Science ZJU scholars realize quantum topological state manipulation of light
Light is quantized. Using this property, people have built laser pens, printers, code sweepers and optical radar, and also tried to explore new scientific horizons through it. The quantum optics research team and the superconducting quantum computing team of Zhejiang University have collaborated to introduce the quantum property of light into the field of topological photonics, and have achieved the first quantum topological manipulation of light on a newly designed superconducting quantum chip.
The paper "Observing the quantum topology of light" was published as a Research Article in Science on Dec. 2, 2022.
In 2016, when the Nobel Prize jury announced the winners of that year's physics prizes, it presented different shapes of bread to the public. These breads were tasked with explaining the "topological phase transition" that won the prize at the time. The analogy between "doughnuts" and "coffee cups" was also made: in the topological world, doughnuts and coffee cups are "equal" because they both have one and only one hole. A "donut" can be stretched into a "coffee cup", but not into a "German knot" with two holes.
Topology was originally a dormant branch of mathematics, used to describe the properties of objects that remain unchanged under continuous deformation. It was not until physicists discovered the quantum Hall effect in 1980, which could not be explained by traditional energy band theory, that physicists found the new "language" of "topology" in the treasury of mathematics. In topological insulator materials, some electrons "run" along the edges of the material, and the material as a whole exhibits the characteristics of intermediate insulation and edge conductivity, and this characteristic is not affected by material defects or impurities, making the material appear very "robust" (robust). (usually translated as "robustness" in academic terms). In topological "parlance," this "robustness" or robustness is because it is "topologically protected. Think of a doughnut. No matter how much you stretch it and crush it, the property that it "has a hole" remains the same. It was soon realized that when the "donut" of the topological world met the "electron" of the material world, it was possible to manipulate the electron by modulating the topological properties of the material. This heralded great theoretical and application prospects, and developed into a popular direction in condensed matter physics, namely topological states.
In recent years, topological "doughnuts" have been moving further and further in the world of physics. Professor Haldane, who was awarded the Nobel Prize in 2016, had the audacity to introduce topology into the optical system in 2008 and to build a "topological insulator" in the optical world. The reason is that Maxwell's equations describing the fluctuations of light and Schrödinger's equations describing the motion of electrons have similarity. By virtue of this similarity, the topological "doughnut" has "jumped" from condensed matter into the world of optics, where scientists can use classical light transport in periodic media to simulate the topological edge states of electrons in a lattice. This led to a series of theoretical and experimental investigations that opened up the field of topological photonics.
In the view of researcher David Wang from the School of Physics, Zhejiang University, there are still some shortcomings in topological photonics research: light is essentially quantum, but we do not know what new horizons the quantum properties of light will bring to topological physics. Previously, topological photonics research mainly used the classical properties of light, such as its color, polarization and vortex, and "omitted" the quantum properties of light. David Wang hopes to let light "release" its quantum nature in the topological world.
We are all familiar with light, which is our main tool for understanding the world, yet its quantum properties have not been revealed until the last hundred years. What is the quantum "nature" of light? It was unveiled by Planck, Einstein and Bose. Their research confirmed that the statistical laws of particles in the microscopic world are completely different from those in the macroscopic world. For example, when we go to a meeting, we basically have to find an empty seat and assume that a seat is occupied, you cannot sit in that seat; but in the world of photons, it is very strange: particles and particles prefer to stay together, so when a particle enters the "meeting place", it is crowded wherever there are many people, and then plays in the same position. "stacking high". Particles with this magical "cohesion" effect are called bosons, of which photons are the most typical representatives. It is based on the quantum property that photons "like to stay together" that people invented laser, which led to the development of laser pens, scanners, code readers, light radar and other technologies and products. In a laser beam, all the photons are "consciously" lined up together and "move" in the same direction at the same pace.
David Wang needed to go back to the starting point of Professor Haldane's thinking and rethink how to make topological "doughnuts" meet quantumized light. Back in 2010, David Wang was inspired by Professor Jen-Paul Liu of the Chinese University of Hong Kong to investigate how to use quantum optical systems coupled with light and atoms to study topological physics. He still cannot hide his excitement when he mentions Prof. Renbao Liu's suggestion to construct a lattice using Fock states: the dimensionality of such a lattice can be arbitrary and not limited by three-dimensional space. In the many years that followed, they collaborated to come up with several interesting results. But the question of how to use the quantum properties of light to construct new topological states has always troubled David Wang. He revisited the quantum properties of light in the classical Jaynes-Cummings (JC) model in the field of quantum optics and has been exploring it for years with Cai Han, who is currently a researcher in the 100-member program of the School of Optoelectronics at Zhejiang University.
The JC model describes how a photon "runs" when an optical cavity (in a Fock state containing an integer number of photons) and an atom are coupled: the atom absorbs a photon, changes from the ground state to the excited state, "returns" a photon to the cavity, and the atom returns to the ground state. The photon returns to the ground state and "runs" back and forth between the cavity and the atom. The frequency of the run depends on the number of photons n in the cavity, which is proportional to the root n. The higher the number of photons, the stronger the coupling.
The situation becomes complicated when there are two optical cavities coupled to an atom. Both cavities want to exchange photons with the atom, so with whom does the atom choose to make the exchange? This is where the cohesive property of bosons comes into play: the more photons there are in the cavity, the stronger the coupling between the atom and it, and the more willing it is to give the photons to it. What is reflected here is the Matthew effect in the world of quantum optics. But the world of quanta is a superposition of many possibilities. Considering all possible cases, the quantum states of two cavities and atoms form a one-dimensional chain in Fock space, where each lattice point in the chain is a Fock state, and the coupling between the lattice points depends on the number of photons inside the Fock state.
Figure: SSH model of a one-dimensional Fock state lattice
The situation becomes more complex and interesting when there are three cavities, and the three cavities competing for photons from atoms form a honeycomb lattice structure in the Fock state space similar to graphene. The coupling between each lattice point and the three surrounding lattices depends on the number of photons inside the three cavities in the Fock state, which varies with position.
While listening to a presentation by Zhaju Yang, David Wang realized that the honeycomb lattice was equivalent to a "stress field", and the image of n under the root reminded him of the Landau energy level of electrons in graphene in a magnetic field, and a strained honeycomb structure caused by the boson condensation property was laid out in his mind. Dawei Wang and Han Cai immediately started to calculate the "stress field" in the JC model Fock state lattice as the "magnetic field" in the Landau energy level of graphene through the Dirac equation. This inspiration led to the encounter between topology and light quanta.
Figure: Three resonant cavities coupling a two-energy level atom and its Fock state lattice
In October 2020, Han Cai and David Wang published a paper in National Science Review revealing the topological states based on the quantum properties of light. They predicted that in a JC model with one atom and three cavity modes coupled, a Fock state lattice composed of photons undergoes a semimetallic-to-insulator topological phase transition on an inner tangent circle at the edge of a triangle.
"Can the quantum properties of light lead to topological states that cannot be explained by classical optics?" This question has been answered theoretically for the first time.
Three years ago, a superconducting quantum computing team led by Haohua Wang, Chao Song and Zhen Wang at the School of Physics of Zhejiang University decided to invest resources in experimentally realizing "topological states based on the quantum properties of light", officially starting this "magnificent adventure". The team is experienced in designing multi-quantum bit superconducting chips and is at the international leading level. At the same time, they also collaborate with theoretical physicists to "tailor" various novel circuits to explore novel physical phenomena according to the needs of theoretical research.
Photo: PhD student Jinfeng Deng, first author of the paper, in the lab
"It's a completely new circuit that has not been done before, and it's not too difficult." Researcher Chao Song said. The theoretical team and the experimental team began to work closely together, while Jinfeng Deng, co-first author of the thesis and the first PhD student of David Wang, was stationed directly in the superconducting quantum computing lab to receive the necessary training in experimental skills, both in close communication with the theoretical collaborators and in collaboration with a number of students from the experimental team, including Hang Dong, Chuanyu Zhang and Yaozu Wu, overcame various difficulties to build the measurement and control circuit of the chip and develop the The experimental observation and manipulation of the theoretically predicted topological states was achieved in three years.
Superconducting quantum chip diagram
The team has proposed a new "quantum signal toroid" chip, designed by co-author Hang Dong and prepared by Hekang Li, a former postdoctoral fellow at Zhejiang University and current technology development expert at the International Science and Innovation Center of Zhejiang University. The core of the chip consists of a central bit coupled by three tunable couplers and three resonant cavities, capable of presenting a one- and two-dimensional Fockian lattice.
When atoms on a quantum bit are coupled to photons in two resonant cavities simultaneously, the cavities can "spit out" a series of photons and jump to different Fock states, which are connected to form a chain-like Fock state lattice, which is the famous Su-Schrieffer-Heeger (SSH) lattice in topological physics. This is the famous Su-Schrieffer-Heeger (SSH) model in topological physics. In the experiments, the team demonstrated the adiabatic transport of topological zero-energy states predicted by the theory, allowing the coherent transfer of photons from one resonant cavity to another and the preparation of arbitrary two-mode binomial states.
Figure: Observation of Haldane edge flow in a Fock state lattice
The team also experimentally implemented the highly acclaimed Haldane model, which is the first implementation of the Haldane model in the photonic regime. As predicted by the theory, by periodically adjusting the coupling strength, the researchers observed the rotational trajectory of photons on the inner tangent circle of the Fock state lattice.
Can the quantum properties of light lead to topological states that cannot be explained by classical optics? This is the first answer and verification experimentally after the theoretical answer published by Han Cai and David Wang at NSR in 2020.
"When the quantum properties of light are added to the topological world for consideration, we find a new world." Chao Song said, "We dug out a huge 'fishing net' to describe the behavior of photons, which can lead to very rich and novel findings that are incomparable to classical optical systems." The team believes that this window into the quantum topological nature of light has only just opened, and that there are many novel physical phenomena waiting to be discovered beyond it. "We have achieved in our experiments to construct a one-dimensional lattice structure with two cavities, a two-dimensional lattice structure with three cavities, and if we have four cavities, we can construct a three-dimensional lattice ...... Expanding in this way, we can construct a high-dimensional space that does not exist in the material world, providing a topological matter states to provide a new research platform." Deng Jinfeng said.
Song Chao said, in this study, the experimental team also gained a lot, from the point of view of quantum manipulation, the quantum topological state of light regulation experiments, perhaps in the future to add a regulatory "handle" for quantum computing.
Figure: Group photo of some members of the research team
The co-first authors of this paper are Jinfeng Deng and Hang Dong, PhD students in the School of Physics, Zhejiang University, and the corresponding authors are Chao Song, Professor Haohua Wang and David Wang, Researcher of the Hundred Talents Program, Zhejiang University. This work was supported by the National Key Research and Development Program, National Natural Science Foundation of China, Zhejiang Provincial Key Research and Development Program, Special Funds for Basic Research Operations of Central Universities, and Quantum Science and Technology Innovation Project.
