1. Introduction

As an essential resource in the field of quantum optics, single photon sources play an important role in quantum simulation [1], quantum information processing, and quantum metrology [2–5]. The photon blockade effect is one of the main physical mechanisms for generating single-photon sources, which can convert classical light into non-classical light [6,7]. Photon blockade [8,9] means that the absorption of the first or few photons will block the transmission of subsequent photons.

It has two types of photon blockade effect, according to the physical mechanism of production: conventional photon blockade (CPB) and unconventional photon blockade (UPB). The physical mechanism of CPB generation is the anharmonicity of the system’s eigenenergy spectrum. In 2005, the CPB was first observed successfully in the system of cavity quantum electrodynamics (QED) [10]. From then on, photon blockade has been studied in various systems, such as cavity QED systems [11–13], circuit-QED systems [14,15], quantum dot cavity systems [16–19], superconducting qubit systems [20,21], and quantum optomechanical systems [22–26]. Different from CPB, UPB arises from the physical mechanism of the destructive quantum interference between different quantum transition pathways in weakly nonlinear systems. Liew and Savona first proposed the concept of UPB by weak nonlinearities [27]. Over the past few decades, the UPB effect has been theoretically investigated in quantum dots [28–30], a nanomechanical resonator [31], a quantum well [32], optomechanical systems [33,34], an optical parametric amplifier system [35], two-tunnel coupled cavity systems [36–40], and a non-Hermitian indirectly coupled resonator system [41]. Recently, the UPB effect has been experimentally demonstrated in two coupled superconducting resonators [7].

Cavity QED system is an important topic in the study of light-matter interactions today and shows unique advantages in quantum information processing, photonic devices and other applications. As an essential model in the cavity QED system, the T-C model can be used to study the interaction between light and N two-level systems. In hybrid systems consisting of optical cavity and two-level system, the majority of work has been based on resonant coupling to investigate the PB effect [42,43]. However, it is experimentally difficult to achieve a perfect optical cavity where the cavity frequency is completely resonant with the transition frequency of the two-level system. Therefore, the effect of detuning between the two-level system and cavity field on the statistical property of the cavity field has recently been investigated [44,45]. It is worth noting that the detuning between the two-level system and the cavity field is relatively small, the system would therefore not enter the dispersive regime. In the dispersive limit, the disappearance of photon nonlinearity resulting in the system unable to produce the CPB effect [46,47]. Very recently, the retrieval of the CPB effect for the Jaynes-Cummings model in the dispersive limit has been proposed theoretically [48] and implemented experimentally via superconducting quantum circuits [49]. However, the T-C model in the dispersive limit can be reduced approximately as the dispersive T-C model, and its PB effect has been rarely studied. Thus, it becomes an interesting question how to recover the photon blockade effect in the dispersive T-C model by using appropriate quantum manipulations.

In this paper, we study the CPB effect in the dispersive limit for T-C model. The optical nonlinearity in the system can be recovered by introducing a transverse drive to the two-level qubit, where the two qubits are not required to be homogeneous. The single excitation resonance conditions and the corresponding optimal qubit driving strength are also given analytically. According to numerically solving the quantum master equation of the open quantum system, we obtain the average photon number of the cavity field and the equal-time n-order correlation functions of the cavity field in the steady state. The strongest PB effect and largest average photon number can be produced as we analyzed. Furthermore, the two-photon blockade effect is also observed in the case of two-photon resonance transition. Hence, our scheme is able to achieve both single-photon blockade and two-photon blockade effects in the same system. Interestingly, the conventional two-photon blockade effect is relatively robust to thermal noise. This work will provide a new and reliable method for generating the CPB effect in the dispersively coupled quantum optical systems.

The organization of the paper is as follows: In Sec. 2, we describe the physical model and the Hamiltonian of the dispersive T-C system. Subsequently, we solve analytically the eigenvalues of the driven dispersive T-C Hamiltonian. In Sec. 3, we investigate the one-photon blockade effect and the two-photon blockade effect numerically by using the method of the quantum master equation. We also study the relationship between equal-time n-order correlation function of cavity field and various adjustable parameters. Finally, a conclusion is given in Sec. 4.

2. System and Hamiltonian

We consider a T-C model in the dispersive limit, which consists of two qubits (with transition frequency $\omega _j$) coupling to an optical cavity (with single-mode frequency $\omega _c$), as illustrated in Fig. 1(a). The dispersive limit is characterized by a large detuning $\Delta _j$=$\omega _j$ - $\omega _c\gg g_j$ as compared to the qubit$_{j}$-cavity coupling strength $g_{j}$ ($j=1,2$). At large detuning of the two qubits from the cavity, qubits cannot exchange energy directly with the cavity field, and both have an offset in frequency. Since the cavity and qubits are dispersively coupled, this results in the cavity frequency with a qubit-state-dependent shift $\chi _j$. In this limit, the system with the two qubits and the cavity can be described by the dispersive T-C Hamiltonian ($\hbar =1$) [50]

 

Fig. 1. (a) Schematic of the driven dispersive T-C system, which is composed of two two-level qubits coupled to an optical cavity via the dispersive T-C type of interaction. (b) Diagram of the eigenenergy levels of the Hamiltonian $H_{\mathrm {d}}$ in the subspaces associated with zero, one, two, and three photons, where $|\varepsilon _{n}^{\pm,0}\rangle$ is the corresponding eigenstates ($n=0, 1, 2, 3$).

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In the dispersive T-C model, the system anharmonicity vanishes due to the absence of photon nonlinearity. We recover the photon nonlinearity in the system by introducing transverse drive with drive frequency $\omega _{d j}$ and drive intensity $\Omega _{R j}$ to the qubits, $\Omega _{R j}=\sqrt {2P_{j}\gamma /\hbar \omega _{d j}}$, where $P_{j}$ is the drive field power. In the frame rotating at the driving frequency $\omega _{d 1}$ and $\omega _{d 2}$, respectively, the driven dispersive T-C system Hamiltonian can be reduced as

The physical mechanism of CPB is the anharmonicity of the system’s eigenenergy spectrum. In order to analyse the CPB effect in the system, it is necessary to know the eigensystem of the driven dispersive T-C Hamiltonian $H_{d}^{(n)}$. Using the collective states as basis ($|gg,n\rangle$, $|\pm,n\rangle$=$(|eg,n\rangle \pm |ge,n\rangle )/\sqrt {2}$, $|ee,n\rangle$), the Hamiltonian in the $n$-photon space can be expressed in the following matrix form:

We obtain the eigenenergy of the driven dispersive T-C Hamiltonian $H_{d}^{(n)}$ in the $n$-photon space, according to the eigenequation $H_{d}^{(n)}|\varepsilon _{n}^{\pm,0}\rangle$=$E_{n}^{(\pm,0)}|\varepsilon _{n}^{\pm,0}\rangle$ of matrix $H_{d}^{(n)}$

Equation (5) shows that the eigenenergy of the system is a nonlinear function of the number of photons $n$. However, when the driving strength of the qubit is very strong or extremely weak, the anharmonicity of the system all becomes weak. The eigenenergy of the system be approximated as

In this paper, we mainly consider two single-photon resonance transition paths $\Delta _{c}=\Delta ^{1,+}_{0,+}$ and $\Delta _{c}=\Delta ^{1,-}_{0,-}$. The detuning between the energy level transitions corresponding to these two paths are

3. Photon blockade effect

In order to study the conventional photon blockade effect, we calculate the equal-time $n$-order correlation function of the optical cavity by solving the quantum master equation numerically. For open quantum systems, the physical system inevitably interacts with the external environment. The full dissipative dynamics of the system are described by the master equation

For exhibiting the quantum behavior of the photons, we investigate the statistical properties of the photons, which can be characterized by the average photon number in the cavity and equal-time $n$-order correlation functions in the steady state ($n$ = 2,3)

3.1 Single-photon blockade effect

Firstly, we study the single-photon blockade effect of the driven dispersive T-C system in the case of cavity drive. As shown in Fig. 1(b), when the pump field energy satisfies the system from ground state to one-photon state, the first photon is resonance absorbed by the system. However, the second photon is blocked due to nonlinearity resulting in energy level anharmonicity, this causes the conventional single-photon blockade effect.

For simplicity, we consider the case of zero-temperature environments ($\overline {n}_{\mathrm {th}} = 0$). When the energy of the driving field resonates with the energy of the system transition from the ground state to the single-photon state, single excitation resonance conditions can be obtained for single-photon blockage, also known as optimal detuning of the CPB. Driving detuning has therefore become an important parameter in the study of photon blockade. To study the statistical properties of the cavity field, we plot the average photon number $N$ as functions of the driving detuning $\Delta _{c}/\kappa$ in Fig. 2(a). As shown in Fig. 2(a), there are nine peaks for the average photon number $N$. By analyzing the eigenenergy spectrum, we find that the locations of the nine peaks correspond to the single-photon resonant transitions $|\varepsilon _{0}^{0}\rangle \rightarrow |\varepsilon _{1}^{\pm,0}\rangle$, $|\varepsilon _{0}^{+}\rangle \rightarrow |\varepsilon _{1}^{\pm,0}\rangle$, $|\varepsilon _{0}^{-}\rangle \rightarrow |\varepsilon _{1}^{\pm,0}\rangle$, with the single excitation resonance conditions $\Delta _{c}=\Delta ^{1,\pm }_{0,0}=\mp \sqrt {(\Delta ^{'}+2\chi )^{2}+4\Omega _{R}^{2}}$, and $\Delta _{c}=\Delta ^{1,0}_{0,0}=0$, and $\Delta _{c}=\Delta ^{1,\pm }_{0,+}= \sqrt {(\Delta ^{'})^2+4\Omega _{R}^{2}}\mp \sqrt {(\Delta ^{'}+2\chi )^{2}+4\Omega _{R}^{2}}$, and $\Delta _{c}=\Delta ^{1,\pm }_{0,-}=-\sqrt {(\Delta ^{'})^2+4\Omega _{R}^{2}}\mp \sqrt {(\Delta ^{'}+2\chi )^{2}+4\Omega _{R}^{2}}$, and $\Delta _{c}=\Delta ^{1,0}_{0,\pm }=\pm \sqrt {(\Delta ^{'})^2+4\Omega _{R}^{2}}$, respectively. In addition, it can be seen that the corresponding average photon number reaches $N\simeq 10^{-3}$ in the weak-driving case. As a result, our model can obtain single-photon sources with high brightness. To clearly see the single-photon blockade effect in the cavity, and find the optimal detuning of the CPB effect, as shown in Fig. 2(b), we plot the equal-time second-order correlation function $g^{(2)}{(0)}$ as a function of the driving detuning $\Delta _{c}/\kappa$. Obviously, it has eight dips correspond to the single-photon resonant transitions and the optimal CPB effect ($g^{(2)}{(0)}\ll 1$) takes place at single excitation resonance conditions $\Delta _{c}=\Delta ^{1,\pm }_{0,0}$; $\Delta _{c}=\Delta ^{1,\pm }_{0,+}$; $\Delta _{c}=\Delta ^{1,\pm }_{0,-}$; and $\Delta _{c}=\Delta ^{1,0}_{0,\pm }$, respectively. It is worth noting that the photon bunching effect observed at $\Delta _{c}=0$, which is attributed to the resonance transition of the two-photon $|\varepsilon _{0}^{0}\rangle$ →$|\varepsilon _{1}^{0}\rangle$ →$|\varepsilon _{2}^{0}\rangle$.

 

Fig. 2. (a) Average photon number $N$ as functions of the driving detuning $\Delta _{c}/\kappa$. (b) Equal-time second-order correlation function $g^{(2)}(0)$ as a function of the driving detuning $\Delta _{c}/\kappa$. Here, we chose $\gamma /\kappa = 0.5$, $\chi /\kappa = 15$, $\Omega _{R}/\chi = 1.1$, $\Delta ^{'}=0$, $\eta /\kappa = 0.1$, and $\overline {n}_{\mathrm {th}} = 0$.

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Single-photon blockade effect can also be effectively characterized by a time-delayed second-order correlation function $g^{(2)}{(\tau )}={\langle \hat {a}^{\dagger }(t)\hat {a}^{\dagger }(t+\tau )\hat {a}(t+\tau )\hat {a}(t)\rangle }/{\langle \hat {a}^{\dagger }(t)\hat {a}(t)\rangle }{\langle \hat {a}^{\dagger }(t+\tau )\hat {a}(t+\tau )\rangle }$, which represents the probability of detecting two photons in the presence of a delay time $\tau$. When $\tau =0$, $g^{(2)}{(0)}$ is the equal-time second-order correlation function. Thus, we plot in Fig. 3 the evolution of $g^{(2)}{(\tau )}$ with $\Delta _{c}=\Delta ^{1,-}_{0,-}$. It can be observed that $g^{(2)}{(0)}\ll 1$ and $g^{(2)}{(0)}<g^{(2)}{(\tau )}$, which indicates that the photon is in the antibunching state. As $\tau$ increases, $g^{(2)}{(\tau )}\longrightarrow 1$, which further verifies the appearance of the single-photon blockade effect of the system. Specially, there is a characteristic time around $\kappa \tau \sim 5$ when a second photon is more likely to be emitted than would be expected at random (i.e., $g^{(2)}{(\tau )}>1$). This is related to the energy level structure of the system. At a particular time point, there is a change in the transition probability between energy levels in the system, resulting in an increased probability of emitting the second photon.

 

Fig. 3. The time-delayed second-order correlation function $g^{(2)}(\tau )$ versus the time-delay $\kappa \tau$. Here, we chose $\Delta _{c}=\Delta ^{1,-}_{0,-}$, $\gamma /\kappa = 0.5$, $\Delta ^{'}= 0$, $\Omega _{R}/\chi = 1.1$, $\chi /\kappa = 15$, $\eta /\kappa = 0.1$, and $\overline {n}_{\mathrm {th}} = 0$.

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In order to further investigate the effect of controllable parameters on the single-photon blockade effect, we select two single-photon resonant transitions paths ($\Delta _{c}=\Delta ^{1,+}_{0,+}$; $\Delta _{c}=\Delta ^{1,-}_{0,-}$) and plot the function $\mathrm {log}_{10}[g^{(2)}(0)]$ versus dispersive coupling strength $\chi /\kappa$ and the ratio $\Omega _{R}/\chi$ of the atomic-driving strength $\Omega _{R}$ over the dispersive coupling strength $\chi$ in Fig. 4. The numerical results show that different controllable parameters correspond to different values of the second-order correlation function. Particularly, the strong photon blockade effect is observed at $\Omega _{R}/\chi \approx 1.1$. Simultaneously, when $\Omega _{R}/\kappa$ is very small or large, the value of the second-order correlation function approaches 1, indicating the existence of optimal controllable parameters in the system.

 

Fig. 4. Equal-time second-order correlation function $\mathrm {log}_{10}[g^{(2)}(0)]$ as a function of $\chi /\kappa$ and $\Omega _{R}/\kappa$ for two single-photon resonant transition cases: (a) $\Delta _{c}=\Delta ^{1,+}_{0,+}$; (b) $\Delta _{c}=\Delta ^{1,-}_{0,-}$. Here, we chose $\gamma /\kappa = 0.5$, $\Delta ^{'}=0$, $\eta /\kappa = 0.1$, and $\overline {n}_{\mathrm {th}} = 0$.

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Based on the above analysis we find that the anharmonicity of photons vanishes when the driving strength of the qubit is either excessively strong or extremely weak. Hence it is important to study the influence of qubit drive strength $\Omega _{R}$ on the photon blockade effect of the system. In Fig. 5, we plot the equal-time second-order correlation function $g^{(2)}(0)$ as a function of the ratio $\Omega _{R}/\chi$ at different single-photon resonant transitions $\Delta _{c}=\Delta ^{1,+}_{0,+}$ and $\Delta _{c}=\Delta ^{1,-}_{0,-}$. Here the red solid curves, blue dashed curves, correspond to the dispersive coupling strengths $\chi /\kappa$= 10 and 15, respectively. As shown in Fig. 5, for a given dispersive coupling strength $\chi$, the value of equal-time second-order correlation function $g^{(2)}(0)$ first decrease and then increase as the ratio $\Omega _{R}/\chi$. Single-photon blockade effect is strongest around $\Omega _{R}/\chi \approx$ 1.1, which correspond to the optimal drive intensity of the qubit in the cases of single-photon resonant transitions $\Delta _{c}=\Delta ^{1,+}_{0,+}$ and $\Delta _{c}=\Delta ^{1,-}_{0,-}$, this agrees well with the analytical solution obtained above. As the same time, we found that single-photon blockade effect is extremely weak and gradually disappears ($g^{(2)}(0)\rightarrow 1$) under the weak and strong coupling regimes ($\Omega _{R}/\chi \rightarrow 0$ and $\Omega _{R}/\chi > 10$). This is consistent with the above system’s eigenenergy analysis results. It is worth noting that, with the increase of $\chi$, the value of $g^{(2)}(0)$ becomes smaller, the single-photon blockade effect is stronger for a larger dispersive coupling strength.

 

Fig. 5. Equal-time second-order correlation function $g^{(2)}(0)$ as a function of the ratio $\Omega _{R}/\chi$ at $\chi /\kappa =10,15$ for two single-photon resonant transition cases: (a) $\Delta _{c}=\Delta ^{1,+}_{0,+}$; (b) $\Delta _{c}=\Delta ^{1,-}_{0,-}$. Here, we chose $\gamma /\kappa = 0.5$, $\Delta ^{'}=0$, $\eta /\kappa = 0.1$, and $\overline {n}_{\mathrm {th}} = 0$.

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Under the resonance condition between the driving field and the transition $|\varepsilon _{0}^{+}\rangle \rightarrow |\varepsilon _{1}^{+}\rangle$ ($|\varepsilon _{0}^{-}\rangle \rightarrow |\varepsilon _{1}^{-}\rangle$), the anharmonicity of the system’s eigenenergy spectrum introduces a detuning $\Delta _{a}$ ($\Delta _{b}$) for the transition $|\varepsilon _{1}^{+}\rangle \rightarrow |\varepsilon _{2}^{+}\rangle$ ($|\varepsilon _{1}^{-}\rangle \rightarrow |\varepsilon _{2}^{-}\rangle$). By solving Eq. (7), it is found that the maximum detuning occurs at $\Omega _{R}/\chi \approx 1.1$, the optimal qubit driving strength for achieving single-photon blockade is obtained. Based on the aforementioned study, we know that different dispersive coupling strength $\chi$ corresponds to different equal-time second-order correlation function $g^{(2)}(0)$. Therefore, we plot the equal-time second-order correlation function $g^{(2)}(0)$ as a function of the ratio $\chi /\kappa$ for two single-photon resonant transition cases $\Delta _{c}=\Delta ^{1,+}_{0,+}$ and $\Delta _{c}=\Delta ^{1,-}_{0,-}$ at $\Omega _{R}/\chi =1.1, 2.5$ in Fig. 6, and the qubit drive strength $\Omega _{R}$ can be controlled by adjusting the power of the driving field. Clearly can be seen, when we choose $\Omega _{R}/\chi$ = 1.1 (red dashed curve) and $\Omega _{R}/\chi$ = 2.5 (blue solid curve) the values of the second-order correlation function $g^{(2)}(0)$ first increase and then decrease with the increase of the ratio $\chi /\kappa$. The physical reason is that the greater the dispersive coupling strength, the stronger the nonlinearity of the system and the better the resulting single-photon blockade effect. Moreover, at appropriate dispersive coupling strength $\chi /\kappa$, the values of the correlation fuctions at the qubit drive strength $\Omega _{R}/\chi$=2.5 larger than at $\Omega _{R}/\chi$=1.1. This characteristic indicates that the dependence of the correlation function on the drive strength is nonmonotonic, and corresponds to the optimal drive intensity of qubit.

 

Fig. 6. Equal-time second-order correlation function $g^{(2)}(0)$ as a function of the dispersive coupling strength $\chi /\kappa$ at $\Omega _{R}/\chi =1.1, 2.5$ for two single-photon resonant transition cases: (a) $\Delta _{c}=\Delta ^{1,+}_{0,+}$; (b) $\Delta _{c}=\Delta ^{1,-}_{0,-}$. Here, we chose $\gamma /\kappa = 0.5$, $\Delta ^{'}=0$, $\eta /\kappa = 0.1$, and $\overline {n}_{\mathrm {th}} = 0$.

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3.2 Two-photon blockade effect

Here we research the two-photon blockade effect of the driven dispersive T-C system with the case of driving the cavity mode. To further study the physical mechanism of the two-photon blockade effect, in Fig. 7(a) we present the $g^{(2)}{(0)}$ and $g^{(3)}{(0)}$ as a function of the ratio $\Omega _{R}/\chi$ of the atomic-driving strength $\Omega _{R}$ over the dispersive coupling strength $\chi$. Clearly, with the increase of $\Omega _{R}/\chi$, the values of $g^{(2)}{(0)}$ and $g^{(3)}{(0)}$ first decrease, then increase and eventually exceed 1. When the value of $\Omega _{R}/\chi$ is in the grey region, we can observe the two-photon blockade effect [i.e., $g^{(2)}{(0)}>1$ and $g^{(3)}{(0)}<1$]. Due to the three-photon transition is highly detuned, we can only observe this distinctive phenomenon in a very narrow frequency range. This quantum effect can also be explained from the eigenenergy spectrum diagram in Fig. 1(b). When the optical cavity is driven at the two-photon resonance, i.e., $\Delta _{c}=\Delta ^{2,0}_{0,+}$, the ground state $|\varepsilon _{0}^{+}\rangle$ can be transitioned to the two-photon state $|\varepsilon _{2}^{0}\rangle$, while the $|\varepsilon _{2}^{0}\rangle \rightarrow |\varepsilon _{3}^{0}\rangle$ transition will be suppressed due to the frequency detuning. Thus, the two-photon blockade effect can be achieved. In addition, in Fig. 7(b), equal-time second-order correlation function $g^{(2)}{(0)}$ and equal-time third-order correlation function $g^{(3)}{(0)}$ are plotted as a function of the dispersive coupling strength $\chi /\kappa$. With the increasing of $\chi /\kappa$, the values of $g^{(2)}{(0)}$ and $g^{(3)}{(0)}$ gradually increase. It is clear that two-photon blockade effect occurs in a grey area ($1.2<\chi /\kappa <2$).

 

Fig. 7. (a) Equal-time n-order correlation function $g^{(n)}(0)$ as a function of the ratio $\Omega _{R}/\chi$ at $\chi /\kappa =10$ for two-photon resonant transition cases: $\Delta _{c}=\Delta ^{2,0}_{0,+}$. (b)Equal-time n-order correlation function $g^{(n)}(0)$ as a function of the dispersive coupling strength $\chi /\kappa$ at $\Omega _{R}/\chi =1$ for two-photon resonant transition cases: $\Delta _{c}=\Delta ^{2,0}_{0,+}$. The black dot line indicate $g^{(2)}{(0)}=1$ for Poissonian statistics and the grey area for the two-photon blockade. Here, we chose $\gamma /\kappa = 0.5$, $\Delta ^{'}=0$, $\eta /\kappa = 1$, and $\overline {n}_{\mathrm {th}} = 0$.

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In the discussion above, we do not consider the influence of the average thermal excitation numbers $\overline {n}_{\mathrm {th}}$ on the photon statistical characteristics (i.e., $\overline {n}_{\mathrm {th}}=0$). For optical cavities, the number of thermal photons is negligible, so our assumption of a zero temperature environment above is reasonable. In order to present how the average thermal excitation numbers affects the two-photon blockade effect, we plot the equal-time second-order correlation function $g^{(2)}{(0)}$ and third-order correlation function $g^{(3)}{(0)}$ versus the average thermal excitation numbers $\overline {n}_{\mathrm {th}}$, as shown in Fig. 8. We find that the equal-time second-order correlation function $g^{(2)}{(0)}$ and equal-time third-order correlation function $g^{(3)}{(0)}$ gradually decrease as the average thermal excitation numbers $\overline {n}_{\mathrm {th}}$ increases and produce two-photon blockade effect when the value of $\overline {n}_{\mathrm {th}}$ is between 1 and 3 (grey region). The results show that the two-photon blockade effect can be achieved without strong suppression of thermal noise. In other words, the conventional two-photon blockade effect is relatively robust to thermal noise.

 

Fig. 8. Equal-time n-order correlation function $g^{(n)}(0)$ as a function of the average thermal excitation numbers $\overline {n}_{\mathrm {th}}$ for two-photon resonant transition case: $\Delta _{c}=\Delta ^{2,-}_{0,0}$. The black dot line indicate $g^{(2)}{(0)}=1$ for Poissonian statistics and the grey area for the two-photon blockade. Here, we chose $\gamma /\kappa = 0.5$, $\chi /\kappa = 10$, $\Omega _{R}/\chi = 1$, $\Delta ^{'}=0$, and $\eta /\kappa = 0.1$.

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4. Conclusions

In conclusion, we propose a scheme to recover the PB effect in the dispersive T-C model by introducing transversal driving to the qubit. By solving the eigenenergy spectrum of the dispersive T-C system, we obtain analytically the single excitation resonance conditions and the corresponding optimal qubit driving strength. Meanwhile, the numerical simulations are in good agreement with the analytical results, and the single-photon resonant can produce the strongest single-photon blockade effect and largest average photon number. We also research the relationship between equal-time n-order correlation function of cavity field and various adjustable parameters. The results indicate that the single-photon and two-photon blockade effects can be recovered under appropriate qubit driving strength. It is worth noting that two-photon blockade effect is relatively robust to thermal noise. The proposed scheme gives a method to retrieve the CPB effect in the dispersive limit, which could provide a way to construct single-photon sources beyond the traditional limits.