## Abstract

We report dressed intensity noise correlation and intensity-difference
squeezing based on spontaneous parametric four-wave mixing (SP-FWM) in
Pr^{3+}:Y_{2}SiO_{5} crystal both
experimentally and theoretically. We found such intensity noise
correlation and intensity-difference squeezing can be controlled by
using the dressing effect to manipulate the nonlinear optical
coefficient of the SP-FWM process. By changing detuning and power of
the optical field, we manipulate the nonlinear optical coefficient of
the SP-FWM process, thus control the correlation and squeezing. The
results show stronger correlation and squeezing with single dressing,
while weaker near the resonant point due to destructive double
dressing. Furthermore,we observed the dependence of correlation times
on the power of dressing field, and explained by the combination of
the dressing effect and induced dipole-dipole interaction. We also
showed the fourth-order fluorescence signals accompanying with the
SP-FWM process.

© 2015 Optical Society of America

## 1. Introduction

Quantum correlation plays vital role for motivational research for possible
applications of quantum communication and quantum information processing.
The generations of correlated and entangled photon pairs by parametric
processes have been widely studied, including parametric down-conversion
process in nonlinear crystals [1,
2
]. Correlated beams have also been
generated by using an optical parametric amplification process in atomic
media [3]. Besides these, the
correlation switching in an atomic system has been experimentally
demonstrated [4]. The amplitude and
intensity noise correlations of counter-propagating paired photons in an
atomic system have also been discussed theoretically [5]. Simultaneously, the great deal of work
has been done in developing the control mechanism for nonlinear optical
process, such as influence of a dressing field on parametric amplification
of multi-wave mixing processes in an atomic system [6], polarization dressed multi-order fluorescence [7], interaction of double dressed
multi-waves mixing in five level atomic systems [8]. Currently, the most experimental studies of the
parametric FWM processes based on atomic coherence have been carried out
in atomic gases. However, for many practical applications, the
corresponding researches in solid materials are more valuable. The
rare-earth-ion-doped crystals Pr^{3+}:Y_{2}SiO_{5}
(Pr^{3+}:YSO)in which the atomic coherence can be induced easily
when interacting with multiple laser fields, have been used to realize
electromagnetically induced transparency (EIT) [9–12
], coherent storage and light
velocity reduction [13–15
], enhanced
FWM process and all-optically controlled higher-order fluorescence signal
with and without splitting [16].

In this paper, we use the SP-FWM process in
Pr^{3+}:Y_{2}SiO_{5} crystal to generate the
intensity noise correlation and intensity-difference squeezing and
investigate the control mechanism of the noise correlation and
intensity-difference squeezing. The V-type and Λ-type three-level systems
of Pr^{3+}: YSO are compared. We showed that the correlation and
squeezing may be manipulated by the detuning and power of the optical
field participating in the SP-FWM process. But there is some difference
between V-type and Λ-type three-level systems due to difference of
dipole-dipole interaction and dressing effect. We also showed the
fourth-order fluorescence signals accompanying with the SP-FWM process.
Finally, the correlation time of SP-FWM is also investigated by changing
power. The paper is constructed as following: in Sec. 2, we show the
experimental setup for the generation of intensity noise correlation and
intensity-difference squeezing in Pr^{3+}: YSO crystal and
introduce the corresponding theory briefly; in Sec. 3, we present the
experiment results and discuss them in detail; in Sec. 4, we conclude the
paper.

## 2. Basic theory and experimental scheme

#### 2.1 Experimental setup

The sample used in this experiment is 0.05% rare-earth Pr^{3+}
doped Y_{2}SiO_{5} crystal, the triplet energy-level
^{3}H_{4} and singlet energy-level
^{1}D_{2} of Pr^{3+} ions are selected. The
degeneracy of the energy levels of the Pr^{3+} ion is removed
by the crystal field of YSO, where the terms in
^{3}H_{4} and ^{1}D_{2} states are
split into nine and five Stark components, respectively. The
Pr^{3+} ions occupy two nonequivalent cation sites (sites I
and II, respectively) in the YSO crystal lattice. The energy levels
are labeled by a Greek letter with and without asterisk for site II
and I sites, respectively. The coupling between Pr^{3+} ions
localized at different cation vacancies can happen due to
dipole-dipole interactions, so one can treat the two ions as a
heteronuclear-like molecule. Therefore, we can construct a V-type
three-level subsystem
(|0〉(δ_{0})↔|1〉(γ_{0})↔|2〉(γ_{0}*)) and a
Λ-type (|0〉(δ_{0})↔|1〉(${\gamma}_{0}$)↔|3〉(δ_{1})) by coupling the
corresponding laser fields as shown in Fig. 1(a)
.

The sample (a 3-mm Pr:YSO crystal) is held at 77 K in a cryostat
(CFM-102). Three tunable dye lasers (narrow scan with a 0.04
cm^{−1} line width) pumped by an injection locked single-mode
Nd:YAG laser (Continuum Powerlite DLS 9010, 10 Hz repetition rate, 5
ns pulse width) are used to generate the pumping fields
**E**
_{1} (ω_{1}, Δ_{1}),
**E**
_{2} (ω_{2}, Δ_{2}), and
**E**
_{3} (ω_{3}, Δ_{3}). Their
frequency detuning is defined as Δ_{i} =
ω_{mn}−ω_{i} (i = 1, 2, and 3), where ω_{mn}
denotes the corresponding atomic transition frequency and
ω_{i} is the laser frequency. In the V-type (or Λ-type)
three-level subsystem, a SP-FWM processes satisfying the
phase-matching condition **k _{1} + k_{2} =
k_{S1} + k_{aS1}** (or

**k**) can occur, where

_{1}+ k_{3}= k_{S2}+ k_{aS2}**k**and

_{S1}**k**(

_{aS1}**k**and

_{S2}**k**) are the wavevectors of the generated Stokes and anti-Stokes fields in the V-type system (Λ-type system), respectively. Since the SP-FWM process absorbs two photons and produces one Stokes and one anti-Stokes photon simultaneously, the two output photons of the SP-FWM process are highly correlated. Figure 1(b) shows the experimental arrangement. The generated Stokes signal

_{aS2}**E**

_{S1}(or

**E**

_{S2}) and anti-Stokes signal

**E**

_{aS1}(or

**E**

_{aS2}) are reflected by polarized beam splitters (PBS) and detected by photomultiplier tubes. The intensity noises correlation between Stokes and anti-Stokes signals can be calculated by using their time-dependent intensity fluctuations, which are recorded by D1 and D2 and denoted as $\delta {\widehat{I}}_{S}({t}_{S})$ and $\delta {\widehat{I}}_{aS}({t}_{aS})$. The fluorescence signals accompanying with the SP-FWM process is simultaneously detected by D3.

#### 2.2 Basic theory

### 2.2.1 Density matrix elements and nonlinear coefficient

Now we present a brief theory for the generated correlation from
the SP-FWM process both in V-type and Λ-type systems. Signals
**E**
_{aS} and **E**
_{S} are
generated by opening **E**
_{1} and
**E**
_{2} (**E**
_{1} and
**E**
_{3}) beams in the V-type (Λ-type) system.
For the Λ-type system, according to the Liouville pathways [17,18
], the density matrix elements ${\rho}_{13(S2)}^{(3)}$ for Stokes signal
**E**
_{S2} can be obtained as: ${\rho}_{13(S2)}^{(3)}=-i{G}_{3}{G}_{aS2}^{*}{G}_{1}/[({\Gamma}_{13}+i{\Delta}_{3})({\Gamma}_{13}+i{\Delta}_{1}){\Gamma}_{30}]$ via perturbation chain
${\rho}_{33}^{(0)}\stackrel{{E}_{3}}{\to}{\rho}_{13}^{(1)}\stackrel{{E}_{{}_{aS2}}^{*}}{\to}{\rho}_{03}^{(2)}\stackrel{{E}_{3}}{\to}{\rho}_{13(S2)}^{(3)}$, and ${\rho}_{10(aS2)}^{(3)}$ for anti-Stokes signal
**E**
_{aS2} can be obtained as: ${\rho}_{10(aS2)}^{(3)}=-i{G}_{1}{G}_{2S2}^{*}{G}_{3}/[({\Gamma}_{10}+i{\Delta}_{1})({\Gamma}_{10}+i{\Delta}_{3}){\Gamma}_{30}]$ via ${\rho}_{00}^{(0)}\stackrel{{E}_{1}}{\to}{\rho}_{10}^{(1)}\stackrel{{E}_{{}_{S2}}^{*}}{\to}{\rho}_{30}^{(2)}\stackrel{{E}_{3}}{\to}{\rho}_{10(aS2)}^{(3)}$. Here, ${G}_{i}=\mu {E}_{i}/\hslash $ is the Rabi frequency of the
**E**
_{i} field, the term ${\Gamma}_{ij}$ is the decay rate between the energy
levels $|i\u3009$ and $|j\u3009$. If the powers of
**E**
_{1} and **E**
_{3} fields
are strong enough, we should consider dressing effect from
**E**
_{1} and **E**
_{3} fields.
Then the density matrix elements with double dressing effect
should be modified as:

**E**

_{1}and

**E**

_{2}in V-type system can be written as

Once the Stokes and anti-Stokes signals are generated, they will propagate through the nonlinear medium. The nonlinear coefficients ${\kappa}_{S/aS}$ are determined by the nonlinearity susceptibility ${\chi}_{S/aS}^{(3)}$ and the amplitude of incident fields, and can be given as

Where $c$ is speed of light, and ω_{S/aS}is the angular frequency. Because of the relation of ${\chi}_{S/aS}^{(3)}=N\mu {\rho}_{(S/aS)}^{(3)}/({\epsilon}_{0}{E}_{1}{E}_{j}{E}_{aS/S}^{*})$, where j = 2 (V-type) or 3(Λ-type), $N$is atomic density, $\mu $ is corresponding dipole moment, and ${\epsilon}_{0}$ is permittivity of free space, the SP-FWM process can be controlled by the fields

**E**

_{1}and

**E**

_{2}(or

**E**

_{3}). Then the output photon number from the nonlinear medium can be written as

^{2}(κ

_{S/aS}L) is the gain coefficient with the medium length L.

### 2.2.2 Intensity noise correlation and intensity difference squeezing

The measured photon number at each output channel can be obtained
by $<{\widehat{a}}_{i}^{\text{+}}{\widehat{a}}_{i}>$ and the corresponding intensity I∝
$<{\widehat{a}}_{i}^{\text{+}}{\widehat{a}}_{i}>$. Since the two output photons of the
SP-FWM process are highly correlated, the intensity noise
correlation function ${G}_{}^{(2)}(\tau )$ between **E**
_{S}
and **E**
_{aS} signal can be calculated by [19]

_{1}= |R

_{S}R

_{aS}

**E**

_{S}

**E**

_{aS}|

^{2}, R

_{2,4}= R

_{S}|

**E**

_{S}|

^{2}, R

_{3,5}= R

_{aS}|

**E**

_{aS}|

^{2}with R

_{aS/S}= V

^{1/3}/[(2π)υ

_{aS/S}] and

**E**

_{aS/S}= (ħω

_{aS/S}/2ε

_{0}V)

^{1/2}(here, V is the quantization volume and υ

_{aS/S}is group velocity). For the parameters in above expressions, only A is related to τ.

We also investigate the squeezing in V and Λ-type systems, which is governed by [20].

The generated intensity noises correlation and intensity difference
squeezing in the SP-FWM process are related to the nonlinear
coefficient κ, which can be modified by the dressing effect
induced by **E**
_{1} and
**E**
_{2} (or **E**
_{3}).
Specially, the dressing effects can be manipulated by the detuning
and power of the incident fields. So both correlation and
squeezing can be changed via the detuning and power.

### 2.2.3 Coherence time and decay rate of Stokes and anti-Stokes

Besides, we investigate the coherence time of the generated intensity noise correlation. The intensity of Stokes or anti-Stokes signal is related to the respective number of photon and can be expressed by

where Γ_{S}/Γ

_{aS}are decay rates whose values are different in Λ and V type system. In the Λ system, Γ

_{S2}= Γ

_{13}+ Γ

_{30}+ Γ

_{10}and Γ

_{aS2}= Γ

_{10}+ Γ

_{30}+ Γ

_{10}, and for V level system Γ

_{S1}= Γ

_{20}+ Γ

_{00}+ Γ

_{20}and Γ

_{aS1}= Γ

_{10}+ Γ

_{00}+ Γ

_{20}, in which Γ

_{00}= (2πT

_{1})

_{0}

^{−1}+ (2π${T}_{2}^{\ast}$)

_{0}

^{−1}is the transverse dephasing rate of the ground state |0〉.

## 3. Results and discussions

#### 3.1 Intensity noise correlation and intensity difference squeezing with changing detuning

We first investigate the intensity noise correlation between the Stoke
and anti-Stokes signals in the Λ-type level system. Figure 2(a1) and 2(a2)
show the measured Stokes signal and the fourth order
fluorescence signal, respectively. These signals are obtained by
scanning Δ_{1} from −200GHz to 200 GHz and keeping
Δ_{3} = 0. The **E _{1}** and

**E**fields have horizontal polarization and their powers keep 2 mW. The fluorescence signal appears a suppression dip with a weak peak at resonance. This phenomenon can be explained by the dressing effect, which will change from single dressing (from

_{3}**E**

_{3}field) to double dressing (from

**E**

_{3}and

**E**

_{1}field) when Δ

_{1}is changed from −200/200 GHz to 0 GHz. Since the generated Stokes signal is less sensitive to dressing effect than fluorescence signal, so we cannot observed the double dressing from it [21].

Figures 2(b1-b7) show the
intensity noise correlations of Stokes and anti-Stokes versus delayed
time τ with different detuning Δ_{1}. The square points in
Fig. 2(d1) show the dependence
of correlation (with $\tau =0$) on detuning of Δ_{1}. It is
found that the correlation values ${G}_{}^{(2)}(0)$ become weaker when Δ_{1} is
tuned from larger detuning ( ± 200GHz) to near resonance ( ± 92GHz)
with the energy level $|1\u3009$, there exists a poorest correlation at
Δ_{1 =} −92/92 GHz. Then the correlation will slightly
increase when Δ_{1} is at resonance (0GHz). According to Eq. (5-8)
, ${G}_{}^{(2)}(0)$ depends on the nonlinear susceptibility
${\chi}_{S/aS}^{(3)}$. This result reflects the induced
modulation of nonlinear susceptibility (${\chi}_{S/aS}^{(3)}$) by the dressing effect. The
${\chi}_{S/aS}^{(3)}$ is function of the density matrix
elements ${\rho}_{(S/aS)}^{(3)}$, in which dressing terms
${G}_{3}{|}^{2}/[{\Gamma}_{13}+i({\Delta}_{1}-{\Delta}_{3})]$ of **E**
_{3} and
${G}_{1}{|}^{2}/[{\Gamma}_{13}+i{\Delta}_{1}]$ of **E**
_{1} in Eq. (1-2)
will affect ${\chi}_{S/aS}^{(3)}$. When we tune Δ_{1} near the two
dressed states, the nonlinear optical susceptibility${\chi}_{S/aS}^{(3)}$ can be enhanced due to the two-photon
resonance [22]. So we can
control the intensity-noise correlation by altering Δ_{1}.
When Δ_{1} is set to −200/200 GHz, the
**E**
_{1} field will be near-resonant to the two
dressed states, therefore, the ${\chi}_{S/aS}^{(3)}$ can be enhanced. Hence the correlation
is the highest at −200/200 GHz. When Δ_{1} is tuned away from
the two dressed states, the ${\chi}_{S/aS}^{(3)}$ will gradually decrease as shown at
points −170/170 GHz and −92/92 GHz. According to the above
dressed-state analysis, at Δ_{1} = 0, the correlation should
be the poorest. However, the correlation at Δ_{1} = 0 is
higher than that at −92/92 GHz. This is because the dressing from
**E**
_{1} field is also active at Δ_{1} = 0,
where the higher correlation is induced by double dressing from
**E**
_{1} and **E**
_{3}. These
results are also shown through theoretical simulation of dressed
correlation function of Eq.
(8) in Fig. 2(f1-f4) in
accordance with Fig. 2(b1-b4),
respectively. The experimental results agree well with the theoretical
simulated results.

At the meantime, by substituting the detected intensity data into Eq. (10), we can also obtain
the intensity-difference squeezing of Stokes and anti-Stokes signal as
shown in Figs. 2(c1-c7), where
the intensity-difference squeezing ${\delta}^{2}({\widehat{N}}_{S}-{\widehat{N}}_{aS})$ and the total sum of noise spectra
${\delta}^{2}({\widehat{N}}_{S}+{\widehat{N}}_{aS})$ versus $\text{\omega}$ are shown by the lower curves and the
higher curves, respectively. According to Eq. (5) and (10)
, the squeezing also depends on
${\chi}_{S/aS}^{(3)}$. Figure
2(d2) gives the degree of squeezing amount at different
detuning Δ_{1} when the analysis frequency $\text{\omega}$ is set at 1.5MHz. One can easily see
that the intensity-difference squeezing in Fig. 2(c) have the same behavior with that of
correlation in Fig. 2(b).
Hence, by changing Δ_{1} and then the dressing effect, the
degree of intensity-difference squeezing of the output
**E**
_{S} and **E**
_{aS} fields can
also be controlled. Figures
2(f5-f8) show theoretical simulation of squeezing by Eq. (10) corresponding to
experimental result of squeezing ((Fig. 2(c1-c4)). The experimental results can be well explained
by the theoretical model.

Now we investigate the intensity noise correlation in a V-type level
system with the same power and polarization defined for Λ-type level
system. The intensities of Stokes signal and fourth order fluorescence
signal are shown in Figs. 3(a1) and
(a2)
, respectively, with Δ_{1} scanned (−200 to 200 GHz) and
Δ_{2}(Δ_{2} = 0) fixed. Differentiating from the
signal in Λ-type level system (a suppression dip), the fluorescence
signal in V-type level shows an emission peak. This indicates the
energy levels of V-type system are less sensitive to dressing effect
than that in Λ-type system, because the dressing effect between levels
of individual ion is stronger than hetero-nuclear-like
configuration.

Following the same procedure just as in the Λ–type system, the
intensity noise correlations between Stokes and anti-Stokes and their
intensity difference squeezing are obtained as shown in Figs. 3(b1-b7) and 3(c1-c7),
respectively. Figures 3(d1) and
3(d2) show the dependence of correlation function
${G}_{}^{(2)}(0)$ at $\tau =0$ and squeezing at $\omega =1.5MHz$ versus Δ_{1}, respectively. In
Figs. 3(b1-b7), it is found
that the correlation value ${G}_{}^{(2)}(0)$ has large value at ± 200GHz and
decreases when Δ_{1} is tuned to ± 170 GHz. However, it
increases with further decrease of Δ_{1}, and then slightly
decreases when Δ_{1} is set at resonance. This result also
reflects the dressing-induced modulation of ${\chi}_{S/aS}^{(3)}$, but the phenomenon is not exactly the
same to the Λ–type system. From Eq. (3-4)
we can find
a different nested dressing term $|{G}_{2}{|}^{2}/[{\Gamma}_{20}+i({\Delta}_{2}-{\Delta}_{1})+|{G}_{1}{|}^{2}/({\Gamma}_{01}-i{\Delta}_{1})]$ in the V–type system. When Δ_{1}
is tuned near the 0GHz, the higher-order nonlinear process becomes
strong and interferes with the SP-FWM process. Hence oscillation of
the correlation can be observed near the 0GHz. Again, squeezing in
Fig. 3(c) has the same behavior
as the correlation. Comparing V–type with Λ–type system, besides the
oscillation of correlation and squeezing, the maximum value of the
correlation and squeezing are obtained in Λ–type system is larger than
that in V–type system.

#### 3.2 Intensity noise correlation and intensity difference squeezing with changing power

Subsequently, we investigate the power dependence of the correlation
and squeezing. Five curves in Fig.
4(a1)
show the intensity of output Stokes signal versus Δ_{1}
(from −200GHz to 200GHz) with fixed Δ_{3} = 0 in the Λ-type
level system, while the power P_{3} are changed from 1mW to
5mW. The signal strength increases with the power P_{3} up to
4mW due to the gain effect of **E**
_{3} field, but
then decrease at 5 mW due to enhanced dressing effect from
**E**
_{3} field. Figure 4(a2) shows the measured fourth-order fluorescence
signals versus Δ_{1} in the same way as the Fig. 4(a1). One can see the depth of
the suppressed dip is same, but the baseline increases with
P_{3} at first, and then decreases when P_{3} = 5mW.
The baseline indicated by short-dashed curve is the non-resonant
fluorescence, which presents similar changing trend with P_{3}
from the gain effect to dressing effect.

Figures 4(b1-b5) show the
correlation functions ${G}_{}^{(2)}(\tau )$ at different powers. The corresponding
intensity-difference squeezing is shown in Figs. 4(c1-c5), Figs. 4(d1) and 4(d2) is the correlation dependence of
${G}_{}^{(2)}(0)$ and squeezing dependence at 1.5 MHz,
respectively. From Figs.
4(b1-b5) we can find the correlation value ${G}_{}^{(2)}(0)$ increases first with power P_{3}
from 1mW to 4mW. But ${G}_{}^{(2)}(0)$ tends to decrease when the power reaches
P_{3} = 5mW. At low power region, **E**
_{3}
field mainly acts as a generation field, nonlinear gain increases with
${G}_{3}=\mu {E}_{3}/\hslash $, so the correlation value
${G}_{}^{(2)}(0)$increases. When the power of
**E**
_{3} field is strong enough, we should consider
dressing effect from **E**
_{3}. According to Eq. (1-2)
, the density matrix elements will
decrease with ${G}_{3}$, so the correlation decreases. The
intensity difference squeezing as shown in Figs. 4(c1-c5) has the same behavior with the
correlation.

Figures 4(e1) and 4(e2) show the
decay rate and the calculated correlation time of SP-FWM,
respectively. Because the decoherence rate Γ_{S2} =
Γ_{13} + Γ_{30} + Γ_{10} and Γ_{aS2} =
Γ_{10} + Γ_{30} + Γ_{10} is caused by the
combination of the dressing effect and induced dipole-dipole
interaction (in turn, *H*-*H** states
and *D*-*D* states, respectively), so
one can see that decoherence rate increases with increasing power
until the dressing effect is not dominant, then begins to decrease
once the dressing effect gets dominant. On the other hand, because the
PC-FWM signals are from the coherent processes, so the correlation
times are determined by decoherence time (or inversely proportional to
decoherence rate) of PC-FWM process, one can see inverse evolution on
power between decay rate and the correlation time.

Figure 5(a1) and (a2)
show the intensities of output Stokes signal and fourth-order
fluorescence signals at different power P_{2} in the V-type
level system, respectively. We can see the fourth-order fluorescence
signals change from a generation peak to a suppressed dip with
P_{2} increasing because the dressing effect of
**E**
_{2} field enhances. The baseline is the
second-order fluorescence from |2〉 to |0〉, which is increased with
P_{2} due to gain effect. At the same time, the SP-FWM signals
also become stronger with the increasing of P_{2}. The
dressing effect on SP-FWM in V-type level system is weaker than that
of Λ-type system. Figures
5(b1-b5) give the correlation functions between Stokes and
anti-Stokes signals with power P_{2} increasing. Following,
the corresponding intensity-difference squeezing at different
P_{2} are shown in Figs.
5(c1-c5). Figures 5(d1) and
5(d2) show the corresponding correlation value ${G}_{}^{(2)}(0)$and the squeezing amount at 1.5 MHz,
respectively. The correlation and squeezing increases with the same
fashion as increased power due to increased nonlinear gain. Unlike the
Λ-type level system, where correlation and squeezing decreases at high
power due to enhanced dressing effect, the V-type system is less
sensitive to dressing of **E**
_{2} field. The power
dependences of decay rate and correlation time (as shown in Figs. 5(e1) and 5(e2)) in V-type
system are as similar as that in Λ-type system.

## 4. Conclusion

The dressed noise correlation and intensity-difference squeezing based on
SP-FWM process in Pr^{3+}:Y_{2}SiO_{5} crystals
have been observed experimentally and theoretically both in Λ-type and
V-type systems. We observed that the degree of correlation and squeezing
of the Stokes and anti-Stokes signals can be controlled by detuning and
power. These results are attributed to dressing-induced modulation of
nonlinear susceptibility. It is also observed difference of correlation
behaviors between Λ-type and V-type systems due to different dressing
effects on levels of individual ion and hetero-nuclear-like configuration.
Further, the noise correlation and the intensity-difference squeezing are
dependent on power of optical field. So we can control them by power
easily. It is clearly seen that the dressed results of squeezing have the
same behavior with the correlation. In addition, we find the dressing
effect can also be observed through the fourth-order fluorescence signals.
We also studied the power dependences of correlation time and decoherence
rate. Results predict that the decoherence rate increases with increasing
power until the dressing effect is not dominant. Once the dressing effect
gets dominant, the decoherence rate starts to decrease. Such controllable
intensity correlation and squeezing of SP-FWM process can be used to
fabricate entangled light sources in quantum communication.

## Acknowledgments

This work was supported by the National Basic Research Program of China (2012CB921804), the National Natural Science Foundation of China (11474228, 61205112), and Key Scientific and Technological Innovation Team of Shaanxi Province (2014KCT-10).

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