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Optics Express

Effective protocol for generating NOON states of resonator modes

Yi‐Hao Kang, Zhe-Ping Lin, Jianqun Yang, Yu Wang, Jie Song, Zhen‐Biao Yang, Yan Xia

Published Nov 23, 2023• 4 citations
Publisher

Abstract

We propose a protocol for the generation of NOON states of resonator modes. The physical model is composed of two Kerr-nonlinear resonators and a four-level qudit. Using the off-resonant couplings between the resonators and the qudit, qudit-level-dependent frequency shifts on the two resonators are induced. The frequency shifts allow us to drive different resonators to the N-photon state when the qudit is in different intermediate levels. Consequently, the generation of NOON states with arbitrary photon number N can be completed in only three steps, i.e., driving the qudit to a superposition state of the two intermediate levels, driving one of the resonators to its N-photon state, and driving the qudit back to its ground level. Numerical simulations show that, in the regime of strong Kerr nonlinearity and coupling strengths, the protocol can produce the NOON state with high fidelity in the cases of different photon numbers. In addition, it is possible for the protocol to produce acceptable fidelity in the presence of systematic errors and decoherence factors. Therefore, the protocol may provide some useful perspectives for effective generation of photonic NOON states.

DOI
10.1364/oe.498836

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We propose a protocol for the generation of NOON states of resonator modes. The physical model is composed of two Kerr-nonlinear resonators and a four-level qudit. Using the off-resonant couplings between the resonators and the qudit, qudit-level-dependent frequency shifts on the two resonators are induced. The frequency shifts allow us to drive different resonators to the N-photon state when the qudit is in different intermediate levels. Consequently, the generation of NOON states with arbitrary photon number N can be completed in only three steps, i.e., driving the qudit to a superposition state of the two intermediate levels, driving one of the resonators to its N-photon state, and driving the qudit back to its ground level. Numerical simulations show that, in the regime of strong Kerr nonlinearity and coupling strengths, the protocol can produce the NOON state with high fidelity in the cases of different photon numbers. In addition, it is possible for the protocol to produce acceptable fidelity in the presence of systematic errors and decoherence factors. Therefore, the protocol may provide some useful perspectives for effective generation of photonic NOON states.
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.
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 concise and deterministic protocol to generate NOON states in a hybrid system consisting of a superconducting qubit, a circuit resonator mode, and two magnonic modes, based on Floquet engineering. In particular, we construct a time-reversal-symmetry broken Hamiltonian for chiral state propagation of the three continuous-variable modes depending on qubit state, by the time modulation over qubit-resonator interaction and magnon frequency. Then, an arbitrary magnonic NOON state can be generated by a typical preparing-and-measurement procedure. We analyze the robustness of our protocol against the systematic errors in the qubit-magnon coupling strength, the Floquet-driving intensity, the frequency mismatch of the magnons, and the counterrotating interactions. We can obtain a high-fidelity NOON state in the presence of quantum dissipation on all components.
Multi-mode NOON states have been attracting increasing attentions recently for their abilities of obtaining supersensitive and superresolved measurements for simultaneous multiple-phase estimation. In this paper, four different methods of generating multi-mode NOON states with a high photon number were proposed. The first method is a linear optical approach that makes use of the Fock state filtration to reduce lower-order Fock state terms from the coherent state inputs, which are jointly combined to produce a multi-mode NOON state with the triggering of multi-fold single-photon coincidence detections (SPCD) and appropriate postselection. The other three methods (two linear and one nonlinear) use N-photon Fock states as the inputs and require SPCD triggering only. All of the four methods can theoretically create a multi-mode NOON state with an arbitrary photon number. Comparisons among these four methods were made with respect to their feasibility and efficiency. The first method is experimentally most feasible since it takes considerably fewer photonic operations and, more importantly, requires neither the use of high-N Fock states nor high-degree of nonlinearity.
We propose a one-step scheme for driving many atoms into a NOON state. In this scheme, two cavities are coupled to each other through the photon-hopping interaction and each cavity contains N four-level atoms. The 2 N atoms are driven into a NOON state via a phase-shift which depends on the collective atomic excitations. Interestingly, the time of generating the NOON state is independent of the atom number, i.e., it is unchanged with the increasing of the atom number. Also, our scheme is insensitive to cavity decay and can effectively suppress atomic spontaneous emission.
Entangled states are self-evidently important to a wide range of applications in quantum communication and quantum information processing. We propose an efficient and convenient two-step protocol for generating Bell states and NOON states of two microwave resonators from merely coherent states. In particular, we derive an effective Hamiltonian for resonators coupled to a superconducting $\mathrm{\ensuremath{\Lambda}}$-type qutrit in the dispersive regime. By the excitation-number-dependent Stark shifts of the qutrit transition frequencies, we are able to individually control the amplitudes of specified Fock states of the resonators associated with relevant qutrit transition, using carefully tailored microwave drive signals. Thereby an arbitrary bipartite entangled state in Fock space can be generated by a typical evolution-and-measurement procedure. We analyze the undesired state transitions and the robustness of our protocol against the systematic errors from the microwave driving intensity and frequency, the quantum decoherence of all components, and the crosstalk of two resonators. In addition, we demonstrate that our protocol can be extended to a similar scenario with a $\mathrm{\ensuremath{\Xi}}$-type qutrit.