Ultranarrow CPO resonance in a Λ-type atomic system

4.7 MB·English

by  T. Lauprêtre

Ultranarrow CPO resonance in a Λ-type atomic system
T. Lauprêtre1, S. Kumar2, P. Berger1,3, R. Faoro1, R. Ghosh2, F. Bretenaker1, and F. Goldfarb1∗
1Laboratoire Aimé Cotton, CNRS-Université Paris Sud 11, 91405 Orsay Cedex, France
2School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India and
3Thales Research and Technology, Campus Polytechnique, 91767 Palaiseau Cedex, France
(Dated: January 19, 2012)
Itiswellknownthatultranarrowelectromagneticallyinducedtransparency(EIT)resonancescan
be observed in atomic gases at room temperature. We report here the experimental observation of
another type of ultranarrow resonances, as narrow as the EIT ones, in a Λ-system selected by light
polarization in metastable 4He at room temperature. It is shown to be due to coherent population
oscillations in an open two-level system (TLS). For perpendicular linearly polarized coupling and
2 probe beams, this system can be considered as two coupled open TLSs, in which the ground state
1
populationsexhibitanti-phaseoscillations. Wealsopredicttheoreticallythatincaseoftwoparallel
0
polarizations,thesystemwouldbehavelikeaclosedTLS,andthenarrowresonanceassociatedwith
2
these oscillations would disappear.

n
a PACSnumbers: 42.50.Gy
J

8
1 Coherent population oscillations (CPO) and electro- (a)m = -1 0 1 3P1 (b) m = -1 0 1 3P1
] mnoamgnenetaictahlalyt cinadnugcievdetrrisaenstpoarreesnocnyan(EceIsTm) uarceh tnwaorropwheer- W dW W c W c
-ph tmhearnhtahpepreenlasxiantitownor-aletveelofaotopmticicalsycostheemresnc(eTsL.ST),hewhfoern- s +wc c X w psp- 3S1 2- W pX W p 2 3S1
m the beatnote between a coupling beam and a coherent 2 2
w , W
o probebeamleadstoatemporalmodulationofthepopu- (c) w , W P P
C C
at lationdifference. Thewidthoftheinducedtransparency PD PBS He cell AO AO
windowisthenlimitedbythepopulationrelaxationrate
.
s [1, 2]. The latter is a two-photon phenomenon that oc-
c
cursforexampleinthree-levelΛsystems,whentwoopti-
i PBS
s caltransitionscoupletwolowerlevelstoacommonupper l /2 l /4 B-field l /4
y
one. When coherent laser beams excite both transitions,
h
p a narrow transparency window appears at Raman reso- FIG. 1: (color online) (a) and (b) Relevant level schemes in
[ nance,thewidthofwhichislimitedbytheRamancoher- thecase ofexcitationbyorthogonal circular(σ⊥σ)and lin-
ence lifetime [3]. As the Raman coherence lifetime can ear(lin⊥lin)polarizations. ΩP (ΩC)andωP (ωC): Rabiand
1
be much longer than the upper level population lifetime, opticalfrequenciesoftheprobe(coupling)beam. δ=ωp−ωc.
v
(c) Experimental setup. AO: acousto-optic modulator. PBS:
2 EIT usually leads to the narrowest resonances. In the
polarizing beam-splitter. PD: photodétector
4 last two decades, such phenomena have raised a lot of
7 interestastheyallowonetoreachveryslowgroupveloc-
3 itiesforlight[4–6], EITbeingevenusedforlightstorage
1. experiments [7–10]. thetransittimeoftheatomsthroughthelaserbeam[11].
This transit time is lengthened thanks to non-dephasing
0
In this Letter, we report the experimental observation
2 collisions with ground-state atoms, leading to an effec-
of ultranarrow resonances in the absorption spectrum of
1 tiveRamancoherencelifetimeoftheorderof100µs[12].
: a hot atomic vapor. These resonances, that cannot be Figure 1(c) gives the schematic of the experimental set-
v
attributed to EIT, are shown theoretically and experi- up. The helium cell, filled with 1Torr of 4He, is 6cm
i
X mentally to be due to CPO in the two coupled TLSs long and has a diameter of 2.5cm. It is placed inside
provided by the Λ system. The two ground state pop-
r a three-layer µ-metal shield for isolation from magnetic
a ulations exhibit anti-phase oscillations, while the total
fieldinhomogeneities. Thecouplingandprobebeamsare
population is conserved. We compare all the features of
derivedfromthesamelaserdiodeat1.083µm. Thebeam
these CPO resonances with those of the EIT ones.
diameters are about 1 cm inside the cell. Helium atoms
The experiment uses metastable helium at room tem- areexcitedtothemetastablestatebyanRFdischargeat
perature. The 23S → 23P transition permits us to 27 MHz. The coupling and probe beams are controlled
1 1
isolate a pure Λ system involving only electronic spins in frequency and amplitude by two acousto-optic mod-
and in which the Raman coherence lifetime is limited by ulators (AOs), and recombined with a polarizing beam-
splitter(PBS).Theprobepowerisabout50µWandthe
coupling power can be varied between 0.5 and 22mW. A
quarter-wave plate (λ/4) located at the entrance of the
∗Electronicaddress: [email protected] cellletsusalternatebetweenorthogonalcircular(σ ⊥σ)
2
and linear (lin⊥lin) polarizations. A variable longitudi- Thefactthatthisunexpectedresonanceoccursatzero
nal magnetic field (B) generated by a solenoid surround- frequency difference δ between the pump and the probe
ing the helium cell lifts the degeneracy of the lower sub- isreminiscentofCPO.However,thewidthofusualCPO
levels. TheLandéfactoris2forthegroundstate,leading resonances is given by the decay rate of the population
to Zeeman shifts of ±2.8kHz/mG for the 23S ,m = ±1 of the upper level. In our case, since the lifetime of the
1
levels. Afterthecell,polarizationopticsallowsdetection excited level is of the order of 100ns, this would lead to
of only the probe. a resonance width of the order of 1MHz. It is clear from
In the usual configuration for EIT experiments along Fig.2(b)thatthewidthofthisextracentralresonanceis
the23S →23P transitionin4He*[12],oneusescircular in the kHz range, and is quite close to the width of the
1 1
polarizations for the pump and probe beams. Since the side EIT resonances in Fig.2(b) or of those in Fig.2(a).
m = 0 → m = 0 transition is forbidden, a σ+ coupling Thus, if we want to interpret this extra resonance as due
beam pumps the atoms into the m = +1 ground state topopulationoscillations, ithastoberelatedtothelife-
sublevelwhichisprobedbyaσ− beam[seeFig.1(a)]. In time of the lower level, which in our case is limited by
contrast, when the coupling beam is linearly polarized, thetransittimeandisthuscompatiblewiththeobserved
atoms are equally pumped into both m = ±1 sublevels, widths.
which can then be probed by a perpendicular linearly A simple and effective way to check whether a reso-
polarized probe beam [see Fig.1(b)]. The experiments nanceisduetopopulationoscillationsornotistoobserve
andsimulationspresentedherecomparetheseσ ⊥σ and whethertheintroductionofadephasingeffect,whichde-
lin⊥lin configurations. creases the lifetime of the coherences, affects it or not.
With this aim, we record the evolution of the widths of
thedifferentresonanceswiththecouplingintensity,inthe
presence of an inhomogeneous magnetic field, simply re-
alizedbytakingthecellpartiallyoutofthemagneticfield
shielding,andthenagainwithpropermagneticshielding.
The result is reproduced in Fig.3(a). The standard EIT
resonance is of course extremely sensitive to magnetic
fieldgradients,becauseitreliesontheRamancoherence.
Incontrast,thecentralresonanceinthelin⊥linconfigu-
ration here is totally unaffected by these gradients. This
FIG.2: (coloronline)(a)Experimentalresultsobtainedwith proves that this resonance is governed by the population
circular polarizations, with and without a 15mG magnetic lifetime in the lower state of the transition, and not by
field, which shifts the m = ±1 Zeeman sublevels by ±∆Z. the Raman coherence lifetime.
(b) Experimental results recorded with linear polarizations,
with (green/grey) and without (black) the magnetic field.
Two slightly off-resonance EIT peaks appear for δ = ±2∆ 50 (a) (b)
Z
(cδor=resωpCon−dωtoP)a,nbyuRtathmeancernetsroanlarnescoen.ance at δ = 0 does not Hz)4300 sion 0.5
dth(k20 nsmis0.45
In the σ ⊥ σ configuration, Fig.2(a) reproduces the Wi10 Tra
experimentally recorded transmission spectrum of the 0 0.4
probe versus δ with and without a magnetic field. As 0 20 40 60 80 -150 -100 -50 0 50 100 150
AverageIntensity(W.m-2) d (kd H(kzH)z)
expected, the Zeeman shift ∆ induced by the magnetic
Z
field shifts the EIT resonance. The Raman resonance is
FIG. 3: (color online) (a) Evolution of the resonance width
obtained for δ = ωC −ωP = 2∆Z, which is in perfect versus average coupling intensity for the standard EIT reso-
agreement with our data. Now, Fig.2(b) shows the re- nance (squares) and forthe central resonancein the lin⊥lin
sults from the same experiment except that the pump configuration (circle). Open (filled) symbols correspond to
and probe beams are now linearly and orthogonally po- measurementsperformedintheabsence(presence)ofamag-
larized (lin⊥lin configuration). Each beam thus excites neticfieldgradient. (b)Simulatedprobetransmissionspectra
equally the transitions ∆m=±1, as seen from Fig.1(b). in the lin ⊥ lin configuration for two values of the Raman
coherence decay rate Γ /2π = 3kHz (continuous blue) and
Here, the two side peaks induced by the magnetic field R
Γ /2π = 12kHz (dashed purple), obtained from a Floquet
occur at ±2∆ and can be interpreted as EIT peaks. R
Z analysis of the three-level system (see text). The transit de-
Theyappearbecausethepumpbeamcouplesbothtran-
cay rate is kept fixed at Γ /2π=2kHz.
t
sitions with a slight optical detuning ±∆ . In contrast,
Z
the central peak does not correspond to any Raman res-
onance. It occurs when the coupling and probe beams Wethusseearesonanceduetopopulationoscillations
have the same frequency, while both transitions expe- in the ground state. This resonance is observable here,
rience opposite frequency shifts induced by the applied and never in the case of CPO in a standard closed TLS,
magnetic field. The appearance of such a peak in the due to the fact that our three levels constitute two open
context of an EIT experiment is thus quite surprising. TLSs. The extra resonance we get is thus linked to the
3
extra resonances predicted by Friedmann et al. [14] in groundstatetootherstates,respectively. Inthepresence
1986 in the case of four-wave mixing (FWM), when an of a pump and a probe beam with a frequency difference
intermediate decaying state is added to a TLS. δ, the total intensity reads I =I +(I e−iδt+c.c.) with
0 1
We could reproduce the experimental results by per- I (cid:28)I . R is the feeding rate of the lower level. At first
1 0
forming a first-order Floquet expansion of the density order, the populations are expanded as N (t) = N +
j 0j
matrix of the three-level system in a manner similar to (N e−iδt +c.c.), where j = g,e. Then the oscillating
1j
Wong et al. [15]. Such simulated spectra are shown partofthepopulationinversionW =N −N isfound
1 1e 1g
in Fig.3(b) for two values of the Raman coherence to be given by
linewidth. These confirm that the central resonance is
−W I Γ (Γ +Γ −2iδ)
not linked to the Raman coherences, unlike the EIT side W = 0 1 0 e g ,
peaks. 1 Isat(Γ0+Γe−iδ)(Γg−iδ)+I0Γ0(Γe+Γg−2iδ)
(3)
where
RI (Γ +Γ )
W =− sat 0 e (4)
0 I Γ (Γ +Γ )+I Γ (Γ +Γ )
sat g 0 e 0 0 g e
is the DC part of the population inversion, and I =
sat
Γ ¯hω/σ is the saturation intensity. When Γ = Γ = 0,
0 e g
Eq.(3)reducestotheusualCPOresonancewithawidth
given by Γ [16]. In contrast, when Γ (cid:28) Γ , assuming
0 g e
also that δ (cid:28)Γ ,Γ , Eq.(3) reduces to:
0 e
(cid:32) (cid:33)
I Γ Γ 1
W =−W 1 0 e . (5)
1 0IsatΓ0+Γe Γg+ ΓΓ00+ΓΓeeIIs0at −iδ
Equation (5) thus exhibits a resonance at δ = 0, with
a width limited by Γ at vanishing coupling intensities
g
FIG. 4: (color online) Simulations of the transmission of an I (cid:28)I . Figure4(a)reproducesthecorrespondingsim-
0 sat
open TLS in the case of (a) Γe/2π = Γ0/2π = 1.6MHz > ulation results, in which R is taken equal to the transit
Γ /2π=Γ /2π=2kHz,and(b)Γ =Γ (cid:28)Γ =Γ /2. Con-
g t e t g 0 rate Γ , Γ = Γ , and Γ = Γ (cid:29) Γ : each TLS along
tinuous blue: simulations with the Floquet expansion of the t g t e 0 g
each leg of the Λ system gives a resonance with a kHz
complete density matrix. Dashed purple: simple rate equa-
width limited by the transit time of the atoms through
tion model analysis. Inset: open TLS. Γ is the optical co-
coh
the beam. Our simple rate equation model (dashed pur-
herencerelaxationrate. (c),(d): Evolutionsoftheoscillating
parts ∆N = (N e−iδt+c.c.) and ∆N = (N e−iδt+c.c.) ple line in Fig.4(a)) is in very good agreement with a
e 1e g 1g
of the excited (continuous purple) and ground (dashed blue) simulation based on a first-order Floquet expansion of
state populations versus δ at a fixed time t = 0.25ms. (c): thefulldensitymatrix(continuousbluelineinFig.4(a)),
same parameters as (a). (d): same parameters as (b). showing the validity of the explanation of the extra res-
onance in terms of lower level CPO. This is confirmed
Ifthecentralresonanceis,aswesuspect,duetopopu- byFig.4(c),whichshowstheevolutionsoftheoscillating
lation oscillations in the lower state sublevels, we should parts ∆Ne =2Re(N1ee−iδt) and ∆Ng =2Re(N1ge−iδt)
be able to reproduce the experimental results in the rate of the excited and ground state populations at a fixed
equationapproximation,i.e.,withallthecoherencesadi- time t. The oscillations of the lower level population ex-
abatically eliminated. Using the notations defined in the hibitaresonancewithafewkHzwidth,whiletheoscilla-
caption of Fig.4, we model one of the legs of the Λ sys- tions of the upper level population have a much smaller
tem(eithertheσ+ ortheσ− transition)asanopenTLS, amplitude and exhibit no visible resonance at this fre-
the other leg of the Λ playing the role of an extra decay quency scale.
channel for the upper level. The rate equations for the It is worth noticing that, in the opposite case where
populations Ne and Ng in the upper and lower levels |e(cid:105) Γg (cid:29)Γe,onepredictstheexistenceofatransmissiondip
and |g(cid:105) are then given by of width Γe (see Fig.4(b)). Similar subnatural absorp-
tionfeatureswerediscussedboththeoreticallyandexper-
dN I imentally by different groups at the end of the eighties
e = −(Γ +Γ )N + σ(N −N ), (1)
dt 0 e e ¯hω g e and the beginning of the nineties [17, 18], with an em-
dN I phasis on FWM, considerably different from the point of
dtg = Γ0Ne+R−ΓgNg− ¯hωσ(Ng−Ne), (2) view developedhere. Figure 4(d)proves thatthenarrow
dip of Fig.4(b) is due to a decrease of the amplitude of
where σ is the absorption cross section, and Γ , Γ , and the oscillations of the lower level population.
0 e
Γ are the population decay rates of the excited state to However, our Λ system is more than an open TLS: it
g
thegroundone,theexcitedstatetootherstates,andthe consists of two open TLSs which are interdependent and
4
CPO resonances induced by the two legs of the Λ then
addconstructively,givingbirthtoasharpresonancelim-
ited by the decay rate of the populations of the ground
states. In contrast, in the lin (cid:107) lin configuration, the
populations of the two ground states oscillate in phase
(seeFig.5(c)),andthesystembehaveslikeaclosedTLS,
showing no resonance in the kHz range. Of course, as
shown in Fig.5(d), the system can still exhibit the much
broader, usualCPOresonancewithawidthgivenbyΓ ,
0
just like an ordinary closed TLS.
It is noted that similar resonances have appeared
in previous works, both experimental and theoretical
[19, 20]. However, these papers focused on electromag-
neticallyinducedabsorptionanddidnotdiscusstheexis-
tence of such sharp CPO-induced transmission windows.
FIG.5: (coloronline)(a)Simulatedprobetransmissionspec- The interest in CPO has been lasting for more than
trum in a Λ system in the lin ⊥ lin (continuous blue) and a decade since many people work on possible applica-
lin(cid:107)lin(dashedpurple)configurations. (b)Evolutionsversus tions of slow and fast light, in particular, for microwave
δ of the oscillating parts ∆N = (N e−iδt+c.c.) of the ex-
e 1e photonics [21–24]. Besides, recent theoretical proposals
citedstate(continuouspurple),and∆N =(N e−iδt+c.c.)
g1 1g1 suggestuseofsuchlong-livedCPOsevenforapplications
(dashed blue) and ∆N = (N e−iδt+c.c.) (dotted green)
g2 1g2 in spatial optical memories [25] or narrowband biphoton
of the two ground states, at a fixed time t in the lin ⊥ lin
generation [26]. The system described here is of interest
configuration. (c),(d) Evolutions versus δ of the oscillating
part ∆N of the excited state (continuous purple) and of the asitcanbemadetobehaveaseitheraclosedoranopen
e
sum ∆N +∆N of the oscillating parts of the two ground TLS by a simple change of the polarization direction of
g1 g2
statepopulations(dashedblue),inthelin(cid:107)linconfiguration. one of the coupling and probe beams. It also has the
advantage of exhibiting conservation of its total popula-
tion, avoiding the need for a repumping laser. Moreover,
excited by the same pair of coupling and probe fields. thedecayrateofthegroundstatepopulationisverylong
One could thus expect the lower level CPO of these two and is not limited by spontaneous emission, but only by
TLSstointerfereconstructivelyordestructively,depend- thetransitoftheatomsthroughthelaserbeam. OtherΛ
ing on the relative signs of their excitation fields. This systems in solids (such as rare-earth ions or NV centers
is why the results of Fig.5 permit us to compare the in diamonds) might even go beyond the present limita-
results of the Floquet simulations in our Λ system for tionsetbythetransittime. SuchcoupledopenTLSsare
perpendicular (lin ⊥ lin) or parallel (lin (cid:107) lin) linearly thus good candidates for the experimental implementa-
polarized pump and probe beams. Figure 5(a) shows tion of the recent theoretical proposals based on narrow
that the ground state CPO resonance is present only in CPO effects.
thelin⊥linconfiguration,butdisappearsinthelin(cid:107)lin
configuration. The authors thank Amrita Madan for interesting dis-
Indeed, in the lin ⊥ lin configuration (see Fig.5(b)), cussions, and acknowledge partial support from the
the populations of the two ground state sublevels oscil- Agence Nationale de la Recherche, the Triangle de la
late in antiphase, due to the fact that they are driven by Physique,andtheIndo-FrenchCenterforthePromotion
intensity modulations which are in antiphase. The two of Advanced Research (IFCPAR/CEFIPRA).
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