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:2204.13300 · Physical Review A

Universal relations for dilute systems with two-body decays in reduced dimensions

Mingyuan He, Chenwei Lv, Qi Zhou

Published Jun 3, 2024• 1 citation
arXivHTMLPDF

Abstract

Physical systems in reduced dimensions exhibit intriguing properties. For instance, the dependences of two-body and many-body physics on scattering lengths are distinct from their counterparts in three dimensions. Whereas many studies of ultracold atoms and molecules in reduced dimensions have been focusing on closed systems, two-body losses may occur in such systems. Here, we show that the two-body inelastic loss rate in reduced dimensions can be expressed in universal relations that are governed by contacts. These universal relations correlate the two-body decay rate with other physical observables at zero and finite temperatures and generic interaction strengths. Our results will provide experimentalists with a new protocol to study inelastic scatterings in both few- and many-body systems in reduced dimensions.

DOI
10.1103/physreva.109.063301

Related papers

Universal relation for the inelastic two-body loss rate

Eric Braaten, H.‐W. Hammer

Strongly interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic two-body loss rate. A simple universal relation between the loss rate and the contact is obtained by truncating the expansion after the lowest dimension operator. We verify the universal relation explicitly by direct calculations in the low-density limit at nonzero temperature. This universal relation can be tested experimentally using ultracold quantum gases of atoms in hyperfine states that have an inelastic spin-relaxation channel.

arXiv:1302.5617•Journal of Physics B Atomic Molecular and Optical Physics•Oct 28, 2013•20 citations

Universal relations for ultracold reactive molecules

Mingyuan He, Chenwei Lv, Hai‐Qing Lin +1 more

The realization of ultracold polar molecules in laboratories has pushed physics and chemistry to new realms. In particular, these polar molecules offer scientists unprecedented opportunities to explore chemical reactions in the ultracold regime where quantum effects become profound. However, a key question about how two-body losses depend on quantum correlations in interacting many-body systems remains open so far. Here, we present a number of universal relations that directly connect two-body losses to other physical observables, including the momentum distribution and density correlation functions. These relations, which are valid for arbitrary microscopic parameters, such as the particle number, the temperature, and the interaction strength, unfold the critical role of contacts, a fundamental quantity of dilute quantum systems, in determining the reaction rate of quantum reactive molecules in a many-body environment. Our work opens the door to an unexplored area intertwining quantum chemistry; atomic, molecular, and optical physics; and condensed matter physics.

arXiv:2005.07861•Science Advances•Dec 18, 2020•31 citations

Universal Loss Processes in Bosonic Atoms with Positive Scattering Lengths

Christian B. Langmack

In experiments with trapped ultracold gases, atoms can be lost through inelastic scattering processes.If the atoms have a scattering length that is much larger than the range of their interactions, then the system exhibits universal behavior that does not depend on details of their interactions.Dramatic enhancements in the loss rate are observed at special negative values of the scattering length for which there is a universal molecule at threshold.In some experiments, enhancements of the loss rate have also been observed at other positive values of the scattering length.

•Jan 1, 2013•1 citation

Ultracold three-body recombination in two dimensions

José Paulo D'Incao, Fatima Anis, Brett D. Esry

We study three-body recombination in two dimensions for systems interacting via short-range two-body interactions in the regime of large scattering lengths. Using the adiabatic hyperspherical representation, we derive semianalytical formulas for three-body recombination in both weakly and deeply bound diatom states. Our results demonstrate the importance of long-range corrections to the three-body potentials by showing how they alter the low-energy and scattering-length dependence of the recombination rate for both bosonic and fermionic systems, which exhibit suppressed recombination if compared to the three-dimensional case. We verify these results through numerical calculations of recombination for systems with finite-range interactions and supporting a few two-body bound states. We also study finite-range effects for the energies of the universal three-identical-bosons states and find a slow approach to universal predictions as a function of the scattering length.

arXiv:1411.2321•Physical Review A•Jun 23, 2015•17 citations

Atom-dimer scattering and collisional stability in two-dimensional quantum gases

Yirong Wang, Jiaqi Yi, 高奎意 +1 more

Abstract The characterization of few-body interactions is fundamental for understanding the properties and collisional stability of ultracold quantum gases in reduced dimensions. In this work, we theoretically investigate the atom-dimer scattering and three-body recombination processes in a two-dimensional quantum gas. By generalizing the Skorniakov–Ter-Martirosian equations to two dimensions, we obtain the exact atom-dimer scattering amplitude and systematically evaluate the validity of common theoretical approximations, revealing a distinct feature of two-dimensional (2D) collisions: while mean-field theory fails rapidly with increasing interaction strength, the single-pole approximation remains remarkably accurate across a broad interaction regime. Furthermore, we extend our exact framework to non-zero incident momenta to calculate the three-body recombination rate. Our results demonstrate that the lifetime of the 2D quantum gas exhibits a power-law dependence on the 2D gas parameter n a 2D 2 with an exponent of approximately − 2.45 , showing a significant reduction in stability as interactions are enhanced. This study bridges the gap between exact few-body theory and practical many-body approximations, offering a robust benchmark for predicting the stability of cold atomic mixtures and guiding future experimental explorations of universal few-body physics in highly controllable 2D environments.

Communications in Theoretical Physics•May 15, 2026•0 citations

General relations for quantum gases in two and three dimensions. II. Bosons and mixtures

Félix Werner, Yvan Castin

We derive exact general relations between various observables for $N$ bosons with zero-range interactions, in two or three dimensions, in an arbitrary external potential. Some of our results are analogous to relations derived previously for two-component fermions and involve derivatives of the energy with respect to the two-body $s$-wave scattering length $a$. Moreover, in the three-dimensional case, where the Efimov effect takes place, the interactions are characterized not only by $a$, but also by a three-body parameter ${R}_{t}$. We then find additional relations which involve the derivative of the energy with respect to ${R}_{t}$. In short, this derivative gives the probability of finding three particles close to each other. Although it is evaluated for a totally lossless model, it also gives the three-body loss rate always present in experiments (due to three-body recombination to deeply bound diatomic molecules), at least in the limit where the so-called inelasticity parameter $\ensuremath{\eta}$ is small enough. As an application, we obtain, within the zero-range model and to first order in $\ensuremath{\eta}$, an analytic expression for the three-body loss rate constant for a nondegenerate Bose gas at thermal equilibrium with infinite scattering length. We also discuss the generalization to arbitrary mixtures of bosons and/or fermions.

arXiv:1210.1784•Physical Review A•Nov 30, 2012•147 citations
Physical systems in reduced dimensions exhibit intriguing properties. For instance, the dependences of two-body and many-body physics on scattering lengths are distinct from their counterparts in three dimensions. Whereas many studies of ultracold atoms and molecules in reduced dimensions have been focusing on closed systems, two-body losses may occur in such systems. Here, we show that the two-body inelastic loss rate in reduced dimensions can be expressed in universal relations that are governed by contacts. These universal relations correlate the two-body decay rate with other physical observables at zero and finite temperatures and generic interaction strengths. Our results will provide experimentalists with a new protocol to study inelastic scatterings in both few- and many-body systems in reduced dimensions.
Strongly interacting systems consisting of particles that interact through a large scattering length satisfy universal relations that relate many of their central properties to the contact, which measures the number of pairs with small separations. We use the operator product expansion of quantum field theory to derive the universal relation for the inelastic two-body loss rate. A simple universal relation between the loss rate and the contact is obtained by truncating the expansion after the lowest dimension operator. We verify the universal relation explicitly by direct calculations in the low-density limit at nonzero temperature. This universal relation can be tested experimentally using ultracold quantum gases of atoms in hyperfine states that have an inelastic spin-relaxation channel.
The realization of ultracold polar molecules in laboratories has pushed physics and chemistry to new realms. In particular, these polar molecules offer scientists unprecedented opportunities to explore chemical reactions in the ultracold regime where quantum effects become profound. However, a key question about how two-body losses depend on quantum correlations in interacting many-body systems remains open so far. Here, we present a number of universal relations that directly connect two-body losses to other physical observables, including the momentum distribution and density correlation functions. These relations, which are valid for arbitrary microscopic parameters, such as the particle number, the temperature, and the interaction strength, unfold the critical role of contacts, a fundamental quantity of dilute quantum systems, in determining the reaction rate of quantum reactive molecules in a many-body environment. Our work opens the door to an unexplored area intertwining quantum chemistry; atomic, molecular, and optical physics; and condensed matter physics.
In experiments with trapped ultracold gases, atoms can be lost through inelastic scattering processes.If the atoms have a scattering length that is much larger than the range of their interactions, then the system exhibits universal behavior that does not depend on details of their interactions.Dramatic enhancements in the loss rate are observed at special negative values of the scattering length for which there is a universal molecule at threshold.In some experiments, enhancements of the loss rate have also been observed at other positive values of the scattering length.
We study three-body recombination in two dimensions for systems interacting via short-range two-body interactions in the regime of large scattering lengths. Using the adiabatic hyperspherical representation, we derive semianalytical formulas for three-body recombination in both weakly and deeply bound diatom states. Our results demonstrate the importance of long-range corrections to the three-body potentials by showing how they alter the low-energy and scattering-length dependence of the recombination rate for both bosonic and fermionic systems, which exhibit suppressed recombination if compared to the three-dimensional case. We verify these results through numerical calculations of recombination for systems with finite-range interactions and supporting a few two-body bound states. We also study finite-range effects for the energies of the universal three-identical-bosons states and find a slow approach to universal predictions as a function of the scattering length.
Abstract The characterization of few-body interactions is fundamental for understanding the properties and collisional stability of ultracold quantum gases in reduced dimensions. In this work, we theoretically investigate the atom-dimer scattering and three-body recombination processes in a two-dimensional quantum gas. By generalizing the Skorniakov–Ter-Martirosian equations to two dimensions, we obtain the exact atom-dimer scattering amplitude and systematically evaluate the validity of common theoretical approximations, revealing a distinct feature of two-dimensional (2D) collisions: while mean-field theory fails rapidly with increasing interaction strength, the single-pole approximation remains remarkably accurate across a broad interaction regime. Furthermore, we extend our exact framework to non-zero incident momenta to calculate the three-body recombination rate. Our results demonstrate that the lifetime of the 2D quantum gas exhibits a power-law dependence on the 2D gas parameter n a 2D 2 with an exponent of approximately − 2.45 , showing a significant reduction in stability as interactions are enhanced. This study bridges the gap between exact few-body theory and practical many-body approximations, offering a robust benchmark for predicting the stability of cold atomic mixtures and guiding future experimental explorations of universal few-body physics in highly controllable 2D environments.
We derive exact general relations between various observables for NNN bosons with zero-range interactions, in two or three dimensions, in an arbitrary external potential. Some of our results are analogous to relations derived previously for two-component fermions and involve derivatives of the energy with respect to the two-body sss-wave scattering length aaa. Moreover, in the three-dimensional case, where the Efimov effect takes place, the interactions are characterized not only by aaa, but also by a three-body parameter Rt{R}_{t}Rt​. We then find additional relations which involve the derivative of the energy with respect to Rt{R}_{t}Rt​. In short, this derivative gives the probability of finding three particles close to each other. Although it is evaluated for a totally lossless model, it also gives the three-body loss rate always present in experiments (due to three-body recombination to deeply bound diatomic molecules), at least in the limit where the so-called inelasticity parameter $\ensuremath{\eta}$ is small enough. As an application, we obtain, within the zero-range model and to first order in $\ensuremath{\eta}$, an analytic expression for the three-body loss rate constant for a nondegenerate Bose gas at thermal equilibrium with infinite scattering length. We also discuss the generalization to arbitrary mixtures of bosons and/or fermions.