Coherent population trapping resonance structure
in paraffin-coated Rb vacuum cells
S. Gateva*, E. Alipieva, E. Taskova and G. Todorov
Institute of Electronics “Academician Emil Djakov”, Bulgarian Academy of Sciences,
72 Tzarigradsko Chaussee, 1784 Sofia, Bulgaria
ABSTRACT
The fast development of CPT applications and the need of good magnetooptical sensors result in an increased interest in
the Coherent Population Trapping (CPT) resonances and the processes that determine their shape. In this work the shape
and width of the CPT resonances are investigated in two different paraffin-coated Rb vapor cells from point of view of
understanding the processes influencing the shape of the resonances and building of miniature and sensitive detector. The
dependence of the shape of the resonances on the laser power is measured. Narrow resonances on three hyperfine
transitions of the D1 87Rb line are registered. For explanation of the bright structure in the resonance shapes at low laser
powers analysis of the influence of different processes is made.
Keywords: coherent population trapping, line shapes and line widths, coated cell, magnetometry
1. INTRODUCTION
During the last decade many applications of Coherent Population Trapping (CPT) resonances in high-resolution
spectroscopy, quantum information storage and processing, metrology (atomic clocks), magnetometry, lasing without
inversion, laser cooling, ultraslow group velocity propagation of light etc. have been demonstrated1-4. Although for
different applications the restrictions for the signals are different, in most of the cases narrow resonances, high signal-tonoise ratios and compact design are needed.
Usually the CPT resonances are measured in alkali atoms cells. CPT resonances, prepared and registered in different
ways have been investigated in vacuum, buffer gas and antirelaxation wall-coated cells. Different narrowing mechanisms
have been developed5.
In vacuum cell, the main decoherence factors are the transit time broadening and the power broadening1. Due to
interaction with the laser beam atoms are prepared in coherent state. Atom-wall collisions destroy the coherence and lead
to atom velocity thermalization (Maxwellian velocity distribution of atoms). The minimum width of the CPT resonance
in the case of uncoated vacuum cell is at low power when the laser beam is expanded to the whole cell. A demonstration
of this is the measured narrow structure due to Rayleigh scattering light6,7.
Two methods are used to reduce resonance broadening due to collisions of the atoms with the cell walls - buffer gas in
the cell and antirelaxation coating of the cell walls. In the first case, the additional buffer gas (neon, argon, helium or
nitrogen) keeps by collisions the alkali atoms from the walls. As these gases are with low polarizability, they have weak
influence on the ground state of the alkali atoms. This method was applied for fabrication of miniature atomic clocks and
magnetometers8. Buffer gas pressure of the order of tens kPa was used. In the second case, an antirelaxation coating is
applied to increase the decoherence time. In paraffin coated cells the atom coherence can survive up to 10 000 collisions
with the cell walls9. Resonance widths less than 1 Hz at room temperature are measured in 3 cm size alkene coated cell10.
In 3 mm size paraffin-coated Cs cell the obtained coherence is 20 Hz11. The measurements in cell with both paraffin wall
coating and buffer gas show that in this case there is slightly narrowing than in the buffer gas cell12.
In this work the dependence of the CPT resonance shape on the laser power is investigated in two different paraffincoated Rb vapor cells from point of view of understanding the processes influencing the resonance widths and
amplitudes, and building of miniature and sensitive magnetooptical detector with antirelaxation paraffin-coated vacuum
cell. Narrow resonances on three hyperfine transitions of the D1 87Rb line are registered. Analysis of the processes that
could be a reason for the measured bright structure in the resonance shape at low laser powers is made.
*[email protected]; phone +359 2 9795924; fax +359 2 9753201
16th International School on Quantum Electronics: Laser Physics and Applications,
edited by Tanja Dreischuh, Dimitar Slavov, Proc. of SPIE Vol. 7747, 77470G · © 2011
SPIE · CCC code: 0277-786X/11/$18 · doi: 10.1117/12.883017
Proc. of SPIE Vol. 7747 77470G-1
2. EXPERIMENTAL SETUP
All measurements are performed by means of Hanle effect configuration. The CPT resonance is created on the Zeeman
sublevels of the ground 52S1/2 87Rb state after excitation with linear polarized laser light resonant to one of the hyperfine
transitions of the D1 line (Fg→Fe=2→1; 2→2; 1→1;1→2). The experimental geometry is shown in Figure 1. A singlefrequency diode laser with the light propagating along the cell’s axis x and polarization in z direction was used. Its
frequency and emission spectrum were controlled by observing fluorescence from a second Rb vapor cell and a FabryPerrot spectrum analyzer. A solenoid created magnetic field collinear to the laser beam. The gas cell and the solenoid
were placed in a three-layer μ-metal magnetic shield. The laser-induced fluorescence was detected by a photodiode in the
Figure 1. Experimental geometry.
y direction and the dependence of the fluorescence on the magnetic field was registered on a digital oscilloscope with
sweep time of the magnetic field 3 s. Resonances in fluorescence were examined in two cylindrical paraffin-coated
vacuum cells. The cell a is with length 2.5 cm and diameter 2 cm. The cell b has the same length (2.5 cm) and diameter
1.4 cm. Both cells contain an enriched 87Rb isotope. All measurements were done at room temperature (250C). The CPT
resonances were detected at laser power densities from 12 μW/cm2 to 1.8 mW/cm2 and magnetic field tuning ranges
from ±1.82 mG to ±1.2 G. This allows us to investigate accurately the measured complex structure of the CPT
resonance.
3. SHAPE OF THE CPT RESONANCES
We have investigated the coherent resonances on all hyperfine transitions of the D1 87Rb line. Resonances were
registered only on the dark transitions: Fg→Fe=2→1; 2→2; 1→1. In Figure 2 the dependence of the shape of the CPT
resonances on the laser power density in cell a and cell b on the D1 87Rb line (Fg=2→Fe=1 transition) is presented. The
magnetic field tuning range ±400mG gives more detail view on the central part of the complex CPT resonance shape.
At 180 μW/cm2 the resonances have dual structure shape in both cells – a narrow resonance superimposed on a broad
pedestal. In cell a the amplitude of the pedestal in this tuning range is equal to the amplitude of the narrow resonance. In
cell b the amplitude of the pedestal is about 30% smaller. The width of the pedestal is the same in both cells. The
amplitude and width of the pedestal decrease with decreasing the laser power. At higher than 180 μW/cm2 powers the
amplitudes of the pedestal and the narrow structure increase and they broaden.
The narrow structure in the resonance shape has the typical for a coated cell resonance shape (Figure 3). In Figure 4 the
power dependences of the narrow structure amplitude and width in cell a and cell b are presented. As the power density
is low, and the power range is small, the measured change in the narrow structure width is small, in the limits of the
accuracy of the measurement. In both cells the resonance amplitudes increase and saturate with power. The width of the
narrowest measured structure is 375 μG in cell a and 180 μG in cell b.
An interesting development of the shape with the laser power density is observed in both cells. At power density lower
than 100 μW/cm2 an additional structure with opposite sign (a bright structure) appears at the center of the resonance
(Figure 2). The bright structure is Gaussian in shape and its amplitude and width increase with decreasing the laser
power density. It is more clearly pronounced in cell a. At 20 μW/cm2 the Gaussian structure is 200 mG wide and the
narrow dark resonance is not registered.
Proc. of SPIE Vol. 7747 77470G-2
cell a
cell b
Figure 2. Shape of the CPT resonance registered in fluorescence at different laser power density in paraffin-coated Rb vapor cell on
the D1 87Rb line (Fg=2→Fe=1 transition).
Proc. of SPIE Vol. 7747 77470G-3
Figure 3. Shape of the narrow CPT resonance in cell b registered in fluorescence on the D1
transition) at different laser power densities.
87
Rb line (Fg=2→Fe=1
Figure 4. Narrow resonance width (black squares) and amplitude (red circles) in cell a and cell b. The line is drawn as a guide
to the eye.
Proc. of SPIE Vol. 7747 77470G-4
4. ANALYSIS OF DIFFERENT FACTORS INFLUENCING THE SHAPE OF THE CPT
RESONANCES IN COATED CELLS
It is well known that CPT resonances in coated cells have a dual structure13. The pedestal is due to atoms interacting with
the laser beam only once during the time they are in a coherent state. As the transit time depends on the thermal velocity
and the beam diameter14, the shape of the pedestal is the same for the two cells and for the uncoated cell we measured
earlier at the same experimental conditions15. The shape of the pedestal is in agreement with the theoretical one, obtained
using the irreducible tensor operator formalism and taking into account the influence of the velocity distribution of the
atoms, the Gaussian distribution of the laser beam intensity and the experimental geometry15 and numerically is well
described by16
RG(δ)∝{1-(δ/S0) arctan(S0/δ)},
(4)
2
where δ is the magnetic field detuning, S0= Ω /(γgγe) and (S0>>1); Ω, the Rabi frequency; γg, the ground state coherence
relaxation rate; γe, the population decay rate from the excited state into the ground states. It has the typical for a Gaussian
beam intensity distribution of the laser beam triangular shape.
The narrow structure is result of multiple atoms interaction with the laser beam. In this case atomic motion induced
narrowing (wall-induced Ramsey effect) of the resonances is observed17. The width of the narrow resonance ΔRRR is
defined by τ, the coherence time of the ground state. ΔRRR=1/(2πτ); τ= nł /v, where n is the number of collisions with the
cell walls; ł =2rcLc/(rc + Lc) Lc is the mean distance between two collisions with the cell walls for cylindrical cell; v is the
mean thermal velocity of the atoms and rb and rc are the beam and the cell radii. The measured widths correspond to 10
collisions with the cell walls for cell a and 30 collisions for cell b. The time for an atom-wall collision (interaction) is
less than 10-10 s and is neglected in these evaluations9.
Theoretically, at equal quality of the coating, as the dimensions of cell a are larger, the mean path between 2 collisions
with the cell walls is longer and the coherence time must be longer. But in larger volume the magnetic field
inhomogeneities are bigger. The reason for the wider structure in cell a could be the noncompensated magnetic field. An
advantage of the coated cells is that there is a “good averaging regime”. When gF ΔBrms τ »1 (gF is the ground state
gyromagnetic factor, ΔBrms is the magnetic field average over the cell volume), because of the many wall collisions
during the time of coherence τ, the atom crosses many times the cell, which leads to averaging of the fields gradients.
Additional compensation of the magnetic field is needed to satisfy this condition18,19.
Different bright resonances are described in the literature. The zero-field-enhanced absorption in the transmitted light
and peak in the fluorescence was measured for systems with Fg≤Fe 20 and explained by accumulation via optical pumping
of the atomic population in ground states maximally coupled to the excited state21. In the real experiment the laser light
polarization is not perfectly linear or circular and this causes changes in the signal shape22. When Fg≥Fe it was shown
experimentally the dark state transforms into a bright one when the laser beam polarization changes from linear to
circular23. In this case (Fg≥Fe) a peak in the fluorescence could be result of a small magnetic field perpendicular to the
laser beam propagation direction23. Inversion phenomena are observed in optically thick vapors24, too. In all these cases,
there is a redistribution of the population causing an enhanced fluorescence. At low laser powers there is a competition
between optical pumping rate to the dark states and the rate at which dark and bright states mix. In our case the
decoherence rate is large due to the nonperfect polarization, noncompensated magnetic fields and this could be the
reason for the registered threshold laser power of the appearance of the dark coherent resonance. This could be the
explanation of the Gaussian shape of the bright structure and that its amplitude and width increase with power decrease.
5. CONCLUSIONS
The performed measurements of the CPT resonances in two different paraffin-coated Rb cells have shown that at low
power, when the optical pumping rate is lower than the decoherence rate, there is a bright structure in the resonance
shape. This structure is with Gaussian shape and it is different in amplitude and width in the two cells. Additional
measurements with better compensation of the magnetic field and numerical calculations of the shape of the resonances
are planned for explanation of the Gaussian peak in the fluorescence at low power densities and the threshold of
registration of the narrow resonances.
ACKNOWLEDGEMENTS
This work was supported by the Bulgarian National Science Fund (Grant No: DO-02-108/2009).
Proc. of SPIE Vol. 7747 77470G-5
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