Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

Quantum computers promise to perform certain tasks that are believed to be intractable to classical computers. Boson sampling is such a task and is considered a strong candidate to demonstrate the ...

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Quantum computational advantage using photons

13. 벼잎선충의 약제처리 방법별 방제 효과

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging and complex landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry, such as the electronic structure of molecules. In the past two decades, significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This Review provides an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing and quantum computing researchers who would like to explore applications in quantum chemistry.

Quantum Chemistry in the Age of Quantum Computing.

Multidimensional quantum walks can exhibit highly nontrivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a two-dimensional (2D) optical quantum walk on a lattice, demonstrating a scalable quantum walk on a nontrivial graph structure. We realized a coherent quantum walk over 12 steps and 169 positions by using an optical fiber network. With our broad spectrum of quantum coins, we were able to simulate the creation of entanglement in bipartite systems with conditioned interactions. Introducing dynamic control allowed for the investigation of effects such as strong nonlinearities or two-particle scattering. Our results illustrate the potential of quantum walks as a route for simulating and understanding complex quantum systems.

http://science.sciencemag.org/content/sci/336/6077/55.full.pdf

A 2D Quantum Walk Simulation of Two-Particle Dynamics

Boson sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require universal control over the quantum system, which favors current photonic experimental platforms. Here, we introduce Gaussian Boson sampling, a classically hard-to-solve problem that uses squeezed states as a nonclassical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the Hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson sampling, a #P hard problem, using squeezed states. This demonstrates that Boson sampling from Gaussian states is possible, with significant advantages in the photon generation probability, compared to existing protocols.

Gaussian Boson Sampling.

Since the development of boson sampling, there has been a quest to construct more efficient and experimentally feasible protocols to test the computational complexity of sampling from photonic states. In this paper, we interpret and extend the results presented previously [Phys. Rev. Lett. 119, 170501 (2017)]. We derive an expression that relates the probability to measure a specific photon output pattern from a Gaussian state to the Hafnian matrix function and use it to design a Gaussian boson sampling protocol. Then, we discuss the advantages that this protocol has relative to other photonic protocols and the experimental requirements for Gaussian boson sampling. Finally, we relate it to the previously most general protocol, scattershot boson sampling [Phys. Rev. Lett. 113, 100502 (2014)].

Detailed study of Gaussian boson sampling

We present the protocol for Gaussian Boson Sampling with single-mode squeezed states. We eliminate heralding and show that our proposal with the Hafnian matrix function can retain the higher photon number contributions at the input.

Gaussian Boson sampling

Quantum optics in combination with integrated optical devices shows great promise for efficient manipulation of single photons. New physical concepts, however, can only be found when these fields truly merge and reciprocally enhance each other. Here we work at the merging point and investigate the physical concept behind a two-coupled-waveguide system with an integrated parametric down-conversion process. We use the eigenmode description of the linear system and the resulting modification in momentum conservation to derive the state generation protocol for this type of device. With this new concept of state engineering, we are able to effectively implement a two-in-one waveguide source that produces the useful two-photon NOON state without extra overhead such as phase stabilization or narrow-band filtering. Experimentally, we benchmark our device by measuring a two-photon NOON state fidelity of $\mathcal{F}=(84.2\ifmmode\pm\else\textpm\fi{}2.6)%$ and observe the characteristic interferometric pattern directly given by the doubled phase dependence with a visibility of ${\mathcal{V}}_{\mathrm{NOON}}=(93.3\ifmmode\pm\else\textpm\fi{}3.7)%$.

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Craig S. Hamilton

Papers

A 2D Quantum Walk Simulation of Two-Particle Dynamics

Gaussian Boson Sampling.

Detailed study of Gaussian boson sampling

Gaussian Boson sampling

Dual-path source engineering in integrated quantum optics