Exceptional sensitivity and transport

    Kohei Kawabata

    • Department of Physics, Princeton University, Princeton, New Jersey, USA

Physics 16, 107

Two experimental studies achieved enhanced atomic sensing and chiral heat transport near exceptional points, singularities inherent in open and non-Hermitian systems.

ODA/C. Cain

Figure 1: Exceptional points are a unique feature of non-Hermitian systems. They define a location where system states overlap, or merge, into one. In this drawing, an exceptional point (pink) is shown as the location where some observables of a system converge. By taking measurements near an exceptional point like this, the researchers demonstrated improved detection and direction-dependent heat transport.Exceptional points are a unique feature of non-Hermitian systems. They define a location where system states overlap, or merge, into one. In this drawing, an exceptional point (pink) is shown as the location where some observables of… Show more

In quantum mechanics, a system is conventionally described by a Hermitian Hamiltonian, the solution of which gives the energy states of the system. Hermiticity is a mathematical property that guarantees several crucial characteristics of a quantum system. From a physical perspective, hermitism is required by the conservation of probability, which further arises from the assumption that the system of interest is isolated. Conversely, when a system is open, in the sense that it exchanges energy, particles or information with its surroundings, it is no longer described by a Hermitian Hamiltonian. Over the past two decades, researchers have discovered numerous new phenomena and features of open classical and quantum systems that have no analogues in conventional Hermitian systems, leading to the emerging research field of non-Hermitian physics [1]. In two separate experimental works, the researchers realized new non-Hermitian phenomena by exploiting a unique feature of non-Hermitian systems called the exceptional point [2, 3]. The first experiment used an exceptional spot to amplify the signal of a magnetic field in an atomic gas. The second experiment demonstrated handedness, or chirality, in transporting heat through a fluid system. These new works may open a new avenue towards active control of the phases of matter.

In closed systems governed by Hermitian Hamiltonians, states are always independent of each other, even if they possess the same spectrum. Conversely, in open systems characterized by non-Hermitian Hamiltonians, states can merge into a single state. This unique and unconventional spectral feature, referred to as an exceptional point, gives rise to exotic spectral singularities inherent in non-Hermitian systems and leads to a wide range of physical phenomena in open systems [1, 4]. For example, an exceptional point accompanies the spontaneous parity-time symmetry breaking [5]. It is also interesting to note that an exceptional point underlies the theory of phase transitions in statistical mechanics [6].

The two new experimental works exploited the potential of exceptional points to advance physics applications. In the first experiment, a research team led by Yong-Chun Liu of Tsinghua University, China used an exceptional point for sensing the magnetic field [2]. While a Hermitian system generally responds linearly to an input signal, a non-Hermitian system at an exceptional point typically generates a response proportional to the square root of the signal. For a small signal, this square root response is qualitatively greater than the conventional linear response, implying that the exceptional point can be exploited to improve the sensitivity of the sensors. [7]. While this improvement in sensitivity has previously been demonstrated in optics and photonics [8]Liu’s team realized it in a thermal atomic ensemble and thus extended its range of potential applications in atomic, molecular and optical physics.

The researchers made an exceptional point in a thermally interacting atomic gas, as had also been done in previous studies [9]. Using a vapor cell of rubidium atoms, they prepared a multilevel thermal atomic array and introduced nonhermiticity by manipulating the decay rate of each energy level with a probe laser. The energy shared between atoms is not conserved and escapes to another energy level, which serves as its surroundings. As a consequence of the interplay between coherent coupling and unbalanced decay rates for different energy levels, the system showed an outstanding point. Specifically, the team observed this through the splitting of a resonance peak in the optical polarization rotation spectrum into two peaks as an input magnetic field was varied. The exceptional point makes the peak division sensitive to the magnetic field, thus providing an opportunity for high-precision sensing.

From a practical point of view, it should be noted that an exceptional point amplifies not only a signal of interest but also noise, which can prevent the improvement of sensitivity [10]. Liu and colleagues’ scheme aimed to overcome this challenge by relying on the optical polarization-rotation signal. Further investigations should evaluate the general applicability of this new scheme and explore possible improvements to the scheme.

In the second experiment, Cheng-Wei Qiu of the National University of Singapore and collaborators explored direction-dependent, or chiral, thermal transport accompanied by an exceptional point [3]. They devised a fluid system in a cylinder involving two thin plates at the top and bottom that rotate in opposite directions (clockwise and counterclockwise) and induce advection in each respective direction. Additionally, the sides of the cylinder are connected to heating and cooling sources that generate heat input. This fluid system is effectively described by a non-Hermitian Hamiltonian in the context of the thermal diffusion equation, where the interaction of intrinsic conduction, advection and influx can give rise to an exceptional point. The team experimentally studied the concomitant heat transport by measuring the temperature distribution of the system under various conditions.

Intuitively, the thermal propagation appears to align with the advection flows induced by the two rotating plates. However, the team observed a directional dependence in heat transport that results from the non-trivial combination of heat influx and the two unbalanced advection flows. Chirality is a hallmark of non-Hermitian systems [11], and the present experimental work demonstrated that non-hermiticity produces chirality also for the heat transport governed by the diffusion equation. Although this chiral heat transport was exclusively observed in the vicinity of the exceptional point, it was suppressed at the very exceptional point, implying a new underlying mechanism.

Chirality finds practical relevance in facilitating the efficient transport of electricity, heat, and other quantities. Early recent examples include topological materials, which exhibit chiral boundary states that are immune to imperfections and inhomogeneities. In contrast, the chiral heat transport realized by Qiu and colleagues relies on a different mechanism intrinsic to open systems, which may inspire new ideas for actively manipulating transport phenomena and for developing new devices.

Conventionally, dissipation has been viewed as a nuisance that obscures interesting physics, forcing physicists to purge it from laboratory setups and practical applications. However, these two new experimental studies exemplify the utility of exceptional points in intrinsically dissipative systems. Further theoretical and experimental advances may lead to new physics in open systems that has no parallel in closed systems.


  1. R. El-Ganainy et al.Non-Hermitian physics and PT symmetry, Nat. Phys. 1411 (2018).
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About the author

Image by Kohei Kawabata

Kohei Kawabata received his PhD in physics from the University of Tokyo in 2022. After being a research associate of Gordon and Betty Moore at Princeton University, he joined the faculty of the Institute for Solid State Physics of the University of Tokyo in 2023. the research explores various aspects of condensed matter physics, in particular the fundamental and universal characterization of phases and orders far from equilibrium.

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