Confinement-induced Resonances Research Articles

Controlling the interactions in a cold atom quantum impurity system

We implement an experimental architecture in which a single atom of K is trapped in an optical tweezer, and is immersed in a bath of Rb atoms at ultralow temperatures. In this regime, the motion of the single trapped atom is confined to the lowest quantum vibrational levels. This realizes an elementary and fully controllable quantum impurity system. For the trapping of the K atom, we use a species-selective dipole potential, that allows us to independently manipulate the quantum impurity and the bath. We concentrate on the characterization and control of the interactions between the two subsystems. To this end, we perform Feshbach spectroscopy, detecting several inter-dimensional confinement-induced Feshbach resonances for the KRb interspecies scattering length, that parametrizes the strength of the interactions. We compare our data to a theory for inter-dimensional scattering, finding good agreement. Notably, we also detect a series of p-wave resonances stemming from the underlying free-space s-wave interactions. We further determine how the resonances behave as the temperature of the bath and the dimensionality of the interactions change. Additionally, we are able to screen the quantum impurity from the bath by finely tuning the wavelength of the light that produces the optical tweezer, providing us with a new effective tool to control and minimize the interactions. Our results open a range of new possibilities in quantum simulations of quantum impurity models, quantum information, and quantum thermodynamics, where the interactions between a quantized system and the bath is a powerful yet largely underutilized resource.

Observation of Confinement-Induced Resonances in a 3D Lattice

Observation of Confinement-Induced Resonances in a 3D Lattice

A New Mechanism for Sympathetic Cooling of Atoms and Ions in Atomic and Ion-Atomic Traps

Sympathetic cooling of a Fermi gas with a buffer gas of bosonic atoms is an efficient way to achieve quantum degeneracy in Fermi systems. However, all attempts to use this method for cooling ions until recently were ineffective because of the unremovable ion `"micromotion" in electromagnetic Paul traps, which prevents the realization of a number of hot projects with cold atom-ion systems. In this regard, we propose a new efficient method for sympathetic cooling of ions: the use for this purpose of cold buffer atoms in the region of atom-ion confinement-induced resonances (CIRs) [V.S. Melezhik, Phys. Rev. A103, 53109 (2021)]. We show that the destructive effect of "micromotion" on its sympathetic cooling can, however, be suppressed in the vicinity of the atom-ion CIR. Here, the resonant blocking of a close collision of an atom with an ion also resists its heating due to "micromotion". We investigate the effect of sympathetic cooling around CIRs in atom-ion, and atom-atom confined collisions within the quantum-quasiclassical approach using the Li-Yb$^+$ and Li-Yb confined systems as an example. In this approach, the Schr\"odinger equation for a cold light atom is integrated simultaneously with the classical Hamilton equations for a hotter heavy-ion or atom during a collision. We have found the region near the atom-ion CIR where the sympathetic cooling of the ion by cold atoms is possible in a hybrid atom-ion trap. We also show that it is possible to improve the efficiency of sympathetic cooling in atomic traps by using atomic CIRs.

Impact of ion motion on atom-ion confinement-induced resonances in hybrid traps

We investigate confinement-induced resonances in atom-ion quantum mixtures confined in hybrid traps. Specifically, we consider an ion confined in a time-dependent radio-frequency Paul trap with linear geometry, while the atom is constrained to move into a quasi-one-dimensional optical waveguide within the ion trap. We evaluate the impact of the ion intrinsic micromotion on the resonance position. Thus, we solve the atom-ion dynamics semiclassically, namely the atom dynamics is governed by the three-dimensional time-dependent Schr\"odinger equation, whereas the ion motion is described by the classical Hamilton equations. We find that the energy of the ion provided by the oscillating radiofrequency fields can affect the resonance position substantially. Notwithstanding, the peculiar phenomenology of those resonances regarding perfect transmission and reflection is still observable. These findings indicate that the intrinsic micromotion of the ion is not detrimental for the occurrence of the resonance and that its position can be controlled by the radiofrequency fields. This provides an additional mean for tuning atom-ion interactions in low spatial dimensions. The study represents an important advancement in the scattering physics of compound atomic quantum systems in time-dependent traps.

Confinement-induced resonances in two-center problem via a pseudopotential approach

We study confined scattering of a quantum particle by two centers fixed on the longitudinal axis of a harmonic-waveguide-like trap. The conditions of confinement-induced resonances (CIRs) appearing in these systems, when scattering cross section approaches the unitary limit, are derived for a regularized pseudopotential describing particle interaction with scattering centers. In the limit of a single center, the position of CIR for an even state tends to the well-known result obtained by Olshanii [Phys. Rev. Lett. 81, 938 (1998)]. Our result can be applicable to confined atomic scattering by fixed impurities, such as ions or Rydberg atoms, with possible extension to $N$ impurities, or by two-atomic molecules.

Control of spin-exchange interaction between alkali-earth-metal atoms via confinement-induced resonances in a quasi-(1+0)-dimensional system

A nuclear-spin exchange interaction exists between two ultracold fermionic alkali-earth (like) atoms in the electronic $^{1}{\rm S}_{0}$ state ($g$-state) and $^{3}{\rm P}_{0}$ state ($e$-state), and is an essential ingredient for the quantum simulation of Kondo effect. We study the control of this spin-exchange interaction for two atoms simultaneously confined in a quasi-one-dimensional (quasi-1D) tube, where the $g$-atom is freely moving in the axial direction while the $e$-atom is further localized by an additional axial trap and behaves as a quasi-zero-dimensional (quasi-0D) impurity. In this system, the two atoms experience effective-1D spin-exchange interactions in both even and odd partial wave channels, whose intensities can be controlled by the characteristic lengths of the confinements via the confinement-induced-resonances (CIRs). In current work, we go beyond that pure-1D approximation. We model the transverse and axial confinements by harmonic traps with finite characteristic lengths $a_\perp$ and $a_z$, respectively, and exactly solve the quasi-1D + quasi-0D scattering problem between these two atoms. Using the solutions we derive the effective 1D spin-exchange interaction and investigate the locations and widths of the even/odd wave CIRs for our system. It is found that when the ratio $a_z/a_\perp$ is larger, the CIRs can be induced by weaker confinements, which are easier to be realized experimentally. The comparison between our results and the recent experiment shows that the two experimentally observed resonance branches of the spin-exchange effect are due to an even-wave CIR and an odd-wave CIR, respectively. Our results are advantageous for the control and description of either the effective spin-exchange interaction or other types of interactions between ultracold atoms in quasi 1+0 dimensional systems.

Josephson oscillation and self-trapping in momentum space

A nuclear-spin exchange interaction exists between two ultracold fermionic alkali-earth (like) atoms in the electronic $^{1}{\rm S}_{0}$ state ($g$-state) and $^{3}{\rm P}_{0}$ state ($e$-state), and is an essential ingredient for the quantum simulation of Kondo effect. We study the control of this spin-exchange interaction for two atoms simultaneously confined in a quasi-one-dimensional (quasi-1D) tube, where the $g$-atom is freely moving in the axial direction while the $e$-atom is further localized by an additional axial trap and behaves as a quasi-zero-dimensional (quasi-0D) impurity. In this system, the two atoms experience effective-1D spin-exchange interactions in both even and odd partial wave channels, whose intensities can be controlled by the characteristic lengths of the confinements via the confinement-induced-resonances (CIRs). In current work, we go beyond that pure-1D approximation. We model the transverse and axial confinements by harmonic traps with finite characteristic lengths $a_\perp$ and $a_z$, respectively, and exactly solve the "quasi-1D + quasi-0D" scattering problem between these two atoms. Using the solutions we derive the effective 1D spin-exchange interaction and investigate the locations and widths of the even/odd wave CIRs for our system. It is found that when the ratio $a_z/a_\perp$ is larger, the CIRs can be induced by weaker confinements, which are easier to be realized experimentally. The comparison between our results and the recent experiment shows that the two experimentally observed resonance branches of the spin-exchange effect are due to an even-wave CIR and an odd-wave CIR, respectively. Our results are advantageous for the control and description of either the effective spin-exchange interaction or other types of interactions between ultracold atoms in quasi 1+0 dimensional systems.

Mathematical Modeling of Resonant Processes in Confined Geometry of Atomic and Atom-Ion Traps

We discuss computational aspects of the developed mathematical models for resonant processes in confined geometry of atomic and atom-ion traps. The main attention is paid to formulation in the nondirect product discrete-variable representation (npDVR) of the multichannel scattering problem with nonseparable angular part in confining traps as the boundary-value problem. Computational efficiency of this approach is demonstrated in application to atomic and atom-ion confinement-induced resonances we predicted recently.

Enhancing Kondo coupling in alkaline-earth-metal atomic gases with confinement-induced resonances in mixed dimensions

The Kondo effect describes the spin-exchanging interaction between localized impurity and the itinerant fermions. The ultracold alkaline-earth atomic gas provides a natural platform for quantum simulation of the Kondo model, utilizing its long-lived clock state and the nuclear-spin exchanging interaction between the clock state and the ground state. One of the key issue now is whether the Kondo temperature can be high enough to be reached in current experiment, for which we have proposed using a transverse confinement to confine atoms into a one-dimensional tube and to utilize the confinement-induced resonance to enhance the Kondo coupling. In this work, we further consider the $1+0$ dimensional scattering problem when the clock state is further confined by an axial harmonic confinement. We show that this axial confinement for the clock state atoms not only plays a role for localizing them, but also can act as an additional control knob to reach the confinement-induced resonance. We show that by combining both the transverse and the axial confinements, the confinement-induced resonance can be reached in the practical conditions and the Kondo effect can be attainable in this system.

Multichannel scattering problem with a nonseparable angular part as a boundary-value problem.

We have developed an efficient computational method for solving the quantum multichannel scattering problem with a nonseparable angular part. The use of the nondirect product discrete-variable representation, suggested and developed by V. Melezhik, gives us an accurate approximation for the angular part of the desired wave function and, eventually, for the scattering parameters. Subsequent reduction of the problem to the boundary-value problem with well-defined block-band matrix of equation coefficients permits us to use efficient standard algorithms for its solution. We demonstrate the numerical efficiency, flexibility, and good convergence of the computational scheme in a quantitative description of the Feshbach resonances in pair collisions occurring in atomic traps and the scattering in strongly anisotropic traps. The method can also be used for the investigation of further actual problems in quantum physics. A natural extension is a description of spin-orbit coupling, intensively investigated in ultracold gases, and dipolar confinement-induced resonances.

Tunnel-induced Dipolar Resonances in a Double-well Potential.

A system of two dipolar particles that are confined in a double-well potential and interact via a realistic isotropic interaction potential is investigated as a protoype for ultracold atoms with a magnetic dipole moment or ultracold dipolar heteronuclear diatomic molecules in double-well traps or in optical lattices. The resulting energy spectrum is discussed as a function of the dipole-dipole interaction strength. The variation of the strength of the dipole-dipole interaction is found to lead to various resonance phenomena. Among those are the previously discussed inelastic confinement-induced resonances as well as the dipole-induced resonances. It is found that the double-well potential gives rise to a new type of resonances, tunnel-induced dipolar ones.

Theory of inelastic confinement-induced resonances due to the coupling of center-of-mass and relative motion

A detailed study of the anharmonicity-induced resonances caused by the coupling of center-of-mass and relative motion is presented for a system of two ultracold atoms in single-well potentials. As has been confirmed experimentally, these inelastic confinement-induced resonances are of interest, since they can lead to coherent molecule formation, losses, and heating in ultracold atomic gases. A perturbative model is introduced to describe the resonance positions and the coupling strengths. The validity of the model and the behavior of the resonances for different confinement geometries are analyzed in comparison with exact numerical ab initio calculations. While such resonances have so far only been detected for large positive values of the $s$-wave scattering length, it is found that they are present also for negative $s$-wave scattering lengths, i. e. for attractive interactions. The possibility to coherently tune the resonances by a variation of the external confinement geometry might pave the way for coherent molecule association where magnetic Feshbach resonances are inaccessible.

Confinement-induced resonances in ultracold atom-ion systems

We investigate confinement-induced resonances in a system composed by a tightly trapped ion and a moving atom in a waveguide. We determine the conditions for the appearance of such resonances in a broad region -- from the "long-wavelength" limit to the opposite case when the typical length scale of the atom-ion polarisation potential essentially exceeds the transverse waveguide width. We find considerable dependence of the resonance position on the atomic mass which, however, disappears in the "long-wavelength and zero-energy" limit, where the known result for the confined atom-atom scattering is reproduced. We also derive an analytic and a semi-analytic formula for the resonance position in the "long-wavelength and zero-energy" limit and we investigate numerically how the position of the resonance is affected by a finite atomic colliding energy. Our results, which can be investigated experimentally in the near future, could be used to determine the atom-ion scattering length, the temperature of the atomic ensemble in the presence of an ion impurity, and to control the atom-phonon coupling in a linear ion crystal in interaction with a quasi one dimensional atomic quantum gas.

Finite-temperature fluid–insulator transition of strongly interacting 1D disordered bosons

We consider the many-body localization-delocalization transition for strongly interacting one-dimensional disordered bosons and construct the full picture of finite temperature behavior of this system. This picture shows two insulator-fluid transitions at any finite temperature when varying the interaction strength. At weak interactions, an increase in the interaction strength leads to insulator [Formula: see text] fluid transition, and, for large interactions, there is a reentrance to the insulator regime. It is feasible to experimentally verify these predictions by tuning the interaction strength with the use of Feshbach or confinement-induced resonances, for example, in (7)Li or (39)K.

Kondo effect in alkaline-earth-metal atomic gases with confinement-induced resonances

Alkali-earth atoms have a long-lived electronic excited state, which can be localized in the Fermi sea of ground state atoms by an external potential and serve as magnetic impurities, due to the spin-exchange interaction between the excited and the ground state atoms. This can give rise to the Kondo effect. However, in order to achieve this effect in current atomic gas experiment, it requires the Kondo temperature to be increased to a sizable portion of the Fermi temperature. In this letter we propose that the spin-exchange interaction can be strongly enhanced by utilizing the confinement-induced resonance (CIR). We analyze this system by the renormalization group approach, and we show that nearby a CIR, the Kondo temperature can indeed be increased to the regime attainable by current experiments.

Two-body physics in quasi-low-dimensional atomic gases under spin–orbit coupling

One of the most dynamic directions in ultracold atomic gas research is the study of low-dimensional physics in quasi-low-dimensional geometries, where atoms are confined in strongly anisotropic traps. Recently, interest has significantly intensified with the realization of synthetic spin–orbit coupling (SOC). As a first step toward understanding the SOC effect in quasi-low-dimensional systems, the solution of two-body problems in different trapping geometries and different types of SOC has attracted great attention in the past few years. In this review, we discuss both the scattering-state and the bound-state solutions of two-body problems in quasi-one and quasi-two dimensions. We show that the degrees of freedom in tightly confined dimensions, in particular with the presence of SOC, may significantly affect system properties. Specifically, in a quasi-one-dimensional atomic gas, a one-dimensional SOC can shift the positions of confinement-induced resonances whereas, in quasitwo- dimensional gases, a Rashba-type SOC tends to increase the two-body binding energy, such that more excited states in the tightly confined direction are occupied and the system is driven further away from a purely two-dimensional gas. The effects of the excited states can be incorporated by adopting an effective low-dimensional Hamiltonian having the form of a two-channel model. With the bare parameters fixed by two-body solutions, this effective Hamiltonian leads to qualitatively different many-body properties compared to a purely low-dimensional model.

Analytical approach to atomic multichannel collisions in tight harmonic waveguides

We perform an analytical investigation in the framework of generalized $K$-matrix theory of the scattering problem in tight isotropic and harmonic waveguides allowing for several open scattering channels. The scattering behavior is explored for identical bosons and fermions, as well as for distinguishable particles, the main aspect being the confinement-induced resonances (CIR) which are attributed to different partial waves. In particular, we present the unitarity bounds which emerge when considering a quasi-one-dimensional system. Unitarity bounds are also given for the transition coefficients, which show the limitations for efficient transversal (de)excitations by means of CIRs. We analyze the CIR for $d$ waves and find the intriguing phenomenon of a strong transmission suppression in the presence of more than one open channel, which represents an interesting regime to be applied in the corresponding many-particle systems. The corresponding channel threshold singularities are studied and it is shown that these are solely determined by the symmetry class of the partial wave.

Shifts and widths of p-wave confinement induced resonances in atomic waveguides

We develop and analyze a theoretical model to study p-wave Feshbach resonances of identical fermions in atomic waveguides by extending the two-channel model of Lange et al (2009 Phys. Rev. A 79 013622) and Saeidian et al (2012 Phys. Rev. A 86 062713). The experimentally known parameters of Feshbach resonances in free space are used as input of the model. We calculate the shifts and widths of p-wave magnetic Feshbach resonance of 40K atoms emerging in harmonic waveguides as p-wave confinement induced resonance (CIR). Particularly, we show a possibility to control the width and shift of the p-wave CIR by the trap frequency and the applied magnetic field which could be used in corresponding experiments. Our analysis also demonstrates the importance of the inclusion of the effective range in the computational schemes for the description of the p-wave CIRs contrary to the case of s-wave CIRs where the influence of this term is negligible.

Resonances in ultracold dipolar atomic and molecular gases

A previously developed approach for the numerical treatment of two particles that are confined in a finite optical-lattice potential and interact via an arbitrary isotropic interaction potential has been extended to incorporate an additional anisotropic dipole–dipole interaction (DDI). The interplay of a model but realistic short-range Born–Oppenheimer potential and the DDI for two confined particles is investigated. A variation of the strength of the DDI leads to diverse resonance phenomena. In a harmonic confinement potential some resonances show similarities to s-wave scattering resonances while in an anharmonic trapping potential like the one of an optical lattice additional inelastic confinement-induced dipolar resonances occur. The latter are due to a coupling of the relative and center-of-mass motion caused by the anharmonicity of the external confinement.

Reactive collisions in confined geometries

We consider low energy threshold reactive collisions of particles interacting via a van der Waals potential at long range in the presence of external confinement and give analytic formulas for the confinement modified scattering in such circumstances. The reaction process is described in terms of the short range reaction probability. Quantum defect theory is used to express elastic and inelastic or reaction collision rates analytically in terms of two dimensionless parameters representing phase and reactivity. We discuss the modifications to Wigner threshold laws for quasi-one-dimensional and quasi-two-dimensional geometries. Confinement-induced resonances are suppressed due to reactions and are completely absent in the universal limit where the short-range loss probability approaches unity.