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arXiv:1412.5271 · Optics Letters

Efficient scheme for generation of photonic NOON states in circuit QED

Shao-Jie Xiong, Zhe Sun, Jin-Ming Liu, Tong Liu, Chui-Ping Yang

Published May 4, 2015• 31 citations
arXivHTMLPDF

Abstract

We propose an efficient scheme for generating photonic NOON states of two resonators coupled to a four-level superconducting flux device (coupler). This proposal operates essentially by employing a technique of a coupler resonantly interacting with two resonators simultaneously. As a consequence, the NOON-state preparation requires only N+1 operational steps and thus is much faster when compared with a recent proposal [Su et al, Sci. Rep.4, 3898 (2014)] requiring 2N steps of operation. Moreover, due to the use of only two resonators and a coupler, the experimental setup is much simplified when compared with previous proposals requiring three resonators and two superconducting qubits/qutrits.

DOI
10.1364/ol.40.002221

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We propose an efficient scheme for generating photonic NOON states of two resonators coupled to a four-level superconducting flux device (coupler). This proposal operates essentially by employing a technique of a coupler resonantly interacting with two resonators simultaneously. As a consequence, the NOON-state preparation requires only N+1 operational steps and thus is much faster when compared with a recent proposal [Su et al, Sci. Rep.4, 3898 (2014)] requiring 2N steps of operation. Moreover, due to the use of only two resonators and a coupler, the experimental setup is much simplified when compared with previous proposals requiring three resonators and two superconducting qubits/qutrits.
The generation, manipulation and fundamental understanding of entanglement lies at very heart of quantum mechanics. Among various types of entangled states, the NOON states are a kind of special quantum entangled states with two orthogonal component states in maximal superposition, which have a wide range of potential applications in quantum communication and quantum information processing. Here, we propose a fast and simple scheme for generating NOON states of photons in two superconducting resonators by using a single superconducting transmon qutrit. Because only one superconducting qutrit and two resonators are used, the experimental setup for this scheme is much simplified when compared with the previous proposals requiring a setup of two superconducting qutrits and three cavities. In addition, this scheme is easier and faster to implement than the previous proposals, which require using a complex microwave pulse, or a small pulse Rabi frequency in order to avoid nonresonant transitions.
To generate a NOON state with a large photon number NNN, the number of operational steps could be large and the fidelity will decrease rapidly with NNN. Here we propose a method to generate a type of quantum entangled states, $(|NN00\ensuremath{\rangle}+|00NN\ensuremath{\rangle})/\sqrt{2}$, called ``double NOON'' states, with a setup of two superconducting flux qutrits and five circuit cavities. This scheme operates essentially by employing a two-photon process; i.e., two photons are simultaneously and separately emitted into two cavities when each coupler qutrit is initially in a higher-energy excited state. As a consequence, the ``double'' NOON state creation needs only N+2N+2N+2 operational steps. One application of double NOON states is to get a phase error of 1/(2N)1/(2N)1/(2N) in phase measurement. In comparison, to achieve the same error, a normal NOON state of the form $(|2N,0\ensuremath{\rangle}+|0,2N\ensuremath{\rangle})/\sqrt{2}$ is needed, which requires at least 2N2N2N operational steps to prepare by using the existing schemes. Our numerical simulation demonstrates that high-fidelity generation of the double NOON states with $N\ensuremath{\le}10$ even for imperfect devices is feasible with the present circuit QED technique.
The NOON states are valuable quantum resources, which have a wide range of applications in quantum communication, quantum metrology, and quantum information processing. Here we propose a fast, concise, and reliable protocol for deterministically generating the NOON states of two resonators coupled to a single ▵▵▵-type superconducting qutrit. In particular, we derive the effective Hamiltonians at the points of the multiphoton resonances by virtue of the strong counter-rotating interaction between the resonator modes and the qutrit. Based on these crucial effective Hamiltonians, our protocol simplifies the previous ones using the single-photon resonance and consequently reduces the number of operations for state preparation. To test the robustness of this protocol, we analyze the effects from both the decoherence including dissipation and dephasing and the crosstalk of resonator modes on the state fidelity through a Lindblad master equation in the eigenbases of the full Hamiltonian.
We propose a method for transferring quantum entangled states of two photonic cat-state qubits ( cqubits ) from two microwave cavities to the other two microwave cavities. This proposal is realized by using four microwave cavities coupled to a superconducting flux qutrit. Because of using four cavities with different frequencies, the inter-cavity crosstalk is significantly reduced. Since only one coupler qutrit is used, the circuit resource is minimized. The entanglement transfer is completed with a singlestep operation only, thus this proposal is quite simple. The third energy level of the coupler qutrit is not populated during the state transfer, therefore decoherence from the higher energy level is greatly suppressed. Our numerical simulations show that high-fidelity transfer of two- cqubit entangled states from two transmission line resonators to the other two transmission line resonators is feasible with current circuit QED technology. This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems, such as four microwave or optical cavities, which are coupled to a natural or artificial three-level atom.
The NOON states play a critical role as physical resources in quantum information processing and quantum metrology, yet their preparation efficiency and applicability are often constrained by complicated operational procedures or the requirement for nonlinear interactions. In this paper, we propose an efficient protocol to generate the NOON states within two microwave cavities embedded in a superconducting system, assisted by an auxiliary five-level qudit. The state preparation is accomplished in three steps for an arbitrary photon number NNN by adjusting only external classical fields, while keeping the qudit-cavity coupling strengths and the qudit level spacings fixed. Based on parameters accessible in superconducting systems, numerical simulations show that the protocol achieves relatively high fidelity for the NOON states preparation even in the presence of parameter fluctuations and decoherence effects. Thus, this protocol may provide a practical approach for preparing the NOON states with current technology. Notably, since nonlinear interactions are not required, the protocol is flexible and has the potential to be applied across various physical systems.
In a circuit consisting of two or more resonators, the intercavity crosstalk is inevitable, which could create some problems, such as degrading the performance of quantum operations and the fidelity of various quantum states. The focus of this work is to propose a crosstalk-insensitive method for simultaneously coupling multiple pairs of resonators, which is important in large-scale quantum information processing and communication in a network consisting of resonators or cavities. In this work, we consider 2N2N2N resonators of different frequencies, which are coupled to a three-level quantum system (qutrit). By applying a strong pulse to the coupler qutrit, we show that an effective Hamiltonian can be constructed for simultaneously coupling multiple pairs of resonators. The main advantage of this proposal is that the effect of inter-resonator crosstalks is greatly suppressed by using resonators of different frequencies. In addition, by employing the qutrit-resonator dispersive interaction, the intermediate higher-energy level of the qutrit is virtually excited and thus decoherence from this level is suppressed. This effective Hamiltonian can be applied to implement quantum operations with photonic qubits distributed in different resonators. As one application of this Hamiltonian, we show how to simultaneously generate multiple Einstein-Podolsky-Rosen pairs of photonic qubits distributed in 2N2N2N resonators. Numerical simulations show that it is feasible to prepare two high-fidelity EPR photonic pairs using a setup of four one-dimensional transmission line resonators coupled to a superconducting flux qutrit with current circuit QED technology.