Mechanical qubit-light entanglers in hybrid nonlinear qubit optomechanics

Interfacing between matter qubits and light is a crucial provision for numerous quantum technological applications. However, a generic qubit may not directly interact with a relevant optical field mode, and hence, one could necessitate adjusting frequencies to match resonance conditions between parties. In this work, we show how a parametric coupling of the qubit with a mechanical oscillator, in conjunction with the trilinear radiation pressure coupling of the same object with light, can induce maximal qubit-light entanglement at an optimal time. Furthermore, we show how our method enables conditional (dynamical) nonclassical state preparation of the optical field via qubit measurement in the weak (moderate-to-strong) optomechanical coupling regime. Our scheme benefits from not requiring any cooling of the mechanical component and not needing an adjusting of the detunings and transition frequencies to have resonance between any pairs of quantum systems.

Figure 1

A qubit interacts with a mechanical oscillator [with boson operator ($\widehat{b}$)], while the latter object couples to a quantized light field ($\widehat{a}$). There is no direct qubit-light interaction but that which is mediated through the mechanical subsystem. We wonder in this hybrid tripartite quantum system whether one could reach, dynamically and under Hamiltonian parametric interactions, a high degree of qubit-light quantum entanglement.

Figure 2

Negativity dynamics $\left[\mathcal{N}\right(t\left)\right]$ for different reduced density matrices. We plot the qubit-cavity $[\mathcal{N}{\left(t\right)}_{q,c}$, solid line], the qubit-oscillator $[\mathcal{N}{\left(t\right)}_{q,o}$, dashed line], and the oscillator-cavity negativity $[\mathcal{N}{\left(t\right)}_{o,c}$, dotted line] for different qubit-optomechanical coupling values. Top (bottom) panel considers $g=0.2$ and $\lambda =0.25$ ($g=0.2$ and $\lambda =0.625$); $\beta =1$.

Figure 3

(a) Different bipartite entanglement dynamics for an initial cavity and mechanical oscillator in coherent states. In (b) and (c) we plot the intrinsic entanglement at $t=2\pi$ for the current optics in the coherent case [see Eq. (14)] and the previous optical qubit scenario [see Eq. (7)], respectively. Other values are $\beta =2,\alpha =2,g=0.2,\lambda =0.25.$

Figure 4

Qubit-cavity entanglement dynamics $\mathcal{N}{\left(t\right)}_{q,c}$ mediated by a thermalized mechanical oscillator with $\overline{n}$ phonons on average.

Figure 5

Qubit-cavity entanglement at $t=2\pi$ for different spin relaxation rates $\mathrm{\Gamma }$ as a function of the spin dephasing rate ${\gamma }_{\varphi }$. We fixed ${\gamma }_m={10}^{-5},\kappa ={10}^{-2}$, and other values as in Fig. 3.

Figure 6

Panels (a) and (b) show the Wigner distribution for the generation of nonclassical states for the light field due to its dynamics alone at $t=2\pi$. In (a) we show the two-component cat state for $g=\lambda =0.5$, while (b) corresponds to the five-component cat state for $g\sim 0.32$ and $\lambda \sim 0.8$; (c) illustrates the preparation of nonclassical states via qubit projection $|+\rangle$ at $t=10\times 2\pi$ when operating in the weak optomechanical regime $g\sim 0.013$ and qubit-mechanical coupling $\lambda =1$. In (d) we show the impossibility to obtain a nonclassical state with the same parameters used in (c) by its dynamics alone. In panel (e) we show the displaced Fock number state $\widehat{D}\left(\alpha \right)|1\rangle$ via qubit projection with its corresponding fidelity shown in (f). Other values are $\alpha =3$, and $g^{*}$ the optimal optomechanical strenght to achieve $\widehat{D}\left(\alpha \right)|1\rangle$. In all panels, positive (negatives) values in the Wigner function are blue (red) colored.