Interacting double dark resonances in a hot atomic vapor of helium

Abstract

We experimentally and theoretically study two different tripod configurations using metastable helium (4He*), with the probe field polarization perpendicular and parallel to the quantization axis, defined by an applied weak magnetic field. In the first case, the two dark resonances interact incoherently and merge together into a single electromagnetically induced transparency peak with increasing coupling power. In the second case, we observe destructive interference between the two dark resonances inducing an extra absorption peak at the line center.

Full text

Page 1

PHYSICAL REVIEW A 84, 023811 (2011)
Interacting double dark resonances in a hot atomic vapor of helium
S. Kumar,1T. Lauprˆ etre,2R. Ghosh,1,*F. Bretenaker,2and F. Goldfarb2
1School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
2Laboratoire Aim´ e Cotton, CNRS-Universit´ e Paris Sud 11, F-91405 Orsay Cedex, France
(Received 9 February 2011; published 9 August 2011)
We experimentally and theoretically study two different tripod configurations using metastable helium (4He*),
with the probe field polarization perpendicular and parallel to the quantization axis, defined by an applied weak
magnetic field. In the first case, the two dark resonances interact incoherently and merge together into a single
electromagnetically induced transparency peak with increasing coupling power. In the second case, we observe
destructive interference between the two dark resonances inducing an extra absorption peak at the line center.
DOI: 10.1103/PhysRevA.84.023811 PACS number(s): 42.50.Gy, 42.25.Bs, 42.50.Nn, 42.50.Ct
I. INTRODUCTION
Electromagnetically induced transparency (EIT) in three-
level ? systems is a phenomenon in which an initially
absorbing medium is rendered transparent to a resonant weak
probe laser when a strong coupling laser is applied to a
second transition [1]. In addition to its being a quantum
interference phenomenon of fundamental interest, EIT has
been studied extensively for its numerous applications, such
asinslowandfastlight,lightstorage,sensitivemagnetometry,
and optical information processing. An extension of the
usual three-level EIT to a four-level double-EIT scheme has
been shown to expand the utility of EIT in a number of
additional, potentially useful and easily controllable coherent
nonlinear effects. These include engineering atomic response
by perturbing a dark state [2–4] and control of group velocity
via interacting dark resonances [5]. The interest in four-level
tripodlike atomic configurations started with an early work [6]
showing that in a tripod medium, there exists an internal
state subspace spanned by two orthogonal dark states, which
is immune to spontaneous decay. Subsequently, the creation
and measurement of a superposition of quantum states using
stimulated Raman adiabatic passage in a tripod have been
proposed and demonstrated [7,8]. Simultaneous enhancement
and suppression of a dark resonance have been observed by
nondegeneratefour-wavemixinginasolidinatripodlikelevel
configuration [9]. Large cross-phase modulation induced by
interacting dark resonances in a tripod system of cold87Rb
has also been reported [10]. Tripod configurations with two
probes and a common coupling beam have been studied in
a variety of contexts, theoretically for the magneto-optical
Stern-Gerlach effect [11], for the experimental demonstration
of light storage at dual frequencies [12], in a proposal for
all-optical quantum computation with efficient cross-phase
modulation, and sensitive optical magnetometry [13] and
experimentally for matched slow pulses using double EIT in
Rb [14] and also for the study of nonlinear Faraday effect
in an inverted Y model in Rb vapor [15]. Interacting dark
resonances in tripod configurations with two coupling beams
and a common probe have been used to obtain sub-Doppler
and subnatural narrowing of an absorption line, theoretically
by Goren et al. [16] and experimentally by Gavra et al. in
*rghosh.jnu@gmail.com
Rb [17]. A similar scheme has been suggested for applications
in logic gates and sensitive optical switches [18].
There are several such applications of controllable double
dark resonances in four-level tripod systems, and there are not
many experimental results on tripod systems reported in the
literature so far. In this context, we wish to probe a simple
system of4He* at room temperature. This medium has been
shown to be an ideal candidate for achieving ultranarrow (less
than 10 kHz) EIT in a three-level ? system involving only
electronic spins in the presence of Doppler broadening [19].
We have confirmed the true nature of the two-photon process
of EIT by our observation of asymmetric Doppler-averaged
Fano-like transmission profiles in the presence of single-
photon optical detunings.4He* has some peculiar favorable
properties. (i) Velocity-changing collisions enable us to span
the entire Doppler profile [20]. (ii) The absence of nuclear
spin simplifies the level scheme and eliminates the need
for repumping lasers compensating for losses into the other
ground-state hyperfine levels. (iii) Diffusive motion increases
the transit time of the atoms through the laser beam and
hence the Raman coherence lifetime. (iv) Collisions with
the ground-state atoms do not depolarize the colliding4He*.
Thus, there are no background atoms to contribute to noise.
(v) Penning ionization among identically polarized
atoms is almost forbidden [21]. In the present work, we show
that4He*isasuitablecandidateforrealizingacleanfour-level
tripod system in a room-temperature gas. The excited state
23P0(me= 0, |e?) of4He* can be coupled selectively to the
23S1sublevels, mg= −1 (|g−?), 0 (|g0?), and +1 (|g+?), by
copropagatinglaserbeamsataround1083nm,withσ+,π,and
σ−polarizations, respectively. The energy separation between
the 23P0and the next lower sublevel 23P1is large (29.6 GHz)
compared to the Doppler width (≈1 GHz), allowing one to
ensure that each transition is isolated. This is not the case, for
example, in Rb [17].
We focus on two different tripod configurations based on
the interaction of the atoms with linearly polarized coupling
and probe beams in the presence of a horizontal transverse
magnetic field. In the first case, the probe beam has vertical
linear (V) polarization and the coupling beam has horizontal
linear (H) polarization, while in the second case, the probe
beam has H polarization and the coupling beam has V
polarization. We can easily switch from one configuration
to the other by just a change in the orientation of a wave
plate used in the setup. The difference in the configurations
4He*
023811-1
1050-2947/2011/84(2)/023811(6)©2011 American Physical Society

Page 2

S. KUMAR et al.
PHYSICAL REVIEW A 84, 023811 (2011)
comes from the number of probe transitions used, yielding a
distinctive interplay of double dark resonances in each case.
With4He* at room temperature, using a weak magnetic field
and polarization selective transitions mentioned above, we
experimentally realize a tripod configuration with two probed
transitions in the first case and observe that the double dark
resonances add incoherently, as there is no coherence between
the two populated probe ground levels. This configuration
serves as a useful reference for the second configuration
studied with two coupling transitions. In the second case,
double dark resonances are related to coherent population
trapping in the ground states. As the number of excited states
is less than the number of ground states, transfer of coherence
doesnotplayanyrole[22].Thus,thesedoubledarkresonances
are not stimulated Raman peaks [16,23] but detuned EIT
peaks, interfering destructively with each other, leading to an
absorptiondipbetweenfornonzeromagneticfields.Wemodel
the system successfully and verify our experimental results.
The paper is organized as follows. In Sec. II, we describe
theexperimentalsetup.InSec.III,wepresenttheexperimental
results and compare them with our numerical simulations for
the two different tripod configurations. Our conclusions are
presented in Sec. IV, with hints of potential applications.
II. EXPERIMENTAL SETUP
The experimental setup is shown in Fig. 1. The helium
cell is 6 cm long, has a diameter of 2.5 cm, and is filled
with4He at 1 Torr. The cell is placed in a three-layer μ-
metal shield to isolate the system from Earth’s magnetic-field
inhomogeneities. Helium atoms are excited to the metastable
state by an rf discharge at 27 MHz. We use the 23S1→ 23P0
transitionof4He*(D0line)withthecouplingandprobebeams
derived from a single laser at nearly 1082.9 nm wavelength
(linewidth ? 10 MHz), with a beam diameter of 1 cm after
the telescope. The maximum available power for the coupling
beamisabout27mW,whichislargeenoughduetothefactthat
the saturation intensity in4He* is very low (0.167 mW/cm2).
A probe power of 100 μW has been used throughout. The
frequencies and intensities of the coupling and probe beams
PBS-2
Probe Coupling
AOM-1 AOM-2
λ/2
PBS-1
Laser and
beam shaping
He cell
µ-metal shield
λ/2
λ/4 PBS Photodiode
Rectangular coils
Telescope
FIG. 1. (Coloronline) Experimentalsetup.PBS,polarizingbeam
splitter; AOM, acousto-optic modulator; λ/2, half-wave plate; λ/4,
quarter-wave plate.
are adjusted by the amplitudes and the frequencies of the
rf signals driving the acousto-optic modulators AOM-1 and
AOM-2. In our experiment, a variable weak magnetic field
(B), generated by a pair of rectangular coils surrounding the
helium cell, removes the degeneracy of the lower sublevels.
These coils are able to produce a constant horizontal magnetic
field perpendicular to the direction of propagation of the laser
beams. We theoretically estimate the magnetic field, which is
constant within the cell area and experimentally verify it with
a teslameter.
III. DARK RESONANCE PROFILES IN BASIC
TRIPOD CONFIGURATIONS
We consider two different tripod configurations, with the
magnetic field parallel or perpendicular to the probe beam
polarization. The direction of the static magnetic field is taken
as the quantization axis. For the helium 23S1state, the Land´ e
g factor is 2.002. The magnetic field shifts the metastable
23S1(mJ) state by μBBmJg, where μB= e¯ h/2me= 9.274
× 10−24J/T is the Bohr magneton, and B is the applied mag-
neticfield.ThisgivestheZeemansplitting,?Z≡ μBBmJg/h
= 2.8 kHz for B = 1 mG. The Rabi frequency of the coupling
beam ?Cis much larger than the Zeeman splitting ?Z.
In the rotating-wave approximation [24], the Hamiltonian
of the system can be expressed as
H = H0+ HI.
(1)
H0is the unperturbed Hamiltonian,
H0=
?
i
¯ hωi|i??i|,
(2)
where i = e,g−,g0,g+ corresponds to the different levels,
labeledinFigs.2(b)and4(b).HIistheinteractionHamiltonian
involving the coupling and probe transitions.
The time evolution of the density matrix operator, in the
presence of decay, is obtained from the Liouville equation as
d
dtρ = −i
¯ h[H,ρ] + Rρ,
(3)
where R is the relaxation matrix. The density matrix elements
obey the conditions?
the excited state to the lower states with equal decay rates
?0/3 (?0= 107s−1), transit relaxation of the atoms through
the beams from all allowed states with a rate ?t(≈103s−1),
and Raman coherence decay with a rate ?R(≈104s−1). In
our simple model, we do not explicitly take into account the
Doppler effect but assume that the optical coherence decay
rate ?/2π would effectively be given by the width (≈1
GHz) of the transition in the Doppler-broadened medium.
This approximation has already been shown to be valid
in the case of EIT in a standard three-level system in
4He* [19,20].
iρii= 1 and ρli= ρ∗
il. The sources
of relaxation in our system are spontaneous emission from
A. First configuration
When we set the λ/2 plate in front of our helium cell at 45◦
totheincidentpolarizations,theprobebeamhasVpolarization
(σ), perpendicular to the magnetic field, while the coupling
023811-2

Page 3

INTERACTING DOUBLE DARK RESONANCES IN A HOT ...
PHYSICAL REVIEW A 84, 023811 (2011)
FIG. 2. (Color online) Tripod configuration with V-polarized
(σ±) probes and H-polarized (π) coupling.
beam has H polarization (π), parallel to the magnetic field
(Fig. 2). Levels |e? and |g−?(|g+?) are coupled by the σ+(σ−)-
polarized components of the weak probe beam of frequency
ωPanddetunings?P= ωeg∓− ωP∓ ?Z.Thestrongcoupling
beam of frequency ωCand detuning ?C= ωeg0− ωCcouples
the same excited level |e? with the level |g0?. The Raman
detuning is δ = ?P− ?C.
Weexperimentallymeasuretheevolutionofthetransmitted
probe intensity (in arbitrary units) versus Raman detuning (δ),
as shown in Figs. 3(a)–3(c), for coupling powers of 1, 10, and
22 mW, respectively, with magnetic fields of 0, 10, and 30 mG
at each coupling power.
We model the system by writing the optical Bloch equa-
tions (3) with the relevant interaction Hamiltonian, for a
coupling beam of Rabi frequency ?Cwith horizontal linear
polarization (π) and a probe beam of Rabi frequency ?Pwith
twocountercircularpolarizationcomponents(σ±)withrespect
to the quantization axis (z):
HI= −¯ h
2
??P
√2e−iωPt|e??g+| + H.c.
√2e−iωPt|e??g−| + ?Ce−iωCt|e??g0|
+?P
?
.
(4)
We take ?P? ?Cand consider ?Pto first order.
Weassumethatthecouplingbeamisatresonance(?C=0),
the populations ρg−g−and ρg+g+are approximately equal to
0.50, and ρg0g0≈ 0 ≈ ρee. Then the steady-state solutions of
the six coupled optical Bloch equations for the coherences
ρeg−= ˜ ρeg−e−iωPt, ρeg+= ˜ ρeg+e−iωPt, ρg0g−= ˜ ρg0g−ei(ωC−ωP)t,
(a)
(d)
(b)
(e)
(c)
(f)
FIG. 3. (Color online) (Left column) Experimentally measured
transmitted intensity (arb. units) versus Raman detuning δ, corre-
sponding to the configuration shown in Fig. 2, with magnetic field
B at 0 mG (black open squares), 10 mG (red circles) and 30 mG
(blue triangles), at coupling powers of (a) 1 mW, (b) 10 mW, and
(c) 22 mW. (Right column) (d),(e),(f) Corresponding numerically
calculated transmission profiles, with¯?C≡ 2π?C/?,¯δ ≡ 2πδ/?,
and¯?Z≡ 2π?Z/?.
FIG. 4. (Color online) Tripod configuration with H-polarized (π)
probe and V-polarized (σ±) coupling beams.
023811-3

Page 4

S. KUMAR et al.
PHYSICAL REVIEW A 84, 023811 (2011)
ρg0g+= ˜ ρg0g+ei(ωC−ωP)t, ρg+g−= ˜ ρg+g−, and ρg−g+= ˜ ρg−g+
give
˜ ρeg∓
¯?P
=
w∓/√2
2(a∓+¯?C−i
3) −
|¯?C|2
2(a∓−i¯?R)
,
(5)
where w∓= (ρg∓g∓− ρee) = 0.5, a∓=¯δ ∓¯?Z, and all rates
and frequencies, scaled by ?/2π ≈ 109Hz, are denoted by a
bar over the corresponding symbols.
The probe absorption and dispersion are proportional to the
imaginary and real parts of the susceptibility. We obtain an
expression for the probe susceptibility as
χ(ωP) =
A1
2√2
⎡
⎣
1
(a+−i
3) −
|¯?C|2
⎤
4(a+−i¯?R)
+
1
(a−−i
3) −
|¯?C|2
4(a−−i¯?R)
⎦,
(6)
whereA1= N|μeg|2w∓/¯ h?0,μeg−≈ μeg+= μegisthedipole
matrix element for the probe transitions, and N is the
atomic density. With the above reasonable approximations,
the imaginary part of the susceptibility from Eq. (6) is found
to be
?
Im[χ(ωP)] =3A1
√2
1 −3|¯?C|2
8
?
?
a2
++ ?2+
?
a2
−+ ?2
??
,
(7)
where ? =¯?R+3|¯?C|2
of two Lorentzians with centers at¯δ = ±¯?Zand full widths
at half maxima of 2?. The transmission profiles are generated
from exp[−kLIm[χ(ωP)]], where k is the magnitude of the
wave vector of the probe beam, and L is the length of the
helium cell. The transmission profiles versus scaled Raman
detuning (¯δ) are shown in Figs. 3(d)–3(f), with¯?C= 1.8 ×
10−3,5.7 × 10−3, and 8.6 ×10−3,respectively, corresponding
to the experimental coupling powers, with Zeeman shifts also
corresponding to the experimental values of the magnetic
field.
In this configuration, as seen in Fig. 3, at zero magnetic
field, we observe a single EIT peak at the line center [25].
Whenweapplyaweakmagneticfield,weobservedoubledark
resonances for low coupling powers. The two corresponding
peaks add incoherently. As we increase the coupling power,
these two peaks broaden and eventually merge together into
a single peak at the line center. To observe double dark
resonances, it is required that all population is optically
pumped into the |g−? and |g+? levels. The fact that this
configuration leads to an incoherent sum of two EIT peaks can
be easily understood. Indeed, the weak probe (treated to first
order in the Rabi frequency ?P) cannot create any coherence
betweenthetwopopulatedprobegroundlevels,|g−?and|g+?.
We can thus expect the system to behave as two independent
three-level systems connected by the single coupling beam,
witheachthree-levelsystemexhibitingitsrespectiveEITpeak
for its particular Raman resonance.
4
. The right-hand side of (7) is a sum
B. Second configuration
We now set the λ/2 plate in front of the helium cell at
a specific angle so that this plate behaves as neutral for the
incident polarizations; the probe beam has H polarization (π),
parallel to the magnetic field, while the coupling beam has
V polarization (σ), perpendicular to the magnetic field (see
Fig. 4). Levels |e? and |g−?(|g+?) are coupled by the σ+(σ−)-
polarizedcomponentofthestrongcouplingbeamoffrequency
ωCanddetunings?C=ωeg∓− ωC∓ ?Z.Aweakprobebeam
of frequency ωPand detuning ?P= ωeg0− ωPcouples the
same excited level |e? with the level |g0?.
We again model the system by writing the density-matrix
equations (3), with the corresponding interaction Hamiltonian
for a probe beam of Rabi frequency ?Pwith horizontal linear
polarization (π) and a coupling beam of Rabi frequency ?C
with two countercircular polarization components (σ±) with
respect to the quantization axis:
HI= −¯ h
2
??C
√2e−iωCt|e??g+| + H.c.
√2e−iωCt|e??g−| + ?Pe−iωPt|e??g0|
+?C
?
.
(8)
The main approximations used are to take ?P? ?Cand to
consider ?Pto first order while taking ?Cin all orders.
In our case, ?C= 0, as before. We assume that the
probe ground-level population ρg0g0is approximately equal
to unity, and ρg−g−≈ 0 ≈ ρg+g+≈ ρee. Then the steady-state
solutions of the three coupled optical Bloch equations for the
coherences ρeg0= ˜ ρeg0e−iωPt, ρg−g0= ˜ ρg−g0e−i(ωP−ωC)t, and
ρg+g0= ˜ ρg+g0e−i(ωP−ωC)tgive
˜ ρeg0
¯?P
2b +|¯?C|2
where w0= (ρg0g0− ρee) = 1, a∓=¯δ ∓¯?Z, b =¯δ +¯?C−
i
3, and all rates and frequencies, scaled by ?/2π ≈ 109Hz,
are denoted by a bar on top, as before.
We obtain an expression for the probe susceptibility as
A2(a−− i¯?R)(a+− i¯?R)
2b(a−− i¯?R)(a+− i¯?R) − q|¯?C|2
where q = (¯δ − i¯?R), A2= N|μeg0|2w0/¯ h?0, and μeg0is the
dipole matrix element for the probe transition. The absorption
and dispersion of the probe beam are proportional to the
imaginary and real parts of the susceptibility. With the above
reasonable approximations, we get the imaginary part of the
susceptibility from Eq. (10) as
2a2
4a2
=
w0
4
?
1
(i¯?R−a−)−
1
(a+−i¯?R)
?,
(9)
χ(ωP) =
2
,
(10)
Im[χ(ωP)] = 3A2
−a2
++ 4¯?Rxy + x2¯?2
++¯?Ry(2¯?R+ x) +¯?3
Rx
−a2
R+ 9¯δ2|¯?C|4
4
,
(11)
where x = 2¯?R+ 3|¯?C|2
We plot the experimentally measured transmitted intensity
(arb. units) in Figs. 5(a)–5(c) for coupling powers of 1, 10, and
22 mW. The corresponding numerically calculated transmis-
sion profiles versus scaled Raman detuning are reproduced in
Figs. 5(d)–5(f), with the corresponding values of¯?C= 1.8 ×
10−3, 5.7 × 10−3, and 8.6 × 10−3, respectively. In each case,
we plot the profiles matching the magnetic fields of 0, 10, and
2
and y =¯δ2+¯?2
Z.
023811-4

Page 5

INTERACTING DOUBLE DARK RESONANCES IN A HOT ...
PHYSICAL REVIEW A 84, 023811 (2011)
(a)
(d)
(b)
(e)
(c)
(f)
FIG. 5. (Color online) (Left column) Experimentally measured
transmitted intensity (arb. units) versus Raman detuning δ, corre-
sponding to the configuration shown in Fig. 4, with magnetic field
B at 0 mG (black open squares), 10 mG (red circles), and 30 mG
(blue triangles) for coupling powers of (a) 1 mW, (b) 10 mW, and
(c) 22 mW. (Right column) (d),(e),(f) Corresponding numerically
calculated transmission profiles, with¯?C≡ 2π?C/?,¯δ ≡ 2πδ/?,
and¯?Z≡ 2π?Z/?.
30 mG, as in the experiment. Our numerical simulations are
in good agreement with the experimental results.
This configuration, at zero magnetic field, as shown in
Fig. 5, is equivalent to the degenerate two-level system with
a σ±coupling and a π probe. In this case, we observe
a single EIT peak (black open squares) at the line center
[19]. Note that Kim et al. [26] observed electromagnetically
induced absorption (EIA) for the two-level degenerate system
(Fe= Fg− 1 with Fe? 1 and Fe= Fg) and this anomalous
EIA has been interpreted by the analysis of dressed-atom
multiphoton spectroscopy [27]. In our degenerate two-level
system (Fe= Fg− 1 with Fe= 0), in place of anomalous
EIA, we observe an EIT peak at the line center. This EIT
peak can be explained by the following change of basis,
which is a simple example of Morris-Shore transformation
[28]: Replace the two sublevels |g−? and |g+? with the
usual dark (|NC? = (|g−? − |g+?)/√2) and bright (|C? =
(|g−? + |g+?)/√2) states for coherent population trapping in
a three-level system (|g−?, |g+?, and |e?) for the coupling
beams. Since the transition |NC? → |e? is not allowed, we
have essentially obtained a three-level system (|C?, |g0?, and
|e?) with a probe and a coupling beam. Hence, we observe a
single EIT peak at the line center. The widths and heights of
the EIT windows increase with the coupling power.
When we apply a weak transverse magnetic field,
the degeneracy of the lower levels is removed. In this
case, two dark resonance peaks appear and they shift from
the zero detuning position with increasing magnetic field. The
separation between the two dark resonances varies linearly
with the applied magnetic field. The double dark resonance
cannot be explained in terms of transfer of coherence from
the excited level to the ground level [16,23] but these dark
resonancesaretwoEITpeaksatδ = ±?Z.Whenthecoupling
power is increased in the presence of the magnetic field, an
absorption line appears, much narrower and deeper than that
found in the first configuration, which is the signature of
an interference phenomenon between the two induced EIT
windows [3,18]. This is the main result of this paper. It is
visible both in the experimental data and in simulations that
these EIT peaks are asymmetric at 10- and 22-mW coupling
powers: The absorption dip walls are sharper than the external
transparency window lines. Although it is well known that
EIT profiles become asymmetric when the coupling beam is
optically detuned, the optical detuning given by the Zeeman
shift cannot explain such a shape: Indeed, the detuning in our
caseislessthan100kHzwhilehundredsofMHzarenecessary
to obtain any significant asymmetry in our system [29]. When
comparing these profiles with the ones obtained with the first
configuration (see Fig. 3), one notices here that the double
peak transmissions are much higher. For the two values of
the Zeeman shift used and at high-enough coupling powers
(10 and 22 mW), the transmissions are nearly as large as the
transmissionofthesinglepeakrecordedwithoutanymagnetic
field: Transmissions seem to be given by the total Rabi fre-
quency ?Cwhile the widths are much narrower than the width
expected with such a coupling intensity. The resulting very
deepabsorptionlineseemstonarrowwithincreasingcoupling
power instead of disappearing because of saturation. This is
very different from the first case, where the transmissions cor-
responding to 80 kHz of Zeeman shift remain roughly half the
transmission of this single peak and the saturation broadening
makes the dip disappear for 50 kHz of Zeeman shift. We
have checked that an incoherent addition of susceptibilities or
transmissionswouldgiveabehaviorsimilartothefirstcaseand
cannot explain the data recorded in the second configuration:
The absorption dip appearing at the line center is narrower
and deeper than is possible by adding two independent best-fit
EIT profiles. A common picture for EIT in three-level systems
is to consider that it is the result of interference between two
absorption paths, a direct absorption from the probed level,
and the other which is followed by induced emission and
reabsorptionbythecouplingbeam.Inourtripodconfiguration,
there can be emission and reabsorption with both σ+and σ−
coupling beams. The constructive or destructive nature of this
interferencemechanismdependsonthesignsofthesuperposi-
tionsinthetwodarkstatescorrespondingtothetwothree-level
systems.Inourcase,thecomponentsofthecouplingbeamlead
to opposite signs for the |g−? ↔ |e? and |g+? ↔ |e? transition
amplitudes. As a result, there is a destructive interference
between two EIT peaks at the center and we observe a sharp
absorption dip, looking like (but different in nature from)
EIA [22], flanked by two EIT (detuned) peaks [16]. It is
clear from Fig. 5 that for fixed magnetic fields, the widths
and heights of all the EIT windows increase while the width of
the absorption dip decreases with increasing coupling power
(thefullwidthsathalfmaximaoftheabsorptiondipsareabout
47, 42, and 34 kHz, for coupling powers of 1, 10, and 22 mW,
respectively, at B = 10 mG). In the absence of the magnetic
023811-5

Page 6

S. KUMAR et al.
PHYSICAL REVIEW A 84, 023811 (2011)
field, the narrow absorption dip disappears and the system
becomes transparent at the line center.
IV. CONCLUSIONS
We have been able to carve out a clean four-level tripod
system in a simple system of room-temperature4He* using
a weak magnetic field and polarization-selective transitions.
Interesting interplay between the double dark resonances has
been recorded.
In the firsttripod configuration with two probed transitions,
when the coupling is parallel to the weak magnetic field,
we have observed that two EITs (detuned) add incoherently,
and for large coupling power, these two peaks merge into a
single EIT-like peak at the line center. Such a double-EIT
configuration has potential application in light storage for
two frequencies [12,13] and coupling-induced switch in the
presence of a small magnetic field.
In the second tripod configuration with two coupling
transitions, when the probe is parallel to the weak magnetic
field, we have observed a remarkable destructive interference
between the two EIT peaks, leading to an extra, narrow
absorptionpeakbetweentheEITpeaks.Theabsorptionfeature
is seen to become narrower with increasing coupling power
and could be made subnatural even in the presence of Doppler
broadening [16]. We stress here that our results, shown in
Fig. 5, cannot be obtained from two independent EIT systems,
evenifoneallowsforasymmetricEITwindowsresultingfrom
detuned (by a few tens of kHz) coupling fields. The absorption
dip appearing at the line center is narrower and deeper than
is possible by adding two independent asymmetric EIT fits.
The separation between the observed EIT peaks is determined
by the applied magnetic field. Such a system may be used
as a magnetometer, although the field values used by us are
rather high. The shape of the resonances, however, depends
critically on the direction of the magnetic field, making the
sensoranisotropic.For known directionsofthemagnetic field,
the symmetry of the system offers a specific advantage based
on measurements of differences in frequencies [30]. In the
absenceofthemagneticfield,thenarrowabsorptionmaximum
disappears and the system becomes transparent at the line
center. It thus has the potential to be used as a magneto-optic
switch, with pulsed operation.
Wehavesuccessfullymodeledthesystem.Formixedpolar-
izations of the coupling and the probe along the quantization
axis, the structure of the resonances becomes complex and the
features are under further investigation.
ACKNOWLEDGMENTS
This work is supported by the Indo-French Centre for
Advanced Research (IFCPAR/CEFIPRA), and partiallybythe
Triangle de la Physique. The work of SK is supported by the
Council of Scientific and Industrial Research, India.
[1] S. E. Harris, Phys. Today 50, 36 (1997), and references therein.
[2] M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully,
Phys. Rev. A 60, 3225 (1999).
[3] S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Welch, and
M. D. Lukin, Phys. Rev. A 68, 063801 (2003).
[4] Y. Niu, S. Gong, R. Li, Z. Xu, and X. Liang, Opt. Lett. 30, 3371
(2005).
[5] M.Mahmoudi,R.Fleischhaker,M.Sahrai,andJ.Evers,J.Phys.
B 41, 025504 (2008).
[6] J.Martin,B.W.Shore,andK.Bergmann,Phys.Rev.A54,1556
(1996).
[7] F. Vewinger, M. Heinz, R. Garcia Fernandez, N. V. Vitanov, and
K. Bergmann, Phys. Rev. Lett. 91, 213001 (2003).
[8] R. G. Unanyan, M. E. Pietrzyk, B. W. Shore, and K. Bergmann,
Phys. Rev. A 70, 053404 (2004).
[9] B. S. Ham and P. R. Hemmer, Phys. Rev. Lett. 84, 4080
(2000).
[10] Y. Han, J. Xiao, Y. Liu, C. Zhang, H. Wang, M. Xiao, and
K. Peng, Phys. Rev. A 77, 023824 (2008).
[11] Y. Guo, L. Zhou, L. M. Kuang, and C. P. Sun, Phys. Rev. A 78,
013833 (2008).
[12] L. Karpa, F. Vewinger, and M. Weitz, Phys. Rev. Lett. 101,
170406 (2008).
[13] D. Petrosyan and Y. P. Malakyan, Phys. Rev. A 70, 023822
(2004).
[14] A.MacRae,G.Campbell,andA.I.Lvovsky,Opt.Lett.33,2659
(2008).
[15] R. Drampyan, S. Pustelny, and W. Gawlik, Phys. Rev. A 80,
033815 (2009).
[16] C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and
H. Friedmann, Phys. Rev. A 69, 063802 (2004).
[17] N. Gavra, M. Rosenbluh, T. Zigdon, A. D. Wilson-Gordon, and
H. Friedmann, Opt. Commun. 280, 374 (2007).
[18] J. Q. Shen and P. Zhang, Opt. Express 15, 6484 (2007).
[19] F.Goldfarb,J.Ghosh,M.David,J.Ruggiero,T.Chaneli` ere,J.-L.
Le Gou¨ et, H. Gilles, R. Ghosh, and F. Bretenaker, Europhys.
Lett. 82, 54002 (2008).
[20] J. Ghosh, R. Ghosh, F. Goldfarb, J.-L. Le Gou¨ et, and
F. Bretenaker, Phys. Rev. A 80, 023817 (2009).
[21] G. V. Shlyapnikov, J. T. M. Walraven, U. M. Rahmanov, and
M. W. Reynolds, Phys. Rev. Lett. 73, 3247 (1994).
[22] A.V.Taichenachev,A.M.Tumaikin,andV.I.Yudin,Phys.Rev.
A 61, 011802(R) (1999).
[23] R. Meshulam, T. Zigdon, A. D. Wilson-Gordon, and
H. Friedmann, Opt. Lett. 32, 2318 (2007).
[24] M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge
University Press, Cambridge, 1997).
[25] A. Lezama, S. Barreiro, A. Lipsich, and A. M. Akulshin, Phys.
Rev. A 61, 013801 (1999).
[26] S. K. Kim, H. S. Moon, K. Kim, and J. B. Kim, Phys. Rev. A
68, 063813 (2003).
[27] H. S. Chou and J. Evers, Phys. Rev. Lett. 104, 213602 (2010).
[28] E. S. Kyoseva and N. V. Vitanov, Phys. Rev. A 73, 023420
(2006).
[29] F. Goldfarb, T. Lauprˆ etre, J. Ruggiero, F. Bretenaker, J. Ghosh,
and R. Ghosh, C. R. Phys. 10, 919 (2009).
[30] V. I. Yudin, A. V. Taichenachev, Y. O. Dudin, V. L. Velichansky,
A. S. Zibrov, and S. A. Zibrov, Phys. Rev. A 82, 033807 (2010).
023811-6