image: While usual gapless points that are not geometrically defective i.e. Dirac points (Left column) possess only eigenvalues within [0, 1] (Bottom Left), defective exceptional points (Right column) also exhibit special isolated EB eigenvalues far outside of [0, 1] (Bottom Right). It can be realized by an electric circuit (Right).
Credit: ©Science China Press
This study is led by Dr. Xiangdong Zhang (Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurements of Ministry of Education, Beijing Key Laboratory of Nanophotonics and Ultrafine Optoelectronic Systems and Beijing Institute of Technology), Dr. Ching Hua Lee (National University of Singapore and International Campus of Tianjin University), Dr. Yee Sin Ang (Singapore University of Technology and Design) and Dr. Haiyu Meng (Xiangtan University and National University of Singapore). Entanglement entropy is a measure of how intimately different parts of a quantum system is connected. It tells us how much having information about one part tells us about the other, revealing hidden connections and correlations between particles, which is crucial for developing new technologies in quantum computing and quantum communication.
To understand what negative entanglement entropy means, we will first need to know what entanglement and entropy are.
Entanglement and Entropy in a nutshell
Imagine you have two coins. Normally, if you flip one coin, it doesn't affect the outcomes of flipping the other. But in the quantum world, particles can become "entangled," meaning their states are linked. If two coins are entangled, the entanglement rule can be such that when one coin is flipped into a head, the other coin must show a tail. In essence, knowing the result of one restricts the possible outcomes for the other.
On the other hand, entropy is a concept of statistical physics that measures the disorder or uncertainty of a system. For example, a messy room has high entropy because things are scattered all over, and it is hard to predict where any specific item is. A tidy room has low entropy because everything is in its place, making it easy to find things.
Entanglement Entropy
When putting together, “entanglement entropy” measures how much information you lose about one part of a system if another part of the system suddenly becomes inaccessible i.e. is truncated by a so-called “entanglement cut”. Intuitively, the more highly entangled the two parts are, the more information will be lost.
One simple analogy to understand entanglement entropy is to imagine a pair of socks. You put one sock in one drawer and the other sock in another drawer. If the socks are “entangled”, then knowing the color of the sock in one drawer immediately tells you the color of the sock in the other drawer. Here, two situations can arise:
•High Entanglement: If the colors of the two socks are almost perfectly correlated, then knowing the color of one sock gives you almost perfect information about the other. In particular, if one sock suddenly becomes inaccessible, one would also lose knowledge of the color of the other sock.
•Low Entanglement: If the socks’ colors are essentially uncorrelated, then knowing the color of one sock does not make one more certain about the color of the other. In particular, if one sock suddenly becomes inaccessible, there will not be any more uncertainty i.e. entropy regarding the color of the other sock.
Negative Entanglement Entropy
Conventional quantum mechanics have only been concerned with conservative systems where particles and energy do not get destroyed or made. However, intriguing new physics arise when this restriction is lifted – in the sock analogy, where socks can be removed or added to the system. Such systems as known as “Non-Hermitian” systems.
In non-Hermitian systems, the concept of entanglement needs to be modified, because information can also be lost when the number of particles changes. In particular, gaining new socks and their information can be construed as giving out a negative amount of sock information to others. This leads to the new concept of negative entanglement entropy.
While the theoretical recipe for achieving negative entanglement entropy in a non-Hermitian quantum system has been thought of since a few years ago, actually observing negative entanglement in quantum experiments cannot be easily done. This is due to significant challenges in manipulating intricate quantum states in a way that they gain or lose energy, while at the same time also measuring how entangled they are.
Exceptional bound states and negative entanglement entropy in electrical circuits
Reporting in Science Bulletin, physicists from Singapore and China have experimentally observed elusive states that mathematically possess negative entanglement entropy. Instead of using a quantum system, the research team employed a non-quantum (or classical) electrical circuit to generate ‘sandbox’ system that is mathematically identical to a system with negative entanglement, but without the challenges accompanying true quantum systems. Such classical electrical circuits are built with easily-available electronic components such as resistors, capacitors and operational amplifiers, without the need for ultralow cryogenic cooling and high-precision lasers using needed in a quantum system.
“EB states are highly robust and exhibit prominent measurable signatures, thus greatly facilitating their physical realization in relatively simple classical networks such as electrical circuits without the need for fine-tuning,” said Professor Xiangdong Zhang from the Beijing Institute of Technology whose research team provided the experimental measurements of EB states using electrical circuits.
“A very pertinent question that we have always wanted to answer is: can the esoteric negative entanglement behavior manifest in realistic experiments? In this work, we provide an affirmative “yes” through the novel concept of exceptional bound (EB) states,” said the project leader Assistant Professor Ching Hua Lee from the National University of Singapore.
“EB states are special states that provide the key fingerprints for negative entanglement,” said Professor Haiyu Meng from Xiangtan University, co-Author of this work. Whenever the host system becomes very sensitive due to the non-Hermiticity, EB states may emerge as a direct consequence of negative entanglement.
“This work suggests classical electrical circuits as a new hunting ground for the search of exotic quantum phenomena which are otherwise challenging to realize using atoms and material crystals. Due to their ease of fabrication, electrical circuits may offer a low-cost sandbox for designing and prototyping devices useful for future quantum technology”, said Assistant Professor Yee Sin Ang from the Singapore University of Technology and Design, co-Author of this work.
The demonstration of negative entanglement entropy can have profound impact in many areas of physics and engineering, particularly quantum information technology. Going forward, EB states and electrical circuits can be used to probe exotic physics in higher dimensions, thereby ushering a new fertile arena for the triple interplay of topological, non-Hermitian and EB physics.
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See the article:
Experimental observation of exceptional bound states in a classical circuit network
https://doi.org/10.1016/j.scib.2024.05.036
Journal
Science Bulletin