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 ($^{1}\mathrm{S}_{0}$) and metastable ($^{3}\mathrm{P}$) 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 $^{1}\mathrm{S}_{0}$ state and another atom in the $^{3}\mathrm{P}_{2}$ 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 $^{3}\mathrm{P}_{2}$ 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 $^{3}\mathrm{P}_{2}(F=3/2)$ 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.
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 3P2\ensuremath-3P0 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 3P2\ensuremath-3P0 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 3P2\ensuremath-3P0 Raman coupling, could be of the order of (2\ensuremathπ)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.
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.
A nuclear-spin-exchange interaction exists between two ultracold fermionic alkali-earth-metal-like atoms in the electronic 1S0 state (g state) and 3P0 state (e state) and is an essential ingredient for the quantum simulation of the 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-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 confinement-induced resonances (CIRs). In a previous work, we studied this problem with a simplified pure 1D model [Y. Cheng et al., Phys. Rev. A 96, 063605 (2017)]. In the present work, we go beyond that pure 1D approximation. We model the transverse and axial confinements by harmonic traps with finite characteristic lengths ${a}_{\ensuremath{\perp}}$ and az, 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 ${a}_{z}/{a}_{\ensuremath{\perp}}$ is larger, the CIRs can be induced by weaker confinements, which are easier to be realized experimentally. The comparison between our results and a recent experiment by L. Riegger et al. [Phys. Rev. Lett. 120, 143601 (2018)] 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.
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.
We demonstrate that laser excitations can coherently induce a novel Kondo effect in ultracold atoms in optical lattices. Using a model of alkaline-earth fermions with two orbitals, it is shown that the optically coupled two internal states are dynamically entangled to form the Kondo-singlet state, overcoming the heating effect due to the irradiation. Furthermore, a lack of SU(N) symmetry in the optical coupling provides a peculiar feature in the Kondo effect, which results in spin-selective renormalization of effective masses. We also discuss the effects of interorbital exchange interactions, and reveal that they induce novel crossover or reentrant behavior of the Kondo effect owing to control of the coupling anisotropy. The laser-induced Kondo effect is highly controllable by tuning the laser strength and the frequency, and thus offers a versatile platform to study the Kondo physics using ultracold atoms.
Recently, alkaline-earth (-like) atoms and alkaline earth metals (AEL) gained experimental and theoretical interest principally related to the possibility offered in metrological field by the excitation of visible and UV clock transitions. AEL atoms, in their neutral \nform and in the ground state, have a null total electronic momentum, resulting nearly insensitive to external magnetic fields. While the absence of magnetic coupling does not allow the simply interactions tuning by exploiting Feshbach resonances as it occurs \nin alkaline atoms, these atoms are characterized by highly symmetric ground states allowing the simulation of SU(N) systems. This characteristic, that can be attributed in AEL atoms to the decoupling between electronic and nuclear atomic momenta, can be \nexploited to perform quantum simulation of a wealth of novel systems and constitutes a fundamental property of isotopes that have a nonzero nuclear spin, as it occurs for all the fermionic species and in particular for 173Yb and 87Sr. This feature also ensures the \nabsence of spin-changing collisions in ground state sublevels, implying that nuclear-spin mixtures are observationally stable. This attribute is fundamental for the study of transitions between different nuclear-spin states, for example by exploiting the two-photon \nRaman coupling. The degeneracy related to the SU(N) symmetry can be controllably removed by applying a two-photon Raman coupling, allowing for the simulation of systems with broken symmetries. \nBesides the possibility to induce couplings within the nuclear-spin degree of freedom, AEL atoms also offer the possibility to access a second, electronic degree of freedom; the possibility to address visible doubly-forbidden transitions between long-lived electronic \nclock states comprises a fantastic tool that allowed the building of optical lattice clocks improving metrological measurements and offering a richer platform for simulating complex systems. \nThe main difference between the two internal degrees of freedom offered by AEL atoms is that the possibility to address ultranarrow optical clock transitions exists also for AEL bosonic isotopes in which the nuclear-spin degree of freedom is not present because the \ntotal atomic momentum is absent. \nThe possibilities related to the excitation of long-lived metastable triplet levels, that, referring only to the lowest lying atomic levels are 3P(0;2) (in Russell-Saunders approximation they result doubly forbidden with respect to the electric dipole operator), are \nmultiple. If bosonic atoms are considered, the metrological applications based on the clock transition at the state of the art have performances comparable to optical lattice clocks realized with fermionic isotopes. Bosonic isotopes, requiring external fields in order \nto excite transitions from the ground state to long-lived states, have been proposed as good candidates in order to build a reliable and fast system in which controllable qu-bits could be realized. Most of these applications, and in particular the possibility to create \nquantum computers with neutral atoms, crucially rely on the control of the scattering properties of atoms in different electronic states. \nRegarding fermionic isotopes, the clock transitions recently allowed for the demonstration of spin-orbit coupling and quantum simulation via the synthetic dimension approach. As recently discovered, the clock transitions from the ground to the 3P(0;2) states give rise to rich interactions possibilities between atoms in the fundamental and in the metastable states. The spin-exchange interaction that has been observed between ground and metastable states, supports also a new kind of Feshbach resonance, called Orbital Feshbach Resonance (OrbFR). As occurs in magnetic Feshbach resonances for alkali atoms, also the OrbFR, that occurs in AEL atoms, supports the existence of extremely shallow homonuclear molecules. After considering the (s-wave) scattering parameters of all the AEL atoms that have been characterized experimentally, 173Yb is the only isotope in which the production and manipulation of Orbital Feshbach molecules (produced e.g. with photoassociation) is experimentally viable. Molecules generated by employing this atom, may lead to the investigation of fermionic superfluidity in still-unexplored regimes. In this thesis we report the characterization of interactions in bosonic 174Yb isotope by probing the clock transition between the singlet 1S0 ground state and the triplet 3P0 \nmetastable excited state. Interactions and inelastic losses between ground-state and excited metastable-state atoms have been experimentally determined with high accuracy, resulting consistent with an indipendent evaluation realized in the same period by Yb \nBEC group at LKB. \nThe obtained values for the interactions among ground and metastable atoms for the specified isotope constitute a first step in order to design an experimental system in which quantum information can be realized by means of exploiting the clock transition of bosonic Yb atoms. \nThis work, by exploiting the internal degrees of freedom of 173Yb atoms, reports a study on Orbital Feshbach molecules, showing experimentally the possibility to employ the nuclear degree of freedom in 173Yb atoms to manipulate and precisely detect homo-nuclear photoassociated molecules. \nThis first result regarding this new kind of shallow-bound molecules allowed the characterization of interactions between ground-state and metastable-state of 173Yb atoms. \nThis first intensive study of orbital Feshbach molecules is a fundamental step for future studies on the possibilities offered by these homo-nuclear molecules. \nFinally, we exploited the ground state SU(N) symmetry and its controlled breaking via Raman coupling (in 173Yb N = 1...6) to simulate the physical processes that are supposed to be driven by the hybridation of d-orbitals of iron atoms in iron based-superconductors, \nin which orbital-selective Mott insulating phases have been experimentally observed and are suspected to be the fundamental ingredient to achieve high-temperature superconductivity in these compounds.
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.