Generation of large Fock states from coherent states using Kerr interaction and displacement

TL;DR

The paper addresses deterministic generation of large Fock states from coherent states by applying repeated Kerr nonlinearity and displacement operations. It introduces the scheme $U(\beta,\chi)=\hat{D}(\beta)\hat{U}_K(\chi)$ on $|\alpha\rangle$, with $|\alpha|\approx \sqrt{N}$, and optimizes a sequence of parameters to concentrate the photon-number distribution at $|N\rangle$. Numerically, fidelity $P_N^{(M)}$ exceeds 0.9 for $N\le 6$ with $M=2$ and exceeds 0.95 for $N\le 20$ with $M=3$, illustrating the effectiveness of the iterative approach. The authors analyze experimental feasibility in a Kerr cavity driven by ultrashort pulses and show that, with realistic parameters ($\mathcal{K}/2\pi\approx 12.5$ MHz, $\gamma/\mathcal{K}$ in the $10^{-5}$–$10^{-3}$ range), fidelities above 0.9 are achievable up to $N=20$; the method is compatible with circuit QED and optomechanical platforms. This approach offers a way to generate large Fock states without requiring giant Kerr nonlinearities, with potential impact on quantum information processing and quantum metrology.

Abstract

We discuss a scheme to generate large Fock states. The scheme involves repeatedly applying an experimentally feasible unitary transformation to convert a semiclassical state into a Fock state. The transformation combines Kerr interaction, which is a non-Gaussian operation, and pulsed coherent drives. We identify suitable parameter values (Kerr strength, pulse timings, displacement amplitude) for the physical processes to implement the transformation and generate large Fock states with near-unity fidelity. The feasibility of implementing the scheme in circuit QED architectures is discussed. The method is also suitable for generating Fock states of cavity fields.

Figures (3)

• Figure 1: (a) Description of the repeated application of $\hat{D}(\beta_k)\hat{U}_{K}(\chi_k)$, up to $M=3$, applied on a coherent state $\ket{\alpha}$. (b) The probability distribution $P_n^{(M)}$ (fidelity) for $M=0,1,2$ and $3$ with $\alpha=\sqrt{3}$. After the third operation $(M=3)$, the resultant state has a fidelity of 0.97 with the Fock state $\ket{3}$. (c) Wigner functions of the resultant states after each operation. For $M=3$, the Wigner function displays a ring-like structure with two rings due to its oscillations in the phase space, a characteristic of the Wigner function of the Fock state $\ket{3}$.
• Figure 2: Schematic of a cavity filled with Kerr medium with Kerr strength $\mathcal{K}$. The cavity is driven by a series of ultra-short coherent pulses at $t=-t_1$, $t=-t_2$, and $t=-t_3$ such that they drive the cavity at time $t_1$, $t_2$, and $t_3$ respectively. The setup is equivalent to the unitary transformation of Eq. \ref{['Mthoperation']}.
• Figure 3: (a) Fidelity $(P_N^{(M)})$ of generated states with Fock states for $N=5,10,20$ and $M=3$ as a function of cavity decay rate, normalized to Kerr strength. The horizontal lines correspond to the fidelities in the absence of dissipation. (b) Performance of the protocol shown as a shaded region in the $\gamma/\mathcal{K}$ versus $N$ plot. The shaded region corresponds to the fidelity larger than 0.9, indicating for a given $N$, the range of $\gamma/\mathcal{K}$ for which $P_N^M>0.9$.