非经典光学梳：超短脉冲光的五模量子挤迫态生成与应用

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本文主要探讨了在量子计算的连续变量领域中，非经典光学频率梳（nonclassical optical frequency combs）的重要作用。作者通过一项创新性研究，利用一种双峰型I同步泵浦的光学参量振荡器（degenerate type-I synchronously pumped optical parametric oscillator, OPO）成功生成了时域多模的非经典频梳态（generation of temporal multimode squeezed states）。这些频梳态是针对飞秒脉冲光（femtosecond pulsed light）的，特别关注了前五个模式的量子挤迫现象（squeezing of the leading five temporal modes）。实验结果显示，这些模式的光谱重叠特性表明，它们具有在现实世界量子信息应用中的潜力。通过直接观测，研究人员能够验证和量化这些模式的非经典性质，这对于量子通信、量子信息处理以及量子精密测量等领域具有重要意义。非经典频率梳的实现不仅有助于提升光子源的量子性能，而且对于构建高效的量子网络和量子计算机平台至关重要。文章的作者包括Chihua Zhou（周驰华）、Changchun Zhang（张长春）、Hongbo Liu（刘宏波）、Kui Liu（刘奎）（通讯作者：liukui@sxu.edu.cn）、Hengxin Sun（孙恒信）和Jiangrui Gao（郜江瑞），他们来自中国山西大学的量子光学与量子光学设备国家重点实验室和极端光学协同创新中心，他们的研究成果发表于2017年，被赋予了光学科学分类号270.6570、190.7110和270.5585，doi:10.3788/COL201715.092。这项工作为开发和利用非经典光学频率梳在量子信息处理中的应用迈出了重要一步，展示了其在提高量子通信的可靠性和效率方面可能带来的革命性进展。未来的研究将着重于优化技术，扩大光谱覆盖范围，并探索如何在实际量子通信系统中集成这些非经典光场。

Generation of temporal multimode squeezed states

of femtosecond pulse light

Chihua Zhou (周驰华)

1,2

, Changchun Zhang (张长春)

1,2

, Hongbo Liu (刘宏波)

1,2

Kui Liu (刘奎)

1,2,

*, Hengxin Sun (孙恒信)

1,2

, and Jiangrui Gao (郜江瑞)

1,2

State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics,

Shanxi University, Taiyuan 030006, China

Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

*Corresponding author: liukui@sxu.edu.cn

Received January 22, 2017; accepted May 23, 2017; posted online June 23, 2017

Nonclassical optical frequency combs play essential roles in quantum computation in the continuous variable

regime. In this work, we generate multimode nonclassical frequency comb states using a degenerate type-I syn-

chronously pumped optical parametric oscillator and directly observe the squeezing of the leading five temporal

modes of femtosecond pulsed light. The overlapping spectra of these modes mean that the temporal modes are

suitable for use in real-world quantum information applications.

OCIS codes:: 270.6570, 190.7110, 270.5585.

doi: 10.3788/COL201715.092703.

Nonclassical light is not only a fundamental concept in

physics but also plays a significant role in quantum infor-

mation processing applications

[1,2]

. Recently, considerable

research has been devoted to the sources of multimode

nonclassical states of light, which will not only be of great

value in quantum key sharing and quantum cooperation

but will also be an important tool for the expansion of

the quantum channel capacity. Recently, continuous-

variable (CV) multimode entanglement using a high-

dimensional optical parametric oscillator (OPO) was

demonstrated in both the frequency domain

[3,4]

and the

spatial domain

[5–7]

. These multimode sources can also be

used to generate compact and scalable multipartite en-

tangled states

[8–11]

, which are essential for quantum

communication and computation.

Optical frequency combs, which span thousands of

different frequency modes, have the coherence properties

of continuous-wave (CW) lasers and the high peak powers

of pulsed lasers simultaneously, and have thus become po-

tential tools for temporal multimode nonclassical light

generation. Pinel et al. experimentally demonstrated a

nonclassical frequency comb for the first time in 2012

and obtained amplitude squeezing of −1.2 dB using a

synchronously pumped optical parametric oscillator

(SPOPO)

[12]

. Recently, wavelength-multiplexed quantum

networks and a quantum spectrometer have been realized

based on nonclassical optical frequency combs

[13]

. In 2013,

we observed −2.58 dB phase quadrature squeezing of the

TEM

mode by a type-I degenerate SPOPO that was op-

erating below its oscillation threshold

[14]

. We subsequently

obtained amplitude quadrature squeezing of −0.7 dB us-

ing an SPOPO that operated in a higher-order transverse

mode state in 2016

[15,16]

, which is promising for three-

dimensional space-time measurement applications.

In this work, we generated multimode nonclassical fre-

quency comb states using a degenerate type-I SPOPO and

directly observed the squeezing of the leading five tempo-

ral “supermodes”

[17]

. Unlike transverse spatial modes

[18]

these temporal modes are naturally suited to use with

existing high-efficiency single-mode fiber networks. In ad-

dition, they are insensitive to stationary and slowly vary-

ing medium perturbation effects, such as linear dispersion,

because of their overlapping spectra, which makes them

suitable for use in real-world applications

[19]

We consider a degenerate SPOPO with a type-I nonlin-

ear crystal. The Langevin equation of the intracavity sig-

nal field is given by:

¼ −γ

− γ

m;q



2γ

in;m

: (1)

On the right side of this equation, the first term describes

the effect of cavity damping, and γ

is the decay rate. The

third term is the input coupling term, which reflects the

effects of seed light on the intracavity signal field. The sec-

ond term describes the parametric interaction that occurs

between the two frequency modes.

are the annihilation

operators of the downconversion fields, which are labeled

using the integer index k (where k ¼ m, q), and k ¼ 0 cor-

responds to the phase-matc hed mode. L

m;q

denotes the

coupling matrix, which is related to the phase-mismatch

factor and the frequency domain profile of the pump and

characterizes the coupl ing strengths s

and s

in the non-

linear interaction, and σ is the coupling constant, which is

normalized with respect to the CW threshold for a simple-

mode OPO

[20]

The mode-locked femtosecond pulse laser exports pulse

trains of the order of 10

–10

pulses, so the coupl ing

matrix is very large and complex; this means that the

parameter downconversion procedure is a highly complex

multimode interaction process. The multimode correla-

tions can be simplified into single-mode squeezed states

COL 15(9), 092703(2017) CHINESE OPTICS LETTERS September 10, 2017

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