# Enhanced narrow spectral line and double electromagnetically induced two-photon transparency induced by double dark resonances

**ABSTRACT** We theoretically investigate the features of two-photon absorption

in a five-level atomic system with interacting dark resonances. It

is found that two-photon absorption can be completely suppressed

at two different frequencies due to the application of two

coherent coupling fields and the atomic system exhibits double

electromagnetically induced transparency windows against

two-photon absorption. The position and width of the double

two-photon transparency windows can be controlled via properly

adjusting the frequency detuning and the intensities of the two

coupling fields. In addition, one enhanced narrow central line can

be observed in the two-photon absorption spectra, which may find

applications in high-precision spectroscopy. Form a physical point

of view, we explicitly explain these results in terms of quantum

interference induced by three different two-photon excitation

channels in the dressed-state picture.

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**ABSTRACT:**We propose a scheme for creating atomic coherent superposition states via the technique of stimulated Raman adiabatic passage in a Λ-type system where the final state has twofold levels. With the application of a control field, it is found that the presence of double dark states leads to two arbitrary coherent superposition states with equal amplitude but inverse relative phases, even though the condition of multiphoton resonance is not met. In particular, two orthogonal maximal coherent superposition states are created when the control field is resonant with the transition of the twofold levels. This scheme can also be extended to manifold Λ-type systems.Physical Review A 08/2004; 70(2). · 3.04 Impact Factor - SourceAvailable from: M. Rosenbluh[show abstract] [hide abstract]

**ABSTRACT:**A method is presented for obtaining sub-Doppler and subnatural narrowing and increased absorption of a spectral line. The ultranarrow spectral line is confined between two closely spaced electromagnetically induced transparency windows in a nearly degenerate tripod atomic system formed by an Fg=1→Fe=0 transition, split by a magnetic field. The system is driven by a σ-polarized pump and probed by a tunable π-polarized laser. It can be used to measure small magnetic fields and also as a magneto-optic switch.Physical Review A 06/2004; 69(6). · 3.04 Impact Factor - [show abstract] [hide abstract]

**ABSTRACT:**Doppler-free resonances have been observed in Rb atomic vapor coherently driven by two strong-coupling fields in an intrinsically non-Doppler-free geometry. A four-level theoretical model explains the experimental results. The explanation of the physics is based on the interplay between coherences generated in a four-level system.Physical Review A 03/2002; 65(4):43805. · 3.04 Impact Factor

Page 1

Eur. Phys. J. D 41, 563–569 (2007)

DOI: 10.1140/epjd/e2006-00258-0

THE EUROPEAN

PHYSICAL JOURNAL D

Enhanced narrow spectral line and double electromagnetically

induced two-photon transparency induced by double dark

resonances

J.H. Liaand X.X. Yang

Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, P.R. China

Received 19 August 2006 / Received in final form 19 October 2006

Published online 8 December 2006 – c ? EDP Sciences, Societ` a Italiana di Fisica, Springer-Verlag 2006

Abstract. We theoretically investigate the features of two-photon absorption in a five-level atomic system

with interacting dark resonances. It is found that two-photon absorption can be completely suppressed

at two different frequencies due to the application of two coherent coupling fields and the atomic system

exhibits double electromagnetically induced transparency windows against two-photon absorption. The

position and width of the double two-photon transparency windows can be controlled via properly adjusting

the frequency detuning and the intensities of the two coupling fields. In addition, one enhanced narrow

central line can be observed in the two-photon absorption spectra, which may find applications in high-

precision spectroscopy. Form a physical point of view, we explicitly explain these results in terms of quantum

interference induced by three different two-photon excitation channels in the dressed-state picture.

PACS. 42.50.Hz Strong-field excitation of optical transitions in quantum systems; multiphoton processes;

dynamic Stark shift – 42.50.Gy Effects of atomic coherence on propagation, absorption, and amplification

of light; electromagnetically induced transparency and absorption

Effects of atomic coherence and quantum interference

are currently becoming an important and intensive tool

in resonant nonlinear optical physics. The inhibition of

two-photon and multiphoton absorption based on these

effects in nonlinear optical regime has potential applica-

tions in high-efficiency generation of short-wave length

coherent radiation at pump intensities approaching the

single-photon level [1–7], trapping and manipulating pho-

ton states in atomic ensembles [8], nonlinear spectra at

very low light intensity [9–17], ultraslow optical solitons

in highly resonant media [18], and pulse-preserving prop-

agation in dissipative media [19,20], and so on. In partic-

ular, nonlinear optics assisted by electromagnetically in-

duced transparency (EIT) under few-photon optical field

due to extremely large Kerr nonlinearities and refractive-

index enhancement without absorption has been already

observed [21], and this opens up the possibilities for a

new regime of quantum nonlinear optics. For example,

Harris et al. proposed the use of EIT to suppress ab-

sorption of the short-wavelength light generated in a four-

wave mixing (FWM) scheme and showed that the FWM

efficiency could be greatly enhanced [1]. Agarwal and

Harshawardhanshowed that in a four-level Y-type system,

two-photon absorption could be selectively suppressed or

enhanced [9], and later Gao et al. reported the experimen-

tal observation of the electromagnetically induced inhibi-

tion of two-photon absorption with atomic sodium vapor

ae-mail: huajia li@163.com

as a test medium [10]. In a recent experiment, Yan et al.

demonstrated that EIT in a standard Λ-type configura-

tion could be used to suppress both single-photon and

two-photon absorptions simultaneously [22,23]. Later on,

Wu et al. investigated and discussed a four-wave-mixing

(FWM) scheme in a five-level atomic system and hyper-

Raman scattering (HRS) in resonant coherent media by

the use of EIT, which led to suppressing both two-photon

and three-photon absorptions in both FWM and HRS

schemes and enabling the four-wave mixing to proceed

through real, resonant intermediate states without absorp-

tion loss [2]. Quite recently, he and his coworkers again

analyzed a lifetime-broadened four-state FWM scheme in

the ultraslow propagation regime and put forward a new

type of induced transparency resulted from multiphoton

destructive interference [24]. In reference [25], Zou et al.

investigated two-photon absorption in a three-level ladder

atomic system driven by a pair of bichromatic fields of

equal frequency differences and demonstrated the reduc-

tion of two-absorption absorption.

On the other hand, in recent years a variety of four-

level atomic systems driven by three fields have also shown

that the probe absorption can be characterized by double-

dark resonances [6,26–32]. For the presence of double-

dark resonances, there are basically two different kinds

of atomic configuration. One kind is Λ-configuration sys-

tem where the final state has twofold levels, the other

kind is a tripod atomic system. The interaction of double-

dark states has given rise to some original and significant

Page 2

564The European Physical Journal D

effects. For example, Lukin et al. have shown that in a

Λ-configuration system where the final state has twofold

levels the interaction of double-dark states can result in

a splitting of dark states and the appearance of sharp

spectral features [26]. Recently, Gong and his coworkers

have shown that in the above Λ-configuration four-level

system the presence of double-dark states makes it pos-

sible to prepare arbitrary coherent superposition states

with equal amplitudes but inverse relative phases, even

though the condition of multiphoton resonance is not sat-

isfied [28]. More recently, they have also proposed high

efficiency four-wave mixing induced by double-dark reso-

nances in a five-level system [6]. Yelin et al. experimen-

tally show and theoretically confirm that double dark

resonances lead to the possibility of extremely sharp res-

onances prevailing even in the presence of considerable

Doppler broadening [30]. Alternatively, Goren et al. have

studied the sub-Doppler and subnatural narrowing of the

absorption line induced by interacting dark resonances in

a tripod system [31]. Paspalakis et al. have analyzed co-

herent propagation and nonlinear generation dynamics in

a coherently prepared four-level tripod system [32].

In this paper, we study the two-photon absorption

spectra in a five-level atomic system in the presence of

double dark resonances. The two-frequency transparency

against two-photon absorption occurs in such a system,

which expands the frequency range of two-photon trans-

parency and may improve the controllability of two-

photon transparency. The position and width of two-

frequency transparency windows can be manipulated via

appropriately modulating the frequency detuning and the

intensities of the two coupling fields. Interestingly enough,

one enhanced narrow central line can be observed in the

two-photon absorption spectra, which may find applica-

tions in high-precision spectroscopy.

Let us consider a five-level atomic system driven by

four coherent laser fields, as shown in Figure 1. The atomic

levels are labeled as |0?, |1?, |2?, |3?, and |4?, respectively.

A probe laser field Ep(carrier frequency ωpand Rabi fre-

quency 2Ωp) is applied to the transition |0? ↔ |3? to serve

as the first step of the two-photon excitation of upper

atomic state |4?. A signal laser field Es(carrier frequency

ωsand Rabi frequency 2Ωs) is coupled to the transition

|3? ↔ |4? to complete the two-photon excitation of atomic

state |4?. The transitions |2? ↔ |3? and |1? ↔ |3? are

respectively driven by two coherent coupling laser fields

with Rabi frequencies 2Ωc and 2Ωd (amplitudes Ec, Ed

and carrier frequencies ωc, ωd), which can produce double-

dark resonances. In the interaction picture and under the

electro-dipole interaction and rotating-wave approxima-

tion, with the assumption of ? = 1, the semiclassical

Hamiltonian describing the atom-field interaction for the

system under study can be written as

Hint= (∆p− ∆d)|1??1| + (∆p− ∆c)|2??2|

+ ∆p|3??3| + (∆p+ ∆s)|4??4|

− (Ωp|3??0|+Ωs|4??3|+Ωc|3??2|+Ωd|3??1| + h.c.),

(1)

Fig. 1. (a) Schematic diagram of five-level atoms in a res-

onant coherent medium interacting with a probe laser with

Rabi frequency 2Ωp, a signal laser with Rabi frequency 2Ωs,

two coupling lasers with Rabi frequencies 2Ωc and 2Ωd. The

atomic levels are labeled as |0?, |1?, |2?, |3?, and |4?, respec-

tively. The tripod configuration |0? → |3?, |1? → |3?, and

|2? → |3? owns the property of double-dark resonances [31,32].

∆p, ∆s, ∆c, and ∆d are the frequency detunings of the corre-

sponding probe, signal, and coupling fields, see text for details.

(b) Corresponding dressed-state picture of two coupling fields

Ωc and Ωd.

where h.c. means Hermitian conjugation and for the

sake of simplicity we have taken the ground state |0? as

the energy origin. The quantities Ωn(n = p,s,c,d) stand

for one-half Rabi frequencies for the respective transi-

tions, i.e., Ωp = d30Ep/(2?), Ωs = d43Es/(2?), Ωc =

d32Ec/(2?), and Ωd= d31Ed/(2?), where dij =?dij· ˆ eL

(ˆ eL is the polarization unit vector of the laser field) de-

notes the dipole moment for the transition between levels

|i? and |j?. ∆p= ω30−ωp, ∆s= ω43−ωs, ∆c= ω32−ωc

and ∆d = ω31− ωd, are the frequency detunings of the

four coherent fields from the corresponding two-level tran-

sitions (see Fig. 1). The decay rates from the states |4? to

|3?, |3? to |0?, |3? to |1?, and |3? to |2? are γ43, γ30, γ31,

and γ32, respectively. The relaxation rates of coherence

between the ground states |0?, |1?, and |2? are negligible

and thus can be safely neglected.

In what follows, using the density-matrix formalism

we begin to describe the dynamic response of the reso-

nant coherent medium under study. By the standard ap-

proach [33], we can easily obtain the time-dependent den-

sity matrix equations of motion as follows:

˙ ρ00= γ30ρ33+ iΩp(ρ30− ρ03),

˙ ρ11= γ31ρ33+ iΩd(ρ31− ρ13),

˙ ρ22= γ32ρ33+ iΩc(ρ32− ρ23),

˙ ρ33= −(γ30+ γ31+ γ32)ρ33+ γ43ρ44+ iΩp(ρ03− ρ30)

+ iΩs(ρ43−ρ34) + iΩc(ρ23−ρ32) + iΩd(ρ13−ρ31),

˙ ρ44= −γ43ρ44+ iΩs(ρ34− ρ43),

˙ ρ01= i(∆p− ∆d)ρ01+ iΩpρ31− iΩdρ03,

Page 3

J.H. Li and X.X. Yang: Enhanced narrow spectral line and double EIT565

Fig. 2. Two-photon absorption ρ44 versus frequency detuning ∆p. (a) ∆c = ∆d = 0; (b) ∆c = −γ30 and ∆d = γ30; (c) ∆c =

−1.5γ30 and ∆d = 1.5γ30; (d) ∆c = −2γ30 and ∆d = 2γ30. Other parameters are chosen as Ωp = 0.1γ30, Ωs = 0.2γ30,

Ωc = Ωd= 4γ30, ∆s = 0, γ31 = γ32 = γ30, and γ43 = 0.4γ30, respectively.

˙ ρ02= i(∆p− ∆c)ρ02+ iΩpρ32− iΩcρ03,

˙ ρ03= −

2

− iΩsρ04− iΩcρ02− iΩdρ01,

˙ ρ04= −

2

˙ ρ12= i(∆d− ∆c)ρ12+ iΩdρ32− iΩcρ13,

˙ ρ13= −

2

− iΩpρ10− iΩsρ14− iΩcρ12,

˙ ρ14= −

2

?γ30+ γ31+ γ32

− iΩpρ20− iΩsρ24− iΩdρ21,

˙ ρ24= −

2

?γ30+ γ31+ γ32+ γ43

+ iΩs(ρ44− ρ33) + iΩpρ04+ iΩcρ24+ iΩdρ14, (2)

?γ30+ γ31+ γ32

− i∆p

?

ρ03+ iΩp(ρ33− ρ00)

?γ43

?γ30+ γ31+ γ32

− i(∆p+ ∆s)

?

ρ04+ iΩpρ34− iΩsρ03,

− i∆d

?

ρ13+ iΩd(ρ33− ρ11)

?γ43

− i(∆d+ ∆s)

?

ρ14+ iΩdρ34− iΩsρ13,

?

˙ ρ23= −

2

− i∆c

ρ23+ iΩc(ρ33− ρ22)

?γ43

− i(∆c+ ∆s)

?

ρ24+ iΩcρ34− iΩsρ23,

?

˙ ρ34= −

2

− i∆s

ρ34

where the overdots denote the derivative with respect to

time t and we have assumed that all involving Rabi fre-

quencies are real without loss of generality. Closure of this

atomic system requires that?4

pathway |0? → |3? → |4? is proportional to the popula-

tion distribution in the upper excited state |4?, i.e., σ44.

In the following, we begin with investigating the response

of two-photon absorption by solving the density matrix

equations (2) numerically in the steady-state limit via a

nice Matematica code. Note that, in this paper, all involv-

ing parameters are scaled by γ30, which should be in the

order of MHz for rubidium or sodium atoms.

j=0ρjj= 1 and ρij= ρ∗

ji.

As it is well-known, the two-photon absorption for the

First of all, we will analyze how the interference of the

dark resonance modifies the two-photon absorption spec-

tra via the numerical calculations based on equation (2)

in the steady-state limit. In Figure 2, we plot the two-

photon absorption ρ44 as a function of probe detuning

∆pwith different frequency detuning of the two coupling

fields ∆c and ∆d, while keeping other parameters un-

changed. It is easy to see from Figure 2 that, the spectra

of the two-photon absorption have a convert from single

two-photon transparency window at central frequency to

double two-photon transparency windows at two different

Page 4

566The European Physical Journal D

Fig. 3. Population ρ00 at the level |0? versus frequency detuning ∆p. (a) ∆c = ∆d = 0; (b) ∆c = −γ30 and ∆d = γ30;

(c) ∆c = −1.5γ30 and ∆d= 1.5γ30; (d) ∆c = −2γ30 and ∆d= 2γ30. Other parameters are chosen as Ωp = 0.1γ30, Ωs = 0.2γ30,

Ωc = Ωd= 4γ30, ∆s = 0, γ31 = γ32 = γ30, and γ43 = 0.4γ30, respectively.

side frequencies, moreover the position and width of two-

frequency EIT windows depends strongly on the frequency

detuning of these two coupling fields. Specifically, for the

case that the two coupling fields interacts resonantly with

the corresponding transitions |1? ↔ |3? and |2? ↔ |3?, i.e.,

∆d= ∆c= 0 [see Fig. 2a], the two-photon absorption can

be completely suppressed and the atomic system becomes

transparency only at ∆p= 0. In contrast, when the fre-

quency detuning is varied, for the case that ∆d= −∆c=

γ30 [see Fig. 2b], the effect of the frequency detuning is

seen to cause a further splitting in each of the dynamic

Stark components and gives rise to a three-peak spectral

feature with one narrow central line and two symmetri-

cal normal width side lines. There appear double electro-

magnetically induced two-photon transparency windows.

When the coupling-field frequency detuning continues to

increase [e.g., ∆d= −∆c= 1.5γ30and ∆d= −∆c= 2γ30

in Figs. 2c and 2d], the height of the narrow central spec-

tral line can be enhanced remarkably, meantime the height

of two side spectral lines with normal width change slowly.

As a result, we can see that by adjusting the frequency de-

tuning of the coupling field, such as ∆d= −∆c= 2γ30[see

Fig. 2d], large enhancement of the ultranarrow line can be

achieved in the two-photon absorption spectra. Alterna-

tively, the distance between the double two-photon trans-

parency windows becomes larger with increasing ∆dand

∆c, that is to say, there is an overall shift of the positions

of transparency windows at the opposite direction. These

results will be well explained in the later part. In order to

further verify that the population ρ00 at the level |0? is

not equal to zero, the corresponding curves in Figure 3 is

clearly presented.

In Figure 4, we plot the two-photon absorption ρ44as

a function of probe detuning ∆p with two different in-

tensities of the coupling fields Ωc= Ωd= 2γ30and 4γ30

in the steady-state limit, while keeping other parameters

unchanged. We find that if the coupling-field frequency

detuning is fixed (e.g., ∆d = −∆c = γ30), the positions

of zero two-photon absorption at two different frequencies

are kept unchanged no matter how we vary the inten-

sities of the two coupling fields, but the regimes of two-

frequency EIT windows are enlarged and two side spectral

lines keep away from each other with increasing Ωc and

Ωd. This suggests that the positions of zero two-photon

absorption at two different frequencies depend sensitively

on the frequency detuning of the two coupling coherent

fields, but be independent of their intensities. In order

to explicitly show the influence of frequency detuning

Page 5

J.H. Li and X.X. Yang: Enhanced narrow spectral line and double EIT567

Fig. 4. Two-photon absorption ρ44 versus frequency detuning

∆p for the different intensities of the coupling field: Ωc = Ωd=

2γ30 (sold curve) and Ωc = Ωd = 4γ30 (dashed curve). Other

parameters are chosen as Ωp = 0.1γ30, Ωs = 0.2γ30, ∆s =

0, ∆d = −∆c = γ30, γ31 = γ32 = γ30, and γ43 = 0.4γ30,

respectively.

(∆d= −∆c= ∆) and Rabi frequencies (Ωc= Ωd= Ω) of

the two coupling fields on the central and side peaks, in

Figures 5a and 5b we plot the two-photon absorption spec-

tra for one central peak (solid cure: ∆p= 0) and two side

peaks (dashed curve: ∆p= ±√∆2+ 2Ω2), respectively.

In order to further give the explicit explanations of the

above results from numerical calculations based on equa-

tion (2), we will turn our attention to the dressed-state

picture, generated by the two coherent coupling fields

Ωc and Ωd, namely, the |1? ↔ |3? ↔ |2? transitions to-

gether with the two coupling fields are treated as a cou-

pled “atom+field” system and the energy levels of the

dressed states form a ladder of triplets as shown in Fig-

ure 1b. It is obvious that bare-state level |3? should be

split into three dressed-state sublevels |±?3and |0?3. Such

a subsystem is described by the interaction Hamiltonian

V = ∆d|1??1|+∆c|2??2|+(Ωd|3??1| + Ωc|3??2| + h.c.). The

energy eigenvalues of the three dressed states for the case

that ∆d= −∆c= ∆ and Ωc= Ωd= Ω are given by

?

The corresponding energy eigenstates are written as

λ±= ±

∆2+ 2Ω2

and

λ0= 0.

(3)

|+?3=

1

2√∆2+ 2Ω2

+

∆ +

1

√∆2+ 2Ω2(−∆|3? − Ω|2? + Ω|1?),

1

2√∆2+ 2Ω2

+

∆ −

?

2Ω|3? −

?

∆ −

?

?

∆2+ 2Ω2?

|2?

?

?

∆2+ 2Ω2?

|1?

,

(4a)

|0?3= (4b)

|−?3=

?

2Ω|3? −

?

∆ +

?

?

∆2+ 2Ω2?

|2?

?

?

∆2+ 2Ω2?

|1?

.

(4c)

Fig. 5. Two-photon absorption ρ44 versus (a) frequency de-

tuning ∆ (∆d = −∆c = ∆) and (b) Rabi frequency Ω

(Ωc = Ωd = Ω) for one central peak (sold curve: ∆p = 0)

and two side peaks (dashed curve: ∆p = ±√∆2+ 2Ω2). Other

parameters are chosen as Ωp = 0.1γ30, Ωs = 0.2γ30, ∆s = 0,

γ31 = γ32 = γ30, and γ43 = 0.4γ30, respectively.

When the frequency detuning of the probe field is tuned at

∆p= λ+, 0 and λ−, three stepwise resonant two-photon

excitations happen through the channels in the dressed-

state basis: |0?

|0?

central, and right-side peaks showed in Figures 2 and 4,

respectively. Then the distance between the left and right

side peaks is δ = λ+− λ−= 2√∆2+ 2Ω2. This explains

that the distance between the two side-peaks increases

with the frequency detuning and the Rabi frequency of the

two coupling fields. The central peak corresponding to the

two-photon absorption in the channel |0?

stands at rest at ∆p = 0 for the altering intensities of

the two coupling fields. The double two-photon trans-

parency is induced by the quantum interference among

the three coherent two-photon excitation pathways. This

can be demonstrated by the probability of the two-photon

Ωp

−→ |−?3

Ωs

−→ |4?, which correspond to the left-side,

Ωs

−→ |4?, |0?

Ωp

−→ |0?3

Ωs

−→ |4?, and

Ωp

−→ |+?3

Ωp

−→ |0?3

Ωs

−→ |4?

Page 6

568The European Physical Journal D

absorption according to equations (4a–4c):

?????

E0− ?ωp

+?0|?d ·?Ep|−?3 3?−|?d ·?Es|4?

E−− ?ωp

× δ (?ω4− ?ω0− ?ωp− ?ωs),

????

×

P2=2π

?

?0|?d ·?Ep|+?3 3?+|?d ·?Es|4?

E+− ?ωp

+?0|?d ·?Ep|0?3 3?0|?d ·?Es|4?

?????

2

= 2π

1

∆2+ 2Ω2

????0|?d ·?Ep|3??3|?d ·?Es|4?

where Ei = ?ωp+ ?∆p+ ?λi (i = +,0,−) represents

the relative eigenvalue of the ith dressed state |i?3 to

the ground state |0?. The occurrence of the minimum in

two-photon absorption requires that the part in the first

absolute-value bracket on the right-hand side of equa-

tion (5) should be equal to vanish, which leads to the

following condition after some algebra

?∆2

on the basis of the above analysis, we clearly see that

when ∆d= −∆c= ∆ and Ωc= Ωd= Ω, the two-photon

absorption has minima at ∆p= ±∆ (EIT windows) and

maxima at ∆p= 0 (central peak) and ∆p= ±√∆2+ 2Ω2

(two side peaks or Autler-Townes peaks). This can explain

why the minimum in two-photon absorption is always lo-

cated at ∆p= 0, ±γ30, ±1.5γ30, and ±2γ30in Figures 2

and at ∆p= ±γ30in Figure 4.

Now we give a brief discussion about the possible ex-

perimental realization of our proposed scheme by means

of alkali-metal atoms and appropriate diode lasers. Specif-

ically, we consider for instance the cold atoms87Rb (nu-

clear spin I = 3/2) on the 5S − 5P − 5D transitions as

a possible candidate. The designated states can be cho-

sen as follows: |0? = |5S1/2,F = 1,mF = 1?, |1? =

|5S1/2,F = 1,mF = −1?, |2? = |5S1/2,F = 2,mF = 0?,

|3? = |5P1/2,F = 2,mF = 1?, and |4? = |5D3/2,F =

3,mF= 1?, respectively. In this case, the coherent probe,

signal and coupling laser radiations, whose wavelengths

are, respectively, 795 nm (|0? ↔ |3?, |1? ↔ |3?, and

|2? ↔ |3?) and 762 nm (|3? ↔ |4?), can be obtained from

external cavity diode lasers. The probe and signal fields Ep

and Esis linearly polarized light, other two coupling fields

Ecand Edare right and left circularly polarized light, re-

spectively. Moreover, in order to eliminate the Doppler

broadening effect, atoms should be trapped and cooled by

the magneto-optical trap (MOT) technique.

In summary, we have analyzed and discussed the fea-

tures of the two-photon absorption spectra in a five-level

atomic system in the presence of the interacting dou-

ble dark resonances. Via numerical simulations we clearly

?

Ω2

∆p+ λ+

+

∆2

∆p+ λ0

+

Ω2

∆p+ λ−

?????

(5)

2

???

2

δ(ω4− ω0− ωp− ωs),

p− ∆2??∆2+ 2Ω2?= 0,

i.e.,∆p= ±∆,

(6)

show that the two-photon absorption can be completely

suppressed at two different frequencies and the atomic

system exhibits double electromagnetically induced trans-

parency windows against the two-photon absorption. The

position and width of two-frequency transparency win-

dows can be manipulated via appropriately adjusting the

frequency detuning and the intensities of the two cou-

pling fields. Clearly this control of the two-photon ab-

sorption should be of importance in the context of related

issues like two-photon lasing, pulse-preserving propaga-

tion in dissipative media and two-photon entanglement

in quantum computing and information processing. More

interestingly, one narrow or ultranarrow central spectral

line with high amplitude can be achieved in such a system,

which has potential application for precision spectroscopy.

Form a physical point of view, we well explain these re-

sults in terms of quantum interference induced by three

different two-photon excitation channels in the dressed-

state picture. According to our analysis, these interesting

phenomena should be observable in realistic experiments

by using alkali-metal atoms (e.g., cold Rb or Na atoms)

and appropriate diode lasers.

The research is supported in part by the National Natural Sci-

ence Foundation of China (Grant Nos. 10575040, 90503010,

and 10634060) and by National Basic Research Program of

China under Contract No. 2005CB724508. We would like to

thank Professor Ying Wu for helpful discussion and his en-

couragement.

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