Efficient and flexible preparation of photonic NOON states in a superconducting system

Abstract

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 $N$ 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.

Figures (12)

• Figure 1: (a) The physical model of the superconducting flux qudit coupling to two microwave cavities. Here, $\mathrm{C}_1$ and $\mathrm{C}_2$ are microwave cavities, and $\mathrm{Q}_0$ is a five-level qudit, and $\lambda_k$ indicates the coupling strength between the cavity and the qudit through capacitive coupling ($k=1,2$), where the cavity frequency $\omega_1=\omega_{14}-\Delta_1+\delta_1$ and $\omega_2=\omega_{23}-\Delta_2+\delta_2$. The transition $|1\rangle_0\leftrightarrow|4\rangle_0$ is driven by a classical field with the Rabi frequency (frequency) $\Omega_1$($\omega_{d1}$) and the transition $|2\rangle_0\leftrightarrow|3\rangle_0$ is driven by a classical field with the Rabi frequency (frequency) $\Omega_2$($\omega_{d2}$). (b) The energy level structure of the five-level qudit is shown below. The five energy levels of the qudit are $|0\rangle_0$, $|1\rangle_0$, $|2\rangle_0$, $|3\rangle_0$, and $|4\rangle_0$, respectively.
• Figure 2: The control fields $\mathrm{Re}[\Omega_{\iota}(t)]$ and $\mathrm{Im}[\Omega_{\iota}(t)]$ versus $t'/T$. For Step 1, $\iota=s_1$, $T=\tau_1$, and $t'=t$. For Step 3, $\iota=s_3$, $T=\tau_3-\tau_2$, and $t'=t-\tau_2$.
• Figure 3: Schematic diagram of NOON states preparation, where $|\widetilde{0}\rangle=D(\sqrt{N})|0\rangle$ is the displacement Fock state, and $|n\rangle$ ($n=1,2,\dots,N$) is the Fock state.
• Figure 4: Fidelity $F_p$ of the target state in Step $p$ ($p=1,2,3$) versus $t$ for the photon number $N=2,3,4$.
• Figure 5: Fidelity $F_3$ versus $t$ for the photon number $N=2,3,4$, where $\tau_1=0.01 \mu$s, and $\tau_2=0.31 \mu$s.