Spatial-dependent quantum dot-photon entanglement via tunneling effect

Abstract

Utilizing the vortex beams, we investigate the entanglement between the triple-quantum dot molecule and its spontaneous emission field. We present the spatially dependent quantum dot-photon entanglement created by Laguerre-Gaussian (LG) fields. The degree of position-dependent entanglement (DEM) is controlled by the angular momentum of the LG light and the quantum tunneling effect created by the gate voltage. Various spatial-dependent entanglement distribution is reached just by the magnitude and the sign of the orbital angular momentum (OAM) of the optical vortex beam.

Figure 1

A four-level quantum dot molecule's band diagram. A triple quantum dot molecule is made up of three dots (“QD 1,” “QD 2,” and “QD 3”) with different tunneling rates $T_A$ and $T_B$. The corresponding energy level structure is denoted by levels $\left|1\right.〉$, $\left|2\right.〉,\left|3\right.〉,$ and $\left|4\right.〉$.

Figure 2

(a) DEM plots as a function of $T_A$ and $T_B$. Parameters are ${\mathrm{\Omega }}_1=3\gamma$, and ${\mathrm{\Omega }}_2=7.5\gamma .$ (b) DEM plots as a function of ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$ for $T_A=2\mathrm{\gamma }$, and $T_B=7\mathrm{\gamma }.$ (c) Evolution of the population distribution a function of normalized time $t\gamma$ for ${\mathrm{\Omega }}_1=3\gamma ,{\mathrm{\Omega }}_2=7.5\gamma$, $T_A=2\mathrm{\gamma }$, and $T_B=7\mathrm{\gamma }.$ Other parameters are $\delta ={\mathrm{\Delta }}_1={\mathrm{\Delta }}_2=0$ and ${\omega }_{43}=0.6\gamma$.

Figure 3

Intensity profiles of applied LG fields ${\mathrm{\Omega }}_1$ (a) and ${\mathrm{\Omega }}_2$ (b). DEM density plots as a function of x–y (c), and population distribution as a function of x (y = 0) (d). Parameters are $T_A=2\mathrm{\gamma }$, and $T_B=7\mathrm{\gamma }$, $p=1,{\text{w}}_0=2\text{mm},{\text{C}}_{\text{p}}^{\text{l}}=1,\mathrm{\lambda }=532\times {10}^{-9}\text{m},{\text{I}}_0=10\gamma$, $\mathrm{\delta }={\mathrm{\Delta }}_1={\mathrm{\Delta }}_2=0$ and ${\mathrm{\omega }}_{43}=0.6\gamma$. The parameter y represents the population distribution in presented levels.

Figure 4

DEM density plots as a function of x and y for different modes for $l_i$ $=-2,\dots +2$ $\left(i=1,2\right)$. Parameters are $p=1,w_0=2\text{mm},C_p^l=1,\lambda =532\times {10}^{-9}\text{m},{\text{I}}_0=10\gamma ,\delta ={\mathrm{\Delta }}_1={\mathrm{\Delta }}_2=0,{\omega }_{43}=0.6\gamma ,T_A=2\mathrm{\gamma }\text{and}{T}_B=7\mathrm{\gamma }$.

Figure 5

Steady-state behavior of population versus x (y = 0) for l₂ = 2 and l₁ =  − 1 (a), l₂ = 1 and l₁ = 1 (b) and l₂ =  − 2 and l₁ =  − 1 (c). Parameters are $p=1,{\text{w}}_0=2\text{mm},{\text{C}}_{\text{p}}^{\text{l}}=1,\mathrm{\lambda }=532\ast {10}^{-9}\text{m},I_0=10\gamma ,\mathrm{\delta }={\mathrm{\Delta }}_1={\mathrm{\Delta }}_2=0,{\mathrm{\omega }}_{43}=0.6\gamma ,{\text{T}}_{\text{A}}=2\gamma ,\text{and}{\text{T}}_{\text{B}}=7\gamma .$

Figure 6

Steady-state population distribution as a function of x (y = 0) (a, c), and DEM density plots as a function of x and y (b, d) for ${\text{T}}_{\text{A}}=2\mathrm{\gamma },\text{and}{\text{T}}_{\text{B}}=7\mathrm{\gamma }$ (a, b) and ${\text{T}}_{\text{A}}=6\mathrm{\gamma },\text{and}{\text{T}}_{\text{B}}=1\mathrm{\gamma }$. Other parameters are ${\text{l}}_2=-2,{\text{l}}_1=-1,p=1,w_0=2\text{mm},C_p^l=1,\lambda =532\times {10}^{-9}\text{m},I_0=10\gamma ,\delta ={\mathrm{\Delta }}_1={\mathrm{\Delta }}_2=0,\text{and}{\omega }_{43}=0.6\gamma$.