Quantum Simulation Using Ultracold Ytterbium Atoms
in an Optical Lattice
YOSHIRO TAKAHASHI
DEPARTMENT OF PHYSICS, GRADUATE SCHOOL OF SCIENCE, KYOTO UNIVERSITY
ABSTRACT
I will describe our ongoing projects in our lab for quantum simulation research of quantum manybody systems using ultracold twoelectron atoms of ytterbium (Yb) atoms in an optical lattice, which provides unique possibilities in quantum simulation research. After a brief introduction of the unique features of Yb atoms, we will describe several important results, including the formation of a novel SU(N) Mott insulator, matterwave localization in a Lieb lattice, topological charge pumping, realization of a quantum simulator based on an impurity system with an YbLi(Lithium) atomic mixture, and development of a novel quantum gas microscope.
INTRODUCTION
Quantum Simulations Using Ultracold Atoms
Recently, the technique of manipulating individual single quantum systems such as an atom, ion, and photon has made dramatic progress. The development of an ultraprecise atomic clock is one illustrative example. In contrast to individual quantum systems, many functional materials (e.g., highTc superconductors) are stronglycorrelated quantum manybody systems, which are studied by various approaches in order to obtain an accurate understanding of their novel behaviors. However, quite often, even a qualitative understanding is difficult to obtain for such quantum manybody systems. In addition, topological materials have recently attracted much attention for fundamental research and applications.
Under these circumstances, a system of ultracold atoms in an optical lattice (see Fig. 1) is regarded as an ideal quantum simulator of quantum many body systems, because it possesses a highdegree of controllability of system parameters and it is a quite clean system, free of lattice defects and impurities. It is greatly expected that we can offer indispensable guidelines for novel functional materials, by developing quantum simulation techniques that will enable us to obtain a quantitative understanding of stronglycorrelated manybody systems, using this ideal system of ultracold atoms in an optical lattice. The system is also quite useful for the ideal realization of novel topological phases. Thus, in multiple areas, quantum simulation research can make a significant impact on our society.
Up to now, by using quantum gases of alkali atoms, quantum phase transitions for bosons have been thoroughly studied, and antiferromagnetic ordering for fermions has been now observed by a quantum gas microscopy, which is a recently developed method of siteresolved imaging of individual single atoms. The apparent next step is to lower the temperature of atoms, realizing the expected dwave superfluidity. In addition to the important steps of temperature lowering and the development of measurement and control techniques, a rich variety of interesting research topics are currently being studied, such as topological physics and lownonequilibrium dynamics.
Fig. 1: An optical lattice (periodic potential for atoms created by standing waves of light).
Basic properties of twoelectron atoms of Ytterbium
Instead of using popular alkaliatoms, we have studied quantum degenerate gases by using twoelectron atoms of ytterbium(Yb), because Yb atoms have many unique features that are advantageous in the study of quantum simulation. In the following sections, we will describe the basic properties of twoelectron atoms of Yb. It is noted that some properties are common to twoelectron atoms of alkalineearthmetal atoms. Detailed information on how to generate ultracold Yb atoms can be found in Ref. [1] and [2].
One of the unique features of Yb atoms is the existence of a rich variety of isotopes: two fermions (^{171}Yb and ^{173}Yb) and five bosons (^{168}Yb, ^{170}Yb, ^{172}Yb, ^{174}Yb, and ^{176}Yb). We have so far successfully created BoseEinstein condensates (BEC) of ^{168}Yb, ^{170}Yb, ^{174}Yb, and ^{176}Yb, Fermi degenerate gases of ^{171}Yb and ^{173}Yb, BoseBose mixtures of ^{168}Yb^{174}Yb and ^{174}Yb^{176}Yb, a FermiFermi mixture of ^{171}Yb ^{173}Yb, and BoseFermi mixtures of ^{170}Yb ^{173}Yb, ^{174}Yb ^{173}Yb, and ^{174}Yb ^{171}Yb.
Another unique feature of Yb atoms is the novel energy structure associated with two valence electrons. The two valence electrons result in the spinsinglet ground state ^{1}S_{0} and the metastable spintriplet states ^{3}P_{0} and ^{3}P_{2}, as in shown in Fig. 2. The lifetimes of these metastable states are on the order of 10 s., which are long enough for most cold atom experiments. As a result, these metastable states can be considered as useful orbital states in the Hubbard model. In addition, there are only weakly allowed intercombination transitions with the linewidths on the order of 10 mHz. In fact, we have successfully performed highresolution laser spectroscopy of quantum manybody states in an optical lattice [3].
SU(N) SYMMETRIC FERMI GAS
The isotope of ^{173}Yb has a spin 5/2 originated from the nuclear spin. Since the interatomic interaction of the ground state is independent of the nuclear spin, this system has a high spin symmetry of SU(6). This implies that the spin population should be conserved, for example, even in the presence of interatomic collision. Experimentally we have confirmed that the spin population is actually conserved in a harmonic trap. It should be noted that before the realization of cold atoms, theoretical aspects of the physics of SU(N) with N larger than 2 have been already investigated.
Fig. 2: Relevant energy levels of an Yb atom, connected with ultranarrow optical transitions.
By adiabatically loading a deeply Fermi degenerate gas of ^{173}Yb with 6spin components[4] into an optical lattice, we successfully create a stronglycorrelated system of a Mott insulator state with SU(6) symmetry [5]. Furthermore, a lower temperature is obtained for the SU(6) system compared with those for SU(2), with the same initial entropy in a harmonic trap, which can be explained as the atomic analogue of a Pomeranchuk cooling effect, which is known as an important cooling method for liquid ^{3}He. The result is shown in Fig. 3. During the adiabatic loading process, the entropy flows from the motional degrees of freedom into those of spin, which results in the cooling of the system.
Fig. 3: Pomeranchuk cooling effect for a Fermi gas in an optical lattice.
It is noted that the lowest entropy for one site almost reaches the value of k_{B}log(6), which is the value expected for an uncorrelated spin. This indicates that this temperature regime is close to the observation of the onset of the quantum magnetism of an SU(6) system. The apparent next step is, therefore, the study of novel SU(N) quantum magnetism by lowering the atomic temperature.
OPTICAL LIEB LATTICE
By using several lasers, we can create various nonstandard optical lattices, i.e. lattices other than cubic or square optical lattices, such as triangular, honeycomb, and kagome lattices, which have been successfully demonstrated for alkalimetal atoms. In particular, by combining three different kinds of optical lattices, we successfully realize an optical Lieb lattice[6], in which there are three sites in a unit cell, as shown in Fig. 4. The Lieb lattice has a unique band structure in which there is a flat band and so it is especially important to explore the physics of flatband ferromagnetism and supersolids. It is also noted that the Lieb lattice configuration is basically the same as that of the CuO_{2} twodimensional plane of highT_{c} cuprate superconductors.
Fig. 4: Lieb lattice structure(left) and the band structure(right).
The successful formation of the Lieb lattice is confirmed by the characteristic pattern of the matter wave interference of BEC. By manipulatinga bosonic matterwave in the Lieb lattice, in particular, by controlling the population and phase on each lattice site, we successfully demonstrate the coherent transfer of atoms in the lowest dispersive band into the second flat band and observe the frozen motion of atoms on a specific sublattice, which is a manifestation of the localization of atoms in a flat band[6]. This is shown in Fig. 5.
The next target is to explore the exotic phases expected in the flat band, such as itinerant ferromagnetism, novel superconductivity for fermions, and a supersolid for bosons.
Fig. 5: Localization of matter wave in a flat band.
TOPOLOGICAL CHARGE PUMPING
The high controllability of ultracold atoms in an optical lattice can be also applied for the study of topological quantum physics. So far there have been nice experiments which explored topological physics using cold atoms. In the case of spatial 2D systems, Hofstadter Hamiltonian and Haldane models are realized. Recently, a system of spatial 1D and 1 more synthetic dimension has been realized, leading to the observation of the chiral edge state. In our work, we realized a spatial 1D and temporal 1D system, leading to the observation of Thouless topological charge pumping[7], which shares the same topological features with a twodimensional quantum Hall effect.
Fig. 6: Topological Thouless charge pumping. Dynamical superlattice(left top). Shift of centerofmass of an atom cloud as a function of number of pumping cycle (left bottom). Charge pumping for various pumping schemes A, B, C, and D(right).
More specifically, in our work, we utilize the dynamical controllability of our optical superlattice system, as shown in Fig. 6, and realize a continuous quantum RiceMele pumping of cold fermionic ^{171}Yb atoms. In particular, we successfully reveal the topological feature of this charge pumping[7] by taking various trajectories of the system parameters which are different in topology in the parameter space, shown in Fig. 6.
We can extend our charge pumping scheme to investigate the effect of disorder and interaction. The rich internal degrees of freedom of an Yb atom will also allow us to realize a spin pump with a spinorbit coupling.
ENGINEERED IMPURITY: YBLI MIXTURE
An impurity plays a crucial role in condensed matter physics in phenomena like Anderson localization and the Kondo effect, and it is still important to develop a deeper understanding of these phenomena. Ultracold atomic gases in optical lattices can provide intriguing opportunities to study impurity problems with excellent controllability. For this purpose, we studied a quantum degenerate mixture of Yb atoms and a fermionic isotope of lithium (^{6}Li) atoms in an optical lattice [8], shown in Fig. 7. This mixture has a large mass ratio of about 29. On the one hand, Yb is well localized in an optical lattice and can be considered to be a localized impurity. On the other hand, ^{6}Li is light and as it is so well delocalized in an optical lattice, it is considered as an itinerant carrier. Therefore, this offers an ideal system of controlled impurity in a Fermi system.
Fig. 7: YbLi quantum sim ulator of impurity system.
In our recent work [8], we measured inelastic loss rates of the collisions between Yb in the metastable ^{3}P_{2} state immersed with the Fermi sea of the ground state ^{6}Li.
We have clearly observed fast decay of Yb(^{3}P_{2}) and have determined Yb(^{3}P_{2})Li inelastic loss coefficients in various magnetic fields, indicating Feshbach resonances.
High controllability of the internal state of Yb atoms in an optical lattice by a resonant laser light beam provides the great possibility of dynamical aspects of response of impurity. We can study, for example, the nonequilibrium behavior of a Fermi sea, known as a problem of Anderson's orthogonality catastrophe.
QUANTUM GAS MICROSCOPE
In addition to the sharpening of a quantum simulation technique that utilizes a global or ensemble measurement and control of a quantum manybody system, it also should be important to develop an advanced quantum control technique such as an individual quantum feedback control based on an individual quantum nondemolition(QND) measurement of single atoms in an optical lattice. By successfully combining these two technologies, it is possible to realize an ultimate quantum simulator for a quantum manybody system. We consequently expect the emergence of a new physics of quantum state control of quantum manybody systems.
We have already developed a quantum gas microscope for Yb atoms with a destructive fluorescence detection method[9], and quite recently have demonstrated the siteresolved imaging of single atoms in an optical lattice by Faraday quantum gas microscopy, which utilizes a dispersive, QNDlike interaction of Faraday effect. A typical image is shown in Fig. 8. Boosting the performance of Faraday quantum gas microscopes to a minimally destructive regime will be an important first step toward the realization of the abovementioned ultimate quantum simulator.
Fig. 8: Siteresolved image of single atoms with Faraday quantum gas microscopy.
CONCLUSION
In this article we describe several important results related to quantum simulation of the Hubbard model using ultracold Yb atoms in an optical lattice. We describe the formation of a novel SU(N) Mott insulator, the localization of a matter wave in a flat band of an optical Lieb lattice, the observation of topological Thouless charge pumping, the creation of a quantum simulator based on an impurity system with a YbLi atomic mixture, and the development of a novel quantum gas microscope.
In addition, we have recently studied the behavior of a quantum manybody state under strong dissipation. In particular, we investigated in detail the effect of strong dissipation on the superfluidMott insulator quantum phase transition.
The nonequilibrium dynamics of atoms in an optical lattice is also studied by exploiting the unique ability of a Yb atom system.
Furthermore, by performing an ultraprecise photoassociation spectroscopy of BEC of various Yb isotopes in a harmonic trap, we can set the limit on nonNewtonian shortrange gravity.
Acknowledgements: I would like to thank the collaborators, Y. Takasu, J. Kobayashi, S. Nakajima, S. Taie, F. Schäfer, E. Chae, R. Yamamoto, H. Konishi, H. Ozawa, T. Tomita, H. Asaka, K. Sato, Y. Fukushima, A. Sawada, H. Shiotsu, S. Yamanaka, K. Ono, and Y. Sakura.
References
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YoshiroTakahashi is a professor at Kyoto University. He received his D.Sc. from Kyoto University. Starting in 1990, he worked at Kyoto University as an assistant professor, a lecturer, and an associate professor. Since 2007 he has been a professor at Kyoto University. His research field is atomic physics, especially cold atom research. 
