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Physical Review A

Implementing a cross-Kerr interaction between microwave and optical cavities and its application in generating a hybrid continuous-variable–discrete-variable entangled state

Jin Xu, Tong Liu

Published Mar 7, 2024• 7 citations
Publisher

Abstract

Microwave-optical interactions and hybrid entangled states are crucial for building hybrid quantum networks. In this work, we propose an approach for realizing a cross-Kerr nonlinear interaction between microwave and optical cavities using an ensemble of nitrogen-vacancy centers (NV ensemble). This cross-Kerr interaction is achieved by an NV ensemble dispersively coupled to a microwave cavity and an optical cavity. As an application, we show that the cross-Kerr interaction can be used to create a hybrid entangled state of a discrete-variable (DV) optical qubit and a continuous-variable (CV) optical qubit. The DV optical qubit here refers to a qubit, with two logic states encoded via the vacuum and single-photon states of the optical cavity. The CV optical qubit means a qubit, whose two logic states are encoded through two quasi-orthogonal coherent states or cat states of the microwave cavity. Our method is quite simple because it only requires a single-step operation. Numerical simulations demonstrate that high-fidelity generation of the proposed hybrid state is feasible within current experimental technology. This proposal is universal and the NV ensemble can be replaced by other quantum transducers, such as magnons, rare-earth-doped crystals, and silicon-vacancy centers.

DOI
10.1103/physreva.109.033705

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Microwave-optical interactions and hybrid entangled states are crucial for building hybrid quantum networks. In this work, we propose an approach for realizing a cross-Kerr nonlinear interaction between microwave and optical cavities using an ensemble of nitrogen-vacancy centers (NV ensemble). This cross-Kerr interaction is achieved by an NV ensemble dispersively coupled to a microwave cavity and an optical cavity. As an application, we show that the cross-Kerr interaction can be used to create a hybrid entangled state of a discrete-variable (DV) optical qubit and a continuous-variable (CV) optical qubit. The DV optical qubit here refers to a qubit, with two logic states encoded via the vacuum and single-photon states of the optical cavity. The CV optical qubit means a qubit, whose two logic states are encoded through two quasi-orthogonal coherent states or cat states of the microwave cavity. Our method is quite simple because it only requires a single-step operation. Numerical simulations demonstrate that high-fidelity generation of the proposed hybrid state is feasible within current experimental technology. This proposal is universal and the NV ensemble can be replaced by other quantum transducers, such as magnons, rare-earth-doped crystals, and silicon-vacancy centers.
Quantum conversion between microwave and optical photons is an important area of quantum information science and technology. Here we propose a one-step method to realize a coherent conversion between a microwave cavity and an optical cavity utilizing a nitrogen-vacancy center ensemble (NV ensemble). An NV ensemble considered here acts as a quantum transducer, dispersively coupled to the microwave and optical cavities, enabling transfer of the quantum state and generating entangled states between microwave and optical cavities. With state-of-the-art technology, the numerical simulation is performed to demonstrate that cat states and Fock states can be high-fidelity transferred and a maximally entangled state can be efficiently synthesized between microwave and optical cavities.
Long-distance transmission between spatially separated microwave cavities is a crucial area of quantum information science and technology. In this work, we present a method for achieving long-distance transmission of arbitrary quantum states between two microwave cavities, by using a hybrid system that comprises two microwave cavities, two nitrogen-vacancy center ensembles (NV ensembles), two optical cavities, and an optical fiber. Each NV ensemble serves as a quantum transducer, dispersively coupling with a microwave cavity and an optical cavity, which enables the conversion of quantum states between a microwave cavity and an optical cavity. The optical fiber acts as a connector between the two optical cavities. Numerical simulations demonstrate that our method allows for the transfer of an arbitrary photonic qubit state between two spatially separated microwave cavities with high fidelity. Furthermore, the method exhibits robustness against environmental decay, parameter fluctuations, and additive white Gaussian noise. Our approach offers a promising way for achieving long-distance transmission of quantum states between two spatially separated microwave cavities, which may have practical applications in networked large-scale quantum information processing and quantum communication.
Quantum information processing with hybrid protocols making use of discrete- and continuous-variable currently attracts of great interest because of its promising applications in scalable quantum computer and distant quantum network. By inducing a giant cross-Kerr nonlinearity between two cavities, we propose a general protocol for hybrid quantum gate and quantum entanglement with high fidelity between a stationary, discrete photonic qubit and a flying photonic state. Interestingly, our protocol can be used to conduct a controlled-Z quantum gate between a stationary microwave photon stored in a slowly-decaying microwave cavity and a flying optical photon, and therefore enable to build quantum network for distant superconducting quantum circuits.
We show that a continuous-variable (CV) qudit can be constructed using quasiorthogonal cat states of a bosonic mode, when the phase encoded in each cat state is chosen appropriately. With the constructed CV qudit and the discrete-variable (DV) qudit encoded with Fock states, we propose an approach to generate the hybrid maximally entangled state of a CV qudit and a DV qudit by using two microwave cavities coupled to a superconducting flux qutrit. This proposal relies on the initial preparation of a superposition of Fock states of one cavity and the initial preparation of a cat state of the other cavity. After the initial state of each cavity is prepared, this proposal requires only two basic operations, i.e., the first operation employs the dispersive coupling of both cavities with the qutrit while the second operation uses the dispersive coupling of only one cavity with the qutrit. The entangled state production is deterministic and the operation time decreases as the dimensional size of each qudit increases. In addition, during the entire operation, the coupler qutrit remains in the ground state and thus decoherence from the qutrit is significantly reduced. As an example, we further discuss the experimental feasibility for generating the hybrid maximally entangled state of a DV qutrit and a CV qutrit based on circuit QED. This proposal is universal and can be extended to accomplish the same task, by using two microwave or optical cavities coupled to a natural or artificial three-level atom.
The generation of hybrid entangled states between matter qubits and microwave-field qubits is a fascinating area of quantum science and technology. In this work, we propose an efficient method to deterministically prepare hybrid entangled states between multiple superconducting qubits (matter qubits) and microwave-field qubits (flying qubits), by using a system composed of multiple superconducting qutrits and microwave cavities. Here, each superconducting (SC) qubit is encoded with the two lowest levels of a SC qutrit, while each microwave-field (MF) qubit is encoded using discrete-variable (DV) states (e.g., the vacuum and single-photon states) or continuous-variable (CV) states (e.g., coherent states) of a microwave cavity. Due to the nonpopulation of the qutrits' third energy level during the operation, decoherence from this level is significantly reduced. Moreover, the hybrid entangled states can be generated on a large scale. The operation time is independent of the number of SC qubits and MF qubits. Only two steps of the operation are needed for the preparation of the hybrid Greenberger---Horne---Zeilinger (GHZ) states as long as the initial states of the system are ready. As an example, our numerical results demonstrate that high-fidelity creation of hybrid DV-DV entangled states or CV-DV entangled states of three SC qubits and three MF qubits is feasible with current circuit QED technology. This method is universal and can be extended to generate hybrid entangled states between other matter qubits (such as atoms, ions, quantum dots, NV centers, and magnons) and microwave- or optical-field qubits.
We propose an efficient scheme for transferring quantum states and generating entangled states between two qubits of different nature. The hybrid system consists of a single nitrogen-vacancy (NV) center and a superconducting (SC) qubit, which couple to an optical cavity and a microwave resonator, respectively. Meanwhile, the optical cavity and the microwave resonator are coupled via the electro-optic effect. By adjusting the relative parameters, we can achieve high-fidelity quantum state transfer as well as highly entangled states between the NV center and the SC qubit. This protocol is within the reach of currently available techniques, and may provide interesting applications in quantum communication and computation with single NV centers and SC qubits.