Generation of optical frequency comb squeezed light field
with TEM
01
transverse mode
Nan Huo (霍 楠)
1,2
, Chihua Zhou (周驰华)
1,2
, Hengxin Sun (孙恒信)
1,2
,
Kui Liu (刘 奎)
1,2,
*, and Jiangrui Gao (郜江瑞)
1,2
1
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics,
Shanxi University, Taiyuan 030006, China
2
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
*Corresponding author: liukui@sxu.edu.cn
Received February 2, 2016; accepted April 15, 2016; posted online May 20, 2016
Nonclassical optical frequency combs find tremendous utility in quantum information and high-precision quan-
tum measurement. The characteristics of a type-I synchronously pumped optical parametric oscillator with the
TEM
01
transverse mode below threshold are investigated and a squeezing of 0.7 dB for an optical frequency comb
squeezed light field with the TEM
01
transverse mode is obtained under the pump power of 130 mW. This work
has a promising application in three-dimensional space-time measurement.
OCIS codes: 270.6570, 190.4410, 190.7110.
doi: 10.3788/COL201614.062702.
Optical frequency combs, which span over thousands of dif-
ferent frequency modes, have found tremendous utility in
precision measurement
[1–5]
and quantum information
[6,7]
.In
2008, Fabre et al. put forward a new scheme combining a
balanced homodyne detector (BHD) with mode-locked
ultrafast frequency combs that lead to a new shot noise
limit (SNL) in time transfer and demonstrated that the
time measurement precision is enhanced by taking advan-
tage of the nonclassical optical frequency combs as the
signal field
[8]
. Then this team experimentally prepared a
spatially fundamental mode nonclassical frequency comb
for the first time and obtained −1.2 0.1 dB of the
amplitude squeezing
[9]
. Recently, they have realized
wavelength-multiplexed quantum networks and a quan-
tum spectrometer based on the nonclassical optical fre-
quency combs
[10,11]
.
Spatial transverse modes own a more complex spatial
structure and more information, thus allowing parallel
transfer of quantum information through an optical net-
work
[12]
. Combining the respective advantages of optical
frequency combs and spatial high-order transverse modes,
the quantum network that contains a greater channel
capacity can be achieved by using wavelength division
multiplexing and space division multiplexing
[13,14]
. In addi-
tion, high-order transverse mode nonclassical optical fre-
quency combs will hopefully be used in three-dimensional
(3D) space-time measurements.
In 2013, our group observed − 2.58 dB of the phase
quadrature squeezing of the TEM
00
mode by a type-I
degenerate synchronously pumped optical parametric
oscillator (SPOPO) that operated below its oscillation
threshold
[15]
. In the present work, we obtained the ampli-
tude quadrature squeezing of −0.7 dB by the use of the
SPOPO that operated in a high-order transverse mode
state. This work has had a profound effect on the quantum
network and space-time precision measurement.
Considering a process in which the femtosecond pulse
laser with center frequencies 2ω pumping the SPOPO
with a type-I nonlinear crystal is converted into a down-
conversion field at frequencies around ω, the interaction
Hamiltonian for a type-I SPOPO is expressed by
[16]
ˆ
H
I
¼ i
X
j;q;m
χ
j;q;m
f
j
q;m
a
�
q
ðtÞa
�
m
ðtÞ
ˆ
p
j
ðtÞþH:c; (1)
where
ˆ
a
k
(k ¼ m; q) are annihilation operators of
the downconversion fields with frequency ω þ kΩ,
ˆ
p
j
(j ¼ m þ q) is an annihilation operator of the pump field
with frequency 2ω þ jΩ, and Ω is the free spectral range of
the SPOPO and equal to the repetition of the pumping
laser. f
j
q;m
is the phase-mismatch factor, because the fem-
tosecond pulse has a spectral width of several nanometers,
the perfect phase matching is achieved only at the center
frequency. χ
j;q;m
is the nonlinear coupling constant; it is
dependent on the spatial overlap between the pump
and the downconversion fiel ds and read as
χ
j;q;m
≈ χ
ð2Þ
A
I 01
¼ χ
ð2Þ
ZZ
u
j
u
m
u
q
dxdy; (2)
where u
j
and u
k
(k ¼ m; q) are the transverse distribution
of the pump field and the downconversion fields, respec-
tively, χ
ð2Þ
is the second-order susceptibility of the nonlin-
ear crystal in the center frequency, and A
I 01
is the
interaction area. In our experimental scheme, the down-
conversion fields are operated in the TEM
01
transverse
mode and the pump field is in the TEM
00
transverse mode.
We can get χ
j;q;m
¼ χ
0
∕2, which is much smaller than the
nonlinear coupling constant χ
0
between the TEM
00
pump
field and the TEM
00
downconversion fields
[17,18]
.
Assuming that the pump field is not depleted, the pump
annihilation operator is approximated as h
ˆ
p
j
ðtÞi ≈ εα
j
, ε is
COL 14(6), 062702(2016) CHINESE OPTICS LETTERS June 10, 2016
1671-7694/2016/062702(4) 062702-1 © 2016 Chinese Optics Letters