectroscopy experiment, in which Fermi liquid properties of a strongly interacting atomic Fermi gas were studied. Here we show that by extending the Brueckner-Goldstone model, we can formulate a theory that goes beyond basic mean-field theories and that can be used for studying spectroscopies of dilute atomic gases in the strongly interacting regime. The model hosts well-defined quasiparticles and works across a wide range of temperatures and interaction strengths. The theory provides excellent qualitative agreement with the experiment. Comparing the predictions of the present theory with the mean-field Bardeen-Cooper-Schrieffer theory yields insights into the role of pair correlations, Tan's contact, and the Hartree mean-field energy shift.

arXiv:1411.7207•Scientific Reports•May 5, 2015•16 citations

Universal relations for the strongly-interacting Fermi gas

Eric Braaten, Lucas Platter

Shina Tan has derived some universal relations that hold for any state of a system consisting of fermions with two spin states that have a large scattering length. These relations involve an intensive quantity called the contact that measures the number of pairs of atoms that are very close together. We show how these relations can be derived in the framework of quantum field theory using standard renormalization methods and the operator product expansion. They allow the contact density to be identified as the expectation value of a local operator constructed out of quantum fields.

Laser Physics•Apr 1, 2009•5 citations

Field-theoretical aspects of one-dimensional Bose and Fermi gases with contact interactions

Yuta Sekino, Yusuke Nishida

We investigate local quantum field theories for one-dimensional (1D) Bose and Fermi gases with contact interactions, which are closely connected with each other by Girardeau's Bose-Fermi mapping. While the Lagrangian for bosons includes only a two-body interaction, a marginally relevant three-body interaction term is found to be necessary for fermions. Because of this three-body coupling, the three-body contact characterizing a local triad correlation appears in the energy relation for fermions, which is one of the sum rules for a momentum distribution. In addition, we apply in both systems the operator product expansion to derive large-energy and momentum asymptotics of a dynamic structure factor and a single-particle spectral density. These behaviors are universal in the sense that they hold for any 1D scattering length at any temperature. The asymptotics for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.

arXiv:2011.11971•Physical Review A•Apr 6, 2021•31 citations

Short-Time Operator Product Expansion for rf Spectroscopy of a Strongly Interacting Fermi Gas

Eric Braaten, Daekyoung Kang, Lucas Platter

Universal relations that hold for any state provide powerful constraints on systems consisting of fermions with two spin states interacting with a large scattering length. In radio-frequency (rf) spectroscopy, the mean shift in the rf frequency and the large-frequency tail of the rf transition rate are proportional to the contact, which measures the density of pairs with small separations. We show that these universal relations can be derived and extended by using the short-time operator product expansion of quantum field theory. This is a general method for identifying aspects of many-body physics that are controlled by few-body physics.

arXiv:1001.4518•Physical Review Letters•Jun 4, 2010•103 citations
We investigate properties of an energetic atom propagating through strongly interacting atomic gases. The operator product expansion is used to systematically compute a quasiparticle energy and its scattering rate both in a spin-1/2 Fermi gas and in a spinless Bose gas. Reasonable agreement with recent quantum Monte Carlo simulations even at a relatively small momentum k/kF > 1.5 indicates that our large-momentum expansions are valid in a wide range of momentum. We also study a differential scattering rate when a probe atom is shot into atomic gases. Because the number density and current density of the target atomic gas contribute to the forward scattering only, its contact density (measure of short-range pair correlation) gives the leading contribution to the backward scattering. Therefore, such an experiment can be used to measure the contact density and thus provides a new local probe of strongly interacting atomic gases.
We investigate properties of an energetic atom propagating through strongly interacting atomic gases. The operator product expansion is used to systematically compute a quasiparticle energy and its scattering rate both in a spin-1/2 Fermi gas and in a spinless Bose gas. Reasonable agreement with recent quantum Monte Carlo simulations even at a relatively small momentum $k/{k}_{\mathrm{F}}\ensuremath{\gtrsim}1.5$ indicates that our large-momentum expansions are valid in a wide range of momentum. We also study a differential scattering rate when a probe atom is shot into atomic gases. Because the number density and current density of the target atomic gas contribute to the forward scattering only, its contact density (measure of short-range pair correlation) gives the leading contribution to the backward scattering. Therefore, such an experiment can be used to measure the contact density and thus provides a new local probe of strongly interacting atomic gases.
The momentum distribution in a Fermi gas with two spin states and a large scattering length has a tail that falls off like 1/k4 at large momentum k, as pointed out by Tan. He used novel methods to derive exact relations between the coefficient of the tail in the momentum distribution and various other properties of the system. We present simple derivations of these relations using the operator product expansion for quantum fields. We identify the coefficient as the integral over space of the expectation value of a local operator that measures the density of pairs.
We consider a recent momentum-resolved radio-frequency spectroscopy experiment, in which Fermi liquid properties of a strongly interacting atomic Fermi gas were studied. Here we show that by extending the Brueckner-Goldstone model, we can formulate a theory that goes beyond basic mean-field theories and that can be used for studying spectroscopies of dilute atomic gases in the strongly interacting regime. The model hosts well-defined quasiparticles and works across a wide range of temperatures and interaction strengths. The theory provides excellent qualitative agreement with the experiment. Comparing the predictions of the present theory with the mean-field Bardeen-Cooper-Schrieffer theory yields insights into the role of pair correlations, Tan's contact, and the Hartree mean-field energy shift.
Shina Tan has derived some universal relations that hold for any state of a system consisting of fermions with two spin states that have a large scattering length. These relations involve an intensive quantity called the contact that measures the number of pairs of atoms that are very close together. We show how these relations can be derived in the framework of quantum field theory using standard renormalization methods and the operator product expansion. They allow the contact density to be identified as the expectation value of a local operator constructed out of quantum fields.
We investigate local quantum field theories for one-dimensional (1D) Bose and Fermi gases with contact interactions, which are closely connected with each other by Girardeau's Bose-Fermi mapping. While the Lagrangian for bosons includes only a two-body interaction, a marginally relevant three-body interaction term is found to be necessary for fermions. Because of this three-body coupling, the three-body contact characterizing a local triad correlation appears in the energy relation for fermions, which is one of the sum rules for a momentum distribution. In addition, we apply in both systems the operator product expansion to derive large-energy and momentum asymptotics of a dynamic structure factor and a single-particle spectral density. These behaviors are universal in the sense that they hold for any 1D scattering length at any temperature. The asymptotics for the Tonks-Girardeau gas, which is a Bose gas with a hardcore repulsion, as well as the Bose-Fermi correspondence in the presence of three-body attractions are also discussed.
Universal relations that hold for any state provide powerful constraints on systems consisting of fermions with two spin states interacting with a large scattering length. In radio-frequency (rf) spectroscopy, the mean shift in the rf frequency and the large-frequency tail of the rf transition rate are proportional to the contact, which measures the density of pairs with small separations. We show that these universal relations can be derived and extended by using the short-time operator product expansion of quantum field theory. This is a general method for identifying aspects of many-body physics that are controlled by few-body physics.