Unconventional photon blockade induced by the self-Kerr and cross-Kerr nonlinearities

doi:10.1007/s11467-022-1213-y

Front. Phys.

2023, Vol. 18

Issue (1) : 12304 https://doi.org/10.1007/s11467-022-1213-y

RESEARCH ARTICLE

Unconventional photon blockade induced by the self-Kerr and cross-Kerr nonlinearities

Ling-Juan Feng¹(

), Li Yan²(

), Shang-Qing Gong³(

)

¹. School of Sciences, Shanghai Institute of Technology, Shanghai 201418, China
². School of Physics and Electronic Engineering, Heze University, Heze 274015, China
³. School of Physics, East China University of Science and Technology, Shanghai 200237, China

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Abstract

We study the use of the self-Kerr and cross-Kerr nonlinearities to realize strong photon blockade in a weakly driven, four-mode optomechanical system. According to the Born−Oppenheimer approximation, we obtain the cavity self-Kerr coupling and the inter-cavity cross-Kerr coupling, adiabatically separated from the mechanical oscillator. Through minimizing the second-order correlation function, we find out the optimal parameter conditions for the unconventional photon blockade. Under the optimal conditions, the strong photon blockade can appear in the strong or weak nonlinearities.

Keywords unconventional photon blockade cross-Kerr nonlinearity self-Kerr nonlinearity optomechanical system

Corresponding Author(s): Ling-Juan Feng,Li Yan,Shang-Qing Gong

Issue Date: 03 November 2022

Cite this article:

Ling-Juan Feng,Li Yan,Shang-Qing Gong. Unconventional photon blockade induced by the self-Kerr and cross-Kerr nonlinearities[J]. Front. Phys. , 2023, 18(1): 12304.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1213-y
https://academic.hep.com.cn/fop/EN/Y2023/V18/I1/12304

Fig.1 (a) Schematic diagram of the four-mode optomechanical system, with three optical modes and a single mechanical mode. (b) Schematic diagram of the three-coupled-cavity system.

Fig.2 (a) One set of optimal detuning

Δ o p t

and nonlinearity

U o p t

versus photon tunneling

J

normalized to

κ

. (b) Another set of optimal detuning

Δ o p t

and nonlinearity

U o p t

versus photon tunneling

J

normalized to

κ

Fig.3 Energy-level diagram of the optical system under the Hamiltonian (3) with

J 1 = J 2 = J

and

g 1 = g 2 = g

. States are labeled

| n a 1 n a 2 n c ?

, where

n j

denotes the photon number of the mode

j = a 1, a 2, c

Fig.4 The second-order correlation function

g c (2) (0)

versus the time

κ t

. The red circles show the exact numerical results based on the full Hamiltonian (1) and the master equation (14). The solid blue curve is the approximate numerical results based on the effective Hamiltonian (3) and the master equation (14). The parameters are

J = 2 κ

Δ = Δ o p t

U = U o p t

ω m = 102 κ

N t h = 0

γ = 10 − 3 κ

, and

Ω = 10 − 2 κ

Fig.5 The second-order correlation function

g c (2) (0)

versus the normalized detuning

Δ / κ

for different values of the nonlinearity

U

. The red (or green) circles denote the numerical results based on Eqs. (3) and (14). The solid blue (or black) curve is the analytical results based on Eq. (9). Other parameters are the same as those in Fig.4.

Fig.6 The second- and third-order correlation functions

g c (2) (0)

and

g c (3) (0)

versus the normalized detuning

Δ / κ

. The solid red curve corresponds to the analytical results of

g c (2) (0)

based on Eq. (9). The solid blue curve is the analytical results of

g c (3) (0)

based on Eq. (10). In (a)

U o p t ≈ 13.637 κ

and in (b)

U o p t ≈ 0.096 κ

. Other parameters are the same as those in Fig.4.

Fig.7 The second-order correlation function

g c (2) (0)

versus the normalized detuning

Δ / κ

for different values of the pure dephasing rate

γ p

. These circles show the numerical results based on Eqs. (3) and (14). The red, black, blue circles respectively represent

γ p = 0

γ p = 0.01 κ

γ p = 0.1 κ

. In (a)

U o p t ≈ 13.637 κ

and in (b)

U o p t ≈ 0.096 κ

. Other parameters are the same as those in Fig.4.

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