We report theoretical studies of a Λ-type five-level atomic system. The density matrix equations are set up and solved numerically to obtain the probe absorption line shape of Rb D2 transitions for cold (Doppler-free) and room temperature (Doppler-broadened) atoms. Simulated spectra for Doppler-broadened systems lead to four velocity-selective dips along with an electromagnetic induced transparency (EIT) peak as observed earlier from the co-propagating pump-probe spectroscopy of Rb D2 transitions. Effects of pump power and spontaneous decay rate from the upper levels on the simulated spectra are also studied. For cold atoms a very pronounced EIT peak is observed when the pump frequency is on resonance with one allowed transition. We find that lower pump power leads to a much sharper EIT signal in this case. A simulated dispersion curve shows a rapid variation of the refractive index that may lead to a sharp reduction of the group velocity of photons. © 2007 IOP Publishing Ltd.

BISWAJIT RAY

Physics

D BHATTACHARYYA

P N GHOSH

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Theoretical study of electromagnetically induced transparency in a five-level atom and application to Doppler-broadened and Doppler-free Rb atoms

Journal of Physics B: Atomic, Molecular and Optical Physics

A high contrast (∼48%) Velocity Selective Optical Pumping (VSOP) resonance at the closed transition Fg=4→Fe=5 of Cs-D2 line is obtained in the fluorescence signal under co-propagating pump-probe configuration. We use a 5.2 μm cell operating at reduced temperature (∼55 °C) and the intensity of the pump-laser is kept lower than that of the probe-laser. The observed sharp narrow structure is suitable for side-arms frequency-locking of the cooling- (i.e. probe-) laser in a cold atom experiment, with possibility for "-Γ" to "-4Γ" red-detuning and "+Γ" to "+10Γ" blue-detuning using the standard properties of the commercially available electronics. We have developed a theoretical model corresponding to the thin cell, incorporating the atomic time-of-flight dependent optical pumping decay rate to describe the dimensional anisotropy of the thin cell. The model shows good qualitative agreement with the observation and simulates as well the cases of cells with smaller thickness. It also describes correctly the temperature dependence of the line broadening and shows the potential for further optimization and red-shift detuning above "-4Γ". It may be of interest for further development of miniaturized modules, like the recently developed portable small magneto-optical traps. © 2015 Elsevier B.V.

Optics Communications

Investigation of high-contrast velocity selective optical pumping resonance at the cycling transition of Cs using fluorescence technique

Observation of electromagnetically induced transparency (EIT) and enhanced velocity selective optical pumping (VSOP) signals in a micrometric cell with cesium is reported. The line shape and non-linear features observed in the case of fluorescence in the direction parallel to the cell windows and the transmission spectra observed along the propagation direction of the probe beam show considerable differences in the spectral profile. A theoretical model based on five level optical Bloch equations is used to simulate the spectra. The Doppler convolution includes all possible orientations of atomic velocities with respect to the laser beam direction. Atoms moving nearly parallel to the windows and perpendicular to the collinear pump and probe beams have much lower Doppler shift and hence produce considerable narrowing of the Doppler background in the fluorescence spectra. The coherence decay rate is also low for such atoms as they do not meet with the cell walls. The simulated curves reproduce the observed sharp EIT peaks and enhanced broad VSOP signals for the closed probe transition in the fluorescence and absorption spectra. The observed effect of detuning of the pump frequency on the non-linear features is also reproduced by the simulation. © 2014 IOP Publishing Ltd.

Observation and theoretical simulation of electromagnetically induced transparency and enhanced velocity selective optical pumping in cesium vapour in a micrometric thickness optical cell

Variations of the coherent resonance, i.e. an electromagnetically induced transparency (EIT) peak with the cell temperature in Λ- and V-type systems are observed for the 85Rb-D2 transition. In a Λ-type system, the amplitude of the EIT peak gradually decreases and it is finally masked by the broadened optical pumping dips with the increase of the cell temperature. But for the V-type system, the EIT and the saturation peaks are greatly enhanced with the increase of the cell temperature. The effect of the external magnetic field on the EIT resonance is also investigated considering both types of systems. For the Λ-type system in place of a single EIT resonance, five transparency windows with broadened width and reduced contrast are obtained depending on the Zeeman levels formed by the applied magnetic field. In the V-type system, the coherent resonance peak could not be resolved in the presence of the external magnetic field, but a greater number of saturation peaks with broadened width appear in the probe transmission spectrum. A theoretical model is adopted to represent the experimental results. Good agreement is found between the experimental and numerically simulated results. © 2013 IOP Publishing Ltd.

Temperature and magnetic field effects on the coherent and saturating resonances in Î›- And V-type systems for the 85Rb-D2 transition

We report the experimental observations of double EIT and enhanced EIT signal in a combination of Λ- and V-type multi-level system of the D 2 transition of 85Rb atoms interacting with three laser fields. The EIT formation under a Λ-type and V-type systems is also observed separately. It is found that the EIT width in a V-type system becomes narrower than the Λ-type system. Also the effect of frequency detuning of the control laser on the probe absorption profile is studied in presence of Λ- and V-type EIT systems. © Springer-Verlag 2010.

Applied Physics B: Lasers and Optics

Double EIT and enhanced EIT signal in a combination of Î›- And V-type system of Rb-D2 transition

Atomic coherence resonances such as electromagnetically induced transparency (EIT) and electromagnetically induced absorption (EIA) signals are observed in a Doppler broadened multi-level system for the D2 line of 85Rb atoms in a vapour cell considering different types of atom-laser coupling schemes. Besides the coherence resonances, the nonlinear resonances like velocity selective optical pumping (VSOP) dips and velocity selective resonances (VSR) are also observed for the non-zero velocity selective groups of atoms. In the presence of pump, control and probe laser fields, we observe two EIT signals in a double Λ-type system and two EIA signals in a double V-type system. We are able to see the EIA signal for the non-zero velocity group of atoms when the pump laser is locked with an open transition by a small red detuning. We also report the experimental observation of simultaneous EIT and EIA signals in a (Λ+V)-type system. The effect of frequency tuning of the control laser is also studied in the presence of the frequency locked pump laser. A simple theoretical analysis explains the experimental results. © 2011 IOP Publishing Ltd.

Nonlinear resonances caused by coherent, optical pumping and saturating effects in the presence of three laser fields for the 85Rb-D 2 line

Pump-probe double resonance spectroscopy of Rb D2 transitions are reported for co and counter propagating lasers with tunable frequencies. A perturbative analytical solution of the optical Bloch equations is derived for the five-level atomic system to reproduce the experimental results. The optical pumping effect has been taken into account in the theoretical model. Velocity selective peaks can be observed for all velocity groups of atoms by choosing the appropriate pump frequency. The peaks can be narrowed by varying the lower level hyperfine decay rate. © 2007 Elsevier B.V. All rights reserved.

Chemical Physics Letters

Velocity dependent pump-probe spectroscopy for a five-level system: An application to Rb D2 transitions

It is shown that the pump-probe spectroscopy of Λ-type system for the D2 transition of 87Rb exhibits additional absorption enhancement peaks due to velocity selective optical pumping along with the electromagnetically induced transparency (EIT). The separation of these peaks is consistent with the hyperfine splitting of the upper levels. For 85Rb the peaks are not clearly discernible since the hyperfine splitting is much smaller. © 2005 IOP Publishing Ltd.

Velocity selective optical pumping effects and electromagnetically induced transparency for D2 transitions in rubidium

The interaction of a four-level atomic system with two electromagnetic radiations has been studied. The two intermediate levels are closely spaced such that a single radiation frequency can induce transitions from the ground state to both of them. In a cascade-type double resonance, the pump electric-field amplitude is much stronger than the amplitude of the signal field, which can induce transitions from both of the intermediate levels to the upper state. The 15 optical Bloch equations obtained from the Liouville equations are solved analytically to obtain the Doppler-free signal line shape. The computed signals, exhibiting two Lorentzian line profiles, are presented for different pump frequencies. In addition to these one-photon transitions, we obtain a weak two-photon resonance peak. The two-photon resonance becomes weaker when the detuning of the pump frequency from a resonance frequency is increased. When the pump frequency p is intermediate between the pump resonance frequencies 1 and 2, the two-photon resonance is very weak and almost vanishes when p=(1+2)/2. When the pump frequency is on resonance with one of the transition frequencies, the Rabi splitting of the signal shows asymmetry because of the presence of a close-lying transition which is pumped off resonance. The intensity-dependent shifts of the transitions are such that they repel each other more and more as the intensity of the pump field is increased. These shifts arise from the nonresonant interaction between the atom and the field. © 1993 The American Physical Society.

Physical Review A

Line shape, frequency shift, Rabi splitting, and two-photon resonances in four-level double-resonance spectroscopy with closely spaced intermediate levels

The interaction of two electromagnetic radiations with a four-level atom with two closely spaced common levels is studied for the cascade system. The spacing between the close levels is assumed to be small so that the radiation frequency can act simultaneously on the two closely spaced resonances. Fifteen Bloch equations are developed for the four-level atom and a computer program is written for their solution in the steady state. Numerical computations for the line shape of the signal having the closely spaced levels at the lower level and a single upper level are reported. The closely spaced levels are the upper levels for the pump transition. When the signal is on-resonance with one of the transitions, a Rabi splitting is observed, but the presence of a nearby transition produces an asymmetry between the Rabi components. The asymmetry depends on the transition moment of the nearby transition and disappears when the other transition is weak. In the case of off-resonance pumping a weak two-photon signal is found in addition to the two signals. The intensity of the two-photon signal depends on the pump radiation frequency. © 1992.

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ISSN	0953-4075