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arXiv:2001.05064 · Electronic Proceedings in Theoretical Computer Science

Quantum Walk and Dressed Photon

Misa Hamano, Hayato Saigo

Published Apr 1, 2020• 6 citations
arXivHTMLPDF

Abstract

A physical model called dressed photons, a composite system of photons and excitation of electrons in the nano-particles, is effectively used in the realm of near-field optics. Many interesting behaviors of dressed photons are known, especially the rapid energy transfer and the accumulation to singular points, e.g., points with strong dissipation. We propose a new modelling of dressed photons based on quantum walks, especially Grover walks on semi-infinite graphs which we call jellyfish graphs, and show a universal accumulation phenomena around the point with strong dissipation.

DOI
10.4204/eptcs.315.9

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Quantum optics, the study of light at the level of its building blocks, \nhas been one of the frontiers of science. The arena of quantum optics \nhas been fruitful for investigations of a wide range of interesting questions, \nfrom those on the fundamental structures in driven dissipative \nsystems to those on applications of quantum information processing \nand quantum communication. \nThe first part of this thesis is concerned with one of the holy grails \nof quantum optics: an efficient transfer of energy (coupling) between \nsingle photons and matter degrees of freedom. From a certain point \nof view, the problem of efficient coupling is purely geometrical. The \nefficiency of coupling between an atom and light is difficult because \nit is difficult to shape the wavefunction of a single photon such \nthat it overlaps perfectly with the matter degree of freedom (emitter). \nThe first contribution of this thesis is addressing this issue by considering \nan emitter which perfectly matches the single photon plane-wave. \nMoreover, luckily, such an emitter is already realized in nature in the \nform of a two-dimensional crystal. We show that a new generation \nof two-dimensional semiconductors, transition metal dichalcogenide \n(TMD) monolayers, have especially favorable characteristics for allowing \nhighly efficient coupling between photons and matter degrees \nof freedom. \nOne of the most important goals in realizing an efficient coupling \nbetween photons and matter degrees of freedom is that unlike photons, \nmatter excitations interact with each other. Hence, if we would \nlike to have photons which act as if they interact, one possible way \nis to first convert them into matter excitations, and then transfer the \ncorrelations due matter interactions back to photons. As the second \ncontribution of this thesis, we demonstrate that TMD monolayers placed \nwithin a cavity can help us create photons which avoid each other \nas if they interact. The effect can be simply understood as the TMD \nmonolayer acting as a filter for photons, such that it only allows the \npassage of one photon at a time. \nBesides being the fundamental building block of light, photons also \nserve as mediators of interactions between charged particles. In a \nsense, two positive charges repel each other because there is always \na photon which lets them know that they are close to one another. \nOn the other hand, systems of many interacting particles behave in \na completely different way then when they are alone. It may even be \nargued that all physical phenomena at some level emerge from the \nbehavior of many interacting constituents. Given this point of view, \nit is crucial to find ways to control photons in order to control the \ninteractions that they mediate between matter degrees of freedom. \nAs the third contribution of this thesis, we analyze an experimental \nscheme where the control of photonic degrees of freedom can allow \nan experimentalist to modify the strength and range of interactions \nbetween matter. In particular, we propose squeezed photon states as \na resource to control such interactions. \nThe second part of this thesis is concerned with the emergent phenomena \narising in a system of many interacting particles. In particular, \nthe fourth contribution of this thesis considers the combination \nof two fascinating phenomena which emerges such condensed matter \nsystems: superconductivity and geometric effects in lattice band \nstructures. Separately, both superconductivity and the non-trivial geometrical \neffects in lattice systems are well-established subfields of condensed \nmatter physics. Yet only more recently, the combination of \nthese two phenomena were investigated in the context of topological \nsuperconductors, as well as other superconducting states which emerge \non top of band structures with non-trivial geometry. In our study, \nwe attempt at clarifying one of the ways that the non-trivial geometry \nassociated with the lattice band structure may affect the dynamics of \nan emergent superconducting state. Surprisingly, our analysis shows \nthat one of the most robust characteristics of the superconductor, vortices \nenclosing a quantum of magnetic flux, can be modified due to \ngeometrical effects.

•Nov 1, 2019•0 citations
A physical model called dressed photons, a composite system of photons and excitation of electrons in the nano-particles, is effectively used in the realm of near-field optics. Many interesting behaviors of dressed photons are known, especially the rapid energy transfer and the accumulation to singular points, e.g., points with strong dissipation. We propose a new modelling of dressed photons based on quantum walks, especially Grover walks on semi-infinite graphs which we call jellyfish graphs, and show a universal accumulation phenomena around the point with strong dissipation.
Several interesting physical phenomena and industrial applications explained by the dressed photon have been reported in recent years. These require a novel concept in an off-shell science that deviates from the conventional optics, satisfying energy and momentum conservation laws. In this paper, starting from an original model that captures dressed-photon characteristics phenomenologically, the dynamics of the dressed photon in a nanomatter system and the mechanism for extracting internal degrees of freedom of the dressed photon to an external space have been examined by theoretical and numerical approaches. Our proposal is that basis states of the dressed photon can be transformed to the form that reflects the spatial distribution of the dressed-photon steady state in the system, and some of basis states with predetermined spatial distribution can relate to the dissipation components in the external space by means of the renormalization technique. From the results of numerical simulation, it is found that quasi-static states are regarded as the photon with light mass or massless, and the extraction of active states strongly affects the spatial distribution in a new steady state. The concept for extracting dressed-photon energy to an external space will contribute to a detailed understanding of dressed-photon physics and future industrial applications.
The discrete quantum walk in N dimensions is analyzed from the perspective of its dispersion relations. This allows understanding known properties, as well as designing new ones when spatially extended initial conditions are considered. This is done by deriving wave equations in the continuum, which are generically of the Schrödinger type, and allows devising interesting behavior, such as ballistic propagation without deformation, or the generation of almost flat probability distributions, which is corroborated numerically. There are however special points where the energy surfaces display intersections and, near them, the dynamics is entirely different. Applications to the two- and three-dimensional Grover walks are presented.
Driven-dissipative phase transition in an open quantum systems nowdays is among the most rapidly developing fields of quantum optics. An example of such a system is depicted in Fig. 1 (a) , which shows a superconducting microwave cavity undergoing two-photon driving at g rate as well as two-photon dissipation at γ rate [1] . In this system, the presence of the two-photon dissipation does not destroy, but stabilizes the quantum state, also known as Schrödinger cat state, and it is possible to prepare a dynamically protected qubit on its basis [2] . Numerical methods are commonly applied to study such quantum systems. However, their use typically does not allow to uncover physical phenomena underlying the evolution of the system. In the limit of a large number of photons, a qualitative picture of the occurring phenomena can be obtained using the so-called semiclassical approximation. Nevertheless, this approach completely neglects the quantum fluctuations, which can play a significant role, even in the case of large average number of photons in the system.
This article reviews recent progress in theoretical studies of dressed photons. For providing concrete physical images of dressed photons, several experimental studies are demonstrated. They are applications of dressed photons to novel optical functional devices, nano-fabrication technologies, energy conversion technologies, and photon breeding devices. After these experimental demonstrations, as the main part of this review, quantum-field theoretical formulation of dressed photons is attempted in use of the newly introduced Clebsch-dual variable of electromagnetic field. The reason for introducing the new formulation will be explained in the final section from the viewpoint to exhibit the contrast between free and interacting quantum fields in regard to their energy-momentum supports which are seldom touched upon (or forgotten) in the common physical discussions about quantum fields.
Quantum optics, the study of light at the level of its building blocks, \nhas been one of the frontiers of science. The arena of quantum optics \nhas been fruitful for investigations of a wide range of interesting questions, \nfrom those on the fundamental structures in driven dissipative \nsystems to those on applications of quantum information processing \nand quantum communication. \nThe first part of this thesis is concerned with one of the holy grails \nof quantum optics: an efficient transfer of energy (coupling) between \nsingle photons and matter degrees of freedom. From a certain point \nof view, the problem of efficient coupling is purely geometrical. The \nefficiency of coupling between an atom and light is difficult because \nit is difficult to shape the wavefunction of a single photon such \nthat it overlaps perfectly with the matter degree of freedom (emitter). \nThe first contribution of this thesis is addressing this issue by considering \nan emitter which perfectly matches the single photon plane-wave. \nMoreover, luckily, such an emitter is already realized in nature in the \nform of a two-dimensional crystal. We show that a new generation \nof two-dimensional semiconductors, transition metal dichalcogenide \n(TMD) monolayers, have especially favorable characteristics for allowing \nhighly efficient coupling between photons and matter degrees \nof freedom. \nOne of the most important goals in realizing an efficient coupling \nbetween photons and matter degrees of freedom is that unlike photons, \nmatter excitations interact with each other. Hence, if we would \nlike to have photons which act as if they interact, one possible way \nis to first convert them into matter excitations, and then transfer the \ncorrelations due matter interactions back to photons. As the second \ncontribution of this thesis, we demonstrate that TMD monolayers placed \nwithin a cavity can help us create photons which avoid each other \nas if they interact. The effect can be simply understood as the TMD \nmonolayer acting as a filter for photons, such that it only allows the \npassage of one photon at a time. \nBesides being the fundamental building block of light, photons also \nserve as mediators of interactions between charged particles. In a \nsense, two positive charges repel each other because there is always \na photon which lets them know that they are close to one another. \nOn the other hand, systems of many interacting particles behave in \na completely different way then when they are alone. It may even be \nargued that all physical phenomena at some level emerge from the \nbehavior of many interacting constituents. Given this point of view, \nit is crucial to find ways to control photons in order to control the \ninteractions that they mediate between matter degrees of freedom. \nAs the third contribution of this thesis, we analyze an experimental \nscheme where the control of photonic degrees of freedom can allow \nan experimentalist to modify the strength and range of interactions \nbetween matter. In particular, we propose squeezed photon states as \na resource to control such interactions. \nThe second part of this thesis is concerned with the emergent phenomena \narising in a system of many interacting particles. In particular, \nthe fourth contribution of this thesis considers the combination \nof two fascinating phenomena which emerges such condensed matter \nsystems: superconductivity and geometric effects in lattice band \nstructures. Separately, both superconductivity and the non-trivial geometrical \neffects in lattice systems are well-established subfields of condensed \nmatter physics. Yet only more recently, the combination of \nthese two phenomena were investigated in the context of topological \nsuperconductors, as well as other superconducting states which emerge \non top of band structures with non-trivial geometry. In our study, \nwe attempt at clarifying one of the ways that the non-trivial geometry \nassociated with the lattice band structure may affect the dynamics of \nan emergent superconducting state. Surprisingly, our analysis shows \nthat one of the most robust characteristics of the superconductor, vortices \nenclosing a quantum of magnetic flux, can be modified due to \ngeometrical effects.