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arXiv:1908.08323 · Photonics Research

Nonreciprocal transition between two nondegenerate energy levels

Xun‐Wei Xu, Yan-Jun Zhao, Hui Wang, Aixi Chen, Yu-xi Liu

Published Mar 12, 2021• 10 citations
arXivHTMLPDF

Abstract

Stimulated emission and absorption are two fundamental processes of light–matter interaction, and the coefficients of the two processes should be equal. However, we will describe a generic method to realize the significant difference between the stimulated emission and absorption coefficients of two nondegenerate energy levels, which we refer to as a nonreciprocal transition. As a simple implementation, a cyclic three-level atom system, comprising two nondegenerate energy levels and one auxiliary energy level, is employed to show a nonreciprocal transition via a combination of synthetic magnetism and reservoir engineering. Moreover, a single-photon nonreciprocal transporter is proposed using two one-dimensional semi-infinite coupled-resonator waveguides connected by an atom with nonreciprocal transition effect. Our work opens up a route to design atom-mediated nonreciprocal devices in a wide range of physical systems.

DOI
10.1364/prj.412904

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Stimulated emission and absorption are two fundamental processes of light–matter interaction, and the coefficients of the two processes should be equal. However, we will describe a generic method to realize the significant difference between the stimulated emission and absorption coefficients of two nondegenerate energy levels, which we refer to as a nonreciprocal transition. As a simple implementation, a cyclic three-level atom system, comprising two nondegenerate energy levels and one auxiliary energy level, is employed to show a nonreciprocal transition via a combination of synthetic magnetism and reservoir engineering. Moreover, a single-photon nonreciprocal transporter is proposed using two one-dimensional semi-infinite coupled-resonator waveguides connected by an atom with nonreciprocal transition effect. Our work opens up a route to design atom-mediated nonreciprocal devices in a wide range of physical systems.
We propose a theoretical scheme to realize nonreciprocal transition in a multi-level atomic system with cyclic four-level transition. The effective transition between two indirectly coupled energy levels become nonreciprocal, when they are coupled to two auxiliary levels simultaneously, by four strong driving fields with the total phase serving as a synthetic magnetic flux and breaking the time reversal symmetry of the system. The nonreciprocal transition can lead to the elimination of a spectral line in the spontaneous emission spectrum, which provide us a simple approach to measure the phenomenon in steady state. This work provides a feasible approach to observe nonreciprocal transition in a wide range of multi-level systems, including natural atoms with parity symmetry.
We propose a theoretical scheme to realize nonreciprocal transition between two energy levels that can not coupled directly. Suppose they are coupled indirectly by two auxiliary levels with a cyclic four-level configuration, and the four transitions in the cyclic configuration are controlled by external fields. The indirectly transition become nonreciprocal when the time reversal symmetry of the system is broken by the synthetic magnetic flux, i.e., the total phase of the external driving fields through the cyclic four-level configuration. The nonreciprocal transition can be identified by the elimination of a spectral line in the spontaneous emission spectrum. Our work introduces a feasible way to observe nonreciprocal transition in a wide range of multi-level systems, including natural atoms or ions with parity symmetry.
We propose how to realize nonreciprocity for a weak input optical field via nonlinearity and synthetic magnetism. We show that the photons transmitted from a linear cavity to a nonlinear cavity (i.e., a linear-nonlinear optical molecule) exhibit nonreciprocal photon blockade but no clear nonreciprocal transmission. Both nonreciprocal transmission and nonreciprocal photon blockade can be observed, when one or two auxiliary modes are coupled to the linear-nonlinear optical molecule to generate an artificial magnetic field. A similar method can be used to create and manipulate nonreciprocal transmission and nonreciprocal photon blockade for photons bidirectionally transport in a nonlinear-nonlinear optical molecule. Additionally, a photon circulator with nonreciprocal photon blockade is designed in cyclic three-nonlinear-mode system. The combination of nonlinearity and synthetic magnetism provides us an effective way towards the realization of quantum nonreciprocal devices, e.g., nonreciprocal single-photon sources and single-photon diodes.
We treat the interaction between an electromagnetic radiation bath and a material system in the semi-classical picture: the radiation is treated according to the Maxwell equations, but the process of emission/absorption is described through the concept of a photon; on the other hand, the material system is modelled according to quantum mechanics, assuming a discrete two-level energy spectrum. This very simple model allows one to elaborate the elementary theory of the absorption/emission coefficients, both for the spontaneous and for the stimulated processes which will be described within the electric dipole approximation. Selection rules for allowed transitions are eventually obtained and the nature of high-order transition is briefly outlined. Finally, a qualitative description of the light amplification by stimulated emission of radiation is presented.
Radiation can change the energy state of matter via three optical processes: spontaneous emission, absorption and stimulated emission. In spontaneous emission, an excited atomic or molecular state decays to a lower energy state with the emission of a photon of energy equal to the difference in the quantum state energies. Photon absorption is the reverse process, with a photon causing excitation from a lower to an excited quantum state. Stimulated emission was first proposed by Einstein in a paper published in 1917. He attempted to balance spontaneous emission and photon absorption, but could not get the correct balance without the postulated process of stimulated emission (see Section 4.2). With stimulated emission, an excited quantum state is stimulated to decay to a lower quantum state by an impinging photon. The existing photon survives with another identical photon being created (so that energy is conserved). The rates at which radiative transitions occur can be calculated using quantum mechanics. The time-dependent Schrodinger equation is used with the system wavefunction comprising time-varying linear combinations of the two wavefunctions for the lower and upper quantum states. In semi-classical treatments, an atom is treated quantum mechanically with the radiation field treated classically. There is a perturbation in energy associated with, say, the electric field of the radiation interacting with the electric dipole of the atom, though other interactions can be significant if the electric dipole interaction energy is small. In absorption, for example, a differential equation representing the change in ‘weighting’ of the wavefunction from the lower to upper state is obtained. A ‘time constant’ for the speed of change represents the rate of the radiative process. We examine the quantum mechanical nature of radiation absorption in Section 10.1 before discussing (Section 10.3) another important parameter arising with radiative transitions between discrete bound quantum states: the lineshape function. Quantum Theory of the Atom–Radiation Interaction An expression for the Einstein B-coefficient for photo-absorption is derived using quantum mechanics in this section. Einstein determined the detailed balance relationship between the rates of spontaneous emission, photo-absorption and stimulated emission when light interacts with an atom by considering an atomic system of two energy levels which are in equilibrium with a black-body radiation field. We use a semi-classical treatment where the atom is treated quantum mechanically and the radiation field is treated as a classical oscillating electric field.
We study the transport of a single photon in two coupled one-dimensional semi-infinite coupled-resonator waveguides (CRWs), in which both end sides are coupled to a dissipative cavity. We demonstrate that a single photon can transfer from one semi-infinite CRW to the other nonreciprocally. Based on such nonreciprocity, we further construct a three-port single-photon circulator by a T-shaped waveguide, in which three semi-infinite CRWs are pairwise mutually coupled to each other. The single-photon nonreciprocal transport is induced by the breaking of the time-reversal symmetry and the optimal conditions for these phenomena are obtained analytically. The CRWs with broken time-reversal symmetry will open up a kind of quantum device with versatile applications in quantum networks.