Exploring the properties and applications of topological quantum states is essential to better understand topological matter. Here, we theoretically study a quasi-one-dimensional topological atom array. In the low-energy regime, the atom array is equivalent to a topological superatom. Driving the superatom in a cavity, we study the interaction between light and topological quantum states. We find that the edge states exhibit topology-protected quantum coherence, which can be characterized from the photon transmission. This quantum coherence helps us to find a superradiance-subradiance transition, and we also study its finite-size scaling behavior. The superradiance-subradiance transition also exists in symmetry-breaking systems. More importantly, it is shown that the quantum coherence of the subradiant edge state is robust to random noises, allowing the superatom to work as a topologically protected quantum memory. We suggest a relevant experiment with three-dimensional circuit QED. Our study may have applications in quantum computation and quantum optics based on topological edge states.
Exploring the properties and applications of topological quantum states is essential to better understand topological matter. Here, we theoretically study a quasi-one-dimensional topological atom array. In the low-energy regime, the atom array is equivalent to a topological superatom. Driving the superatom in a cavity, we study the interaction between light and topological quantum states. We find that the edge states exhibit topology-protected quantum coherence, which can be characterized from the photon transmission. This quantum coherence helps us to find a superradiance-subradiance transition, and we also study its finite-size scaling behavior. The superradiance-subradiance transition also exists in symmetry-breaking systems. More importantly, it is shown that the quantum coherence of the subradiant edge state is robust to random noises, allowing the superatom to work as a topologically protected quantum memory. We suggest a relevant experiment with three-dimensional circuit QED. Our study may have applications in quantum computation and quantum optics based on topological edge states.
In this dissertation we focused on two topics: 1. atomic cooperative effect, including superradiance, subradiance and collective Lamb shift in an atomic ensemble; 2. novel topological effect in quantum optics system, such as Haldane model, synthetic magnetic field in superradiance lattice and synthetic spin-orbit interaction in Fock-state lattices. \n\nIn the first part, we start from the Dicke state, an N-particle atomic ensemble excited by a single photon. Due to the interaction of the atoms with a continuum of vacuum modes, the Dicke state has a larger decay rate compared with an isolated atom, termed the single photon superradiance. In the “opposite” case, the single-photon subradiance state does not decay because of the destructive interference of the atomic transitions. We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance in an extended ensemble. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.\n\nIn the second part, we start from introducing the concepts, methods, and models from quantum optics or condensed matter physics. They include the timed-Dicke states, electromagnetically induced transparency, coupled wave equations, tight-binding model, band theory, Floquet theory, superradiance lattice, integer quantum Hall effect, Haldane model, etc.. Based upon these tools, we study three topological quantum optics systems: (i) a Haldane model with in situ tunable topological properties in a two-dimensional momentumspace superradiance lattice composed of timed Dicke states in electromagnetically induced transparency; (ii) a spin-orbit coupled Fock-state lattice, which introduce a novel quantum operation to generate mesoscopic superposition states, e.g., the NOON states and cat states; (iii) a synthetic magnetic field created in a quasi one dimensional superradiance lattice, which is predicted to be observed in thermal vapours of alkali atoms instead of only in cold atoms (as in previous experiments). This study aims to provide a novel, highly tunable platform simulating exotic phenomena in condensed matter physics and offers a basis of topological quantum optics and novel photonic devices.
The ordered atomic array emerges as a versatile atom-photon interface for exquisite control of light-matter interaction at the nanoscale. In particular, the one-dimensional atom-waveguide system can achieve strong coupling between a single atom and a photon, where two atomic mirrors coupled to waveguide act as a high-finesse cavity. In this work we show that under the strong-coupling regime, the mirror atoms arranged in the form of a Su-Schrieffer-Heeger chain are advantageous in decoherence suppression compared to a nontopological Bragg configuration, manifesting a significant increase in the lifetime of dressed states, substantial narrowing of the spectral linewidth, and order-of-magnitude enhancement of the cooperativity of light-matter interaction. Furthermore, subradiant dressed states with a decay rate smaller than the emission rate of a free-space atom are found in the dissipationless atomic cavity with a few mirror atoms, which cannot be achieved with a Bragg atomic mirror. A theory of the local density of states (LDOS) of the atomic cavity is presented and reveals that the decoherence suppression is directly related to the negative LDOS in a wide frequency range contributed by the bulk modes of the topological atomic cavity. This peculiar feature of the LDOS indicates the destructive quantum interference of photon scattering by the topological edge- and bulk-state channels. Our work demonstrates the great potential of topology in engineering quantum states and enhancing quantum coherence for future applications in quantum computing and quantum information processing.
The combination of topological photonics and quantum optics has promising applications. In previous works, the role of the edge states of conventional topological optical structure in the coherent coupling between atoms has been discussed. Besides the optimistic results, we find that if the coupling coefficient between the atom and element-cavity exceeds the coupling coefficient between cavities in the array, atoms cannot be effectively coupled with each other through the edge states. Here, we generalize to higher-order structures and explore the dynamics of three atoms interacting with the cavity array based on the kagome-type optically coupled-cavity array with topologically protected corner states. Three atoms are theoretically coupled in three corner cavities, and various quantum behaviors can be displayed in different parameters. It is shown that three atoms mediated by the corner state can be coherently coupled with each other, without the constraint of the coupling coefficient, and can induce entanglement, which shows that the high-order topological optical structure has more advantages than the conventional topological optical structure in coherent coupling among qubits. In addition, we also studied atoms mediated by edge states. The results show that the atoms mediated by edge states can be coherently coupled only in the weak coupling regime, and the entanglement effect induced by the edge states is not as good as that of the corner state. It indicates that the corner state is more useful than the edge state in the second-order optical topological structure. Our results can offer references for applying optical topological structure in quantum computing and quantum communication.
Abstract Efficient manipulation of quantum states is a key step towards applications in quantum information, quantum metrology, and nonlinear optics. Recently, atomic arrays have been shown to be a promising system for exploring topological quantum optics and robust control of quantum states, where the inherent nonlinearity is included through long-range hoppings. Here we show that a one-dimensional atomic array in a periodic magnetic field exhibits characteristic properties associated with an effective two-dimensional Hofstadter-butterfly-like model. Our work points out super- and sub-radiant topological edge states localized at the boundaries of the atomic array despite featuring long-range interactions, and opens an avenue of exploring an interacting quantum optical platform with synthetic dimensions.
The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.
Topological insulators are materials that have a gapped bulk energy spectrum but contain protected in-gap states appearing at their surface. These states exhibit remarkable properties such as unidirectional propagation and robustness to noise that offer an opportunity to improve the performance and scalability of quantum technologies. For quantum applications, it is essential that the topological states are indistinguishable. We report high-visibility quantum interference of single-photon topological states in an integrated photonic circuit. Two topological boundary states, initially at opposite edges of a coupled waveguide array, are brought into proximity, where they interfere and undergo a beamsplitter operation. We observe Hong-Ou-Mandel interference with 93.1 ± 2.8% visibility, a hallmark nonclassical effect that is at the heart of linear optics-based quantum computation. Our work shows that it is feasible to generate and control highly indistinguishable single-photon topological states, opening pathways to enhanced photonic quantum technology with topological properties, and to study quantum effects in topological materials.