Observation of Autler−Townes Splitting of Second-OrderFluorescence in Pr3+:YSODan Zhang, Huayan Lan, Changbiao Li, Huaibin Zheng, Chengjun Lei, Ruimin Wang, Imran Metlo,and Yanpeng Zhang*
Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information PhotonicTechnique, Xi’an Jiaotong University, Xi’an 710049, China
ABSTRACT: We investigate the second-order fluorescence (FL) signals of Pr3+:YSOboth theoretically and experimentally. For the first time, the Autler−Townes (AT) splittingeffect of FL spectrum induced by itself and/or external fields and the polarizationdependence of FL signals in two-level, V-level, and N-level atomic systems are observedand explained. The AT splitting distance can be modulated by the frequency detunings,power, and polarization configurations of the incident fields which are well explained byusing the presented theoretical model.
1. INTRODUCTION
Atomic Autler−Townes (AT) splitting was first studied on aradio frequency transition1 and then in calcium atoms.2 Such anAT splitting effect was also observed in four-wave mixing(FWM) process in two-level systems.3 Besides, progressesrelated to atomic coherence4 in solid-state materials haveprovided bases for potential applications, such as opticalstorage,5 optical velocity reduction and reversible storage ofdouble light pulses,6 and controllable erasing of optically storedinformation.7 Also, the polarization properties of two-photonresonant FWM have been well investigated previously.8−11
Polarization states of the involved laser beams can play animportant role in FWM processes with atomic media involvingmulti-Zeeman sublevels.12 Several previous experimental andtheoretical studies have shown that FWM processes can beeffectively controlled by changing the polarization states andfrequency detunings of the involved laser beams.13,14
In this work, we show the all-optically-controlled fluores-cence (FL) process of Pr3+:YSO in a heteronuclear-likemolecule system theoretically and experimentally. The ATsplitting of FL spectrum induced by itself and/or external fieldsand the polarization dependence of FL signals in a two-level,three-level, and N-level atomic system are investigated. The ATsplitting distances can be modulated by the frequencydetunings, power, and polarization configurations of theincident fields. A theory model based on the second-order FLprocess is developed to explain these results, which agree withthe experimental data well. The paper is constructed as follows:in section 2, we show the experimental setup and introduce thetheory briefly; in section 3, we show and explain the experimentresults in detail; in section 4, we conclude the paper.
2. EXPERIMENTAL SETUP AND BASIC THEORYA. Experimental Setup. Figure 1a shows the relevant two-
energy-level diagram of 0.05% rare-earth Pr3+-doped Y2SiO5(Pr:YSO) crystal. Since it is easy to identify them reliably byinvestigating the optical spectrum of the Pr3+ ions, we confineourselves to a detailed analysis of the triplet energy level 3H4and singlet energy level 1D2 in the current work. Under theaction of the crystal field of YSO, the terms in 3H4 and 1D2states are split into nine and five Stark components, as shown inFigure 1a1, respectively. The Pr3+ impurity ions occupy twononequivalent cation sites (sites I and II, respectively) in theYSO crystal lattice. Considering the two nonequivalent cationsites, we can construct simplified energy-level and dressed-stateenergy-level diagrams for Pr3+ ion associated with the energybands for YSO crystal (see Figure 1a2), where the energy levelof the site is labeled by the one with an asterisk. In this work,the pump fields for the excitation processes of FL signals arecoupled into the transition δ0 (|0⟩)↔γ0 (|1⟩). Meanwhile, forFL processes, two hyperfine states ±5/2 (|0⟩) and ±3/2 (|2⟩)of δ0 and γ0 (|1⟩) are involved. In addition, with T = 77 K, thephonons in the crystal matrix participate in the nonradiativeenergy transport between Pr3+ ions localized at different cationvacancies in the YSO crystal.Figure 1b1 shows the simplified energy-level diagram of
0.05% rare-earth Pr:YSO crystal. The interaction between Pr3+
ions localized at different cation vacancies in the YSO crystalcan happen,15 and then one can treat the two ions asheteronuclear molecules. Considering the two nonequivalent
Received: March 7, 2014Revised: June 6, 2014Published: June 9, 2014
cation sites, we can construct a V-type three-level and dressed-state energy-level system (|0⟩↔|1⟩↔|2⟩) (see Figure 1b2),where the energy level of site I is labeled by a Greek letterwithout asterisk and the one for site II is labeled by the onewith an asterisk. Otherwise, the ground state |0⟩ of such aheteronuclear molecule is a degenerate state constituted by δ0and δ0* while the level |1⟩ (γ0) is from site I and |2⟩ (γ0*) fromsite II. Figure 1c shown the frequency domain of the typicalfluorescence signals, and the controlled results are monitoredby two photomultiplier tubes (PMTs).The sample (a 3 mm Pr:YSO crystal) is held at 77 K in a
cryostat (CFM-102). Three tunable dye lasers pumped by aninjection 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 E1 (ω1,Δ1), E2, andE2′(ω2,Δ2), and E3 (ω3, Δ3) with the frequency detuning of Δi= ωmn − ωi (i = 1, 2, and 3), respectively, where ωmn denotesthe corresponding atomic transition frequency.
B. Theoretical Calculations for FL. The FL signal can beused to monitor the interaction among the incident fields, andthe intensity of this signal can be expressed by the diagonalelements of the density matrix. Considering the dressing effect
of E1 (E2), via two probable pathways ρ00(0) →
E1ρ10(1) ⎯ →⎯⎯⎯
*E( )1ρ11(2) and
⎯ →⎯⎯⎯*E( )1ρ01(1)→
E1ρ11′(2) (ρ00(0) →
E2ρ20(1) ⎯ →⎯⎯⎯
*E( )2ρ22(2) and ρ00
(0) ⎯ →⎯⎯⎯*E( )2ρ02(1) →
E2
ρ22′(2)), we can obtain ρ11(2) = −|G1|
2/(Γ11d1) and ρ11′(2) = −|G1|2/
(Γ11d1′) (ρ22(2) = −|G2|
2/(d2Γ22) and ρ22′(2) = −|G2|2/(d2′Γ22)),
where d1 = Γ10 + iΔ1, d1′ = Γ01 − iΔ1, d2 = Γ20 + iΔ2, d2′ = Γ02 −iΔ2, Gi = −μijEi/ℏ is the Rabi frequency of Ei with μij theelectric dipole moment between levels |i⟩ and |j⟩, and Γij is thetransverse decay rate. The corresponding intensity of the totalfluorescence signals is IFL = ρ11
(2) + ρ11′(2) + ρ22(2) + ρ22′(2).
Here, we just focus on one of the two perturbation chains toanalyze the physical mechanism of the fluorescence signals. Thediagonal element ρ11
(2) (ρ22(2)) of the fluorescence signal is given
by16
ρ = −| | + | | Γ Γ + | |G d G G d/[( / )( / )]11(2)
12
1 12
00 11 12
1 (1a)
ρ = −| | + | | Γ Γ + | |G d G G d/[( / )( / )]22(2)
22
2 22
00 22 22
2 (1b)
With both beams on, the corresponding intensity of the totalFL signals is IFL = ρ11
(2) + ρ22(2).
In the V-type atomic system, Considering the interplay ofprocesses ρ11
(2) and ρ22(2), the diagonal element ρ11
(2) (ρ22(2)) can be
modified as follows:
ρ =−| |
+ | | Γ + | | Γ + Δ − Δ Γ + | |G
d G G i G d[ / /( ( ))]( / )11(2) 1
2
1 12
11 22
12 1 2 11 12
1
(2a)
ρ =−| |
′ + | | Γ + | | Γ + Δ − Δ Γ + | | ′G
d G G i G d[ / /( ( ))]( / )22(2) 2
2
2 22
22 12
21 2 1 22 22
2
(2b)
From eq 2, one can see that the output signal is a combinedsignal of the self-dressing effect of FL excited by E1 and theexternal-dressing effect of FL excited by E2 with mutualinteractions between them.
C. Dressed-State Picture with Generating FieldsScanned. We can obtain the absorption dip in FL signalswhen the frequency detuning of the generating field (i.e., Δ2) isscanned. The AT splitting of the emission peak can be observedif the signal is dressed by self- and external-dressing fields Eiand Ej (i, j = 1, 2, 4, and i ≠ j). The primary AT splittingcorresponds to the primary dressed states |±⟩ created by Ei,while the secondary one corresponds to the secondary dressedstates |+±⟩ (|−±⟩) created by Ej from |+⟩ (|−⟩) with Δ1 < 0(with Δ1 > 0).First, the self-dressing field Ei splits the state |1⟩ into two
primary dressed states |G±⟩. If we set |1⟩ as the frequencyreference point, the Hamiltonian can be written as
= −ℏ* − Δ
⎡⎣⎢⎢
⎤⎦⎥⎥H
G
G
0
( 1)
i
ii
i
From the equation H|G±⟩ = λ±|G±⟩, we can obtain
Figure 1. (a1) Simplified two-energy-level diagram of Pr3+ ions in aYSO crystal. (a2) Diagram of Pr3+ ions in a YSO crystal. The primaryand secondary dressed states are the solid purple and dotted−dashedred lines, respectively. The inset is the dressed-state picture. (b1) V-type three-level atomic system (|0⟩↔|1⟩↔|2⟩) for the interactionbetween two FL signals. (b2) V-type three-level system diagram ofPr3+ ions in a YSO crystal. The inset is the dressed-state picture. (c)Frequency domain of typical fluorescence signals. (d) Experimentalsetup scheme. The small blue piece is a half-wave plate (HWP) orquarter-wave plate (QWP) to change the polarization of E3.Abbreviations: PMT, photomultiplier tube; PBS, polarized beamsplitter; L, lens. (e) Zeeman structure of the ladder-type atomic systemin the experiment and various transition pathways in it. Solid, dotted,dashed−dotted, and dashed lines are transitions for linearly polarizeddressing beams, left-circularly-polarized FL beam, right-circularly-polarized FL beam, and linearly polarized beam, respectively.
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λ = − Δ + Δ + | |+ G[( 1) ( 4 ) ]/2ii i i
2 2 1/2(3a)
λ = − Δ − Δ + | |− G[( 1) ( 4 ) ]/2ii i i
2 2 1/2(3b)
Next, the external-dressing field Ej splits |G+⟩ into |G′+±⟩ if Δ1> 0 or splits |G−⟩ into |G′−±⟩ if Δ1 < 0. The Hamiltonian canbe written as
′ = −ℏΔ′ ′
′ *
⎡⎣⎢⎢
⎤⎦⎥⎥H
G
G( ) 02
From the relation H′|G±±⟩ = λ±±|G±±⟩, we can obtain
λ = − Δ′ ± Δ′ + | |−± G[( 1) (( ) 4 ) ]/2jj j j
2 2 1/2(3c)
with Δj′ = Δj − (−1)jλ − or
λ = − Δ′ ± Δ′ + | |+± G[( 1) (( ) 4 ) ]/2jj j j
2 2 1/2(3d)
with Δj′ = Δj − (−1)jλ+.D. Polarization Theory. For clearly understanding the
influences of the incident beams on AT splitting of FLprocesses, we also report the corresponding experimentalobservations which can be effectively controlled by thepolarization states of the pumping laser beams using a HWPor QWP in front of the FL signals. Due to the periodic changeof the polarization states of the pumping beam, the intensity ofthe FL beam also evolves periodically.For second-order electric susceptibility tensor crystal there
are 27 nonzero quantities, because the YSO crystal is amonoclinic biaxial crystal system, the space point group is C2h
6 ,so the second-order electric susceptibility tensors are ninenonzero amounts. Considering that we only trigger the FLsignals using the x-direction and x-direction polarization in ourexperiments, we inspire four components corresponding to xxy,xyx, yxx, and yyy, respectively. The density-matrix elements canbe written as follows:
Considering the dressing effect, the equations are modified into
ρ ρ ρ
μ θμ θ μ θ
= =
=− | |
+ | | Γ Γ + | |G
d G G d
cos 2
( cos 2 / )( cos 2 / )
xxy
x
x x
FL(2)
FL( )(2)
11(2)
21
2 2
12
12 2
00 112
12 2
1
ρ ρ ρ
μ μ θ θ
μ θ μ θ
= =
=− | |
Γ + | | +
G
d G d
cos 2 sin 2
[ ( cos 2 sin 2 )/ ]
xyx
x y
y x
FL(2)
FL( )(2)
11(2)
12
1 11 12 2 2 2 2
1
ρ ρ ρ
μ μ θ θ
μ θ μ θ
= =
=− | |
Γ + | | +
G
d G d
cos 2 sin 2
[ ( cos 2 sin 2 )/ ]
yxx
x y
x y
FL(2)
FL( )(2)
11(2)
12
1 11 12 2 2 2 2
1
ρ ρ ρ
μ θ
μ θ μ θ
= =
=− | |
+ | | Γ Γ + | |
G
d G G d
sin 2
( sin 2 / )( sin 2 / )
yyy
y
y y
FL(2)
FL( )(2)
11(2)
21
2 2
12
12 2
00 11 12 2 2
1
In two-level atomic systems, the intensity of this signal can beexpressed by the diagonal elements of the density matrix. In thecurrent system, when the polarizations of the pumping fieldsare changed by using half-wave plates, the density-matrixelement ρ11
(2) is given by
ρ ρ ρ ρ ρ= + + +xxy xyx yxx yyy11(2)
FL( )(2)
FL( )(2)
FL( )(2)
FL( )(2)
(4a)
For the N-level atomic system, it contains three second-orderfluorescence systems. When we change the polarization of E3,the density-matrix element ρ11
(2) is modified to
where d12 = Γ12 + i(Δ1 − Δ2), d21 = Γ21 + i(Δ2 − Δ1), d30 = Γ30+ i(Δ1 − Δ3), d31 = Γ31 + iΔ3, d30′ = Γ30 + i(Δ3 − Δ1), d23 = Γ23+ i(Δ2 − Δ1 + Δ3), and d32 = Γ32 + i(Δ3 − Δ1 + Δ2).Quarter-wave plates are used for changing the polarizations
of the pumping fields as follows.17
For the V-level atomic system, by simply substituting thecorresponding dressing terms into eq 4b, we can obtain anexpression of the density-matrix element, which induces the FLsignal of the linearly polarized component.
Γ3M0M + i(Δ1 − Δ3), and d3M1M = Γ3M1M + iΔ3).When the polarization is 45°, the FL signal becomes circular,
and the expression of the density-matrix element can be writtenas
where d3M0M−1= Γ3M0M‑1
+ i(Δ1 − Δ3) and (M = −5/2, −3/2,−1/2, 1/2, 3/2, 5/2).Since the CG coefficients18 are different for different
transitions between Zeeman sublevels, the Rabi frequenciesare different even with the same laser field. For example,considering CG coefficient values, the Rabi frequency is |G3M−1
+ |2.When we consider M = −1/2, |G3
+| = 4/√35, which indicatesthat the circularly polarized FL signal is mainly dressed by G3
±
not G3. And from the CG coefficients, we can also obtain that |G3M−1+ |2 > |G3M−1
|2 (|G3(−1/2)| = 3(1/35)1/2), which indicates thatthe dressing effects in the circularly polarized subsystems aregreater than those in the linearly polarized subsystems.
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It can be also used in the N-type four-level atomic system.When we change the polarization of k1, the linearly density-matrix element ρ11
Γ2M1M + i(Δ2 − Δ1), and the circular one is given by
where d31M−1= Γ3M−11M + iΔ3.
Similarly, when the angle is 45° the circularly polarized FLsignal is mainly dressed by G3
± not G3 due to the term |G3M−1+ |2.
And the dressing effects in the circularly polarized subsystemsare greater than in the linearly polarized subsystems due to theterm |G3M−1
+ |2 > |G3M−1|2.
3. EXPERIMENTAL RESULTS AND DISCUSSIONSA. Power Dependence. In Figure 2a,b, we show two kinds
of AT-like splitting results of the FL signals by changing P1 and
P2, respectively. Parts c and d of Figure 2 clearly show therelative width of AT-like splitting corresponding to Figure 2a,b.Figure 2a presents the AT-like splitting with P1 set as 0.5, 1, 1.5,2, 2.5, and 3 μW from bottom to top. When the power of E1increases, the intensity of the FL signal also increasesaccordingly. To explain the effects, we turn to the density-matrix element related to the FL signal. In eq 1a, the term |G1|
2/d1 can determine the self-dressing effect when Δ1 isscanned. The primary AT splitting distance corresponding tothe primary dressed states |±⟩ can be written as Δa = λ+ − λ− =(Δ1
2 + 4|G1|2)1/2 where G1 = μ(2P1/ε0cA)
1/2/ℏ. With P1increasing, the distance of AT-like splitting increases due tothe term |G1|
2, as shown in Figure 2a,c. For the case shown inFigure 2a1, there is no obvious AT-like splitting because of theweek self-dressing effect (low P1).Similarly with Figure 2a, we show the AT-like splitting by
changing the power of E2 (P2) in Figure 2b. The splittingdistance also increases with P2 (Figure 2d), and there is no
obvious dressing effect in Figure 2b1 because of the low P2.Here the primary AT splitting distance is Δa′ = λ+ − λ− = (Δ2
2 +4|G2|
2)1/2. Figure. 2e is the theory model corresponding toFigure 2b.Equation 2b displays the expression of the corresponding
density-matrix element related to FL processes, in which |G1|2/
Γ00 and |G2|2/d2 mean a primary AT splitting and a secondary
AT splitting in the spectrum, respectively. The term |G1|2/Γ00 is
constant, and it can suppress the FL signal. One way to explainthe effects is to use the dressed-state picture as shown in Figure1a2. First, E1 splits |1⟩ into two primary dressed states |G±⟩.Then the external-dressing field E2 splits |G+⟩ into |G′+±⟩ if Δ2> 0 or |G−⟩ into |G′−±⟩ if Δ2 < 0. We can obtain theeigenvalues λ± = ±G (measured from |1⟩) of |±⟩ with G = G1and λ+±
(3) = (Δ2′ ± (Δ2′2+ 4|G′|2)1/2)/2) (λ−±(3)(Δ2′ ± ((Δ2′)2 + 4|G′|2)1/2/2) with G′ = G1 + G2 (measured from level |+⟩ (|−⟩))of |+±⟩ (|−±⟩), where Δ2′ = Δ2 − λ+ (Δ2′ = Δ2 − λ−). When Δ1is scanned from negative to positive, the resonance of the FLfield with |G±⟩ will produce two peaks of the primary ATsplitting. And the satisfaction of two-photon resonant conditioncreates the dip in FL intensity signal at Δ1 = 0. So, in Figure3a,c, by scanning Δ1 with relatively low P1, the separation Δa of
the primary AT splitting and secondary one is caused by E1 andE2 together. We can obtain the expression of the splittingdistance Δa = λ+ − λ− = (Δ2
2 + 4|G′|2)1/2. Among these peaks,the pair formed by resonating with |G′++⟩ and |G′+−⟩ are thesecondary AT splitting ones. Δa will become larger when P1increases. The distance of the AT splitting nearly disappears atP1 = 0.5 μW because of the low primary AT splitting as shownin Figure 3a1.On the other hand, we investigate the AT splitting of FL
signal versus Δ2 at discrete P1 shown as in Figure 3b atrelatively high P2. The distance of the AT splitting is obvious atP1 = 3 μW because of the strong primary AT splitting as shownin Figure 3b1 compared with the signals in Figure 3a1. It isobvious that the AT splitting distance undergoes a strengthen-ing process as depicted by the dashed line by setting P1discretely from negative to positive when scanning Δ2. It isobserved that the secondary AT splitting peaks change fromsmall to big as depicted by Figure 3d. In order to demonstratethe phenomena more clearly, we present the correspondingtheory model of fluorescence signals in Figure 3e whichconfirm our experimental results.
B. Detuning Dependence. Figure 4a shows the dressingeffect of E2 on the FL signal at various fixed Δ2 in a two-level
Figure 2. (a) Block E2, scan Δ1 when P1 is (1) 0.5, (2) 1, (3) 1.5, (4)2, (5) 2.5, and (6) 3 μW from bottom to top. (b) Block E1, scan E2when P2 is (1) 0.5, (2) 1, (3) 1.5, (4) 2, (5) 2.5, and (6) 3 μW frombottom to top. (c and d) Relative width of AT-like splitting distancecorresponding to a and b, respectively. (e) Theory model of b.
Figure 3. Measured intensity of FL signals (a) versus Δ1 with P2 being(a1) 0.5, (a2) 5.3, (a3) 10.1, (a4) 14.0, (a5) 18.2, and (a6) 23.4 μWfrom bottom to top and (b) versus Δ2 with P1 being (b1) 3.0, (b2) 6.4,(b3) 9.5, and (b4) 12.7 μW from bottom to top, in a V-type three-level system. (c and d) Relative width of AT splitting corresponding toa and b, respectively. (e) Theory model of b.
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system. The profile connecting the baselines of the signals withdifferent Δ2 is the FL signal excited by E2, where the curveshows the AT-like splitting due to its strong power. For thecase shown in Figure 4a1, when Δ2 is far away from theresonant region, the FL signal has no AT splitting and is nearlynot affected by E2. As Δ2 gets closer to the resonant point, thebaseline raises gradually due to the competed excitations of theparticles by E1 and E2 (dashed−dotted line in Figure 4a), andthe intensity of the FL signal reduces. At the two peaks of AT-like splitting of the FL signal profile, E2 dominates thecompetition and dresses the FL signal. At the near-resonantregion, the competition of E1 on particles increases graduallyuntil Δ1 ∼ 0 due to the self-dressing effect of the FL signal.However, the dressing effect of E2 on the FL signal increasesgradually and the AT-splitting distance and the splitting depth(dashed line in Figure 4a) reaches the maximum at Δ1 = Δ2 ∼0. Such mutual interaction between self-dressing FL signals andextra-dressing FL signals can be well interpreted by eq 2. Dueto the low E1 power, the dressing effect of E1 (|G1|
2/(Γ10 + iΔ1)and |G1|
2/Γ00) can be neglected in eq 2. Therefore, the outputsignals are controlled via the competed action of E2 on theparticles of the ground state (|G2|
2/Γ00) and the dressing effecton the energy-level position (|G2|
2/(Γ10 + iΔ2)).Figure 4b shows the dressing effect of E2 on the FL signal
(with the self-dressing AT splitting) at various fixed Δ2 in athree-level system. The curve shows the strong self-dressing ATsplitting caused by the strong P1 even though the FL signal isnot affected by E2 when Δ2 is far away from the resonantregion. As the baseline of the signals raises gradually with Δ2getting closer to the resonant point, the intensity of the FLsignal reduces, and the AT-splitting distance and the splittingdepth (dashed line in Figure 4b) increases because of theincreasing secondary dressing effect of E2.Figure 5a presents the dressing effect of E1 on the FL signal
with the self-dressing AT splitting versus Δ1 at differentdetuning Δ2 in the two-level system. In the region being faraway from the resonance (|Δ1| ≫ 0) we can get a pure FLsignal with the self-dressing AT splitting as shown in Figure5a1,a6. From Figure 5c, we can observe the AT-splittingdistance increases from Figure 5a1 to Figure 5a3 and thendecreases from Figure 5a4 to Figure 5a6 which contain the self-dressing and external-dressing AT splittings.Comparing with the case in Figure 5a, the splitting distance is
also determined by the combination of self-dressing ATsplitting and the external-dressing one. When Δ1 is far awayfrom the resonance, the distance of the two peaks nearlydisappears because of the weak self-dressing effect as shown inFigure 5b1,b6. The external-dressing effect is enhanced when
Δ2 is close to the resonant point and reaches the maximum atthe resonant point (|Δ1 − Δ2| = 0) which can be explained byeq 2 well. That leads to the AT-splitting distance increase fromFigure 5b1 to Figure 5b3 and then decrease from Figure 5b4 toFigure 5b6, as shown in 5d.
C. Polarization Dependence. For clearly understandingthe influences of the incident beams to AT spitting distance ofFL processes, we investigate the signals in P and S polarizationsseparately. The total intensity is the sum of two components asthe two FL signals are captured by one PMT. Figure 6a
represents the signal strength of the FL signal with no dressingfield versus Δ1 and a different polarization angle of E1 from θ =0° to θ = 90° by rotating HWP. The corresponding equation iseq 4a, in which the term |G1|
2cos 2θ/Γ10 + iΔ1 determines thedistance of AT splitting. When we change the angle from θ = 0°to θ = 90°, the AT splitting distance decreases and thenincreases as shown in Figure 6a1−a6. When θ = 45°, the ATsplitting disappears due to the term cos2 2θ = 0 as shown inFigure 6a3.The dependences of the dressing effects on the polarization
of the FL signals are shown in Figure 6b, in which thepolarization angle of E3 changes from −45° to 0° from bottomto top by rotating the QWP in the three-level system. It isobvious that the AT-splitting distance decreases from bottomto top which can be well explained by the term |G3 + G3
+ + G3−|2
cos2 2θ/Γ13 + i(Δ1 − Δ3) in eq 4c. When θ = 0°, G3± = 0 and G3
≠ 0, while when G3 = 0, G3± reaches its maximum when θ =
±45°, which can be well explained by the polarization theory.
Figure 4. Measured intensity of FL signals versus Δ1 at differentdetuning Δ2 values: (a) −600, −400, −200, 0, 200, 400, and 600 GHzfrom left to right in a two-level system, respectively; (b) −600, −400,−200, 0, 200, 400, and 600 GHz from left to right in a three-levelsystem, respectively (the dashed line is the profile of the baseline, andthe dashed-dotted line is the splitting height).
Figure 5. FL signals versus Δ1 at different Δ2 values: (a1) −20, (a2)−10, (a3) 0, (a4) 10, (a5) 20, and (a6) 30 GHz in the two-levelsystem; (b1) −60, (b2) −30, (b3) 0, (b4) 30, (b5) 60, and (b6) 90GHz in the V-type three-level system. (c and d) Relative widths of ATsplitting corresponding to a and b, respectively.
Figure 6. Variations of the relative FL intensities versus the rotationangle of the wave plate: (a) FL signals of the two-level system with theHWP; (b) FL signals of the V-type three-level system with the QWP.(c and d) Relative widths of AT splitting corresponding to a and b,respectively.
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The linearly polarized signal only exists when θ = 0° whichleads to the small AT-splitting distance as shown in Figure 6b6.If the signals are polarized along the same direction, themaximum signal intensity is observed when θ = ±45°. Toclearly depict the splitting distance, parts c and d of Figure 6present the relative widths of AT splitting corresponding toparts a and b, respectively.Figure 7a is versus Δ1 with the rotating angle θ of HWP
setting from −45° to 0° from bottom to top in a three-level
system. According to eq 4b, the changing of the AT-splittingdistance is caused by the term |G3|
2 cos2 2θ, which determinesthe decreasing of the splitting distance with increasing θ asshown in Figure 7a1−a6.Similar to Figure 6b, the dressing effect of E3 in the N-type
four-level system (in Figure 7c) is clearly revealed in Figure 7b,which leads to the AT splitting of FL signals. When QWP isrotated, the linearly circularly polarized transitions graduallytransform into circularly polarized ones, which lead to thenonlinear dressing effect partly instead of the linear one.Consequently, the dressing effect gets bigger and the AT-splitting distance becomes bigger as QWP is rotated from 0° to45° and reaches a maximum at θ = 45° as shown in Figure7b1−b4, which can be well explained by the term |G3 + G3
+ +G3−|2 cos2 2θ/Γ13 + i(Δ1 − Δ3) in eq 4b. When we change the
angle from 45° to 90°, G3 becomes bigger but G3± decreases,
which cause the whole dressing effect to decrease as shown inFigures 7b4−b6.Figure 7c is FL versus Δ1 with all beams on (solid line),
block E3 (dashed line) and block E1 and E3 (dashed−dottedline) from bottom to top, respectively. From Figure 7c, we canfind that the whole strength of the AT splitting is induced byboth the self-dressing field E1 and the extra-dressing field E3.
4. CONCLUSIONIn summary, we have experimentally and theoreticallydemonstrated the AT spatial splitting of the all-optically-controlled second-order fluorescence processes of Pr3+:YSO ina heteronuclear-like molecule system. By the comparisonbetween the two-level and V-type three-level system, theinfluence of the dressing field to the AT-splitting distance isdemonstrated. By changing the detuning and power of thecontrolling field, desirably modulated results of the FL signalcan be obtained, such as the changing of the splitting distanceof the splitting peaks, which has a potential application tofabricate all-optical switch devices. In addition, we investigated
the FL processes with different polarizations by rotating HWPand QWP in two-level, three-level, and N-type four-levelsystems.
■ ACKNOWLEDGMENTSThis work was supported by the 973 Program (Grant2012CB921804), KSTITSP (Grant 2014KCT-10), NSFC(Grants 61308015, 11104214, 61108017, 11104216, and61205112), and XJTUIT (Grant cxtd2014003).
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Figure 7. Polarization dependence of the FL signals versus Δ1 andchange of the angle of E3 (a) with the HWP rotation angle θ set from−45° to 0° in the three-level system and (b) with the QWP rotationangle θ set as (1) 0°, (2) 20°, (3) 35°, (4) 45°, (5) 75°, and (6) 90° inthe four-level system. (c) FL signals versus Δ1 with all beams on,without E1 and without E1 and E3 from top to bottom in the four-levelsystem, respectively. (d) N-type four-level system diagram.
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