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

arXiv:1212.5274 · Physical Review Letters

Lifetime of the Bose Gas with Resonant Interactions

Benno S. Rem, Andrew T. Grier, Igor Ferrier-Barbut, Ulrich Eismann, Tim Langen, Nir Navon, Lev Khaykovich, Félix Werner, Dmitry S. Petrov, Frédéric Chevy, Ch Salomon

Published Apr 16, 2013• 149 citations
arXivHTMLPDF

Abstract

We study the lifetime of a Bose gas at and around unitarity using a Feshbach resonance in lithium 7. At unitarity, we measure the temperature dependence of the three-body decay coefficient ${L}_{3}$. Our data follow a ${L}_{3}={\ensuremath{\lambda}}_{3}/{T}^{2}$ law with ${\ensuremath{\lambda}}_{3}=2.5(3{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }(\ensuremath{\mu}\mathrm{K}{)}^{2}\text{ }{\mathrm{cm}}^{6}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ and are in good agreement with our analytical result based on zero-range theory. Varying the scattering length $a$ at fixed temperature, we investigate the crossover between the finite-temperature unitary region and the previously studied regime where $|a|$ is smaller than the thermal wavelength. We find that ${L}_{3}$ is continuous across the resonance, and over the whole $a<0$ range our data quantitatively agree with our calculation.

DOI
10.1103/physrevlett.110.163202

Related papers

The Road to the Unitary Bose Gas

Benno S. Rem

Ultracold gases have become versatile systems to study quantum many-body effects. Their high degree of control and the tunability of the atomic interactions led to important advances in the understanding of strongly correlated matter. In the regime of strong interactions, unlike fermions, the study of bosons is hampered by three-particle recombination that leads to atom losses and keeps the system from reaching a real equilibrium state. In this thesis, we have performed the first quantitative comparison between theory and experiment on the three-particle loss coefficient L_3(a,T), for arbitrary scattering length a and temperature T. For unitary two-particle scattering (|a| → ∞), we show that the three-particle loss coefficient follows the law L_3(∞, T ) = λ_3/T^2, that we have tested using a trapped non-degenerate ^{7}Li gas maintained at constant temperature. The measured value of λ_3 = 2.5(3)_{stat}(6)_{cyst} × 10^{−20}(μK)^2cm^6s^{−1} is, within the error bars in good agreement with the theory prediction λ_3^{th} = 1.52 × 10^{−20}(μK)^2cm^6s^{−1}. We have extended our measurements to arbitrary values of the scattering length a. For a < 0, the theory predicts a smooth connection between the previously derived zero-temperature model for L_3(a, 0) and the unitarity limited loss coefficient L_3(∞, T ). We also show that a second Efimov resonance in 7Li should be observable near a = − 500 a0 for a temperature of 1 μK. Finally, we compare our theoretical prediction with measurements performed at Innsbruck with ^{133}Cs and at Cambridge with ^{39}K. The theory also shows remarkable quantitative agreement with these measurements.

•Jan 1, 2013•1 citation

Stability of a Unitary Bose Gas

Richard J. Fletcher, Alexander L. Gaunt, Nir Navon +2 more

We study the stability of a thermal (39)K Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length a exceeds the thermal wavelength λ. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive a<<λ we find agreement with three-body theory. However, for a<0 and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, L(3) proportional λ(4), is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes (39)K particularly promising for studies of many-body physics in a unitary Bose gas.

arXiv:1307.3193•Physical Review Letters•Sep 20, 2013•108 citations

Unitarity-limited behavior of three-body collisions in a p -wave interacting Fermi gas

Muhammad Waseem, Jun Yoshida, Taketo Saito +1 more

We experimentally investigate the unitarity-limited behavior of the three-body loss near a $p$-wave Feshbach resonance in a single-component Fermi gas of $^{6}\mathrm{Li}$ atoms. At the unitarity limit, the three-body loss coefficient ${L}_{3}$ exhibits universality in the sense that it is independent of the interaction strength and follows the predicted temperature scaling law of ${L}_{3}\ensuremath{\propto}{T}^{\ensuremath{-}2}$. When decreasing the interaction strength from the unitarity regime, the three-body loss coefficient as a function of the interaction strength and temperature can be described by the theory based on the association of an excited resonant quasibound state and its relaxation into a deep stable dimer by collision with a third atom in the framework of the standard Breit-Wigner theoretical approach. The results reported here are important to understand the properties of a resonant $p$-wave Fermi gas in the prospect of quantum few- and many-body physics.

arXiv:1803.07530•Physical Review A•Aug 8, 2018•32 citations

Quenching to unitarity: Quantum dynamics in a three-dimensional Bose gas

A. G. Sykes, John Corson, José Paulo D'Incao +5 more

We study the dynamics of a zero-temperature Bose condensate following a sudden quench of the scattering length from noninteracting to unitarity (infinite scattering length). We apply three complementary approaches to understand the momentum distribution and loss rate. First, using a time-dependent variational ansatz for the many-body state, we calculate the dynamics of the momentum distribution. Second, we demonstrate that, at short times and large momenta compared to those set by the density, the physics can be understood within a simple, analytic two-body model. We make a quantitative prediction for the evolution of Tan's contact and find features in the momentum distribution that are absent in equilibrium. Third, we study three-body loss at finite density under the same dynamic scenario. We find lifetimes that are long compared to the saturation times of large-momentum modes, and we relate this result to the three-body inelasticity parameter.

arXiv:1309.0828•Physical Review A•Feb 3, 2014•85 citations

Properties of a dilute Bose gas near a Feshbach resonance

Lan Yin, Zhenhua Ning

In this paper, properties of a homogeneous Bose gas with a Feshbach resonance are studied in the dilute region at zero temperature. The stationary state contains condensations of atoms and molecules. The ratio of the molecule density to the atom density is $\ensuremath{\pi}{\mathrm{na}}^{3}.$ There are two types of excitations, molecular excitations and atomic excitations. Atomic excitations are gapless, consistent with the traditional theory of a dilute Bose gas. The molecular excitation energy is finite in the long-wavelength limit as observed in recent experiments on ${}^{85}\mathrm{Rb}.$ In addition, the decay process of the condensate is studied. The coefficient of the three-body recombination rate is about 140 times larger than that of a Bose gas without a Feshbach resonance, in reasonably good agreement with the experiment on ${}^{23}\mathrm{Na}.$

arXiv:cond-mat/0304548•Physical Review A•Sep 19, 2003•8 citations

Crossover from weak to unitarity-limited interactions in Bose gases

J. J. R. M. van Heugten, Henk T. C. Stoof

We develop an analytical approach for the description of the crossover of an atomic Bose gas from small to infinitely large scattering length where the two-body interactions satisfy the unitarity bound. We obtain several properties of the Bose gas as a function of interaction strength, namely the chemical potential, the contact, the speed of sound, the condensate density, the effective interatomic interaction and the three-body recombination rate. Also, the energy dependence of the effective interaction at unitarity and the evolution of the Feshbach bound state are discussed. It is shown how the approach can be systematically improved with renormalization-group methods and how it reduces to the Bogoliubov theory in the weak-coupling limit.

arXiv:1306.1104•Jun 5, 2013•0 citations
We study the lifetime of a Bose gas at and around unitarity using a Feshbach resonance in lithium 7. At unitarity, we measure the temperature dependence of the three-body decay coefficient L3{L}_{3}L3​. Our data follow a L3=\ensuremathλ3/T2{L}_{3}={\ensuremath{\lambda}}_{3}/{T}^{2}L3​=\ensuremathλ3​/T2 law with \ensuremathλ3=2.5(3)stat(6)syst\ifmmode×\else\texttimes\fi10\ensuremath−20  (\ensuremathμK)2 cm6 s\ensuremath−1{\ensuremath{\lambda}}_{3}=2.5(3{)}_{\mathrm{stat}}(6{)}_{\mathrm{syst}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}20}\text{ }\text{ }(\ensuremath{\mu}\mathrm{K}{)}^{2}\text{ }{\mathrm{cm}}^{6}\text{ }{\mathrm{s}}^{\ensuremath{-}1}\ensuremathλ3​=2.5(3)stat​(6)syst​\ifmmode×\else\texttimes\fi10\ensuremath−20  (\ensuremathμK)2 cm6 s\ensuremath−1 and are in good agreement with our analytical result based on zero-range theory. Varying the scattering length aaa at fixed temperature, we investigate the crossover between the finite-temperature unitary region and the previously studied regime where ∣a∣|a|∣a∣ is smaller than the thermal wavelength. We find that L3{L}_{3}L3​ is continuous across the resonance, and over the whole a<0a<0a<0 range our data quantitatively agree with our calculation.
Ultracold gases have become versatile systems to study quantum many-body effects. Their high degree of control and the tunability of the atomic interactions led to important advances in the understanding of strongly correlated matter. In the regime of strong interactions, unlike fermions, the study of bosons is hampered by three-particle recombination that leads to atom losses and keeps the system from reaching a real equilibrium state. In this thesis, we have performed the first quantitative comparison between theory and experiment on the three-particle loss coefficient L_3(a,T), for arbitrary scattering length a and temperature T. For unitary two-particle scattering (|a| → ∞), we show that the three-particle loss coefficient follows the law L_3(∞, T ) = λ_3/T^2, that we have tested using a trapped non-degenerate ^{7}Li gas maintained at constant temperature. The measured value of λ_3 = 2.5(3)_{stat}(6)_{cyst} × 10^{−20}(μK)^2cm^6s^{−1} is, within the error bars in good agreement with the theory prediction λ_3^{th} = 1.52 × 10^{−20}(μK)^2cm^6s^{−1}. We have extended our measurements to arbitrary values of the scattering length a. For a < 0, the theory predicts a smooth connection between the previously derived zero-temperature model for L_3(a, 0) and the unitarity limited loss coefficient L_3(∞, T ). We also show that a second Efimov resonance in 7Li should be observable near a = − 500 a0 for a temperature of 1 μK. Finally, we compare our theoretical prediction with measurements performed at Innsbruck with ^{133}Cs and at Cambridge with ^{39}K. The theory also shows remarkable quantitative agreement with these measurements.
We study the stability of a thermal (39)K Bose gas across a broad Feshbach resonance, focusing on the unitary regime, where the scattering length a exceeds the thermal wavelength λ. We measure the general scaling laws relating the particle-loss and heating rates to the temperature, scattering length, and atom number. Both at unitarity and for positive a<<λ we find agreement with three-body theory. However, for a<0 and away from unitarity, we observe significant four-body decay. At unitarity, the three-body loss coefficient, L(3) proportional λ(4), is 3 times lower than the universal theoretical upper bound. This reduction is a consequence of species-specific Efimov physics and makes (39)K particularly promising for studies of many-body physics in a unitary Bose gas.
We experimentally investigate the unitarity-limited behavior of the three-body loss near a ppp-wave Feshbach resonance in a single-component Fermi gas of 6Li^{6}\mathrm{Li}6Li atoms. At the unitarity limit, the three-body loss coefficient L3{L}_{3}L3​ exhibits universality in the sense that it is independent of the interaction strength and follows the predicted temperature scaling law of ${L}_{3}\ensuremath{\propto}{T}^{\ensuremath{-}2}$. When decreasing the interaction strength from the unitarity regime, the three-body loss coefficient as a function of the interaction strength and temperature can be described by the theory based on the association of an excited resonant quasibound state and its relaxation into a deep stable dimer by collision with a third atom in the framework of the standard Breit-Wigner theoretical approach. The results reported here are important to understand the properties of a resonant ppp-wave Fermi gas in the prospect of quantum few- and many-body physics.
We study the dynamics of a zero-temperature Bose condensate following a sudden quench of the scattering length from noninteracting to unitarity (infinite scattering length). We apply three complementary approaches to understand the momentum distribution and loss rate. First, using a time-dependent variational ansatz for the many-body state, we calculate the dynamics of the momentum distribution. Second, we demonstrate that, at short times and large momenta compared to those set by the density, the physics can be understood within a simple, analytic two-body model. We make a quantitative prediction for the evolution of Tan's contact and find features in the momentum distribution that are absent in equilibrium. Third, we study three-body loss at finite density under the same dynamic scenario. We find lifetimes that are long compared to the saturation times of large-momentum modes, and we relate this result to the three-body inelasticity parameter.
In this paper, properties of a homogeneous Bose gas with a Feshbach resonance are studied in the dilute region at zero temperature. The stationary state contains condensations of atoms and molecules. The ratio of the molecule density to the atom density is $\ensuremath{\pi}{\mathrm{na}}^{3}.$ There are two types of excitations, molecular excitations and atomic excitations. Atomic excitations are gapless, consistent with the traditional theory of a dilute Bose gas. The molecular excitation energy is finite in the long-wavelength limit as observed in recent experiments on 85Rb.{}^{85}\mathrm{Rb}.85Rb. In addition, the decay process of the condensate is studied. The coefficient of the three-body recombination rate is about 140 times larger than that of a Bose gas without a Feshbach resonance, in reasonably good agreement with the experiment on 23Na.{}^{23}\mathrm{Na}.23Na.
We develop an analytical approach for the description of the crossover of an atomic Bose gas from small to infinitely large scattering length where the two-body interactions satisfy the unitarity bound. We obtain several properties of the Bose gas as a function of interaction strength, namely the chemical potential, the contact, the speed of sound, the condensate density, the effective interatomic interaction and the three-body recombination rate. Also, the energy dependence of the effective interaction at unitarity and the evolution of the Feshbach bound state are discussed. It is shown how the approach can be systematically improved with renormalization-group methods and how it reduces to the Bogoliubov theory in the weak-coupling limit.