Kensuke Kobayashi (Professor, Institute for Physics of Intelligence / Department of Physics)

Akira Oguri (Professor, Osaka City University / Professor, Yoichiro Nambu Institute of Physics)

Rui Sakano (Assistant Professor, Institute for Solid State Physics)

Key points of the presentation

• Quantum liquid in a tiny artificial atom is investigated by electrical conductivity measurement, and the behavior of three electrons in correlation is detected.
• The universal behavior of quantum liquid in the non-equilibrium regime was experimentally clarified for the first time.
• Contributed to the development of quantum many-body phenomena and nonequilibrium physics, one of the central themes of modern physics.

Summary of Presentations

Professor Kensuke Kobayashi, Graduate School of Science, The University of Tokyo and Graduate School of Science, Osaka University, is joined by Tokuro Hata (at the time of the research: Graduate Student, Graduate School of Science, Osaka University; currently Assistant Professor, Department of Physics, Tokyo Institute of Technology) and Tomonori Arakawa (at the time of the research: Assistant Professor, Graduate School of Science, Osaka University; currently Assistant Professor, Measurement Standards Research Center, National Institute of Advanced Industrial Science and Technology), Meydi Ferrier (Project Researcher at the time of the research, currently Lecturer at the University of Paris-Sud), Akira Oguri (Professor at the Graduate School of Science, Osaka City University and Yoichiro Nambu Institute of Physics, Osaka City University), Yoshimichi Teratani (Project Assistant Professor at the Graduate School of Science, Osaka City University), and Rui Sanno (Assistant Professor at Institute for Solid State Physics, University of Tokyo), through international collaboration, By precisely measuring the electric current in a quantum liquid ^{(Note 1) in} an artificial atom ^(Note2 ) fabricated using microfabrication techniques, they have succeeded in detecting three-body correlations, a measure of the quantum mechanical entanglement of electrons.

Quantum liquids, which are formed by the quantum mechanical interactions of many particles, exhibit a wide variety of behaviors that are unimaginable from a single particle. In this study, we have clarified the behavior of a local Fermi liquid, a type of such quantum liquid, ^{in a} non-equilibrium state ^{(Note 3)}. We generated a quantum liquid by ^the Kondo effect ^{(Note 4)} in an artificial atom created in a tiny electronic circuit and demonstrated that its behavior is determined by the entanglement of three particles (three-body correlation).

Such studies are the key to quantitatively understanding quantum many-body phenomena in non-equilibrium states.

Publication details

Background of Research
According to quantum mechanics, when there is only one particle such as an electron or an atom, the behavior of the particle can be precisely predicted. However, when there are many particles and they interact with each other in a quantum mechanical manner, it is a very difficult problem to predict their behavior accurately. Not only is it difficult, but in reality, such a group of particles may behave in ways that are completely unpredictable from the properties of a single particle. This is called quantum many-body phenomena. In particular, the group may act as if it were a liquid in unison. Such a liquid state produced by a quantum many-body phenomenon is called a quantum liquid.

The Kondo effect is a typical example of a quantum many-body phenomenon that produces a quantum liquid. The Kondo effect is a phenomenon in which localized spins in a solid combine with the spins ^{(Note 5)} of the surrounding conduction electrons to form a special quantum state called the Kondo state ^{(Note 4)}. From the 1960s to the present, the Kondo effect has been one of the important topics in condensed matter physics and has been the subject of numerous studies. Theoretically, it is established that the Kondo state can be described as a type of quantum liquid called a "local Fermi liquid". Therefore, studying the behavior of Kondo states can also be considered as studying quantum liquids governed by strong electronic correlations.

Details of Research
The research group has precisely investigated the properties of quantum liquid formed by the Kondo effect from the equilibrium state to the nonequilibrium state. Until now, most experimental studies of the Kondo effect have used macroscopic samples to investigate the average properties of a population containing a large number of spins. In contrast, in microscopic electronic circuits called "artificial atoms," which are fabricated using microfabrication techniques, the number of electrons can be controlled one by one, allowing the Kondo effect caused by a single spin to be studied while controlling all the parameters involved in the phenomenon. Thus, artificial atoms in the Kondo state are ideal electronic circuits that can test theories about quantum liquids, including nonequilibrium states, with a high degree of accuracy and fidelity to theory.

The research group studied the Kondo effect in artificial atoms fabricated using carbon nanotubes (Figure 1(a) ). By connecting a conductor to an artificial atom and measuring the current passing through it, the state of the artificial atom can be precisely investigated. In this research, the ideal Kondo state was achieved by controlling the voltage and magnetic field applied to the artificial atom. In our research, we injected electrons into a quantum liquid and placed it in a non-equilibrium state to detect interactions between particles (Figure 1(b) ).

Figure 1: (a) Electron micrograph of the sample used in the experiment. The white streak in the area surrounded by the yellow dotted line is an artificial atom made of carbon nanotubes. A quantum liquid was generated by confining a single electron to this artificial atom and the resulting Kondo effect. This quantum liquid is confined between the source and drain electrodes. The electrical conductivity of this quantum liquid was precisely measured (the measurement results are shown in Figure 2(a) ).
(b) Schematic diagram of a quantum liquid. It is composed of many particles (electrons). The interaction between two particles (two-body correlation) and the interaction between three particles (three-body correlation) are schematically represented in blue and red.

The results of the electrical conductivity measurements are shown in Figure 2(a). Analysis of the experimental results shows that in the absence of an applied magnetic field, the quantum liquid can be described from the equilibrium state to the nonequilibrium state only by the interaction between the two particles (two-body correlation, Figure 1(b )). This "two-body correlation" is a quantity corresponding to the magnetic susceptibility, which has been established experimentally and theoretically by previous studies. However, when a magnetic field is applied, we found that we must incorporate a new "three-body correlation" (Fig. 1(b )), an interaction of three particles, in order to explain the properties of quantum liquid in a non-equilibrium state with an applied current. This result is found to be quantitatively consistent with the recently published theory of quantum liquid in non-equilibrium regime (local Fermi liquid theory) (Fig. 2(b )). This study represents the first successful experimental detection of three-body correlations by precisely examining the properties of quantum liquid in nonequilibrium.

Figure 2: (a) Measured electrical conductivity of the quantum liquid when the bias voltage is varied (the bias voltage is normalized by the energy scale of the Kondo effect). Each curve is measured when the magnetic field is varied stepwise from 0 T to 2.5 T. As the bias voltage or magnetic field is increased, the conductivity of the quantum liquid changes significantly. This change in the conductivity of the quantum liquid allows us to detect the interaction of particles in the quantum liquid.
(b) Two-body and three-body correlations obtained by analyzing the measurement results shown in (a) are plotted. Red indicates experimental results, solid blue indicates theoretical calculations based on the local Fermi liquid theory in the nonequilibrium regime, and green indicates a free-particle model that does not take quantum many-body effects into account. You can see that the free-particle model cannot explain the experimental results at all, and that the three-body correlations increase (in a negative direction) as the magnetic field increases.

Significance
This is the first detection of a quantity called three-body correlation between three particles by experimentally investigating the non-equilibrium behavior of quantum liquid resulting from strong interactions. Understanding nonequilibrium states is one of the greatest challenges in modern physics. There are many phenomena around us that are inherently non-equilibrium. The interaction of light and matter, electronics as represented by transistors, and even life and human society itself are non-equilibrium phenomena. Such non-equilibrium phenomena are caused by the complex interactions of various unique components. In comparison, the particles that make up a quantum liquid are simple, and the nature of their interactions is well understood. Therefore, understanding the behavior of quantum liquid in a non-equilibrium state is a good touchstone for understanding non-equilibrium phenomena quantitatively. This study presents one of the methodologies to unravel non-equilibrium, which will contribute to the future development of research on quantum many-body phenomena.

Acknowledgments: This work was supported in part by Grant-in-Aid for Scientific Research on Innovative Areas ( Proposal-type ) "Control and Function of Quantum Liquid Crystals" ( JP19H05826), Grant-in-Aid for Scientific Research (A) ( JP19H00656), Grant-in-Aid for Basic Research (B) ( JP18H01815), Grant-in-Aid for Basic Research (C) ( JP (JP18K03495), Young Scientists ( JP19K14630 ), Grant-in-Aid for Young Scientists ( JP18J10205), and JST CREST (No.JPMJCR1876 ). It was also conducted as part of a joint project research at the Research Institute of Electrical Communication, Tohoku University.

Journals

Journal name	Nature Communications
Title of paper	Three-body correlations in nonlinear response of correlated quantum liquid.
Authors	Tokuro Hata∗, Yoshimichi Teratani, Tomonori Arakawa, Sanghyun Lee, Meydi Ferrier, Richard Deblock, Rui Sakano, Akira Oguri, and Kensuke Kobayashi∗
DOI Number	10.1038/s41467-021-23467-4
URL	https://doi.org/10.1038/s41467-021-23467-4

Explanation of Terms

Note 1 Artificial atoms

When a tiny region is fabricated between two electrodes using microfabrication technology, the number of electrons in the region can be changed one by one by controlling the voltage of the attached electrodes. This region is called an artificial atom because it has atom-like properties. Using artificial atoms, the properties of a single electron can be investigated by measuring electrical conductivity. The present results are based on experiments with artificial atoms fabricated using a single carbon nanotube molecule. ↑up

Note 2: Quantum liquid and quantum many-body phenomena

A quantum liquid is a situation in which a large number of particles interact and behave as one in a quantum mechanical manner. A quantum liquid may exhibit properties that are essentially different from those of a single particle, and such phenomena are called quantum many-body phenomena. Superconductivity, superfluidity, and the Kondo effect are representative examples of quantum many-body phenomena, which have long been studied as a central topic in physics. ↑up

Note 3: Equilibrium and nonequilibrium states

When an object of interest is in a completely stable state with no flow or change (of particles or heat), we say that the object is in equilibrium. A non-equilibrium state is called a non-equilibrium state. In physics, the theoretical framework for describing equilibrium states is fairly well established, but the question of how to deal with nonequilibrium states is a major challenge in physics today. ↑up

Note 4 Kondo effect and Kondo states

The Kondo effect is a phenomenon in metals containing magnetic impurities in which the spin of the impurity and the spin of the conduction electrons combine through interaction to form a spin singlet ("Kondo state"), which exhibits increased resistance at low temperatures . The Kondo effect is a typical example of quantum many-body phenomena and has been the subject of numerous studies in strongly correlated electron systems (heavy fermion systems and high-temperature superconductivity). It has been established that the Kondo state is a "local Fermi fluid," a quantum liquid that extends the idea of "Fermi liquid" by L.D. Landau. In this study, the behavior of a local Fermi fluid in a non-equilibrium state is experimentally detected and quantitatively compared with the latest theory. ↑up

Note 5 Spin

Electrons have an electric charge, but they also have another quantity called spin. Because of the spin, each electron behaves like a small magnet. Spin as well as charge is a very important factor in quantum many-body phenomena. The Kondo effect is another quantum many-body phenomenon in which spin plays a major role. ↑up