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:2306.09236

Potential and Feshbach sss-wave resonances in coupled atomic collision channels

Grover Andrade-Sánchez, Vı́ctor Romero-Rochı́n

Published Jun 15, 2023• 0 citations
arXivHTMLPDF

Abstract

We discuss $s$-wave scattering in an atomic binary collision with two coupled channels, tunable by an external magnetic field, one channel open and the other closed for the incident energies considered. The analysis is performed with a stylized model of square-well potentials. This simplification allows for a pedagogically thorough discussion of the different scattering resonances that appear in coupled channels. One of the them, the potential resonances at vanishing energy, occur as a bound state of the coupled system emerges, in turned tuned at a very precise value of the external field. The other resonances, described by Feshbach theory, occur when the incident energy is near a bound state of the closed channel, as if it were decoupled from the open channel. These resonances exist for values of the external field above a particular threshold value. Besides the potential intrinsic value of this study in a quantum mechanics course, as the analysis can be performed with minor numerical calculations, it is also an aid for the understanding of current research advances in the exciting field of ultracold gases.

DOI
10.48550/arxiv.2306.09236

Related papers

Potential and Feshbach s-wave resonances in coupled atomic collision channels

Grover Andrade-Sánchez, Vı́ctor Romero-Rochı́n

Abstract We discuss s-wave scattering in an atomic binary collision with two coupled channels, tunable by an external magnetic field, one channel open and the other closed for the incident energies considered. The analysis is performed with a stylized model of square-well potentials. This simplification allows for a pedagogically thorough discussion of the different scattering resonances that appear in coupled channels. One of them, the potential resonances at vanishing energy, occurs as a bound state of the coupled system emerges, in turn, tuned at a very precise value of the external field. The other resonances, described by Feshbach theory, occur when the incident energy is near a bound state of the closed channel, as if it were decoupled from the open channel. These resonances exist for values of the external field above a particular threshold value. Besides the potential intrinsic value of this study in a quantum mechanics course, as the analysis can be performed with minor numerical calculations, it is also an aid for the understanding of current research advances in the exciting field of ultracold gases.

European Journal of Physics•Sep 7, 2023•0 citations

Feshbach Resonance without a Closed-Channel Bound State

Y. Avishai, Y. B. Band, Marek Trippenbach

The physics of Feshbach resonance is analyzed using an analytic expression for the s-wave scattering phase shift and the scattering length a which we derive within a two-channel tight-binding model. Employing a unified treatment of bound states and resonances in terms of the Jost function, it is shown that, for strong interchannel coupling, Feshbach resonance can occur even when the closed channel does not have a bound state. This may extend the range of ultracold atomic systems that can be manipulated by Feshbach resonance. The dependence of the sign of a on the coupling strength in the unitary limit is elucidated. As a by-product, analytic expressions are derived for the background scattering length, the external magnetic field at which resonance occurs, and the energy shift ε-ε(B), where ε is the scattering energy and ε(B) is the bound-state energy in the closed channel (when there is one).

arXiv:1306.0144•Physical Review Letters•Oct 11, 2013•4 citations

Microscopic many-body theory of atomic Bose gases near a Feshbach resonance

R. A. Duine, Henk T. C. Stoof

A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.

arXiv:cond-mat/0210544•Journal of Optics B Quantum and Semiclassical Optics•Apr 1, 2003•49 citations

Feshbach resonances and the three-body problem

L.G. Cook

By applying a magnetic field across a trapped ultracold gas of alkali metal atoms, it is possible to alter the binding energies of near threshold molecular states. The proximity of molecular states to the scattering threshold has a strong effect on the threshold scattering characteristics. Because of this the magnetic field strength can be used to control low energy scattering within the gas. This resonant phenomena is referred to as a magnetically tuneable Feshbach resonance. This thesis looks at these and related phenomena in the context of trapped potassium atoms. First, we perform coupled-channels calculations in order to characterise a group of previously unreported Feshbach resonances, occurring in a host of different collision channels. Next, we compare these characterisations to empirical data, and more simplified models. Second, a detailed investigation into the photodissociation of weakly bound Feshbach molecules is carried out. This allows us to gain new insights into the structure of the exit channel interaction. We make semi-classical arguments which enable experimentalists to directly measure the height of potential barriers. We also perform detailed numerical calculations which, in conjunction with experimental data, allow us to develop a fine-tuned potential model for the exit state. Third, we model weakly bound triatomic states and their impact on near threshold scattering. Then, we discuss the use of three body recombination as a tool for observing Efimov states. Furthermore, we model the three body recombination rate using a simplified two channel model. Finally we suggest a method intended to provide the basis for numerical calculations using realistic Born-Oppenheimer potentials. It could also be used to analytically study near threshold three body physics.

•Jun 28, 2012•1 citation

The two-body collision controlled by the magnetic field and laser field near magnetic Feshbach resonance

Bing-Kuan Lyu, Bo-Wen Si, Zong-Han Yu +2 more

It is crucial to control the collision between ultracold atoms by applying external fields. We developed a theoretical model for investigating the s-wave scattering of ultracold atoms controlled by the magnetic field and laser field. The calculation is performed by using the close-coupling method and mapped Fourier grid method. Due to the interference between the photoassociation and bound-to-bound transitions, the bound state in the continuum, which is a resonance with a vanishing width, occurs at the magnetic field position near the magnetic Feshbach resonance. The widths of resonances in the neighborhood of the bound state in the continuum are narrow. Changing the laser intensity can shift the magnetic field position where the bound state in the continuum occurs through modifying the ground molecular state to induce wide resonances at desired magnetic field positions. By increasing the resonance width, the tunability of the real part of the scattering length at resonances can be significantly improved. Changing the laser intensity can also adjust the coupling between the ground and excited molecular states. When the coupling between the ground and excited molecular states approaches zero, a resonance is induced, and the photoassociation and bound-to-bound transitions are both significantly suppressed at this resonance. Therefore, the atomic loss peak due to spontaneous emission does not appear at this resonance. The magnetic field position of this resonance is stable against the change in laser frequency.

Frontiers in Physics•Jul 5, 2023•0 citations

Exactly solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics

Andrey M. Pupasov-Maksimov, B. F. Samsonov, Jean-Marc Sparenberg

Starting from a system of $N$ radial Schr\"odinger equations with a vanishing potential and finite threshold differences between the channels, a coupled $N\ifmmode\times\else\texttimes\fi{}N$ exactly solvable potential model is obtained with the help of a single nonconservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as does its Jost matrix. It depends on $N(N+1)/2$ unconstrained parameters and on one upper-bounded parameter, the factorization energy. A detailed study of the model is done for the $2\ifmmode\times\else\texttimes\fi{}2$ case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has zero, one, or two bound states, and zero or one resonance; a compact formula for the open-channel scattering length is obtained. As a first physical application, exactly solvable $2\ifmmode\times\else\texttimes\fi{}2$ atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interacts with a bound or virtual state close to threshold, which results in a large background scattering length.

arXiv:0709.0343•Physical Review A•Jan 30, 2008•14 citations
We discuss sss-wave scattering in an atomic binary collision with two coupled channels, tunable by an external magnetic field, one channel open and the other closed for the incident energies considered. The analysis is performed with a stylized model of square-well potentials. This simplification allows for a pedagogically thorough discussion of the different scattering resonances that appear in coupled channels. One of the them, the potential resonances at vanishing energy, occur as a bound state of the coupled system emerges, in turned tuned at a very precise value of the external field. The other resonances, described by Feshbach theory, occur when the incident energy is near a bound state of the closed channel, as if it were decoupled from the open channel. These resonances exist for values of the external field above a particular threshold value. Besides the potential intrinsic value of this study in a quantum mechanics course, as the analysis can be performed with minor numerical calculations, it is also an aid for the understanding of current research advances in the exciting field of ultracold gases.
Abstract We discuss s-wave scattering in an atomic binary collision with two coupled channels, tunable by an external magnetic field, one channel open and the other closed for the incident energies considered. The analysis is performed with a stylized model of square-well potentials. This simplification allows for a pedagogically thorough discussion of the different scattering resonances that appear in coupled channels. One of them, the potential resonances at vanishing energy, occurs as a bound state of the coupled system emerges, in turn, tuned at a very precise value of the external field. The other resonances, described by Feshbach theory, occur when the incident energy is near a bound state of the closed channel, as if it were decoupled from the open channel. These resonances exist for values of the external field above a particular threshold value. Besides the potential intrinsic value of this study in a quantum mechanics course, as the analysis can be performed with minor numerical calculations, it is also an aid for the understanding of current research advances in the exciting field of ultracold gases.
The physics of Feshbach resonance is analyzed using an analytic expression for the s-wave scattering phase shift and the scattering length a which we derive within a two-channel tight-binding model. Employing a unified treatment of bound states and resonances in terms of the Jost function, it is shown that, for strong interchannel coupling, Feshbach resonance can occur even when the closed channel does not have a bound state. This may extend the range of ultracold atomic systems that can be manipulated by Feshbach resonance. The dependence of the sign of a on the coupling strength in the unitary limit is elucidated. As a by-product, analytic expressions are derived for the background scattering length, the external magnetic field at which resonance occurs, and the energy shift ε-ε(B), where ε is the scattering energy and ε(B) is the bound-state energy in the closed channel (when there is one).
A Feshbach resonance in the s-wave scattering length occurs if the energy of the two atoms in the incoming open channel is close to the energy of a bound state in a coupled closed channel. Starting from the microscopic Hamiltonian that describes this situation, we derive the effective atom–molecule theory for a Bose gas near a Feshbach resonance. In order to take into account all two-body processes, we have to dress the bare couplings of the atom–molecule model with ladder diagrams. This results in a quantum field theory that exactly reproduces the scattering amplitude of the atoms and the bound-state energy of the molecules. Since these properties are incorporated at the quantum level, the theory can be applied both above and below the critical temperature of the gas. Moreover, making use of the true interatomic potentials ensures that no divergences are encountered at any stage of the calculation. We also present the mean-field theory for the Bose–Einstein condensed phase of the gas.
By applying a magnetic field across a trapped ultracold gas of alkali metal atoms, it is possible to alter the binding energies of near threshold molecular states. The proximity of molecular states to the scattering threshold has a strong effect on the threshold scattering characteristics. Because of this the magnetic field strength can be used to control low energy scattering within the gas. This resonant phenomena is referred to as a magnetically tuneable Feshbach resonance. This thesis looks at these and related phenomena in the context of trapped potassium atoms. First, we perform coupled-channels calculations in order to characterise a group of previously unreported Feshbach resonances, occurring in a host of different collision channels. Next, we compare these characterisations to empirical data, and more simplified models. Second, a detailed investigation into the photodissociation of weakly bound Feshbach molecules is carried out. This allows us to gain new insights into the structure of the exit channel interaction. We make semi-classical arguments which enable experimentalists to directly measure the height of potential barriers. We also perform detailed numerical calculations which, in conjunction with experimental data, allow us to develop a fine-tuned potential model for the exit state. Third, we model weakly bound triatomic states and their impact on near threshold scattering. Then, we discuss the use of three body recombination as a tool for observing Efimov states. Furthermore, we model the three body recombination rate using a simplified two channel model. Finally we suggest a method intended to provide the basis for numerical calculations using realistic Born-Oppenheimer potentials. It could also be used to analytically study near threshold three body physics.
It is crucial to control the collision between ultracold atoms by applying external fields. We developed a theoretical model for investigating the s-wave scattering of ultracold atoms controlled by the magnetic field and laser field. The calculation is performed by using the close-coupling method and mapped Fourier grid method. Due to the interference between the photoassociation and bound-to-bound transitions, the bound state in the continuum, which is a resonance with a vanishing width, occurs at the magnetic field position near the magnetic Feshbach resonance. The widths of resonances in the neighborhood of the bound state in the continuum are narrow. Changing the laser intensity can shift the magnetic field position where the bound state in the continuum occurs through modifying the ground molecular state to induce wide resonances at desired magnetic field positions. By increasing the resonance width, the tunability of the real part of the scattering length at resonances can be significantly improved. Changing the laser intensity can also adjust the coupling between the ground and excited molecular states. When the coupling between the ground and excited molecular states approaches zero, a resonance is induced, and the photoassociation and bound-to-bound transitions are both significantly suppressed at this resonance. Therefore, the atomic loss peak due to spontaneous emission does not appear at this resonance. The magnetic field position of this resonance is stable against the change in laser frequency.
Starting from a system of NNN radial Schr\"odinger equations with a vanishing potential and finite threshold differences between the channels, a coupled $N\ifmmode\times\else\texttimes\fi{}N$ exactly solvable potential model is obtained with the help of a single nonconservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as does its Jost matrix. It depends on N(N+1)/2N(N+1)/2N(N+1)/2 unconstrained parameters and on one upper-bounded parameter, the factorization energy. A detailed study of the model is done for the $2\ifmmode\times\else\texttimes\fi{}2$ case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has zero, one, or two bound states, and zero or one resonance; a compact formula for the open-channel scattering length is obtained. As a first physical application, exactly solvable $2\ifmmode\times\else\texttimes\fi{}2$ atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interacts with a bound or virtual state close to threshold, which results in a large background scattering length.