Abstract The idea of manipulating the interaction between ultracold fermionic alkaline-earth (like) atoms via a laser-induced periodical synthetic magnetic field was proposed in Kanász-Nagy et al (2018 Phys. Rev. B 97, 155156). In that work, it was shown that in the presence of the shaking synthetic magnetic field, two atoms in 1S0 and 3P0 states experience 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 173Yb atoms which have a large natural scattering length. Here we examine 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 λ of the synthetic magnetic field being of the order of (2π) 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 cm3 · 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.
Abstract The idea of manipulating the interaction between ultracold fermionic alkaline-earth (like) atoms via a laser-induced periodical synthetic magnetic field was proposed in Kanász-Nagy et al (2018 Phys. Rev. B 97, 155156). In that work, it was shown that in the presence of the shaking synthetic magnetic field, two atoms in 1S0 and 3P0 states experience 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 173Yb atoms which have a large natural scattering length. Here we examine 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 λ of the synthetic magnetic field being of the order of (2π) 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 cm3 · 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.
Ultracold gases of fermionic alkaline-earth(-like) atoms are hopeful candidates for the quantum simulation of many-body physics induced by magnetic impurities (e.g., the Kondo physics), because there are spin-exchange interactions (SEIs) between two atoms in the electronic ground (1S0) and metastable (3P) state, respectively. Nevertheless, this SEI cannot be tuned via magnetic Feshbach resonance. In this paper, we propose three methods to control the SEI between one atom in the 1S0 state and another atom in the 3P2 states or $^{3}\mathrm{P}_{2}\text{\ensuremath{-}}^{3}\mathrm{P}_{0}$ dressed states, with one or two laser beams. These methods are based on the spin-dependent ac-Stark shifts of the 3P2 states or the $^{3}\mathrm{P}_{2}\text{\ensuremath{-}}^{3}\mathrm{P}_{0}$ Raman coupling. We show that due to the structure of alkaline-earth (like) atoms, the heating effects induced by the laser beams of our methods are very weak. For instance, for ultracold Yb atoms, ac-Stark-shift difference of variant spin states of the 3P2(F=3/2) level, or the strength of the $^{3}\mathrm{P}_{2}\text{\ensuremath{-}}^{3}\mathrm{P}_{0}$ Raman coupling, could be of the order of $(2\ensuremath{\pi})\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, while the heating rate (photon scattering rate) is only of the order of Hz. As a result, the Feshbach resonances, with which one can efficiently control the SEI by changing the laser intensity, may be induced by the laser beams with a low-enough heating rate, even if the scattering lengths of the bare interatomic interaction are so small that they are comparable with the length scale associated with the van der Waals interaction.
Most of the current theories on the p-wave superfluid in cold atomic gases are based on the effective-range theory for the two-body scattering, where the low-energy p-wave scattering amplitude f1(k) is given by ${f}_{1}(k)=\ensuremath{-}1/[\mathit{ik}+1/(\mathcal{V}{k}^{2})+1/\mathcal{R}]$. Here k is the incident momentum, V and R are the k-independent scattering volume and effective range, respectively. However, due to the long-range nature of the van der Waals interaction between two colliding ultracold atoms, the p-wave scattering amplitude of the two atoms is not described by the effective-range theory [J. Math. Phys. 4, 54 (1963); Phys. Rev. A 58, 4222 (1998)]. In this paper we provide an explicit calculation for the p-wave scattering of two ultracold atoms near the p-wave magnetic Feshbach resonance. We show that in this case the low-energy p-wave scattering amplitude ${f}_{1}(k)=\ensuremath{-}1/[\mathit{ik}+1/({\mathcal{V}}^{\mathrm{eff}}{k}^{2})+1/({\mathcal{S}}^{\mathrm{eff}}k)+1/{\mathcal{R}}^{\mathrm{eff}}]$ where Veff,Seff, and Reff are k-dependent parameters. Based on this result, we identify sufficient conditions for the effective-range theory to be a good approximation of the exact scattering amplitude. Using these conditions we show that the effective-range theory is a good approximation for the p-wave scattering in the ultracold gases of 6Li and 40K when the scattering volume is enhanced by the resonance.
Ultracold collisions of spin-polarized 24Mg, 40Ca, and 88Sr in the metastable 3P2 excited state are investigated based on molecular potentials obtained from ab initio calculations. We calculate the long-range interaction potentials and estimate the scattering length and the collisional loss rate as a function of magnetic field. The scattering lengths show resonance behavior due to the appearance of a molecular bound state in a purely long-range interaction potential and are positive for magnetic fields below 50 mT. A loss-rate model shows that losses should be smallest near zero magnetic field and for fields slightly larger than the resonance field, where the scattering length is also positive.
We study the magnetic-field dependence of the interactions between two alkaline-earth(-like) Rydberg atoms, 88Sr and 174Yb. Considering the pair of Rydberg states ∣ns,3S1,mJ⟩ and ∣(n+1)s,3S1,mJ⟩, we show that the effective Hamiltonian takes the form of an {\it XXZ}-type quantum spin model, as in the alkali-atom case [M. Kunimi and T. Tomita, Phys. Rev. A {\bf 112}, L051301 (2025)]. We find that the behavior of the anisotropy parameter for 174Yb at zero magnetic field is significantly different from that for other atomic species. This behavior arises from the interplay of strong spin-orbit coupling and the resulting multichannel redistribution of Förster defects in 174Yb. We systematically calculate the interaction parameters of the {\it XXZ} model in the presence of a magnetic field and show that they can be tuned by the field. As applications to quantum many-body problems, we investigate one-dimensional systems in the large-anisotropy regime and show that the folded {\it XXZ} model can be realized in 174Yb systems without fine-tuning of the field. We also investigate two-dimensional square-lattice systems and show that a supersolid phase can emerge in the ground state at the mean-field level.
Ultracold neutral atoms in optical lattices are rich systems for the investigation of many-body physics as well as for the implementation of quantum information processing. While traditionally alkali atoms were used for this research, in recent years alkaline-earth-like atoms have attracted considerable interest. This is due to their more complex but tractable internal structure and easily accessible transitions. Furthermore, alkaline-earth-like atoms have extremely narrow 1S→3P intercombination transitions, which lend themselves for the implementation of next generation atomic clocks. In this dissertation, I show that exquisite control of alkaline-earth-like atoms can be reached with optical methods, and elucidate ways to use this controllability to further different aspects of research, mainly quantum information processing. Additionally, the control of alkaline-earth-like atoms is very interesting in many-body physics and the improvement of atomic clocks. Since heating usually degrades the performance of quantum gates, recooling of qubits is a necessity for the implementation of large scale quantum computers. Laser cooling has advantages over the usually used sympathetic cooling, given that it requires no additional atoms, which have to be controlled separately. However, for qubits stored in hyperfine states, as usually done in alkali atoms, laser cooling leads to optical pumping and therefore to loss of coherence. On the other hand, in the ground state, the nuclear spin of alkaline-earth-like atoms is decoupled from the electronic degrees of freedom. As I show in this dissertation, this allows for the storage of quantum information in the nuclear spin and laser cooling on the electronic degrees of freedom. The recooling protocol suggested here consists of two steps: resolved sideband cooling on the extremely narrow 1S0→3P0 clock transition and subsequent quenching on the much shorter lived 1P1 state. A magnetic field is used to overcome the hyperfine interaction in this excited state and thus ensures decoupling of the nuclear spin degrees of freedom during the quenching. The application of this magnetic field also allows for photon scattering on the 1P1 state, while preserving the nuclear spin, e. g. for electronic qubit detection. The manipulation of the scattering properties of neutral atoms is an important aspect of quantum control. In contrast to alkali atoms, whose broad linewidths cause large losses, this can be done with purely optical methods via the implementation of an optical Feshbach resonance for alkaline-earth-like atoms. Here, the scattering length resulting from the application of an optical Feshbach resonance on the 1S0→3P1 intercombination line, including hyperfine interaction and rotation is calculated for 171Yb. Due to their different parities, the p-wave scattering length can be controlled independently from the s-wave scattering length, thus allowing for unprecedented control over the scattering properties of neutral atoms. Furthermore, I also show how optical Feshbach resonances in alkaline-earth-like atoms can be used together with the underlying quantum symmetry to implement collisional gates between nuclear-spin qubits over comparatively long ranges.
We study the two-body problem of ultracold fermionic alkaline-earth-metal-(like) atoms in the electronic 1S0 state (g-state) and 3P0 state (e-state) which are confined in a quasi-one-dimensional (quasi-1D) tube simultaneously, where in the axial direction the g-atom experiences a 1D optical lattice and the e-atom is localized by a harmonic potential. Due to the nuclear-spin exchange interaction between the g- and e-atoms, one can use such a quasi-(1+0)D system to realize the Kondo effect. We suggest two tight-binding models for this system, for the cases that the odd-wave scattering between the g- and e-atoms is negligible or not, respectively. Moreover, we give a microscopic derivation for the interatomic interaction parameters of these models, by explicitly calculating the quasi-(1+0)D low-energy scattering amplitude of the g- and e-atoms in this system and matching this exact result with the ones given by tight-binding models. We illustrate our results for the experimental systems of ultracold 173Yb and 171Yb atoms and show the control effect of the confinement potentials on these model parameters. Furthermore, the validity of the simple ``projection approximation'' is examined. In this approximation, one derives the interaction parameters of the tight-binding models by directly projecting the three-dimensional (3D) Huang-Yang pseudopotential on the ground state of the confinement and the lowest band of the optical lattice. This approximation is supposed to be correct when the 3D interatomic scattering length as is much smaller than the characteristic lengths (CLs) of the confinements. However, we find that for our system this approximation already does not work when as is only of the order of 10% of the confinement CLs. Using the exact two-atom scattering amplitude, we also calculate the spin-exchanging rate (i.e., the cross section of the spin-exchanging collision between the g- and e-atoms) for the recent experiment [L. Riegger et al., Phys. Rev. Lett. 120, 143601 (2018)] of 173Yb atoms in this quasi-(1+0)D system and investigate finite-quasimomentum effect of the g-atoms in this experiment. Our results show that this effect is very significant.