Berry and Pancharatnam topological phases of atomic and optical systems

Ben‐Aryeh, Y.

doi:10.1088/1464-4266/6/4/r01

Cited by 42 publications

(54 citation statements)

References 198 publications

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“…However, many previous classical works invoke the theory of Hermitian line bundles or gauge theory (see, e.g., [17], [23]), and here we avoid those topics and consider Berry properties from a relatively simple electromagnetic perspective [30]. Furthermore, as described in [31], before the Berry phase was understood as the general concept it is now, in various fields this extra phase had been found.…”

Section: Introductionmentioning

confidence: 99%

Berry Phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material From a Classical Electromagnetics Perspective

Gangaraj

Silveirinha

Hanson

2017

IEEE J. Multiscale Multiphys. Comput. Tech.

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Abstract-The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical Schrödinger equation, writing both in Hamiltonian form. However, the aforementioned quantities are not necessarily quantum in nature, and for photonic systems they can be explained using only classical concepts. Here we provide a derivation and description of PTI quantities using classical Maxwell's equations, we demonstrate how an electromagnetic mode can acquire Berry phase, and we discuss the ramifications of this effect. We consider several examples, including wave propagation in a biased plasma, and radiation by a rotating isotropic emitter. These concepts are discussed without invoking quantum mechanics, and can be easily understood from an engineering electromagnetics perspective.Index Terms-Berry Phase, surface wave, photonic topological insulator.

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Section: Introductionmentioning

confidence: 99%

Berry Phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material From a Classical Electromagnetics Perspective

Gangaraj

Silveirinha

Hanson

2017

IEEE J. Multiscale Multiphys. Comput. Tech.

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“…Different from the Hermitian Hamiltonian in quantum mechanics, the twisted transfer operatorĤ u are non-Hermitian such that its left eigenvector ϕ u | is not the Hermitian conjugate of the corresponding right eigenvector |ψ u , but only biorhonormal with each other. Therefore, writing ϕ A |ψ B = | ϕ A |ψ B |e iφ AB (χ) and ϕ B |ψ A = | ϕ B |ψ A |e iφ BA (χ) with angle φ AB and φ BA as the analogy of Pancharatnam's topological phase [31,32], we have φ AB = φ BA generally. This is different from from those in Hermitian quantum mechanics, where φ AB is always equal to φ BA [33].…”

Section: Seebeck Effect Pyroelectric Effectmentioning

confidence: 99%

The Third Way of Thermal-Electric Conversion beyond Seebeck and Pyroelectric Effects

Ren

2014

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Thermal-electric conversion is crucial for smart energy control and harvesting, such as thermal sensing and waste heat recovering. So far, people are aware of only two ways of direct thermal-electric conversion, Seebeck and pyroelectric effects, each with distinct working conditions and limitations. Here, we report the third way of thermal-electric conversion beyond Seebeck and pyroelectric effects. In contrast to Seebeck effect that requires spatial temperature difference, the-third-way converts the time-dependent ambient temperature fluctuation into electricity, similar to the behavior of pyroelectricity. However, the-third-way is also distinct from pyroelectric effect in the sense that it does not require polar materials but applies to general conducting systems. We demonstrate that the-third-way results from the temperature-fluctuation-induced dynamical charge redistribution. It is a consequence of the fundamental nonequilibrium thermodynamics and has a deep connection to the topological phase in quantum mechanics. The findings expand our knowledge and provide new means of thermal-electric energy harvesting.About 90 percent of the world's energy is utilized through heating and cooling, which makes energy waste a great bottleneck to the sustainability of any modern economy [1]. In addition to developing new technology of smart heat control [2], the global energy crisis can be alleviated by recovering the wasted thermal energy. In view of the inconvenient truth that more than 60% of the energy utilization was lost mostly as wasted heat [3], harvesting the thermal energy becomes critical to provide a cleaner and sustainable future [1].Thermal-electric energy harvesting mainly relies on two principles: Seebeck effect (Fig. 1A) and pyroelectric effect (Fig. 1B). The Seebeck effect utilizes the spatial temperature difference between two sides of materials to drive the diffusion of charge carriers so as to convert heat into electricity [4,5]. Besides recovering waste heat, Seebeck effect with its reciprocal has wide applications of cooling, heating, power generating [6] and thus has revitalized an upsurge of research interest recently [7,8]. However, when the ambient temperature is spatially uniform, we have to resort to the pyroelectric effect [9], which utilizes the time-dependent temperature variation to convert heat into electricity but is restricted to pyroelectric materials [10]. This is due to the fact that the temporal temperature fluctuation modifies the spontaneous polarization of polar crystals, which consequently redistributes surface charges and produces temporary electric current [11,12]. In addition to thermal-electric energy harvesting [13][14][15][16][17], pyroelectric effect has widespread applications in long-wavelength infrared sensing, motion detector, thermal image [11], and even nanoscale printing [18].However, since Seebeck and pyroelectric effects have been known for quite a long time, one cannot help wondering: Does Nature only offer us these two means for thermal-electric energy harvestin...

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“…The Berry phase has very interesting applications, such as the implementation of quantum computation by geometric means [3,4,5]. Recently, it has been recognized that large-scale quantum computers are hard to construct because quantum systems easily lose their coherence through interaction with the environment [2].…”

Section: Introductionmentioning

confidence: 99%

“…These types of systems, however, are very unrealistic and almost never occur in practice. In some applications, however, in particular geometric fault tolerant quantum computation [3], mixed state cases are important. From a mathematical point of view, Uhlmann was the first to address the issue of mixed state holonomy [22,23].…”

Section: Introductionmentioning

confidence: 99%