Enhancement of squeezing in resonance fluorescence of a driven quantum dot close to a graphene sheet

We investigate squeezing of the resonance fluorescence of a laser-driven quantum dot (QD) close to a graphene sheet. The coupling between the QD and the surface plasmon around the graphene sheet is frequency dependent in the terahertz region, which can be adjusted by the laser intensity. Distinct decay rates in different transition channels of dressed QDs can be achieved due to the tailored photon reservoir, which can be used to improve the squeezing. It is found that increases in both the dephasing rate and the environmental temperature are harmful to the squeezing. Meanwhile, an enhancement in the QD-plasmon coupling strength may reduce the fragility of squeezing against the decoherence process. Additionally, in the strong light-matter coupling region, squeezing can be largely enhanced by tuning the strength of the pump field and its detuning from the QD.

Figure 1

Geometry of the system. The $z$ axis is taken normal to the graphene sheet with its origin located on the surface, and the QD is situated in the upper space at a distance $d$ above the graphene, with a $z$-polarized dipole and excitation frequency ${\omega }_0$, which corresponds to the transition between the excited state $\left|e\right.〉$ and the ground state $\left|g\right.〉$. A classical laser beam, whose polarization is assumed to be parallel to the dipole momentum of the QD, has central frequency ${\omega }_l$ and acts as the pump field.

Figure 2

The Purcell factor vs the frequency. The case ${\mu }_f=90$ meV at different environmental temperatures, $T=0$ K (solid blue line) and $T=300$ K (dashed red line), is considered. Inset: The case ${\mu }_f=120$ meV, at environmental temperatures of $T=0$ K (solid green line) and $T=300$ K (dashed pink line), is considered in comparison to the former case. Locations of peaks are shown by arrows, and different QD-graphene distances are investigated: (a) $d=20$ nm; (b) $d=10$ nm.

Figure 3

The Purcell factor vs the QD's position. The case where ${\mu }_f=90$ meV and $T=0$ K at the QD's excitation frequency is investigated, both the enhancement of the total decay rate (solid blue line) and the decay through SPF (dashed red line) are plotted. Inset: The case where ${\mu }_f=120$ meV at the same temperature.

Figure 4

Noise spectrum of the fluorescence field for ${\mu }_f=90$ meV, $\mathrm{\Omega }=20$ meV, $T=0$ K, and (a) $d=20$ nm and $\mathrm{\Delta }=25$ meV or (b) $d=10$ nm and $\mathrm{\Delta }=20$ meV. The solid purple line represents the weaker-dephasing-rate case $\left({\gamma }_0=5\mu \mathrm{eV}\right)$ and the dashed green line represents the stronger-dephasing case $({\gamma }_0=0.1$ meV).

Figure 5

Population difference $\langle {\tilde{\sigma }}_z\rangle$ vs detuning for ${\mu }_f=90$ meV, $\mathrm{\Omega }=20$ meV, $T=0$ K, and (a) $d=20$ nm or (b) $d=10$ nm. Different dephasing rates, ${\gamma }_0=5\mu \mathrm{eV}$ (solid purple line) and ${\gamma }_0=0.1$ meV (solid green line), are considered; the dashed black line denotes the values of $-\mathrm{\Delta }/\overline{\mathrm{\Omega }}$.

Figure 6

Noise spectrum of the driven system for ${\mu }_f=90$ meV, $\mathrm{\Omega }=20$ meV, $d=10$ nm, and (a) ${\gamma }_0=5\mu \mathrm{eV}$ and $\mathrm{\Delta }=25$ meV or (b) ${\gamma }_0=0.1$ meV and $\mathrm{\Delta }=-15$ meV. The solid blue line and the dashed red line are used to highlight different environmental temperatures: the former represents zero temperature; the latter, room temperature.

Figure 7

Scaled quadrature fluctuation of resonance fluorescence vs the Fermi energy of graphene, for $d=10$ nm, $\mathrm{\Omega }=20$ meV, $\mathrm{\Delta }=10$ meV, and ${\gamma }_0=5\mu \mathrm{eV}$; both the zero-temperature (solid blue line) and the room-temperature (dashed red line) cases are considered.

Figure 8

Reservoir-assisted decay rates and the scaled quadrature fluctuation vs the QD detuning and Rabi frequency, for ${\mu }_f=120$ meV, ${\gamma }_0=5\mu \mathrm{eV}$, and $T=300$ K. (a) The decay rate ${\gamma }^{\overline{n}+1}\left({\omega }_l^{+}\right)$, which corresponds to the transition channel $\left|+\right.〉\to \left|-\right.〉$. (b) The decay rate ${\gamma }^{\overline{n}+1}\left({\omega }_l^{-}\right)$, which corresponds to the symmetrical transition channel $\left|-\right.〉\to \left|+\right.〉$. (c) Total normal-order invariance of in-phase quadrature.