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In a remarkable scientific achievement, scientists from the University of Science and Technology of China, including Jian-Wei Pan, Chao-Yang Lu, Ming-Cheng Chen, and others, have successfully realized strong nonlinear interaction between photons using an innovative device—based on the indigenously developed Plasmonium-type superconductive highly non-linear optical resonator arrays. With the support of this technology, the team has built an artificial gauge field acting on photons, used to create artificial gauge fields. This groundbreaking experiment has, for the first time, demonstrated the anomalous quantum Hall state of photons, marking an important advance in the “bottom-up” approach in the field of quantum simulation research. These exciting research results were published in the prestigious international academic journal Science on May 2nd, in the form of a full-length article.
Physicists have adopted the traditional method of starting from easily understandable phenomena, through hypotheses, abstraction, and ultimately deducing universal laws, to explain this complex phenomenon. Typically, they are inspired by common everyday objects, such as a falling apple, and then extend to the vast cosmic phenomena, revealing how the law of gravitation governs the motion of macroscopic celestial bodies. However, although the story of Newton and the apple might not be factual, the example precisely captures the exploratory spirit of physicists—applying laws extracted from specific phenomena to entirely new systems.
Just as we no longer use apples but rely on small balls and blocks of wood to learn the principles of mechanics in high school physics experiments, the stories we discuss today also follow a similar path from the concrete to the abstract. The Hall effect—as the “falling apple” of the scientific field, will once again be put on the agenda.
When we look back at the discovery journey of the Hall effect, we can trace a path from specific experimental phenomena to theoretical research development. In 1879, E. H. Hall, while studying the interaction between electric currents and magnets, uncovered the basic principle of the Hall effect: when an electric current passes through a conductor perpendicular to an external magnetic field, a potential difference appears on the side of the conductor, as a result of the current carriers being deflected to one side by the Lorentz force.
1879, E.H. Hall discovered the Hall effect
But on top of the Hall effect, the scientific community discovered a more advanced form of the Hall effect—the Quantum Hall effect. In 1980, the scientist K. Klitzing observed the quantum Hall effect under strong magnetic field and low-temperature conditions, finding that the relationship between Hall resistance and the magnetic field was no longer linear but showed step-like quantization at certain values. This milestone discovery revealed that, under certain conditions, the movements of carriers would exhibit quantum characteristics.
Related research and discoveries were led by the phenomenon accidentally found by Tsui Chee, a Chinese-American physicist, during his quest for the electron crystal. He ultimately shared the 1998 Nobel Prize in Physics with Horst Störmer and Robert B. Laughlin for their contributions to the fractional quantum Hall effect. Although they initially thought they had discovered quarks, it turned out that their discovery was of equal importance in the field of physics.
The quantum Hall effect is favored by scientists for its unique physical properties, which stimulate the exploration of the mysterious quantum mechanisms behind it. In a two-dimensional electron gas system, due to the action of a strong magnetic field, electrons fill up the Landau levels, leading to resistance showcasing quantized plateaus proportional to the strength of the magnetic field, forming the basis of the integer quantum Hall effect theory. This phenomenon is not only relatively intuitive to understand but also has wide application value in precision measurement and electronics.
To the surprise of many, barely a year after the discovery of the integer quantum Hall effect, the fractional quantum Hall effect was discovered by Tsui and Horst Störmer, showcasing even more magical phenomena: unlike the integer step values of the Hall resistance in the integer quantum Hall effect, the fractional quantum Hall effect shows fractions as step values, seemingly splitting the electron charge into multiple parts, prompting Tsui to jokingly claim that he had discovered particles akin to quarks.
Nobel Prize winner Robert B. Laughlin, in trying to explain the fractional quantum Hall effect, proposed a microscopic wave function and conceived a physical picture that is easy to comprehend: in this state, electrons form bonds with magnetic flux, thereby creating quasiparticles or quasiholes that carry fractional charge. These quasiparticles bear charges that are fractions of the elementary charge, though it is worth noting that Laughlin’s model only explains cases where the denominator of the fractional charge is odd.
At the same time, the American physicist Frank Wilczek also proposed a corresponding theory. He introduced a type of fractional statistical particle called anyons, whose statistical behavior is different from traditional fermions or bosons, and they are restricted to move in two dimensions. Subsequent scientific developments have confirmed that the fractional charge-carrying quasiparticles mentioned by Laughlin are essentially anyons. What’s even more exciting is that anyons are considered the potential foundation for constructing topological qubits and realizing fault-tolerant quantum computers.
In recent years, the quantum Hall effect has continuously shown new phenomena in experiments, such as being present without the need for strong magnetic fields or under room temperature conditions, known as the quantum anomalous Hall effect. Although there have been theoretical predictions, experimental detection remains challenging. Chinese physicist Shoucheng Zhang believed that magnetic topological insulators might be the key material to achieve this effect. In 2013, Chinese physicist Xue Qikun and his colleagues were the first to observe the integer quantum anomalous Hall effect, and the fractional quantum anomalous Hall effect was also independently observed by different research groups in the following decade.
Currently, more and more systems are showing the potential to achieve the quantum Hall effect, not limited to solid-state systems. In this context, Chinese physicist Wen Xiaogang proposed an understanding that whether it is the fractional quantum Hall effect under two-dimensional and strong magnetic field conditions or the high-temperature superconductivity phenomena that are difficult to explain with traditional BCS theory, they are essentially “phenomena.” Just as the fall of apples and the motion of celestial bodies are different aspects of the unified theory of gravity.
In the strange quantum world, a particularly special state of matter has attracted widespread attention, which is topological order. Unlike the disordered state of particles inside materials under normal conditions, under extreme conditions, such as very low temperatures, high purity two-dimensional materials, and sufficiently strong magnetic fields, the behavior of particles will deviate from the predictions of traditional physical theories. Especially electrons, at this time, they no longer act independently; instead, they interact with each other in an organized manner to form a new state of matter called the fractional quantum Hall state. In this state, the spins of the electrons resemble a delicate quantum waltz.
To delve into this state of matter, scientists have introduced the new concept of topological order. Topological order describes the special ordered phase that matter exhibits under extreme conditions, characterized by strong topological properties and correlations, based on long-range many-body quantum entanglement. This discovery not only provides a foundational understanding for many wondrous phenomena such as quantum spin liquids and the quantum Hall state, but also promotes the study of important states of matter related to topology, such as topological insulators, that do not contain topological order. Examining the quantum Hall state from a topological perspective is not just for understanding the phenomenon itself, but also helps us recognize and understand other various novel physical phenomena and explore their connections. Additionally, studying topological order involves deeper issues, such as the true nature of quantum entanglement.
In order to understand the fractional quantum Hall effect (FQHE), scientists used a method analogous to fundamental physics experiments. Just as middle school students experience the force of gravity when an apple falls, researchers have created an FQHE system with photons to explore the essence of the quantum Hall state. Due to various limitations of traditional two-dimensional solid-state materials in studying Hall states, such as the requirement of low temperatures and strong magnetic fields, as well as the materials’ own imperfections and challenging manipulation, researchers adopted a ‘bottom-up’ strategy from simple to complex. For example, a research team from Harvard University successfully simulated the fractional quantum Hall effect using ultracold atoms in an optical lattice. Meanwhile, scientists in China have established a superconducting cavity QED lattice, a 4×4 chessboard-like platform that makes the system’s Hamiltonian clearly visible and allows precise photonic manipulation, generating the FQH effect without the need for an external magnetic field.
The reason no external magnetic field is needed is because the system utilizes the Aharonov-Bohm effect (A-B effect). This effect shows that in the absence of a magnetic field, if the magnetic flux enclosed by the paths of two photons is non-zero, their phase difference can manifest in interference. On this special platform, the magnetic flux can be altered through precise control, indicating that physicists can use photons to simulate and study the fractional quantum Hall effect, which may hint at deeper secrets of the quantum world.
On the path to achieving quantum information processing, scientists have taken a unique approach: constructing a four-by-four superconducting cavity lattice, each site comprised of innovatively developed new superconducting quantum bits or “little boxes.” The design of these quantum bits feature anharmonicity, which means that the energy level spacing is uneven. Therefore, when a photon enters the little box, it excites the quantum bit to transition from the lower energy level to the next higher one. However, since the gap between the third and second energy levels is larger, subsequent arriving photons will be unable to match the existing energy level difference and are thus rejected.
With the aid of the interaction coupler between the quantum bits, we have successfully created an equivalent magnetic field on the two-dimensional chessboard, enabling the control of photons jumping between boxes and realizing precise manipulation of the movement and flow of photons.
Using this platform, we are able to uncover important information about the behavior of photons on a two-dimensional lattice chessboard. First, through the influence of the constructed artificial magnetic field, we can assess the capability to control the dynamics of photons. Experimental results show that under different strength magnetic fields, photons experience varying Lorentz forces, leading to different deflection angles within the lattice. Scientists further observed the “butterfly” shaped spectrum of the single-photon energy spectrum as it changes with the magnetic field, which is in agreement with theoretical predictions.
Delving deeper, we attempted to formally prepare the fractional quantum Hall effect (FQH) state in the experiment. By adjusting the system’s coupling and magnetic field strength, the system undergoes an adiabatic evolution process, with photons transitioning from a naive state to a new quantum state of matter. As the strength of the magnetic field increases, a topological phase transition occurs, and when the intensity of the magnetic field reaches a certain threshold, the anticipated FQH state emerges.
For this emerging FQH state, we are more concerned with its inherent long-range correlated properties and topological nature. In the past, these properties were mainly derived through theoretical calculations, but now, through an artificially constructed quantum system, we can directly observe these properties in experiments. The research indicates that photons in the system, after transitioning to the FQH state, tend to appear between two distant lattice points. Moreover, there is a significant change in the pattern of photon movement; in the FQH state, density flow with opposite chiralities inside and along the edges has been observed, while radial density flow is effectively suppressed, all consistent with the theoretical description of the FQH state.
Particularly noteworthy is the presence of quasi-particle characteristics within the FQH state. In traditional two-dimensional materials, since charged particles struggle to cross magnetic field lines, capturing and manipulating quasi-particles is a significant challenge. However, in current research, through precise control of the lattice potential structure, scientists have been able to track the formation process of quasi-particles. Quasi-particle “traps” constructed at the edge of the chessboard affect the gathering of photons in the normal state, and when the trap becomes deep enough, the accumulation of photons is linearly related to the depth of the trap.
In the fascinating realm of the fractional quantum Hall effect (FQH), when we observe a not-so-deep potential well, we note that the rate of increase in the number of photons is limited. However, once the depth of the potential well exceeds a certain threshold, we see a sharp rise in the number of photons, forming a distinct step phenomenon. This phenomenon is caused by the incompressibility of the quasi-particles.
In the FQH state, the Hall conductivity is a key indicator, which can be determined by the photon average number in response to changes in magnetic flux—that is, the bulk density at the center of the lattice. In recent experiments, the measured value of fractional quantum Hall conductivity was 0.52, which is very close to the ideal thermodynamic limit of 0.5 and the finite-size theoretical simulation value of 0.6.
All these findings undoubtedly point to one conclusion: The FQH state can be achieved in a photon-filled lattice. Today, our scientists have successfully prepared fractional quantum Hall states using photons on a checkerboard of gauge fields formed by superconducting circuits. This two-dimensional system is programmable, and photons can be precisely controlled through our manipulation. This precise control over photons goes far beyond its significance in studying Hall states; it also makes bottom-up research of other strongly correlated topological states of matter possible and indicates directions for fault-tolerant operations in topological quantum computing. This high-precision manipulation ability for microscopic particles is a core part of the “second quantum revolution.”
Let us not forget that Laughlin’s description for fractional quantum Hall states can only explain fractional charges with odd denominators. For cases with even denominators, in 1991, Gregory Moore and Nicholas Read proposed the Moore-Read (MR) states, which can describe these situations. In such states, quasiparticles not only have fractional charge but also follow non-Abelian statistics. The interactions between electrons create an energy gap between the ground and excited states, which protects the degeneracy of the ground state from being affected by slight perturbations of the Hamiltonian.
This resistance to change is similar to the concept of topology in mathematics, where a shape maintains its topological geometric properties despite transformations. Therefore, physicists refer to substances with FQH states as topological states of matter. Based on their robust nature, topological quantum computing becomes possible. In the degenerate space protected by topology, information storage is non-local, while the majority of interactions between the system and its environment are local. Hence, the stored information is protected from decoherence effects by its degeneracy.
An increasing number of experiments show that topological quantum computing using fractional quantum Hall systems is feasible. By braiding the non-Abelian anyons of different types of FQH states, various universal quantum logic gates can be implemented. The combination of topological protection and universal quantum logic gates makes fault-tolerant quantum computing an important prospective application in FQH states and other topological states of matter.
In the future, this artificially constructed chessboard will become bigger, capable of generating larger and more complex FQH states. The localized topologically coherent movement of quasiparticles will benefit from single-point programming and performing braiding operations on multiple non-Abelian quasiparticles in larger systems has profound implications for building fault-tolerant quantum information storage and processing devices.
Mozi, as an outstanding thinker and scientist in ancient China, left behind a rich legacy of thoughts and scientific achievements, representing an important aspect of early Chinese scientific thought. The Mozi Salon, named after him, is dedicated to inheriting and developing this precious scientific tradition and promoting the spirit of science.
Mozi Salon is committed to enhancing the public’s scientific literacy and helping to build a society that admires science. The salon mainly targets those who love science, eager to explore and discover. Through offline events and a variety of new media platforms, the salon enables more people to access cutting-edge scientific discoveries and advanced scientific concepts worldwide, thereby continuously advancing on the path of scientific pursuit, enjoying the joy and beauty that science brings.
The platform has received support from institutions including the University of Science and Technology of China Shanghai Research Institute, Pudong New Area Southern Seven Quantum Technology Exchange Center, and is also supported by the USTC Alumni Foundation, University of Science and Technology of China Education Foundation, Pudong New Area Association for Science & Technology, China Association for Science and Technology, and the Pudong New Area Commission of Science Technology and Economy.
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