Competition between Polarization-Dressing and Phonon Effects inFourth-Order Fluorescence of Pr3+:Y2SiO5

Ruimin Wang,* Tianyi Xie, Xinghua Li, Wei Li, Yameng Li, Jianyong Mao, and Yanpeng Zhang*

School of Science, Key Laboratory for Physical Electronics and Devices of the Ministry of Education, and Shaanxi Key Lab ofInformation Photonic Technique, Xi’an Jiaotong University, Xi’an 710049, China

ABSTRACT: We report modulating spontaneous four-wave mixing, fourth-order fluorescence, and intensity noise correlation by polarization-dressingeffect at different temperatures in a Pr3+:Y2SiO5 crystal. The delay time,Autler−Townes splitting, and shape of correlation curve are changedobservably with temperature and polarization state of dressing field. Theseresults demonstrate competition between polarization-dressing and phononeffects. The impact of temperature on nonlinear response is very important forthe stability of quantum optical devices.

I. INTRODUCTION

Rare-earth ion-doped crystal has been widely studied becauseof its advantages for coherent excitation and because it is moreappropriate for practical applications. Recent researches onquantum coherence effect in rare-earth ion have been reported,including electromagnetically induced transparency (EIT),1,2

stimulated Raman adiabatic passage,3 light velocity reduction,coherent storage,4,5 and all-optical routing.6 A Pr3+-dopedY2SiO5 crystal has long coherence time and narrow spectralwidth as compared to traditional nonlinear crystals. So, theatomic coherence can be induced easily in Pr3+:Y2SiO5. Rare-earth ion-doped crystal can find potential applications in all-optical communication and optical information processing onthe photonic chip.In practical applications, coherent excitation processes are

required to be controlled reliably. Polarization-dressing effectoffers a method to modulate the coherent transition. Becausedifferent polarization states of pumping field correspond todifferent transition ways in Zeeman levels, the EIT processescan be controlled via polarization-dressing effect.7,8 Weinvestigated polarization-dressed multi-order fluorescence(FL) and spontaneous four-wave mixing (SFWM) in thePr3+:Y2SiO5 crystal at low temperature.9,10 We can controldressing signals by changing power, detuning, and polar-ization.11 The correlation and squeezing of FWM signal canalso be modulated via polarized dark states.12 Correlation andanticorrelation have been observed at different polarizationstates.13 Such polarization-dressed signals have potentialapplications such as all-optical switch and route devices.14

Recently, hybrid correlation between different types of stateswas identified as a useful resource for optical quantuminformation processing and quantum computing.15,16 Hybridcorrelation between SFWM and multi-order fluorescence hasalso been obtained in the Pr3+:Y2SiO5 crystal.

17

In our previous works, all experiments were carried out atlow temperature, so the phonon effect has never been

considered. In practical applications, temperature plays animportant role in device stability. Phonon effect cansignificantly affect the nonlinear response of quantum opticaldevices with increasing temperature. In this paper, weinvestigate the polarization-dressing effect of fourth-orderfluorescence at different temperatures. In this case, phononeffect must be considered. Our results indicate that thepolarization-dressing effect competed with phonon effect. Wealso modulate the hybrid correlation shape by cross-phasemodulation. Research about competition between polarization-dressing and phonon effects is very important for obtaining ahybrid signal resource, controlling quantum optical devices,and improving the stability of all-optical devices.

II. THEORETICAL MODELIn a V-type three-level system with two pumping fields E1 andE2 opening, the four-wave mixing and fluorescence signals aregenerated simultaneously. The intensity of FWM is propor-tional to the third-order nonlinear density matrix elements.The third-order nonlinear density matrix elements for StokesES and anti-Stokes EAS signals can be written as

ρ =−

Γ + + + +| | | | | |Γ

| |Γ( )( )( )

iG G G

d dGd

Gd

G GS1(3) 2 AS2 1

00 2 12

2

2

12

1

22

22

12

11 (1)

ρ =−

+ + Γ + +| |Γ

| |Γ

| | | |( )( )( )iG G G

d dG G Gd

Gd

AS2(3) 2 S1 1

2 1 002

2

22

12

11

22

2

12

1

(2)

where d1 = Γ10 + iΔ1 and d2 = Γ20 + iΔ2. Γij is the transversedecay rate. Gi = μiEi/ℏ is the Rabi frequency of the incident

Received: October 11, 2018Accepted: January 2, 2019Published: January 15, 2019

Article

http://pubs.acs.org/journal/acsodfCite This: ACS Omega 2019, 4, 1215−1220

© 2019 American Chemical Society 1215 DOI: 10.1021/acsomega.8b02770ACS Omega 2019, 4, 1215−1220

This is an open access article published under an ACS AuthorChoice License, which permitscopying and redistribution of the article or any adaptations for non-commercial purposes.

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field Ei. In eqs 1 and 2, we consider the self-dressing effect ofE1 and the external-dressing effect of E2 simultaneously. In thissystem, the detected signal intensity is the sum of twofluorescence signals, FL1 and FL2. The density matrixelements of fourth-order fluorescence are

ρ =| |

+ + Γ + +

×| |

+ + Γ +

| |Γ

| | | | | |

| |Γ

| | | |

( )( )

( )( )

G

d

G

d

G Gd

Gd

Gd

G Gd

Gd

FL1(4) 2

2

2 00

12

1 11

22

00

12

21

12

1

22

2

12

00

22

12

12

1 (3)

ρ =| |

+ + Γ + +

×| |

+ + Γ +

| |Γ

| | | | | |

| |Γ

| | | |

( )( )

( )( )

G

d

G

d

G Gd

Gd

Gd

G Gd

Gd

FL2(4) 1

2

1 00

22

2 22

12

00

22

12

12

1

22

2

22

00

12

21

22

2 (4)

where d12 = Γ12 + i(Δ1 − Δ2) and d21 = Γ21 + i(Δ2 − Δ1).Similarly, in a Λ-type three-level system, the third-order

nonlinear density matrix elements for Stokes and anti-Stokessignals ES1 and EAS3 are given by

ρ =−

+ + +

×Γ + +

| |Γ

| | | |Γ

| | | |′( )

( )( )iG G G

d d

1

G Gd

G

Gd

G

d

S1(3) 3 AS3 1

3 13

03

32

11

12

30

12

03

12

13

32

10 (5)

ρ =−

+ + +

×Γ + +

| | | |Γ

| |Γ

| | | |

( )( )

( )

iG G G

d d

1

Gd

G G

Gd

Gd

AS3(3) 3 S1 1

1 10

30

32

30

12

11

32

30

32

10

12

13 (6)

The density matrix elements of FL1 are

ρ =| |

+ +

×| |

+ + Γ + +

| |Γ

| |

| |Γ

| | | | | |

( )

( )( )

G

d

G

d

G Gd

G Gd

Gd

Gd

11(4) 1

2

1

32

3 11

2

12

11

32

30

32

11

12

30

32

3

12

1 (7)

where d3 = Γ13 + iΔ3, d30 = Γ03 + i(Δ3 − Δ1), d13 = Γ13 + iΔ1,and d10

′ = Γ01 − iΔ3.In the experiment, generated FWM signals are reflected by a

polarized beam splitter, and the vertically polarized componentof FWM signals is detected. So, the effective density matrixelements can be written as ρ(y)

(3) = ρ(xxyy)(3) + ρ(yyyy)

(3) . We use a half-wave plate (HWP) to modulate the polarization direction ofincident field Ei, and the dependence of Rabi frequency onpolarization angle can be described as cx

2|Gi|2cos22θ for ρ(xxyy)

(3)

and cy2|Gi|

2sin22θ for ρ(yyyy)(3) . When a quarter-wave plate (QWP)

is used to change the polarization state of incident field, theRabi frequency is cx

2|Gip|2 (cos4 θ + sin4 θ) for ρ(xxyy)

(3) and cy2|

Gip|2 sin2 θ cos2 θ for ρ(yyyy)

(3) , respectively, where θ is defined asthe rotated angle of the WP’s axis from the x axis and cx,y is the

anisotropic factor in different directions of crystal. Gip(p =−,0,

+) is the Rabi frequency of a pumping field with left circular,linear, and right circular polarization, respectively. Differentlaser polarization states have different Clebsch−Gordan (CG)coefficients.When strong pumping fields couple with energy levels,

energy levels will split as induced by the dressing effect. In theV-type three-level system, ground state |0⟩ is split into |±⟩dressing levels by E2. Considering the excitation of pumpingfield E1 and dressing effect of E2, there are two spontaneousemissions from |2⟩ to |±⟩ dressing levels. The wavelength oftwo spontaneous emis s ions can be wr i t ten as

λ = [ − Δ ± Δ + | | ]± G( 1) 4 /2i2 2

22

2 .18 Therefore, the split-

ting distance between |+⟩ and |−⟩ is Δ = Δ + | |± G422

22 .

Moreover, considering the self-dressing effect of E1, the

splitting distance can be expressed as Δ = | | + | |± G G2 12

22

when Δ1 = Δ2 = 0. Similarly, in the Λ-type three-level system,excited state |1⟩ is split into |±⟩ dressing levels by E3 and E1

with distance Δ = | | + | |± G G2 12

32 .

The linewidth (Γ) of the measured fluorescence signal isdetermined by the longitudinal relaxation time (T1) andtransverse relaxation time (T2), that is, Γ = (2πT1)

−1 +(2πT2)

−1, where T1 is determined by the width of energy leveland T2 by the dephasing rate. Considering the dressing level,the broadened linewidth of the fluorescence signal can befurther described as Γ = Γpop + Γion‑spin + Γion‑ion + Γphonon −Γ(Δ±), where Γpop = (2πT1)

−1 depends on the location of theenergy level in phase space, Γion‑spin relates to the ion-spincoupling effect of the individual ion, and Γion‑ion is determinedby the interaction among the rare-earth ions, which can becontrolled by the power of external field and impurityconcentration. Phonon relaxation rate is given by Γphonon ∝2π[n(ω, T) + 1]/h, where n(ω, T) = 1/[exp(ω/kBT) − 1] isthe thermal occupation of phonon mode. So, Γphonon is relatedto the temperature of the sample. Γ(Δ±) represents thelocation of the energy level induced by dressing fields.In our experiment, the FWM and fourth-order FL signals

were illuminated by the same pumping fields and weregenerated simultaneously, so the correlation exists betweenthem. The intensity noise correlation function G(2)(τ) can beexpressed as

τδρ δρ

δρ δρ

φ

=⟨ [ ]⟩

⟨[ ] ⟩⟨{ [ ]} ⟩

Δ

Gt t

t t( )

( )Im ( )

( ) Im ( )

cos( )

(2) FL(4)

FL S/AS(3)

S/AS

FL(4)

42

S/AS(3)

S/AS2

(8)

where Δφ = φS/AS − φFL, φS/AS is the initial phase of FWM,and φFL is the dressed phase of fourth-order FL. So, thecorrelation functions change with the dressing nonlinear phasevia cross-Kerr effect.

III. RESULTS AND DISCUSSION

Figure 1 shows FL signals in a time domain detected byphotomultiplier tube D3 in Λ-type (Figure 1a−c) and V-type(Figure 1d−f) three-level systems. There are two peaks inthese hybrid signals. The right peak is attributed to theadiabatic population transfer between dressed states, whereasthe left peak is the contribution of SFWM without adiabaticpopulation transfer. In the Λ-type three-level system, excited

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state |1⟩ is split into |G1±⟩ caused by E1. Dressing level |G1+⟩ isfurther split into |G2+±⟩ induced by E3. The transfer ofpopulation can occur between dressing levels through phonon-assisted nonradioactive transition. We attribute the delay ofright peak to the transfer of residual particles between |G2++⟩and |G1−⟩. The delay time of right peak is determined by thedistance between |G2++⟩ and |G1−⟩. One can see that the delaytime decreases with the increase of temperature both in Λ-typeand V-type three-level systems. This effect results from thecompetition between dressing and phonon effects. Phononrelaxation rate Γphonon ∝ 2π[n(ω, T) + 1]/h includes puredephasing contributions from temperature-dependent phononscattering. At high temperature, dressed state levels arebroadened by the phonon effect, which causes the splittingdistance of dressed state to decrease. Considering the phononbroadening, we can write the expression of the splitting

distance as Δ = | | + | | − Γ± G G2 ( )12

2,32

phonon2 . At room

temperature, the dressing effect is balanced by the phononeffect, so two peaks combine into one peak. At lowtemperature, phonon relaxation rate Γphonon decreases, whichcauses the transition distance between dressing levels toincrease. As a result, the right peak presents obvious delay. Inaddition, the proportion of FWM and FL in hybrid signals alsochanges with temperature.Next, we investigate the polarization-dressing effect on delay

time when the dressing field E2 (or E3) is changed by QWP. At77 K, when the polarization state of dressing field changes fromcircular to linear, one can see that the delay time of right peakincreases. In this case, the splitting distance is replaced by

θ θΔ = | | + | | +± G c G2 (cos sin )xi

12 2

2,32 4 4 . Because the

Rabi frequency of a linearly polarized state (cx2G2,3

0) is greaterthan that of a circularly polarized state (cx

2G2,3+ / 2), the delay

time of the linearly polarized state is longer than that of thecircularly polarized state. With the temperature increasing,polarization dependence of delay time becomes not obviousbecause of competition between dressing and phonon effects.Such splitting and delay hybrid signals can be exploited for all-optical transistor switching applications.14,19

Figure 2 shows FL signals in a frequency domain detected atdifferent polarization-dressing states and different temper-atures. The detuning Δ2,3 is set at Δ2,3 = 0, and Δ1 is scanned.One can observe the obvious decrease in linewidth withtemperature decreasing, and FL curves show Autler−Townes(AT) splitting at low temperature. The linewidth of thefluorescence signal depends on Γ = Γpop + Γion‑spin + Γion‑ion +Γphonon − Γ(Δ±), whereas AT splitting is caused by thedressing effect. One can easily predict that phonon effect

Γphonon is dominant at room temperature, so the linewidth ofthe FL curve increases. Moreover, the splitting distance of

dressed state level Δ = | | + | | − Γ± G G2 ( )12

2,32

phonon2 is

decreased because of the phonon broadening effect, so ATsplitting disappears. When the temperature is below 110K, thephonon effect Γphonon decreases, and the dressing effect isdominant, which result in obvious AT splitting.Now, we compare the polarization-dressing effect on AT

splitting when the polarization state of dressing field E2 (or E3)is changed by QWP. With the rotation angle of QWP changingfrom 0 to 45°, the depth of the suppressed dip reduces. Theexternal-dressing effect of E2,3 on spectra splitting is reflectedby |G2,3|

2/d2,3 (in eqs 3 and 7). Because of different CGcoefficients, the dressing effect of the linearly polarized field(cx

2|G2,30|2/d2,3) is stronger than that of the circularly polarized

field (cx2|G2,3

+ |2/2d2,3), which leads to the decrease of ATsplitting depth from 0 to 45°.At room temperature, AT splitting disappears due to

phonon effect. The fluorescence emission peaks increasegradually from linear to circular polarization in the Λ-typesystem. On the contrary, they decrease from linear to circularpolarization in the V-type system. In the Λ-type system, thereis only one signal FL1 from site I, and E3 acts as an external-dressing field. The suppression dressing effect of linearpolarization is stronger than circular polarization, sofluorescence emission peak increases from linear to circularpolarization. In the V-type system, there are two signals, FL1and FL2, from sites I and II, respectively. E3 acts as theexternal-dressing field for FL1 and the generating field for FL2simultaneously. The generating effect becomes weak fromlinear to circular polarization, which causes the intensity offluorescence emission peak to decrease.Next, we modulate the fourth-order FL signal by changing

the frequency detuning Δ2 of dressing field (as shown in Figure3). At 77 K, the FL peak evolves from AT splitting to puresuppression dip, with Δ2 changing from large detuning toresonance. When Δ2 is tuned close to the resonant point, thedress terms |G2|

2/d2 and |G2|2/d12 in eqs 3 and 4 increase.

Because of the satisfaction of suppression condition Δ1 + Δ2 =0 in the experiment, the suppression effect and AT splittingdepth increase. Because the temperature increased to 110 K,the evolution of FL peak with frequency detuning Δ2 was lessobvious. This is attributed to the dressing phonon interactionterm |G2|

2/(Γ20 + iΔ2). With the temperature increasing, Γ20 isincreased because of the phonon broadening effect, whichcounteracts the dressing effect. As a result, the spectrum is lesssensitive to the frequency detuning of dressing field at high

Figure 1. FL composite signals in a time domain detected at differenttemperatures and polarization states. (a−c) Λ-Type three-levelsystem. (d−f) V-type three-level system. 1−3 represent linearlypolarized, elliptically polarized, and circularly polarized states ofdressing field, respectively.

Figure 2. FL composite signals in a frequency domain detected atdifferent temperatures and polarization states. 1−3 represent linearlypolarized, elliptically polarized, and circularly polarized states ofdressing field, respectively. (a−c) Λ-Type three-level system. (d−f) V-type three-level system.

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temperature. Such controllable splitting and suppressionsignals have potential applications in all-optical router andswitching devices.Finally, we investigate the intensity noise correlation of

hybrid signals. Correlation properties of hybrid signals can beused to reduce the noise level of quantum optical devices.Figure 4a,b shows the intensity noise correlation function

G(2)(τ) between Stokes and FL composite signals at 110 and77 K, respectively. An HWP is used to change the polarizationdirection of E1. When the polarization direction of E1 ischanged from horizontal (0°) to vertical polarization (45°), wefind that the correlation values G(2)(0) decrease both at 77 and110 K. With θ changing from 0 to 45°, the generating termscx2|G1|

2 in eqs 1 and 3 change to cy2|G1|

2, and the intensities ofSFWM and FL signals decrease. As a result, the correlationvalues decrease.For correlation curves at 77 K, it is shown obviously that a

sharp peak superimposed on each curve of the correlation at τ= 0. As shown in Figure 1, FL composite signals have twopeaks in the time domain. The left peak is the contribution ofSFWM, whereas the right peak is caused by the phonon-assisted FL process. The shape of the hybrid correlationfunction for SFWM and FL composite signals is determined by

τ= | | [ +

− Ω | | ]

ζ τ ζ τ

ζ τ

− Γ +Γ + | | − Γ +Γ + | |

− Γ +Γ +Γ +Γ + | |

+ + − −

+ + − −A R A e e

e2 cos( )e

1 12 2( ) 2( )

2( )

S FL S FL

S FL S FL (9)

The parameter ζ represents the bandwidth of the laser source.Correlation shape is primarily affected by the decay rates Γ ofSFWM and FL signals, and decay rates can be affected by thephonon and dressing effects. We observe that the shape ofcorrelation curve follows the intensity of the composite signaland the competition between SFWM and FL signals. At 77 K,the phonon effect decreases, and the proportion of SFWM incomposite signal is large, so the sharp peak of correlation curveis more obvious. With the temperature increase, the phonon-assisted FL process is enhanced, and the proportion of SFWM

is reduced. Therefore, the sharp peak of correlation curve issmall.Figure 5 shows the correlation functions of ES-FL and ES-

EAS at 110 K when a QWP is used to change the polarization

state of E2. In Figure 5a, we find that the maximum correlationbetween ES and FL is obtained at the linearly polarized state (θ= 0o). When the polarization state of dressing field E2 changesfrom linearly polarized to right circularly polarized (θ = 45°),the correlation peaks decrease at first and then switch fromcorrelation to anticorrelation. This result may be explained bythe cross-phase modulation (XPM) induced by dressing fieldE2. In eq 8, the nonlinear phase shift between ES and FL can be

characterized as Δφ = 2(kSn2S − kFLn2

FL)|E2|2e−r

2

z/n1, where n2 =Re χ(3)/ε0cn1 is the nonlinear refractive index of the Kerrmedium, r is the beam radius of dressing field, and z is thelength of the YSO crystal. When the polarization of thedressing field E2 is changed from linearly polarized to rightcircularly polarized, the effective Rabi frequency and third-order effective susceptibility can be modulated. Therefore, thenonlinear phase shift between ES and FL is changed.Correspondingly, the correlation value switches from positiveto negative.Figure 5b shows the correlation functions between ES and

EAS signals. When the polarization state of E2 changes fromlinearly polarized to circularly polarized, the correlation valueG(2)(0) decreases first and then increases at 45°. G(2)(0)achieves its minimum value at an elliptically polarized state.The variation of G(2)(0) results from the competition betweengain and dressing effect of E2. Moreover, anticorrelation effectwas not observed between ES and EAS. For the SFWM process,it is insensitive to dressing effect, and the phase differencebetween ES and EAS is smaller because of the coherent natureas compared to the incoherent FL signal. So, all values ofG(2)(0) are positive.

IV. CONCLUSIONSIn summary, we have investigated hybrid signals includingfourth-order fluorescence and SFWM in both time andfrequency domains at different temperatures and modulatedby different polarization-dressing fields. By changing theexperiment temperature and polarization states of dressingfields, the delay time, AT splitting, and proportion of SFWMand FL in hybrid signals are modulated desirably. Ourexperiment data are in good agreement with the theoreticalresults of competition between polarization-dressing andphonon effects.

Figure 3. FL composite signals in a frequency domain detected atdifferent detuning of dressing field E2 in the V-type three-level system.

Figure 4. (a, b) Intensity noise correlation function G(2)(τ) betweenES and FL signals in the V-type three-level system detected at (a) 110K and (b) 77 K, respectively. The polarization direction of E1 ischanged by HWP.

Figure 5. Correlation function G(2)(τ) in the V-type three-levelsystem detected at 110 K. The polarization state of E2 is changed byQWP. (a) Correlation between Stokes and fluorescence signals (ES-FL). (b) Correlation between Stokes and anti-Stokes signals (ES-EAS).

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In addition, the polarization dependences of hybridcorrelation are compared at different temperatures. It isfound that the competition between SFWM and FL signalsdetermines the correlation shape and can be modulated bydressing and phonon effects. The switches between correlationand anticorrelation of hybrid signals are observed at differentpolarization states and attributed to cross-phase modulationinduced by the dressing field. Our results demonstrate thatphonon effect can significantly affect the nonlinear response ofquantum optical devices. The dressing phonon interactionplays a vital role in determining the controlling parameters ofquantum optical devices.

V. EXPERIMENTAL SETUPOur experiments are carried out in a rare-earth Pr3+-dopedY2SiO5 crystal, the concentration of Pr

3+ ion is about 0.05 atom%. The energy levels 3H4 and

1D2 of Pr3+ ion are selected to

couple with the pumping field. There are two crystallographicsites (denoted as sites I and II) of Pr3+ ions in the Y2SiO5crystal; Figure 6a shows their energy levels. Because two

crystallographic sites have different Stark splitting, we candetect two fluorescence signals, FL1 (γ0 to δ0) and FL2 (γ0* toδ0*). Because of the dipole−dipole interactions, we treat ionsPr3+(I) and Pr3+(II) as heteronuclear molecules. Therefore, wecan construct the Λ-type three-level |0⟩ ↔ |1⟩ ↔ |3⟩ (Figure6c) and V-type three-level |0⟩ ↔ |1⟩ ↔ |2⟩ systems.The experimental setup is shown in Figure 6b. As pumping

fields, we used three tunable dye lasers (narrow scan with a0.04 cm−1 linewidth) pumped by an injection-locked single-mode Nd:YAG laser (Continuum Powerlite DLS 9010, 10 Hzrepetition rate, 5 ns pulse width). The pumping fields E1 (ω1,Δ1), E2 (ω2, Δ2), and E3 (ω3, Δ3) have the frequency detuningΔi = ωmn − ωi (i = 1, 2, and 3), where ωmn denotes thecorresponding atomic transition frequency and ωi is the laserfrequency. Two strong beams, E1 and E2 (or E3), counter-propagate through the YSO crystal, and the generated forwardStokes ES and backward anti-Stokes EAS signals satisfy thephase-matching condition k1 + k2,3 = kS1 + kAS2,3, where k1,2 isthe wavevector of the pumping fields and kS, AS is thewavevector of generated ES and EAS beams. The FL signal

can be detected at any direction, but it diminishes quickly withdistance. To detect pure SFWM signals, two photomultipliertubes (D1 and D2) are placed at far position, wherefluorescence almost vanished. Another PMT (D3) placed atnear position is used to collect the hybrid signal (FL +SFWM). The polarization state of pumping fields is changedby quarter-wave plate (QWP) and half-wave plate (HWP).

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: wangrm@mail.xjtu.edu.cn (R.W.).*E-mail: ypzhang@mail.xjtu.edu.cn (Y.Z.).ORCIDYanpeng Zhang: 0000-0002-0954-7681NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis work was sponsored by the National Key R&D Programof China (2017YFA0303700), the National Natural ScienceFoundation of China (11474228, 61605154, and 11604256),and the Key Scientific and Technological Innovation Team ofShaanxi Province (2014KCT-10).

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Figure 6. (a) Simplified energy-level diagram of Pr3+ ions in a YSOcrystal. (b) Experimental setup. D: photomultiplier tube; PBS:polarized beam splitter; WP: wave plate; L: lens. (c, d) Λ-Type andV-type three-level systems in Pr3+:Y2SiO5.

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