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Advances in Photonics of Quantum Computing, Memory, and Communication

Single-channel Hadamard gate by exploiting frequency conversion of single-photon Raman scattering in chiral quantum nanophotonics

Zihao Chen, Yao Zhou, Jung‐Tsung Shen

Published Mar 4, 2019• 2 citations
Publisher

Abstract

To enhance the spatial utility of typical two-port Hadamard gate, we propose a novel single-channel scheme through frequency conversion in Λ-atom-mediated single-photon Raman scattering process in chiral quantum nanophotonics. We demonstrate faithful and efficient gate operations, and quantitatively analyze gate performance. Moreover, by manipulating photon-emitter coupling and frequency detuning, it is confirmed that an arbitrary unitary single-qubit operations are achieved in the presented configuration, including most representative single-qubit Hadamard, X, Z, S, and T gates. Due to the advent of directional emission techniques, the chiral condition is readily experimentally feasible. In addition, we further propose an alternative N-type atom architecture to perform Hadamard operations that are enabled by hyperfine structure in the strong-coupling regime.

DOI
10.1117/12.2517090

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To enhance the spatial utility of typical two-port Hadamard gate, we propose a novel single-channel scheme through frequency conversion in Λ-atom-mediated single-photon Raman scattering process in chiral quantum nanophotonics. We demonstrate faithful and efficient gate operations, and quantitatively analyze gate performance. Moreover, by manipulating photon-emitter coupling and frequency detuning, it is confirmed that an arbitrary unitary single-qubit operations are achieved in the presented configuration, including most representative single-qubit Hadamard, X, Z, S, and T gates. Due to the advent of directional emission techniques, the chiral condition is readily experimentally feasible. In addition, we further propose an alternative N-type atom architecture to perform Hadamard operations that are enabled by hyperfine structure in the strong-coupling regime.
Abstract Single-photon frequency conversion in the system composed of a Λ -type three-level giant atom chiral couples to a one-dimensional waveguide is investigated. Two configurations, i.e. one of the atomic transitions couples to the waveguide at two separated points while the other one either directly or indirectly couples to the waveguide at a single point, are considered. The scattering amplitudes for representing the frequency conversion in the two kinds of coupling schematics are obtained analytically with the real-space approach. The results show that perfect nonreciprocal transmission with preserving frequency and ideal directional frequency conversion can be realized due to the time-reversal symmetry broken induced by the chiral coupling as well as the self-interference comes from the giant atom. In particular, in the indirect coupling configuration, the scattering spectra exhibit two directional frequency conversion windows due to the atom-cavity coupling, which enables the present system suitable for the simultaneous manipulation of incident photons with different frequencies. These results may have potential applications in various quantum information processing and quantum network engineering.
To resolve the intrinsic trade-off between the deterministic nature and scalability of controlled phase gate implementation in the linear optics regime, we propose a novel deterministic two-photon controlled phase gate scheme in chiral quantum nanophotonics. The essential ingredient here is that, a non-linear π-phase shift is imprinted during the photonic molecule generations. On one hand, the gate operates in a deterministic way without the assistance of probabilistic ancilla qubit measurement. On the other hand, the gate implementation is of low complexity to be highly scalable. To date, the chiral coupling is readily underpinned by the advent of directional emission technique. Potential implementation platforms include QD, superconducting qubit, Rydberg atom, or N-V center that is coupled to a PhC waveguide, transmission line, or optical fiber.
We present a scheme to achieve efficient single-photon frequency conversion by exploiting quantum interference between different transition pathways for single-photon states. As an example, we discuss the single-photon frequency-conversion process in the configuration wherein a $\ensuremath{\Lambda}$-type (Lambda-type) three-level quantum emitter is coupled to a Sagnac interferometer. It is shown that the efficiency of the frequency conversion approaches unity in the ideal case. A real-space theoretical approach and a pseudospectral numerical method are developed, which facilitate the computation for the full spatiotemporal dynamics of the scattering process.
We present a quantum nanophotonic scheme to achieve efficient single-photon frequency conversion. This mechanism is essential for integrated nanophotonics, as it can provide access to frequency regimes in which no single-photon sources are currently available. Moreover, such a device could be used as the basis of a photonic frequency-shift-keyed quantum information scheme. The proposed scheme uses a Sagnac interferometer to exploit quantum interference between two transition pathways in a three-level quantum dot. In the proposed scheme, an input photon induces a complete population state transfer on the Lambda-type quantum dot, causing a frequency shift in the outgoing photon. The Sagnac interferometer is used to put the input photon into a superposition of counterpropagating states which interfere at the quantum dot, providing the necessary quantum interference to make the process efficient. We have developed a real-space theoretical approach and a computationally efficient pseudospectral numerical method to invegtigate the full spatiotemporal dynamics of the scattering process. It is shown that the efficiency of the frequency-conversion process approaches unity in the ideal case, and is greater than 80% even in the presence of realistic dissipation.
In this paper, we begin with a model of a $\mathrm{\ensuremath{\Lambda}}$-type atom whose both transitions are chirally coupled to a wave guide and then extend the model to its giant-atom version. We investigate the single-photon scatterings of the giant-atom model in both the Markovian and the non-Markovian regimes. It is shown that the chiral atom-wave-guide couplings enable nonreciprocal, reflectionless, and efficient frequency conversion, while the giant-atom structure introduces intriguing interference effects to the scattering behaviors, such as ultranarrow scattering windows. The chiral giant-atom model exhibits quite different scattering spectra in the two regimes and, in particular, demonstrates non-Markovicity-induced nonreciprocity under specific conditions. These phenomena can be understood from the effective detuning and decay rate of the giant-atom model. We believe that our results have potential applications in integrated photonics and quantum network engineering.
Unitary transformations are the fundamental building blocks of gates and operations in quantum information processing, allowing the complete manipulation of quantum systems in a coherent manner. In the case of photons, optical elements that can perform unitary transformations are readily available only for some degrees of freedom, e.g., wave plates for polarization. However, for high-dimensional states encoded in the transverse spatial modes of light, performing arbitrary unitary transformations remains a challenging task for both theoretical proposals and actual implementations. Following the idea of multi-plane light conversion, we show that it is possible to perform a broad variety of unitary operations at high quality by using only a few phase modulation planes. More importantly, we experimentally implement several high-dimensional quantum gates for up to five-dimensional states encoded in the full-field mode structure of photons. In particular, we realize cyclic and quantum Fourier transformations, known as Pauli X ^ -gates and Hadamard H ^ -gates, respectively, with an average visibility of more than 90%. In addition, we demonstrate near-perfect “unitarity” by means of quantum process tomography, unveiling a process purity of 99%. Last, we demonstrate the benefit of the two independent spatial degrees of freedom, i.e., azimuthal and radial, and implement a two-qubit controlled-NOT quantum operation on a single photon. Thus, our demonstrations open up new paths to implement high-dimensional quantum operations, which can be applied to various tasks in quantum communication, computation, and sensing schemes.