Confinement-induced Resonance Research Articles

Solution of the BEC to BCS Quench in One Dimension.

A gas of interacting fermions confined in a quasi one-dimensional geometry shows a BEC to BCS crossover upon slowly driving its coupling constant through a confinement-induced resonance. On one side of the crossover the fermions form tightly bound bosonic molecules behaving as a repulsive Bose gas, while on the other they form Cooper pairs, whose size is much larger than the average interparticle distance. Here we consider the situation arising when the coupling constant is varied suddenly from the BEC to the BCS value. Namely, we study a BEC-to-BCS quench. By exploiting a suitable continuum limit of recently discovered solvable quenches in the Hubbard model, we show that the local stationary state reached at large times after the quench can be determined exactly by means of the quench action approach. We provide an experimentally accessible characterization of the stationary state by computing local pair correlation function as well as the quasiparticle distribution functions. We find that the steady state is increasingly dominated by two-particle spin singlet bound states for stronger interaction strength, but that bound state formation is inhibited at larger BEC density. The bound state rapidity distribution displays quartic power-law decay suggesting a violation of Tan's contact relations.

Interaction-modulated tunneling dynamics of a mixture of Bose-Fermi superfluid

In this paper, we study the interaction-modulated tunneling dynamics of a Bose-Fermi superfluid mixture, where a Bose-Einstein condensate (BEC) with weak repulsive interaction is confined in a symmetric deep double-well potential and an equally populated two-component Fermi gas in a harmonic potential symmetrically is positioned in the center of the double-well potential. The tunneling between the two wells is modulated by fermions trapped in a harmonic potential. When the temperature is adequately low and the bosonic particle number is adequately large, we can employ the mean-field theory to describe the evolution of the BEC in the double-well potential through the time-dependent Gross-Pitaevskii equation. For the Fermi gas in the harmonic potential trap, we consider the case where the inter-fermion interaction is tuned on the deep Bose-Einstein condensate of the inter-fermion Feshbach resonance, where two fermions of spin-up and spin-down form a two-body bound state. Within the regime, the Fermi gas is well described by a condensate of these fermionic dimers, and hence can be simulated as well by a Gross-Pitaevskii equation of dimers. The inter-species interactions couple the dynamics of the two species, which results in interesting features in the tunneling oscillations. The dynamic equations of the BEC in the double-well potential is described by a two-mode approximation. Coupling it with time-dependent Gross-Pitaevskii equation of the harmonically potential trapped molecular BEC, we numerically investigate the dynamical evolution of the Boson-Fermi hybrid system under different initial conditions. It is found that the interaction among fermions in a harmonic potential leads to strong non-linearity in the oscillations of the bosons in the double-well potential and enriches the tunneling dynamics of the bosons. Especially, it strengthens macroscopic quantum self-trapping. And the macroscopic quantum self-trapping can be expressed in three forms: the phase tends to be negative and monotonically decreases with time, the phase evolves with time, and the phase tends to be positive and increases monotonically with time. This means that it is possible the tunneling dynamics of the BEC in double-well potential is adjustable. Our results can be verified experimentally in a Bose-Fermi superfluid mixture by varying different interaction parameters via Feshbach resonance and confinement-induced resonance.

Two distinguishable fermions entanglement generation and fermionization

We propose a procedure for entanglement generation which could be implemented in current experiments performed with two distinguishable interacting fermions confined in a 1D harmonic trap [Phys. Rev. Lett. 108 , 075303 (2012)]. Our results indicate that entangled states could be obtained by preparing a non-interacting non-entangled product state of the trap and then properly controlling the scattering length by means of the magnetic field. Entanglement could be generated when the prepared non-entangled initial state undergoes a turn on and off interaction procedure in which the state is brought into the interacting regime and then back to the absence of interaction point. Entanglement could also be generated when reaching the strongly repulsive regime by tuning the scattering length near the confinement-induced resonance (CIR), i.e. when the two distinguishable fermions are fermionized. We give exact upper bounds for the entanglement and show that maximally entangled states could be produced. Moreover, our results suggest that the maximum entanglement could be reached by repeatedly turning on and off the interaction or by repeatedly crossing the CIR, being the latter the most convenient procedure because it ensures the obtention of maximally entangled states with a higher probability. The turn on and off procedure, the fermionization of the states, and the CIR crossing constitute three basic experimentally realizable main steps upon which several paths for entanglement generation could be diagrammed. • Entanglement generation in a two distinguishable interacting fermion system. • Entangled states are obtained tuning the interaction strength with a magnetic field. • Entanglement could be generated with three basic experimental main steps. • Several paths for entanglement generation could be diagrammed. • Maximum entanglement could be generated by repeatedly crossing the resonance.

Asymmetric conductivity of the Kondo effect in cold atomic systems

Motivated by recent theoretical and experimental advances in quantum simulations using alkaline earth (AE) atoms, we put forward a proposal to detect the Kondo physics in a cold atomic system. It has been demonstrated that the intrinsic spin-exchange interaction in AE atoms can be significantly enhanced near a confinement-induced resonance (CIR), which facilitates the simulation of Kondo physics. Since the Kondo effect appears only for antiferromagnetic coupling, we find that the conductivity of such system exhibits an asymmetry across a resonance of spin-exchange interaction. The asymmetric conductivity can serve as the smoking gun evidence for Kondo physics in the cold atom context. When an extra magnetic field ramps up, the spin-exchange process near Fermi surface is suppressed by Zee-man energy and the conductivity becomes more and more symmetric. Our results can be verified in the current experimental setup.

Improving efficiency of sympathetic cooling in atom-ion and atom-atom confined collisions

We propose a new way for sympathetic cooling of ions in an electromagnetic Paul trap: it implies the use for this purpose of cold buffer atoms in the region of atom-ion confinement-induced resonance (CIR). The problem is that the unavoidable micromotion of the ion and the long-range nature of its interaction with the environment of colder atoms in a hybrid atomic-ion trap prevent its sympathetic cooling. We show that the destructive effect of ion micromotion on its sympathetic cooling can however be suppressed in the vicinity of the atom-ion CIR. The origin of this is the "fermionization" of the atom-ion wave function near CIR, where the atom-ion pair behaves as a pair of noninteracting identical fermions. This prevents the complete approach of the atom with the ion near resonance and does not enhance the ion micromotion, which interferes with its sympathetic cooling. We investigate the effect of sympathetic cooling around CIRs in atom-ion and atom-atom confined collisions within the qusiclassical-quantum 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 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.

Entanglement and fermionization of two distinguishable fermions in a strict and non strict one-dimensional space

The fermionization regime and entanglement correlations of two distinguishable harmonically confined fermions interacting via a zero-range potential is addressed. We present two alternative representations of the ground state that we associate with two different types of one-dimensional spaces. These spaces, in turn, induce different correlations between particles and thus require a suitable definition of entanglement. We find that the entanglement of the ground state is strongly conditioned by those one-dimensional space features. We also find that in the strongly attractive regime the relative ground state is a highly localized state leading to maximum entanglement. Our analysis shows that in the strongly repulsive regime the ground state changes smoothly from a superposition of Slater-like states to a finite superposition of Slaters, this lack of accessible states yields to Pauli blocking as a strong signature of fermionization. Our results indicate that entangled states could be obtained in current experiments by reaching the non-interacting regime from the interacting regime. Entangled states could also be obtained when a state is brought from the interacting regime into the strongly repulsive regime by changing the scattering length near the confinement-induced resonance (CIR). Finally, we show that the first excited state obtained in the absence of interactions and the third excited fermionized state are maximally entangled.

Confinement-induced resonance (CIR) in classical vs. quantum scattering under 2D harmonic confinement

Using complex analysis, we have investigated classical quasi-one-dimensional atom–atom scattering under 2D harmonic confinement with two different interaction potentials (Yukawa and Lennard-Jones) and found that the confinement-induced resonance (CIR) that occurs in the quantum system seems to have a classical analogue. We observed CIR in our classical results in the sense that a clear minimum appeared in the transmission coefficient for the different interaction potentials. We also investigated the changes in the value and position of this minimum by varying the characteristic parameters of the system including the angular momentum $$L_z$$ along the longitudinal axis. In the quantum case, it has already been shown that for the zero range Huang potential, CIR occurs only for $$L_z = 0$$. Our results indicate that classical CIR can also occur for $$L_z \ne 0$$ using finite range potentials. We have endeavoured to provide extensive physical arguments to explain the observed results and to support the proposed analogy between the classical and quantum regimes where applicable.

Confinement-induced resonance with weak background interaction

We studied the scattering problem of two distinguishable atoms with unequal mass, where one atom (atom $\ensuremath{\alpha}$) is trapped in a quasi-one-dimensional (quasi-1D) tube and the other one (atom $\ensuremath{\beta}$) is localized by a 3D harmonic trap. We show that in such a system if atom $\ensuremath{\alpha}$ is much heavier than $\ensuremath{\beta}$, confinement-induced resonance (CIR) can appear when the 3D $s$-wave scattering length ${a}_{s}$ of these two atoms is much smaller than the characteristic lengths (CLs) of the confinements, for either ${a}_{s}>0$ or ${a}_{s}<0$. This is quite different from the usual CIRs which occur only when ${a}_{s}$ is comparable with the CL of confinement. Moreover, the CIRs we find are broad enough to serve as a tool for the control of effective interatomic interaction. We further show the mechanism of these CIRs via the Born-Oppenheimer approximation. Our results can be used for the realization of strongly interacting systems with ultracold atoms with weak 3D background interaction (i.e., small ${a}_{s}$), e.g., the realization of ultracold gases with strong spin-dependent interaction at zero magnetic fields.

Confinement Induced Resonance with Weak Bare Interaction in a Quasi 3+0 Dimensional Ultracold Gas

Confinement induced resonance (CIR) is a useful tool for the control of the interaction between ultracold atoms. In most cases the CIR occurs when the characteristic length atrap of the confinement is similar as the scattering length as of the two atoms in the free three-dimensional (3D) space. If there is a CIR which can occur with weak bare interaction, i.e., under the condition $a_{\rm{trap}}\gg a_s$, then it can be realized for much more systems, even without the help of a magnetic Feshbach resonance, and would be very useful. In a previous research by Massignan and Castin (Phys Rev A 74:013616, 2006), it was shown that it is possible to realize such a CIR in a quasi-(3+0)D system, where one ultracold atom is moving in the 3D space and another one is localized by a 3D harmonic trap. In this work we carefully investigate the properties of the CIRs in this system. We show that the CIR with $a_{\rm{trap}}\gg a_s$ can really occur, and the number of the CIRs of this type increases with the mass ratio between the moving and localized atoms. However, when $a_{\rm{trap}}\gg a_s$ the CIR becomes extremely narrow, and thus are difficult to be controlled in realistic experiments.

Tunneling dynamics of a Bose–Fermi superfluid mixture

We study the tunneling dynamics of a Bose–Fermi superfluid mixture where bosons are confined in a double-well potential and fermions in a harmonic potential symmetrically positioned at the center of the double-well. By focusing on the deep Bose–Einstein condensate side of the inter-fermion Feshbach resonance where the fermions can be well described as molecular bosons, we employ a mean-field method and numerically investigate the dynamical evolution of bosons under different parameters and initial conditions. We find that the interaction with background fermions can enrich the tunneling dynamics of the bosons, and specifically, lead to a re-entrant macroscopic quantum self-trapping state by varying different parameters. Our results can be observed in Bose–Fermi superfluid mixture by tuning interactions via Feshbach resonance and confinement-induced resonance.

Dimensional crossover for the beyond-mean-field correction in Bose gases

We present a detailed beyond-mean-field analysis of a weakly interacting Bose gas in the crossover from three to low dimensions. We find an analytical solution for the energy and provide a clear qualitative picture of the crossover in the case of a box potential with periodic boundary conditions. We show that the leading contribution of the confinement-induced resonance is of beyond-mean-field order and calculate the leading corrections in the three- and low-dimensional limits. We also characterize the crossover for harmonic potentials in a model system with particularly chosen short- and long-range interactions and show the limitations of the local-density approximation. Our analysis is applicable to Bose-Bose mixtures and gives a starting point for developing the beyond-mean-field theory in inhomogeneous systems with long-range interactions such as dipolar particles or Rydberg-dressed atoms.

Confinement-induced resonance of alkaline-earth-metal-like atoms in anisotropic quasi-one-dimensional traps

We study the confinement-induced resonance (CIR) of $^{173}$Yb atoms near an orbital Feshbach resonance in a quasi-one-dimensional tube with transversal anisotropy. By solving the two-body scattering problem, we obtain the location of CIR for various anisotropy ratio and magnetic field. Our results show that the anisotropy of the trapping potential can serve as an additional knob to tune the location of CIR. In particular, one can shift the location of CIR to the region attainable in current experiment. We also study the energy spectrum of the system and analyze the properties of CIR from the perspective of bound states. We find that as the orbital Feshbach resonance acquires two nearly degenerate scattering channels, which in general have different threshold energies, CIR takes place when the closed channel bound state energy becomes degenerate with one of the thresholds.

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.

Width of the confinement-induced resonance in a quasi-one-dimensional trap with transverse anisotropy

We theoretically study the width of the s-wave confinement-induced resonance (CIR) in quasi-one-dimensional atomic gases under tunable transversely anisotropic confinement. We find that the width of the CIR can be tuned by varying the transverse anisotropy. The change in the width of the CIR can manifest itself in the position of the discontinuity in the interaction energy density, which can be probed experimentally.

Stretching p -wave molecules by transverse confinements

We revisit the confinement-induced p-wave resonance in quasi-one-dimensional (quasi-1D) atomic gases and study the induced molecules near resonance. We derive the reduced 1D interaction parameters and show that they can well predict the binding energy of shallow molecules in quasi-1D system. Importantly, these shallow molecules are found to be much more spatially extended compared to those in three dimensions (3D) without transverse confinement. Our results strongly indicate that a p-wave interacting atomic gas can be much more stable in quasi-1D near the induced p-wave resonance, where most weight of the molecule lies outside the short-range regime and thus the atom loss could be suppressed.

Tuning an effective spin chain of three strongly interacting one-dimensional fermions with the transversal confinement

Strongly interacting one-dimensional fermions form an effective spin chain in the absence of an external lattice potential. We show that the exchange coefficients of such a chain may be locally tuned by properly tailoring the transversal confinement. In particular, in the vicinity of a confinement-induced resonance (CIR) the exchange coefficients may have simultaneously opposite ferromagnetic and antiferromagnetic characters at different locations along the trap axis. Moreover, the local exchanges may be engineered to induce avoided crossings between spin states at the CIR, and hence a ramp across the resonance may be employed to create different spin states and to induce spin dynamics in the chain. We show that such unusual spin chains have already been realized in the experiment of Murmann et al. [Phys. Rev. Lett. 115, 215301 (2015)].

Spin-orbit-induced resonances and threshold anomalies in a reduced-dimension Fermi gas

We calculate the reflection and transmission probabilities in a one-dimensional Fermi gas with an equal mixing of the Rashba and Dresselhaus spin-orbit coupling (RD-SOC) produced by an external Raman laser field. These probabilities are computed over multiple relevant energy ranges within the pseudo-potential approximation. Strong scattering resonances are found whenever the incident energy approaches either a scattering threshold or a quasi-bound state attached to one of the energetically closed higher dispersion branches. A striking difference is demonstrated between two very different regimes set by the Raman laser intensity, namely between scattering for the single- minimum dispersion versus the double-minimum dispersion at the lowest threshold. The presence of RD-SOC together with the Raman field fundamentally changes the scattering behavior and enables the realization of very different one-dimensional theoretical models in a single experimental setup when combined with a confinement-induced resonance.

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.

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.

Two-body state withp-wave interaction in a one-dimensional waveguide under transversely anisotropic confinement

We theoretically study two atoms with $p$-wave interaction in a one-dimensional waveguide, and investigate how the transverse anisotropy of the confinement affects the two-body state, especially, the properties of the resonance. For bound-state solution, we find there are totally three two-body bound states due to the richness of the orbital magnetic quantum number of $p$-wave interaction, while only one bound state is supported by $s$-wave interaction. Two of them become nondegenerate due to the breaking of the rotation symmetry under transversely anisotropic confinement. For scattering solution, the effective one-dimensional scattering amplitude and scattering length are derived. We find the position of the $p$-wave confinement-induced resonance shifts apparently as the transverse anisotropy increases. In addition, a two-channel mechanism for confinement-induced resonance in a one-dimensional waveguide is generalized to $p$-wave interaction, which was proposed only for $s$-wave interaction before. All our calculations are based on the parameterization of the $^{40}$K atom experiments, and can be confirmed in future experiments.