Electromagnetically Induced Transparency in optically trapped rubidium atoms

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by  Bernd Kaltenhäuser

Electromagnetically Induced Transparency
in optically trapped rubidium atoms
∗
Bernd Kaltenha¨user, Harald Ku¨bler, Andreas Chromik, Ju¨rgen Stuhler, and Tilman Pfau
5. Physikalisches Institut, Universit¨at Stuttgart, 70550 Stuttgart, Germany.†
Atac Imamoglu
Institute of Quantum Electronics, ETH-Zu¨rich, 8093 Zu¨rich, Switzerland
Wedemonstrateelectromagnetically inducedtransparency(EIT)inasampleofrubidiumatoms,
trapped in an optical dipole trap. Mixing a small amount of σ−-polarized light to the weak σ+-
polarizedprobepulses,weareabletomeasuretheabsorptiveanddispersivepropertiesoftheatomic
mediumatthesametime. Featuresassmallas4kHzhavebeendetectedonanabsorptionlinewith
7 20MHz line width.
0
PACSnumbers:
0
2

n INTRODUCTION We have measured 4kHz features in the EIT response.
a
This is an important step towards long storage times
J
of quantum information in an atomic ensemble and the
0
Electromagnetically induced transparency allows for investigation of trapped darkstate polaritons.
1
the elimination of absorption in an otherwise opaque

2 medium [1]. The effect is based on a third state, which
v is coupled to the excited state by an additional laser, EXPERIMENTAL SETUP
9
such that all possible absorption paths destructively
4
interfere. On the level of single excitations, the cor- To prepare an absorbing medium of trapped atoms,
0
1 responding collective excitations can be described as wefirstcapture4 109 Rb-87atomsinamagneto-optical
·
0 a quasi-particle, the so-called dark state polariton [2]. trap. Afterwards,weapplyaDark-MOTphase(DM)for
7 Recently,the particlenature ofdarkstatepolaritonshas 25 ms to ensure an efficient transfer of the atoms to the
0
been experimentally demonstrated [3]. dipole trap. For the DM, we ramp up the magnetic gra-
/
h In quantum information processing, photons can be dientfieldfrom13.7to18G/cm,detune the MOT-lasers
p used asrobustinformationcarriers[4], but they lack the to 100MHzfromresonanceandlowertherepumplaser
t- possibility of storage. To overcome this shortcoming, pow−er to 1%. After the DM we have 7 108 atoms at a
n several experiments have used the concept of dark state temperature of 38µK and a density of 1·012atomscm−3
a ·
u polaritons to store photonic information in cold atoms left.
q [5] and vapor cells [6]. Furthermore, as a step towards ThecrossedCO2-laserdipoletrap(DT)isturnedondur-
: storage in a solid, EIT has been demonstrated in a ingtheloadingstepsdescribedabove. Afterswitchingoff
v
i room-temperature solid [7]. It has also been shown theDMandadditional80msthermalizationtimewecap-
X theoretically that EIT in atomic ensembles can be used ture2 107atomsatadensityof2 1011atomscm−3inthe
· · ·
r to enhance the possibilities of long-distance quantum DT. Due to optical pumping, the atoms are distributed
a
communication [8]. overthe5magneticsubstatesofthe5S , F =2ground
1/2
Spin squeezing is often regarded as a benchmark for state. Because the potential of the DT is much steeper
the control of atom-light-states. This effect has already thanthe one ofthe DM,the cloudheatsup to atemper-
been demonstrated in a vapor cell via a quantum ature of 110µK. The cloud provides a medium with an
nondemolition measurement [9]. In magneto-optically opticaldensityupto0.76forasingleZeemancomponent
trapped cold atoms it has been demonstrated in a on resonance.
similar way [10], as well as by mapping the squeezed
state of light onto the atomic ensemble[11]. Recently, de For the EIT-measurements, a magnetic offset field of
Echaniz and co-workers have shown that this effect can 129G is applied parallel to the laser beam propagation.
be significantly increased in an optical dipole trap [12]. Atthisfieldstrength,themagneticsubstatesofthe5S
1/2
ground state can be addressed individually. This al-
Here, we report on the first experimental demon- lows to perform the EIT-measurement only between the
stration of EIT in an optical dipole trap. Contrary to (5S , F =2, m = 1) and (5S , F =1, m =+1)
1/2 F 1/2 F
−
magneto-optical and magnetic traps, our setup allows substates. WeuseaRamanlasersystemtoaddressthese
for arbitrary magnetic fields. A homogeneous magnetic transitions, which are shown in figure 1.
field can be used to address different magnetic substates
of the medium. ThesetupfortheEIT-measurementsisshowninfigure2.
2
THEORY
As described above, the first λ/4-plate mixes a rel-
ative intensity a2 of σ−-polarization into the otherwise
σ+-polarizedprobebeam. Duetobirefringenceintheop-
−
ticalviewportsofthevacuumchamber,theσ -polarized
beam collects an additional phase φ relative to the σ+-
polarized beam. The total electric field acting on the
atoms can then described via
|Ein|2 = Ein,σ+ +Ein,σ− 2
(cid:12) (cid:12) 2
FIG. 1: Level scheme of the EIT transition. The probe laser = (cid:12) 1 a2E +aE(cid:12) exp iφ
0 0
couples to the 5S1/2, F = 2, mF = −1 ←→ 5P1/2, F = (cid:12)(cid:12)p − { }(cid:12)(cid:12)
21,, mmFF ==+01t←ra→nsi5tiPo1n/,2,thFe=co2u,pmlinFg=la0setrratnostithioen5.S1/2, F = = (cid:12)E02(cid:16)1+2ap1−a2cosφ(cid:17) .(cid:12) (1)
Whenwetunethecouplinglasertoresonance,thesingle-
photon and two-photon detuning of the probe laser be-
comeidenticalandthesusceptibilityfortheσ+-polarized
probe laser is given by [14]
µ2̺
χ(+) = | |
ǫ ~
0
4δ(Ω2 4δ2 γ2)
c − −
×(cid:20) Ω2+(Γ+i2δ)(γ+i2δ)2
| c |
8δ2Γ+2γ(Ω2+γΓ)
+i c . (2)
Ω2+(Γ+i2δ)(γ+i2δ)2(cid:21)
| c |
To derive this equation, we have also assumed that the
relevant atomic population stays mainly in the initial
5S , F =2, m = 1state. Thisisfulfilled,ifastrong
1/2 F
−
couplinglaserorweakprobepulses(N N )
photons atoms
≪
FIG.2: Setupfortheexperiment: theprobeandthecoupling are used. Here, δ is the probe laser detuning, Ωc the
laserareoverlappedinapolarizingbeamsplitter(PBS).With Rabi-frequency of the coupling laser, Γ the spontaneous
the following λ/4-plate the polarization of the pulses are ad- emission rate between the excited state and the respec-
justedbeforetheyenterthecloud. Withthesecondλ/4-plate tive ground state, γ the collisional decay rate between
thepolarizationsareturnedagaintoseparatetheprobefrom
the two ground states and µ the dipole matrix element
the coupling beam in the following polarizing beamsplitter. | |
between the ground and the excited state.
Duetolenses(notshown inthepicture),thecloudisimaged
−
Due to the large Zeeman-shift, the σ -polarized beam
onto a high efficiency CCD camera.
doesnot fulfillthe Raman-conditionandthus its suscep-
tibility can be described by the two-level atom. As can
be seen in figure 3, one has to sum over the susceptibil-
ities of all four independent two-level systems, that can
interact with the beam. Due to the large detuning from
Forrevealingthedispersivepropertiesofthemedium,the
− resonance, absorption can be neglected (<0.04% in our
first λ/4-plate is turned, until a σ -polarized intensity
admixture of a2 = 8.7% to the probe beam is obtained. system), but the phase shift can become considerable.
The susceptibility is then described by [15]
The second λ/4-plate compensates this effect and mixes
bothpolarizationsbacktolinearlypolarizedlight,which
is then measured beyond the second polarizing beam- χ(−) = 4 |µj|2̺j ∆j +iΓ2 . (3)
splitter. This causes the two polarizations to interfere. Xj=1 ~ǫ0 (Γ2)2+∆2j
A similar method has recently been demonstrated with
a vapor cell in a Sagnac interferometer [13]. Here, ̺ are the populations in the respective ground
j
Due tothe largeZeeman-shiftofthe magneticsubstates, states, µ the dipole matrix elements and ∆ the detun-
j j
the Raman-condition is not fulfilled for the wrong po- ingsrelativeto the respectivetransition,while the decay
larizationsand thus the admixture in the coupling beam rateΓisthesameforallofthem. Thedetunings∆ also
j
can be neglected. depend on the probe detuning δ.
3
which finally yields the transmission through the cloud:
+∞
′ ′ ′
T (δ)= T(δ )F(δ δ )dδ (8)
P
Z −
−∞
Unfortunately, there is no analytic solution to this inte-
gral.
EXPERIMENTAL RESULTS
FIG. 3: Level scheme for the σ−-polarized component of the
We have measured the EIT-resonance spectrum for
probe light: the detunings of the respective transitions j are
three different lengths of the probe pulse: τ = 5µs,
marked as ∆ .
j
τ =20µs and τ =100µs. Figure 4 shows the data of one
measurementwitha pulselengthof20µsanda coupling
The electric output field is then given by laser Rabi-frequency of 1200kHz. In this measurement,
itcanbeseen,thatthesignalcontainsanabsorptive(the
|Eout|2 = Eout,σ+ +Eout,σ− 2 peakitself)aswellasadispersive(the asymmetry)part.
(cid:12) (cid:12)
(cid:12) (cid:12)
= 1 a2E exp iχ(+)kz/2
0
(cid:12)p − { } 1
(cid:12) 2
+(cid:12) aE exp iφ exp iχ(−)kz/2
0 { } { }(cid:12) 0.9
(cid:12)
(cid:12)
= a2exp Imχ(−)kz n T0.8
+ (1 a2{)−exp Im}χ(+)kz missio0.7
− − s
+ 2a 1 a2e(cid:0)xp Imχ(−(cid:1))+Imχ(+) kz/2 Tran0.6
p − n−(cid:0) (cid:1) o
cos φ+ Reχ(−) Reχ(+) kz/2 . (4) 0.5
× n (cid:0) − (cid:1) o
0.4
It can be seen that the first two terms of the equation −7.7 −7.6 −7.5 −7.4 −7.3 −7.2 −7.1 −7 −6.9 −6.8
δ / MHz
describetheusualbehavior,describedtherespectivesus-
ceptibility, while the last term is responsible for the in-
FIG.4: Transmission spectrumofa20µspulseatacoupling
terferenceandresultsintheappearanceofthedispersive
laserRabi-frequencyof1200kHz. Theabsorptiveanddisper-
properties of the medium.
sivepartsinthesignalcanberecognized. Thefrequencyoffset
Together with equations 1 and 2, this yields the total of δ0 = −7.27MHz corresponds to the differential quadratic
transmission through the medium via Zeemanshiftbetweenthetwogroundstatelevels. Thisoffset
does not depend on the lasers and can thus be used to cali-
E 2 brate the magnetic offset field. For the fit we used equation
out
T(δ)= | | . (5)
E 2 5 as an approximation.
in
| |
Because we are probing the sample with relatively short The value for the phase φ = 4.95 was obtained from
pulses, the pulse length limits the minimal EIT band- the fits of all measurements. The curve was fitted
width. The Gaussian pulses are defined as with equation 5 and yielded σ = 100kHz, γ = 8kHz
and δ = 7.27MHz for the frequency offset due to the
t2 0
I(t)=I exp . (6) quadratic Zeeman shift. The ground state decay rate γ
0 (cid:26)−τ2(cid:27)
usually corresponds to collisions between the atoms as
Toincludethislimitation,onehastoevaluatetheconvo- well as collisions with the background gas. The colli-
lutionintegraloverthe Fouriertransformedofthe Gaus- sionrateratecanusuallybe neglected,especiallyincase
sian pulse of large coupling laser Rabi-frequencies. But it can also
correspond to a transient effect: for low coupling laser
+∞ Rabi-frequencies, a steady state in the atomic popula-
F(δ)= I(t)exp I2πδt dt=√πτexp π2τ2δ2 , tion cannot be reached within the time of a short probe
Z { } −
−∞ (cid:8) (cid:9) pulse. Thiseffectshowsthesameempiricbehaviorasthe
(7) collisional loss of polaritons and leads to non-negligible
4
values of γ. opticaldensityof0.76predicts. Weattributethesesmall
The data in figures 5 and 6 show the results of the mea- discrepancies to a decrease in the optical density of the
surements with the 5µs and the 20µs pulses. For large trapped cloud during the experimental measurements.
couplinglaserRabi-frequencies,thecouplinglaserbroad- Smaller optical densities can be caused by a reduced
ens the line width, while for lower Rabi-frequencies, the number of optically trapped atoms, which is typically
pulse length is the limiting factor. observed in the course of the day, and lead to broader
theoretically expected line widths. The theory curve is
plotted for an optical density of 0.76.
The lack of sufficient coupling light results in an uncom-
200
plete transparency and limits the relative depth of the
EIT dip in the signal. This can be seen in figure 7.
Hz150
k
h /
dt
n wi100
o
bti
or
s
Ab 50
1
00 0.05 0.1 0.15 0.2 0.25 0.8 20 µs→ ← 5 µs
Ωc / Γ pth
e
d0.6
p
FIG.5: TheorycurveandEITmeasurementwith5µspulses. e Di
The figure shows the transparency width (Gaussian 1/e- ativ0.4
radius)dependingontheRabi-frequencyofthecouplinglaser. Rel
The probe pulses contain 3·105 photons within the size of 0.2
the cloud, which correspond to a maximum Rabi-frequency
of190kHz. Theerrorbarsreflecttheuncertaintyinthephase
0
φ. 0 0.05 0.1 0.15 0.2 0.25
Ω / Γ
c
FIG. 7: EIT measurement with 5µs and the 20µs pulses.
ThefigureshowstherelativedepthoftheEITdipdepending
350 on the Rabi-frequency of the coupling laser. The decrease
for small Rabi-frequenciescorresponds tothetransient effect
300 thatasteadystatecannotbereachedherewithinthetimeof
z a short probepulse.
H250
k
h /
dt200
wi
n
orbtio150 To obtain a very narrow line width, a measurement was
Abs100 made with 100µs long pulses, containing 3.9 106 pho-
·
50 tons within the size of the cloud, which corresponds to
a maximum Rabi-frequency of 360kHz. Figure 8 shows
0
0 0.05 0.1 0.15 0.2 0.25 theresultforacouplinglaserRabi-frequencyof590kHz.
Ω / Γ
c For lower values, the induced transparency was too low.
Due to inefficient EIT,the absorptivepartis so low that
FIG. 6: Theory curve and EIT measurement with 20µs
it is not visible anymore. Instead, due to a large phase
pulses. The figure shows the transparency width (Gaussian
shift, the dispersive part of the signal gets enhanced,
1/e-radius) dependingon the Rabi-frequency of the coupling
laser. The pulses contain 2·106 photons within the size of compared to the measurements shown before.
the cloud, which correspond to a maximum Rabi-frequency
of 220kHz. The width is much narrower than the one of the Toenhancethedispersiveeffect,theσ−-intensityadmix-
5µs pulses. ture a2 was increased to 25%, which also resulted in a
different differential phase shift φ = 4.1. With a Gaus-
Thesolidcurvesshowthelinewidththatshouldintheory sian 1/e-half width of 4kHz, this is to our knowledge
be obtainable withoursetup. ForlargeRabi-frequencies the narrowest EIT signal measured in ultracold atoms
applied on 5µs probe pulses, the measurements are in [16, 17]. Narrower signals of 30Hz have been mea-
∼
good accordance with the theory. For all others, the suredinbuffergascells,whereoneisnotlimitedbypulse
measured line widths are broader than the theory for an lengths [18, 19].
5
Baden-Wu¨rttemberg.
∗ Electronicaddress: [email protected]
† URL:http://www.pi5.uni-stuttgart.de
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ACKNOWLEDGEMENTS
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We gratefully acknowledgethe support of the Alexan- 061802(R) (2000).
der von Humboldt foundation and the Landesstiftung