Tight-binding Kondo model and spin-exchange collision rate of alkaline-earth-metal atoms in a mixed-dimensional optical lattice

Zhang, Ren; Zhang, Peng

doi:10.1103/physreva.101.013636

Cited by 12 publications

(10 citation statements)

References 25 publications

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“…3(b), experimentally this situation is realized by the Munich group and a resonant enhanced spin-exchanging scattering amplitude has been observed [45]. Theoretically, this problem can be treated with different degrees of approximations [43,44,[55][56][57], and quantitative results can be systematically improved [56]. The most accurate results are shown in Fig.…”

Section: Control Of Spin-exchanging Interactionmentioning

confidence: 87%

Controlling the interaction of ultracold alkaline-earth atoms

et al. 2020

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Ultracold alkaline-earth atoms have now been widely explored for precision measurements and quantum simulation. Because of its unique atomic structure, alkaline earth atoms possess great advantages for quantum simulation and studying quantum many-body matters, such as simulating synthetic gauge field, Kondo physics and SU (N ) physics. To fully explore the potential of ultracold alkaline-earth atoms, these systems also need to be equipped with the capability of tuning the interatomic interaction to the strongly interacting regime. Recently several theoretical proposals and experimental demonstrations have shown that both spin-independent and spin-exchanging interaction can be tuned to resonance. In this perspective, we will review these progress and discuss the new opportunities brought by these interaction control tools for future quantum simulation studies with ultracold alkaline-earth atoms. arXiv:1908.04973v1 [cond-mat.quant-gas]

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Section: Control Of Spin-exchanging Interactionmentioning

confidence: 87%

Controlling the interaction of ultracold alkaline-earth atoms

et al. 2020

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“…Thus, in the equations Eqs. (9,10) for the short-range wave function, the CoM motion is decoupled with the relative motion and the internal state, as in the case of Sec. II B 1.…”

Section: Multi-component Atoms: Simple Casesmentioning

confidence: 96%

“…Nevertheless, in these calculations the rindependent Zeeman Hamiltonian ĥS (δ) was ignored in the short-range limit r → 0, which means the Zeeman Hamiltonian ĥS (δ) was omitted in Eqs. (9,10), or the coefficients a lj (E, δ) were assumed as a lj (E, δ = 0). In Tab.…”

Section: Ybmentioning

confidence: 99%

“…For instance, the effective inter-atomic interaction of ultracold atoms in quasi low-(or mixed-) dimensional confinements is characterized by the two-body scattering amplitude. As a result, one can control this effective pairwise interaction by tuning the scattering amplitude through the confinement parameter [3][4][5][6][7][8][9][10]. In addition, using the energy spectrum of two ultracold atoms in a three-dimensional (3D) confinement, one can not only qualitatively obtain a primary understanding for the interacting physics, but also quantitatively calculate some important physical parameters for the many-body physics, such as the 2nd Virial coefficient [11,12].…”

Section: Introductionmentioning

confidence: 99%

“…As a result, there are nuclear-spin exchange interactions between these two atoms, with the intensity being proportional to (a − − a + ) in the zero-range limit [13,16,17,19,22]. Thus, the mixture of ultracold atoms in 1 S 0 and 3 P 0 states is a promising candidate for the quantum simulation of many-body physics induced by spin-exchange interaction (e.g., the Kondo physics), and has attracted much attention [6,7,9,17,22,[27][28][29][30][31]. Furthermore, the precise values of a ± are required as basic parameters for the study of this quantum simulation.…”

Section: Introductionmentioning

confidence: 99%

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Universal energy-dependent pseudopotential for the two-body problem of confined ultracold atoms

Xiao,

Zhang,

Zhang

2021

Preprint

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The two-body scattering amplitude and energy spectrum of confined ultracold atoms are of fundamental importance for both theoretical and experimental studies of ultracold atom physics. For many systems, one can efficiently calculate these quantities via the zero-range Huang-Yang pseudopotential (HYP), in which the interatomic interaction is characterized by the scattering length a. Furthermore, when the scattering length is dependent on the kinetic energy εr of two-atom relative motion, i.e., a = a(εr), the results are applicable for a broad energy region. However, when the free Hamiltonian of atomic internal state (e.g., the Zeeman Hamiltonian) does not commute with the inter-atomic interaction, or the center-of-mass (CoM) motion is coupled to the relative motion, the generalization of this technique is still lacking. In this work we solve this problem and construct a reasonable energy-dependent multi-channel HYP, which is characterized by a "scattering length operator" âeff , for the above complicated cases. Here âeff is an operator for atomic internal states and CoM motion, and depends on both the total two-atom energy and the external field as well as the trapping parameter. The effects from the internal-state or CoM-relative motion coupling can be self-consistently taken into account by âeff . We further show a method based on the quantum defect theory, with which âeff can be analytically derived for systems with van der Waals inter-atomic interaction. To demonstrate our method, we calculate the spectrum of two ultracold fermionic alkaline-earth-like atoms (in electronic 1 S0 (|g ) and 3 P0 (|e ) states, respectively) confined in an optical lattice. By comparing our results with the recent experimental measurements for two 173 Yb atoms and two 171 Yb atoms, we calibrate the scattering lengths a± with respect to anti-symmetric and symmetric nuclear-spin states to be a+ = 2012(19)a0 and a− = 193(4)a0 for 173 Yb, and a+ = 232(3)a0 and a− = 372(1)a0 for 171 Yb.

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Scattering amplitude and two-body loss of ultracold alkaline-earth atoms in a shaking synthetic magnetic field

Zhang

2022

Commun. Theor. Phys.

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The idea of manipulating the interaction between ultracold fermionic alkaline-earth (like) atoms via a laser-induced periodical synthetic magnetic field was proposed in [Phys. Rev. B {\bf 97}, 155156 (2018)]. In that work it was shown that in the presence of the shaking synthetic magnetic field, two atoms in $^1$S$_0$ and $^3$P$_0$ states experiences a periodical interaction in a rotated frame, and the effective inter-atomic interaction was approximated as the time-averaged operator of this time-dependent interaction. This technique is supposed to be efficient for $^{173}$Yb atoms which has large natural scattering length. Here we exam this time-averaging approximation and derive the rate of the two-body loss induced by the shaking of the synthetic magnetic field, by calculating the zero-energy inter-atomic scattering amplitude corresponding to the explicit periodical interaction. We find that for the typical cases with shaking angular frequency $\lambda$ of the synthetic magnetic field being of the order of $(2\pi)$kHz, the time-averaging approximation is applicable only when the shaking amplitude is small enough. Moreover, the two-body loss rate increases with the shaking amplitude, and is of the order of $10^{-10}$${\rm cm}^{3}{\rm s}^{-1}$ or even larger when the time-averaging approximation is not applicable. Our results are helpful for the quantum simulations with ultracold gases of fermionic alkaline-earth (like) atoms.

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Tight-binding Kondo model and spin-exchange collision rate of alkaline-earth-metal atoms in a mixed-dimensional optical lattice

Cited by 12 publications

References 25 publications

Controlling the interaction of ultracold alkaline-earth atoms

Controlling the interaction of ultracold alkaline-earth atoms

Universal energy-dependent pseudopotential for the two-body problem of confined ultracold atoms

Scattering amplitude and two-body loss of ultracold alkaline-earth atoms in a shaking synthetic magnetic field

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