Phonon-blockade-based multiple-photon bundle emission in a quadratically coupled optomechanical system

doi:10.1007/s11467-023-1352-9

Front. Phys.

2024, Vol. 19

Issue (3) : 32202 https://doi.org/10.1007/s11467-023-1352-9

RESEARCH ARTICLE

Phonon-blockade-based multiple-photon bundle emission in a quadratically coupled optomechanical system

Ye-Jun Xu¹(

), Hong Xie²(

)

¹. Interdisciplinary Research Center of Quantum and Photoelectric Information, Chizhou University, Chizhou 247000, China
². Department of Mathematics and Physics, Fujian Jiangxia University, Fuzhou 350108, China

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Abstract

We propose a scheme to realize antibunched multiple-photon bundles based on phonon blockade in a quadratically coupled optomechanical system. Through adjusting the detunings to match the conditions of phonon blockade in the photon sidebands, we establish super-Rabi oscillation between zero-photon state and multiple-photon states with adjustable super-Rabi frequencies under appropriate single-phonon resonant conditions. Taking the system dissipation into account, we numerically calculate the standard and generalized second-order functions of the cavity mode as well as the quantum trajectories of the state populations with Monte Carlo simulation to confirm that the emitted photons form antibunched multiple-photon bundles. Interestingly, the desirable n-photon states are reconstructed after a direct phonon emission based on phonon blockade, and thus the single-phonon emission heralds the cascade emission of n-photon bundles. Our proposal shows that the optomechanical system can simultaneously behave as antibunched multiple-photon emitter and single-phonon gun. Such a nonclassical source could have potential applications in quantum information science.

Keywords multiple-photon bundle emission phonon blockade optomechanical system

Corresponding Author(s): Ye-Jun Xu,Hong Xie

About author:

Peng Lei and Charity Ngina Mwangi contributed equally to this work.

Issue Date: 17 November 2023

Cite this article:

Ye-Jun Xu,Hong Xie. Phonon-blockade-based multiple-photon bundle emission in a quadratically coupled optomechanical system[J]. Front. Phys. , 2024, 19(3): 32202.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1352-9
https://academic.hep.com.cn/fop/EN/Y2024/V19/I3/32202

Fig.1 (a) Schematic diagram of a quadratically coupled optomechanical system with a “membrane-in-middle” configuration. (b) Anharmonic energy-level diagram limited in the subspace spanned by the zero- and one-phonon states. States labelled as

| n ~ (m), m ?

denote the cavity mode being in

m

-phonon-dependent displaced Fock state and the mechanical mode being in

m

-phonon state. (c) Frequency spectrogram of the driven optomechanical system with quadratic coupling. There are high-order sidebands due to the nonlinear optomechanical interaction. (d) Illustration of cascade emission of antibunched

n

-photon (

n = 2, 3

) bundles, where the system releases each photon bundle accompanied by single-phonon emission.

Fig.2 (a) Steady-state mean phonon number

? b ? b ?

and mean atomic excited-state probability

? σ ? σ ?

governed respectively by the Hamiltonians (7) and (8) as functions of the detuning

Δ m / Δ g

. (b) Steady-state equal-time second-order phonon correlation function

g b b (2) (0)

as a function of

Δ m / Δ g

. The other parameters are

Δ c / G = 2

Δ g = G 2 / Δ c

κ / G = 0.1

γ = 0.01 κ

ε / κ = 0.1

, and

n ˉ t h = 0

Fig.3 The state populations

P | n ? p | 1 ?

and

P | 0 ? p | 0 ?

(n = 2 and 3)

are plotted as functions of the scaled time

G t

in (a) for

n = 2

Δ c / G = 7.14

Δ m = 2 G 2 / Δ c ? 2 Δ c

and in (b) for

n = 3

Δ c / G = 2.86

Δ m = 2 G 2 / Δ c ? 3 Δ c

, and the common parameter

ε / G = 0.01

. The red and blue curves correspond to the numerical results of the state populations, while the red square and blue circle correspond to the analytical results based on the effective Rabi frequencies

Ω e f f (2)

and

Ω e f f (3)

Fig.4 (a) Zero-delay

n

th-order photon correlation functions

g (n) (0)

versus

Δ m / Δ c

. (b, c) The generalized time-delay second-order correlation functions

g N (2) (τ)

as functions of the scaled evolution time

κ τ

for

N = 2

at (b)

Δ m = 2 G 2 / Δ c ? 2 Δ c

, and at (c)

Δ m = 2 G 2 / Δ c ? 3 Δ c

. The other parameters are

κ = 1

G / κ = 10

Δ c / G = 2

γ / κ = 0.01

, and

ε / κ = 0.1

, and

n ˉ t h = 0

Fig.5 Small fraction of one quantum trajectory of the state populations

P | n ? | 0 (1) ?

(n = 0, 1, 2, 3)

at (a?c)

G / κ = 10

and

Δ m = 2 G 2 / Δ c ? 2 Δ c

, corresponding to the two-photon bundle emission; (d?g)

G / κ = 30

and

Δ m = 2 G 2 / Δ c ? 3 Δ c

, corresponding to the three-photon bundle emission. The other parameters are

Δ c = G

γ / κ = 0.01

ε / κ = 0.2

, and

n ˉ t h = 0

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