# Observation of electromagnetically induced absorption in a vee + ladder
system

Mangesh Bhattarai  Department of Physics, Indian Institute of Science,
Bangalore - 560012  Vineet Bharti  Currently at Institute for Molecular
Science, National Institutes of Natural Sciences, Okazaki, Aichi 444-8585,
Japan Department of Physics, Indian Institute of Science, Bangalore - 560012
Sambit Banerjee  Currently at Department of Physics and Astronomy, Purdue
University, West Lafayette, Indiana 47907, USA Department of Physics, Indian
Institute of Science, Bangalore - 560012  Vasant Natarajan
<EMAIL_ADDRESS>Department of Physics, Indian Institute of
Science, Bangalore - 560012

###### Abstract

We experimentally demonstrate electromagnetically induced absorption (EIA) in
a vee + ladder system. The experiment is done using the low-lying energy
levels of 87Rb. A theoretical model of the system is made that reproduces the
experimental results. We study the dependence of the characteristics of the
EIA resonance on various combinations of the different control powers. We also
explore the contribution of various incoherent phenomena that affect the EIA
signal.

##  I Introduction

The phenomenon of EIT has been well studied over the years in lambda
($\Lambda$), vee (V) and ladder ($\Xi$) type systems. EIT creates transparency
for a weak probe in an otherwise absorbing medium in the presence of a strong
control beam by nonlinear modification of the susceptibility of the medium
FIM2005 . This has led to a variety of applications including in slow light
HHD1999 ; BKR1999 ; KSZ1999 , storage of light LDB2001 ; PFM2001 , lasing
without inversion ZLN1995 , four wave mixing HKD1995 , giant Kerr effect
SCI1996 ; MBB2008 , high resolution spectroscopy KPW2005 , laser frequency
stabilization MLK2004 , and phase stabilization of independent sources BKN2019
.

Similar to the phenomenon of EIT is the phenomenon of electromagnetically
induced absorption (EIA), except that the probe shows an enhanced absorption
and a negative dispersion slope (as opposed to the positive slope in EIT) at
line center. EIA has been reported in four level N type systems YZR2002 ;
GWR2004 ; BMW2009  with two control beams and one probe beam, in degenerate
two level systems CSB2011 ; DBD2016 ; LBA1999  and recently in a three level
system WBK2015 . Recently, we have theoretically proposed a new kind of four-
level EIA system in a vee + ladder configuration BHN2015 . Using this scheme,
we have presented the first theoretical observations of Rydberg EIA BWN2016
and tuning of the group velocity of light between sub- and super-luminal
propagation using a Rydberg state BHN2017 . This system has drawn much
attention, and has been utilized for the investigation of amplitude noise in
non-classical states of light MLY2016 , optical bistability HSK2017 ,
generation of an all-optical diffraction grating BOS2018  and atom
localization HSK2018 . In this work, we report the first experimental
observation of EIA in such a system.

Figure 1: (a) Energy levels depicting the formation of the vee + ladder
system, (b) Levels represented in a dressed state picture.

We begin with a qualitative look at the phenomenon of EIA in terms of the
dressed state picture. The vee + ladder system is formed by 87Rb interacting
with two copropagating fields $\Omega_{v}$ and $\Omega_{p}$ and a
counterpropagating field $\Omega_{l}$, coupling the levels shown in Fig. 1
with detunings $\delta_{v}$, $\delta_{p}$ and $\delta_{l}$, respectively. The
interaction Hamiltonian is given as BHN2015

$\displaystyle H=$
$\displaystyle-\frac{\hbar}{2}\left[\Omega_{v}\ket{1}\bra{2}+\Omega_{p}\ket{2}\bra{3}+\Omega_{l}\ket{3}\bra{4}\right]+\rm
h.c.$ (1)
$\displaystyle-\hbar\left[0\ket{1}\bra{1}-\delta_{v}\ket{2}\bra{2}+(-\delta_{v}+\delta_{p})\ket{3}\bra{3}+(-\delta_{v}+\delta_{p}+\delta_{l})\ket{4}\bra{4}\right]$

The field $\Omega_{v}$ mixes the states $\ket{1},\ket{2}$ to form the dressed
states $\ket{D_{g}^{1}},\ket{D_{g}^{2}}$ and the field $\Omega_{l}$ mixes
$\ket{3},\ket{4}$ creating the dressed states
$\ket{D_{e}^{1}},\ket{D_{e}^{2}}$. The dressed state energy is as indicated in
Fig. 1(b). A weak probe $\Omega_{p}$ scanned across resonance gives 4
absorption peaks at the following values of probe detuning, $\delta_{p}=$

$\displaystyle
1/2(-\delta_{l}+\delta_{v}+\sqrt{\delta_{l}^{2}+\Omega_{l}^{2}}-\sqrt{\delta_{v}^{2}+\Omega_{v}^{2}}),$
(2) $\displaystyle
1/2(-\delta_{l}+\delta_{v}-\sqrt{\delta_{l}^{2}+\Omega_{l}^{2}}+\sqrt{\delta_{v}^{2}+\Omega_{v}^{2}}),$
$\displaystyle
1/2(-\delta_{l}+\delta_{v}-\sqrt{\delta_{l}^{2}+\Omega_{l}^{2}}-\sqrt{\delta_{v}^{2}+\Omega_{v}^{2}}),$
$\displaystyle
1/2(-\delta_{l}+\delta_{v}+\sqrt{\delta_{l}^{2}+\Omega_{l}^{2}}+\sqrt{\delta_{v}^{2}+\Omega_{v}^{2}})$

For an atom moving with a velocity $v$, the position of the peaks are found by
the substitution $\delta_{p}\to\delta_{p}-kv$, $\delta_{v}\to\delta_{v}-kv$,
$\delta_{l}\to\delta_{l}+kv$. Along with the condition $\Omega_{v}=\Omega_{l}$
and $\delta_{v}=-\delta_{l}$, the peaks lie at
$\delta_{p}=\delta_{v},\delta_{v}+\sqrt{\Omega_{v}^{2}+(\delta_{v}-kv)^{2}},\delta_{v}-\sqrt{\Omega_{v}^{2}+(\delta_{v}-kv)^{2}}$.

The first peak has no dependence on the velocity of atom, and the second and
the third peaks lie symmetrically on the right and left side of the first
peak, respectively, for any $v$. In a thermal ensemble, the first peak for all
velocity groups occurs at the same value of the detuning and consequently
grows giving a narrow absorption feature. The peaks on either side get spread
around different values of the detunings, only to give a small rise to the
absorption beyond detuning larger than $\Omega_{v}$ from the first peak. Thus
the resonance condition for EIA can be stated as

$\delta_{p}-\delta_{v}=0\quad{\text{and}}\quad\delta_{p}+\delta_{l}=0$ (3)

which is just a statement about the simultaneous EIT condition for the vee and
ladder branches of the system. When both the control fields are on resonance
($\delta_{v}=\delta_{l}=0$), EIA occurs at $\delta_{p}=0$.

Figure 2: Experimental schematic. Figure key: FI – Faraday isolator; SAS –
saturated absorption spectroscopy; PBS – polarizing beam splitter cube; PD –
photo-diode; $\lambda/2$ – half wave retardation plate; M – dielectric mirror.

##  II Experimental details

The experimental setup is shown in Fig. 2. It consists of three feedback-
stabilized ECDLs — two home-built lasers operating around 780 nm and 795 nm
and a Toptica DL Pro laser operating around 776 nm. The beams from the lasers
are Gaussian and have $1/e^{2}$ diameters of 1.4 mm $\times$ 2.2 mm, 1.9 mm
$\times$ 1.6 mm and 1.9 mm $\times$ 1.6 mm, respectively. The 780 nm laser is
operated around the $F_{g}=2\to F_{e2}=3$ transition in the D2 line of 87Rb. A
portion of the laser goes to a saturated absorption spectrometer used as
frequency reference and the rest to the main experiment. The 795 nm laser on
the D1 line of 87Rb is locked to the $F_{g}=2\to F_{e1}=2$ transition by
modulation of the injection current using another saturated absorption
spectroscopy setup. The 780 nm laser serves as the probe and the 795 nm laser
(henceforth referred to as the vee-control) serves as the control for the vee-
type EIT branch of the total setup. These two beams are combined at PBS3 and
co-propagated to a Rb vapor cell. The vapor cell is cylindrical in shape, of
length 50 mm and diameter 25 mm. It contains the 2 stable Rb isotopes in their
natural abundances (72.17 % 85Rb and 27.83 % 87Rb). It is placed inside a
framework holding three pairs of Helmholtz coils which are used to null the
magnetic field around the cell. Counter propagating to the probe and the vee-
control beams within the Rb vapor cell is the 776 nm laser beam coupling the
$F_{e2}=3\to 5D_{5/2}$ line in 87Rb. This beam forms the control beam for the
ladder EIT branch of the system and will be reffered to as ladder-control. The
PBS2 after the vapor cell serves to counter-propagate the ladder-control beam
as well as separate the probe beam from the vee-control beam. The probe is
collected on the photo-diode PD and the spectrum is recorded on a digital
storage oscilloscope.

##  III Results and discussion

We begin by summarizing EITs in vee and ladder systems and demonstrate
transformation of EIT to EIA when both controls are simultaneously operating.
Figs. 3(a) and (b) show EITs in vee and ladder systems, respectively, for
different powers in the respective control beams.

Figure 3: EIT for different systems. (a) Vee (b) Ladder

The vee system is formed by the probe on $F_{g}=2\to F_{e2}=3$ in the D2 line
and the control on $F_{g}=2\to F_{e1}=2$ in the D1 line. As has been studied
earlier FSM1995 , transparency in the vee system is contributed to by a lot of
other factors besides coherent EIT effects, namely (i) saturation effect which
is ever-present as the control is coupled to the ground state, (ii) optical
pumping to the uncoupled hyperfine level and (iii) optical pumping within the
magnetic sublevels. In the current experiment, optical pumping to the
uncoupled hyperfine level exists because the control couples the $F_{g}=2$
ground state to $F_{e1}=2$ excited state which could decay to the ground state
$F_{g}=1$ not coupled by any light. This adds to probe transparency by loss of
atoms from the interacting levels.

It is seen in Fig. 3(a) that smaller values of the control power (increase
from 0.4 mW to 2 mW) increases the EIT height. Larger control powers (6 mW and
14.6 mW), however, seriously depletes the number of atoms available for EIT
decreasing its strength. A strong control addresses transition for a larger
group of velocities which increases the background transmission by increasing
the probe transparency on either side of the resonance. This process at the
same time decreases the strength and increases the width of the EIT. The
broadening effect is also associated with the increase in the transparency
window caused by higher Rabi frequency of the control. The other effect
contributing to transparency is optical pumping within the magnetic sublevels.
It depends on the polarization combination of the probe and the control beams.
Having orthogonally linearly polarized control and probe adds to transparency
of the probe by Zeeman optical pumping.

Fig. 3(b) shows EIT formed in the ladder system comprised of the probe on the
$F_{g}=2\to F_{e2}=3$ at the D2 line and the control on the $F_{e2}=3\to
F_{e3}=4,3,2$ in the hyperfine levels of 5D5/2 state. In the figure, the
transmission peak at zero detuning of the probe corresponds to the EIT with
the control on the $F_{e2}=3\to F_{e3}=4$ transition. The other two peaks at
the positive value of detunings are EITs corresponding to $F_{e3}=3,2$ levels.
The different powers of control used depicts the transformation of lineshape
of the EIT signal. The EIT corresponding to $F_{e3}=4$ transition
distinctively shows combination of two spectral profiles for powers of 20 mW
and 50 mW. The broad profile is caused by saturation effect on the probe
transition and optical pumping effects due to some population transfer induced
by the probe beam. This has been reported earlier in literature as double
resonance optical pumping (DROP) effect MLK2008 . Over this profile a narrow
EIT feature is formed. The strength of the EIT signal increases with the
control power, as is evident from the figure. For the case of 5 mW power in
the control beam, there is no clear distinction between the DROP effect and
EIT. A similar undifferentiation of the different spectral profiles are seen
in EITs for $F_{e3}=3,2$ levels. Atoms in these levels can decay to the
uncoupled $F_{g}=1$ hyperfine level in the ground state via the intermediate
$F_{e2}=2,1$ hyperfine levels in the 5P3/2 state. It creates an incoherent
transparency window at the expense of the EIT signal. Thus, a narrow EIT
signal is not distinctly visible. This is observed at higher values of the
control powers too.

Figure 4: EIA spectrum. (a) Experimental data with probe and control powers as
shown. (b) Theoretical result with probe and control Rabi frequencies as
shown. The Rabi frequency of the controls does not correspond to the powers
shown in part (a), for the reasons explained in the text.

When the two control beams are acting simultaneously, we observe EIA dip over
the broader vee EIT. This has been illustrated in Fig. 4(a). With both the
control beams at resonance, the EIA occurs at zero probe detuning. When the
vee-control is detuned by about $+25$ MHz from resonance and the ladder-
control by about $-25$ MHz, the EIA occurs at the probe detuning of 25 MHz in
agreement with the condition we stated earlier.

The theoretical analysis has been presented earlier BHN2015  and only the
relevant parts are discussed here. We have considered the three hyperfine
levels in the 5D5/2 manifold with the branching ration of 0.65 HEA1961 . The
theoretical spectrum shown in part (b) of the figure, is shown for the EIA
condition (that Rabi frequencies of the two control beams are equal) — the
Rabi frequencies for the values of the control powers does not reproduce the
experimental data. This is because the theory assumes a uniform intensity for
the two control beams. In addition, magnetic sublevels of the hyperfine levels
are ignored GWR2004 .

For the trace in 4(a), the power in the probe beam is 50 $\upmu$W. The ladder-
control power is $10$ mW (corresponding to a Gaussian peak intensity of $838$
mW/cm2) and the vee-control power is $0.4$ mW (corresponding to a Gaussian
peak intensity of 34 mW/cm2). Theoretically, to obtain an EIA the Rabi
frequencies of the two control beams should be equal. Assuming this condition
FOO2007 , the ratio of the intensities in the ladder- and the vee-control has
to be

$\dfrac{I_{\Xi}}{I_{V}}=\left(\dfrac{\lambda_{V}}{\lambda_{\Xi}}\right)^{3}\dfrac{\tau_{\Xi}}{\tau_{V}}$
(4)

Substituting the values of the wavelengths and the lifetimes of the
transitions SGO2008 ; STE2015 , we see that this ratio is 9.26. The ratio of
intensities at the center of the Gaussian for the result in Fig. 4(a) is
almost three times more. We list a few reasons for this to be so.

  1. 1.

The beams used in the experiment have different Gaussian profiles and we do
not expect them to align within the cell.

  2. 2.

The system under consideration has multiple vee + ladder systems with
different relative strengths of the two controls formed because of the Zeeman
sublevels, thus making the splitting of EIA apparent only at high control
intensties GWR2004 .

  3. 3.

The absorption peak is not entirely a coherent EIA effect but also has
contributions from incoherent phenomena.

One way to understand the contribution of incoherent effects in EIA will be to
consider what effect does the ladder system have on an already present vee
EIT. At large detuning of the probe (larger than width of the ladder EIT), the
presence of the ladder control does not have any effect qualitatively. Near
resonance, when the ladder control is introduced, some additional atoms are
driven out of the interacting levels (by optical pumping effects) and a small
fraction lie on the two excited states ($F_{e2}=3$ and $F_{e3}=4$). This would
decrease the number of atoms in the ground state ($F_{g}=2$). On one hand the
probe transparency is increased just because there are fewer number of atoms
to absorb it, but on the other hand probe absorption could increase due to
reduction in probe saturation as more atoms are excited from $F_{e2}=3$ by the
ladder control. Thus, optical pumping and saturation effects, depending on
which of the phenomena is dominant, either subtract from or add to the EIA
signal. The role of redistribution among the Zeeman sublevels is more
complicated. The strong $\pi$-polarized vee-control induces optical pumping
such that there is maximum population in the $m_{F_{g}}=0$ sublevel, and
decreasing as $|m_{F_{g}}|$ increases. In this configuration, the atoms are
less strongly coupled to both the vee-control and the $\sigma^{\pm}$ polarized
probe beam on the $F_{g}=2\to F_{e2}=3$ transition. Some of the atoms excited
to the $F_{e2}=3$ level by the probe also undergo a rearrangement due to the
strong $\pi$-polarized ladder control. In both cases of $F_{e3}=4$ and
$F_{e3}=3$ levels, the atoms tend to accumulate on the $m_{F_{e2}}=0$
sublevel, but differ quantitatively. Decay from this sublevel contributes to
populate the $m_{F_{g}}=0$ sublevel in the $F_{g}=2$ hyperfine level as it is
most strongly coupled. The other sublevels are less populated due to weaker
couplings to corresponding excited sublevel and fewer number of atoms in them.
Consequently, the number of atoms strongly coupled to the vee-control
decreases. This could thereby contribute to the reduction of the the strength
of the vee plus ladder EIA as well.

Figure 5: EIA spectra for a fixed value of power in the vee-control beam and
varying powers in the ladder-control beam, as listed. (a) $P_{V}=0.4$ mW. (b)
$P_{V}=2.0$ mW. (c) $P_{V}=6.0$ mW. The traces are offset for clarity.

We have studied EIA for different powers in the two control beams, as shown in
Fig. 5. Each of the parts shows the spectrum for a fixed power in the vee-
control and a varying power in the ladder-control. In Fig. 5, it can be seen
that as the power in the ladder-control is increased, the EIA feature gets
broader and eventually splits creating an EIT within. This occurrence of EIT
within EIA has been theoretically predicted as well BHN2015 . The evolution of
the relative heights of the EIT and the EIA signal is interesting. At low vee-
control powers, it is a significantly strong EIT over an EIA feature. With
higher vee-control power, this EIT feature declines in strength and almost
vanishes into the EIA as the vee-control power is further increased. This can
be attributed to optical pumping of atoms from the interaction levels.

Figure 6: EIT spectra for the $F_{e3}=3$ hyperfine level with controls on
resonance, for fixed value of power in the vee-control beam and varying powers
in the ladder-control beam, as listed. The traces are offset for clarity.

We observe that the EIA dip, for $F_{e3}=3$ at resonance shown in Fig. 6, does
not split for any power of the ladder-control. Here, optical pumping to other
hyperfine levels is quite high because of several available decay channels in
the ladder part of the system. The EIA feature remains intact but only
increases in height due to the combined effect of the coherent and incoherent
phenomena, discussed earlier. It is noteworthy that the width of the EIA is
smaller than the corresponding EIT in Fig. 3(b), indicating the coherent
origin of the EIA dip.

##  IV Conclusion

In this paper, we have reported the experimental observation of
electromagnetically induced absorption in a vee + ladder system. We have also
studied the effects of the strengths of the two control beams on the EIA
lineshape. A theoretical analysis has shown that the appearance of an
absorption dip has contributions from several incoherent phenomena besides
EIA, in real experimental systems. The system considered exhibits a conversion
between EIT and EIA, thus enabling the tunability of the light from sub-
luminal to super-luminal transmission. An experimental observation of a vee +
ladder EIA is the first step towards realizing the possibilities mentioned in
the introduction.

## Acknowledgement

We would like to thank Kavita Yadav for insightful discussions on the
interpretation of the results. We would also like to thank Anish Bhattarcharya
for help with the experiment. This work was supported by the Department of
Science and Technology, India.

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