Generation of nonclassical states of light via photon blockade in optical nanocavities

The generation of nonclassical states of light via photon blockade with time-modulated input is analyzed. We show that improved single-photon statistics can be obtained by adequately choosing the parameters of the driving laser pulses. An alternative method, where the system is driven via a continuous-wave laser and the frequency of the dipole is controlled (e.g., electrically) at very fast time scales is presented.

Figure 1

(a) Schematic representation of a single emitter coupled to an optical resonator. The optical resonator has mirrors with different reflection coefficients ($R_{\mathrm{in}}\gg R_{\mathrm{out}}$) such that most of the field coupled into the cavity is emitted at the output port. (b) Schematic representation of the energy eigenstates for a strongly coupled cavity-emitter system.

Figure 2

(a) Nonclassical state generation via pulsed operation in the photon blockade. The properties of the laser pulse coupled at the input port are controlled such that the output field has primarily a single-photon component. (b) Normalized Fock-state coefficients ($\left|c_0\right|{}^2$ for vacuum state, $\left|c_1\right|{}^2$ for single-photon state, and $\left|c_{\mathrm{multi}}\right|{}^2={\sum }_{n=2}^{\infty }\left|c_n\right|{}^2$ for multiphoton probability) for the output field as the intensity of the laser pulse ${\Omega }_0$ is modified and the pulse width is kept constant at $\tau =0.45/\kappa$. The ground state and one of the first-order eigenstates form an effective two-level system [18] so Rabi oscillations are observed in the single-photon character of the output field. The system has parameters $\kappa /2\pi =1\hspace{0.5em}\mathrm{GHz}$, $\gamma /2\pi =0.1\hspace{0.5em}\mathrm{GHz}$, and $g/2\pi =40\hspace{0.5em}\mathrm{GHz}$. (c) Fock-state coefficients for the output field as the duration of the laser pulse ($\tau$) is modified while ${\Omega }_0=10\hspace{0.5em}\mathrm{GHz}$ was kept constant. The system has parameters $\kappa /2\pi =1\hspace{0.5em}\mathrm{GHz}$, $\gamma /2\pi =0.1\hspace{0.5em}\mathrm{GHz}$, and $g/2\pi =40\hspace{0.5em}\mathrm{GHz}$. (d) The same simulation as in panel (b) but for a system with $\kappa /2\pi =5\hspace{0.5em}\mathrm{GHz}$ and $g/2\pi =30\hspace{0.5em}\mathrm{GHz}$.

Figure 3

(a) Second-order correlation function of the output field, for the case $\kappa /2\pi =1\hspace{0.5em}\mathrm{GHz}$ and $g/2\pi =40\hspace{0.5em}\mathrm{GHz}$. (b) Second-order correlation function for $\kappa /2\pi =5\hspace{0.5em}\mathrm{GHz}$ and $g/2\pi =30\hspace{0.5em}\mathrm{GHz}$.

Figure 4

Ratio of single-photon to multiphoton probability in the output field of the nonclassical source with $\kappa /2\pi =1\hspace{0.5em}\mathrm{GHz}$ and $g/2\pi =40\hspace{0.5em}\mathrm{GHz}$ as a function of mean photon number per pulse, $\langle n\rangle$. The results are compared with a coherent pulsed laser source of the same brightness $\langle n\rangle$.

Figure 5

(a) Operation principle for nonclassical state generation using a continuous-wave input and fast control of the dipole frequency using an electric field. (b) Detuning of the dipole frequency with time. The cavity resonance is constant and zero detuning means the dipole is resonant with the cavity. (c) Normalized Fock-state coefficients ($\left|c_0\right|{}^2$ for vacuum state, $\left|c_1\right|{}^2$ for single-photon state, and $\left|c_{\mathrm{multi}}\right|{}^2={\sum }_{n=2}^{\infty }\left|c_n\right|{}^2$ for multiphoton probability) for the output field with varying intensity of the continuous-wave input field (${\Omega }_0$). The system has parameters $\kappa /2\pi =1\hspace{0.5em}\mathrm{GHz}$, $\gamma /2\pi =0.1\hspace{0.5em}\mathrm{GHz}$, and $g/2\pi =40\hspace{0.5em}\mathrm{GHz}$. (d) Normalized Fock-state coefficients for a system with $\kappa /2\pi =5\hspace{0.5em}\mathrm{GHz}$, $\gamma /2\pi =0.1\hspace{0.5em}\mathrm{GHz}$, and $g/2\pi =30\hspace{0.5em}\mathrm{GHz}$.