© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Physical Review A

Properties of magnetic sublevel coherences for precision measurements

I. Y. Chan, A. Andreyuk, Scott Beattie, B. Barrett, C. Mok, M. Weel, Anantharaman Kumarakrishnan

Published Sep 17, 2008• 11 citations

Abstract

We have developed a theoretical description of the evolution of ground state coherences between magnetic sublevels in Rb vapor in the presence of a magnetic field along an arbitrary direction. This formalism uses a rotation matrix approach to describe the evolution of coherences created by two traveling wave laser pulses with orthogonal polarizations. The effect of a magnetic field can be described as a time-dependent rotation of the atomic system about the quantization axis. Predictions based on this theoretical formalism for the functional form of Larmor oscillations in a magnetic field are studied using a coherent transient effect known as magnetic grating free induction decay (MGFID) using room temperature vapor and laser cooled atoms. We find the theoretical predictions to be in excellent agreement with data. The velocity distribution of the cold sample measured from the dephasing time of the MGFID in the absence of magnetic fields is in agreement with the sample temperature obtained by imaging the ballistic expansion of the trapped cloud. By using rate equations to model atomic coherences, it is also possible to predict the evolution of magnetic grating echoes (MGE) in a magnetic field. We compare these predictions with experiments from cold atoms and discuss applications of the MGFID and MGE that relate to a precision measurement of the atomic $g$ factor ratio using $^{85}\mathrm{Rb}$ and $^{87}\mathrm{Rb}$ isotopes.

DOI: 10.1103/physreva.78.033418

Related papers

Magnetic grating echoes from laser-cooled atoms

Anantharaman Kumarakrishnan, S. B. Cahn, Unyob Shim +1 more

We have used two sets of orthogonally polarized traveling-wave pulses separated in time to establish and, subsequently, rephase a spatially periodic coherence grating between the magnetic sublevels of the $F=3$ ground state in a cloud of laser-cooled ${}^{85}\mathrm{Rb}$ atoms. The rephasing results in a magnetic grating echo (MGE). We have used the shape of the signals to determine both transverse and longitudinal velocity distributions and to study the effects of magnetic fields. The amplitude of the MGE with counterpropagating pulses is modulated at the atomic recoil frequency, a consequence of matter wave interference.

Physical Review A•Nov 1, 1998•20 citations

Effects of magnetic fields on magnetic grating free induction decay (MGFID) in a cold Rb vapor

S. B. Cahn, Anantharaman Kumarakrishnan, Unyob Shim +1 more

Summary form only given. The magnetic grating free induction decay (MGFID) may be produced in a sample of room temperature (300 K) /sup 35/Rb, demonstrating the coherence between alternate magnetic sublevels. The decay rate of this coherence is dominated by the dispersal of the atoms and proportional to the most probable velocity u of the atoms. By slowing and confining the atoms in a magnetooptic trap, the decay rate may be reduced by several orders of magnitude.

Quantum Electronics and Laser Science Conference•Jun 2, 1996•0 citations

Magnetic grating echo from room temperature Rb atoms

Anantharaman Kumarakrishnan, S. B. Cahn, Unyob Shim +1 more

We have initiated a new class of coherent transient experiments with Doppler-broadened atoms confined in a vapor cell. A spatially modulated coherence is created between magnetic sublevels of the F=3 ground state of /sup 85/Rb by a standing pulse. This pulse consists of two opposite circularly polarized traveling waves with wave vectors K/sub 1/ and K/sub 2/ at a small angle /spl theta/. The coherence grating is probed by the application of a readout pulse along K/sub 2/. The resulting coherent emission along K/sub 1/ is detected by a heterodyne technique.

Quantum Electronics and Laser Science Conference•Jun 7, 1996•0 citations

Ground-state grating echoes from Rb vapor at room temperature

Anantharaman Kumarakrishnan, Unyob Shim, S. B. Cahn +1 more

We have used two sets of opposite circularly polarized traveling wave pulses separated in time to establish, and subsequently rephase, a spatially modulated coherence between the magnetic sublevels of the $F=3$ ground state in Doppler broadened ${}^{85}\mathrm{Rb}$ vapor. The rephasing results in a magnetic grating echo whose duration is an accurate measure of the velocity distribution. We demonstrate that the time scale of the experiment is determined solely by the transit time of atoms across the laser beam. The shortening of the lifetime due to a perturber (Ar) allows us to infer the Rb-Ar velocity changing collision cross section.

Physical Review A•Nov 1, 1998•13 citations

Dynamics of a stored Zeeman coherence grating in an external magnetic field

D Moretti, D Felinto, J W R Tabosa +1 more

We investigate the evolution of a Zeeman coherence grating induced in a cold atomic cesium sample in the presence of an external magnetic field. The gratings are created in a three-beam light storage configuration using two quasi-collinear writing and reading laser pulses with a counterpropagating pulse after a variable time delay. The phase-conjugated pulse arising from the atomic sample is monitored. Collapses and revivals of the retrieved pulse are observed for different polarizations of laser beams and for different directions of the applied magnetic field. While magnetic field inhomogeneities are responsible for the decay of the coherent atomic response, a five-fold increase in the coherence decay time, with respect to no applied magnetic field, is obtained for an appropriate choice of the direction of the applied magnetic field. A simplified theoretical model illustrates the role of the magnetic field mean and its inhomogeneity on the collective atomic response.

arXiv:1005.0282•Journal of Physics B Atomic Molecular and Optical Physics•May 19, 2010•49 citations

Dynamics of a stored Zeeman coherence grating in an external magnetic field

D. Moretti, D. Felinto, J. W. R. Tabosa +1 more

We investigate the evolution of a Zeeman coherence grating induced in a cold atomic cesium sample in the presence of an external magnetic field. The gratings are created in a three-beam light storage configuration using two quasi-collinear writing and reading laser pulses with a counterpropagating pulse after a variable time delay. The phase-conjugated pulse arising from the atomic sample is monitored. Collapses and revivals of the retrieved pulse are observed for different polarizations of laser beams and for different directions of the applied magnetic field. While magnetic field inhomogeneities are responsible for the decay of the coherent atomic response, a five-fold increase in the coherence decay time, with respect to no applied magnetic field, is obtained for an appropriate choice of the direction of the applied magnetic field. A simplified theoretical model illustrates the role of the magnetic field mean and its inhomogeneity on the collective atomic response.

•Jan 1, 2010•24 citations

We have developed a theoretical description of the evolution of ground state coherences between magnetic sublevels in Rb vapor in the presence of a magnetic field along an arbitrary direction. This formalism uses a rotation matrix approach to describe the evolution of coherences created by two traveling wave laser pulses with orthogonal polarizations. The effect of a magnetic field can be described as a time-dependent rotation of the atomic system about the quantization axis. Predictions based on this theoretical formalism for the functional form of Larmor oscillations in a magnetic field are studied using a coherent transient effect known as magnetic grating free induction decay (MGFID) using room temperature vapor and laser cooled atoms. We find the theoretical predictions to be in excellent agreement with data. The velocity distribution of the cold sample measured from the dephasing time of the MGFID in the absence of magnetic fields is in agreement with the sample temperature obtained by imaging the ballistic expansion of the trapped cloud. By using rate equations to model atomic coherences, it is also possible to predict the evolution of magnetic grating echoes (MGE) in a magnetic field. We compare these predictions with experiments from cold atoms and discuss applications of the MGFID and MGE that relate to a precision measurement of the atomic

g

factor ratio using

^{85}\mathrm{Rb}

and

^{87}\mathrm{Rb}

isotopes.

We have used two sets of orthogonally polarized traveling-wave pulses separated in time to establish and, subsequently, rephase a spatially periodic coherence grating between the magnetic sublevels of the

F=3

ground state in a cloud of laser-cooled

{}^{85}\mathrm{Rb}

atoms. The rephasing results in a magnetic grating echo (MGE). We have used the shape of the signals to determine both transverse and longitudinal velocity distributions and to study the effects of magnetic fields. The amplitude of the MGE with counterpropagating pulses is modulated at the atomic recoil frequency, a consequence of matter wave interference.

We have initiated a new class of coherent transient experiments with Doppler-broadened atoms confined in a vapor cell. A spatially modulated coherence is created between magnetic sublevels of the F=3 ground state of /sup 85/Rb by a standing pulse. This pulse consists of two opposite circularly polarized traveling waves with wave vectors K/sub 1/ and K/sub 2/ at a small angle /spl theta/. The coherence grating is probed by the application of a readout pulse along K/sub 2/. The resulting coherent emission along K/sub 1/ is detected by a heterodyne technique.

We have used two sets of opposite circularly polarized traveling wave pulses separated in time to establish, and subsequently rephase, a spatially modulated coherence between the magnetic sublevels of the

F=3

ground state in Doppler broadened

{}^{85}\mathrm{Rb}

vapor. The rephasing results in a magnetic grating echo whose duration is an accurate measure of the velocity distribution. We demonstrate that the time scale of the experiment is determined solely by the transit time of atoms across the laser beam. The shortening of the lifetime due to a perturber (Ar) allows us to infer the Rb-Ar velocity changing collision cross section.

We investigate the evolution of a Zeeman coherence grating induced in a cold atomic cesium sample in the presence of an external magnetic field. The gratings are created in a three-beam light storage configuration using two quasi-collinear writing and reading laser pulses with a counterpropagating pulse after a variable time delay. The phase-conjugated pulse arising from the atomic sample is monitored. Collapses and revivals of the retrieved pulse are observed for different polarizations of laser beams and for different directions of the applied magnetic field. While magnetic field inhomogeneities are responsible for the decay of the coherent atomic response, a five-fold increase in the coherence decay time, with respect to no applied magnetic field, is obtained for an appropriate choice of the direction of the applied magnetic field. A simplified theoretical model illustrates the role of the magnetic field mean and its inhomogeneity on the collective atomic response.

We investigate the evolution of a Zeeman coherence grating induced in a cold atomic cesium sample in the presence of an external magnetic field. The gratings are created in a three-beam light storage configuration using two quasi-collinear writing and reading laser pulses with a counterpropagating pulse after a variable time delay. The phase-conjugated pulse arising from the atomic sample is monitored. Collapses and revivals of the retrieved pulse are observed for different polarizations of laser beams and for different directions of the applied magnetic field. While magnetic field inhomogeneities are responsible for the decay of the coherent atomic response, a five-fold increase in the coherence decay time, with respect to no applied magnetic field, is obtained for an appropriate choice of the direction of the applied magnetic field. A simplified theoretical model illustrates the role of the magnetic field mean and its inhomogeneity on the collective atomic response.