Spin-exchange narrowing of the atomic ground-state resonances

W. Chalupczak, P. Josephs-Franks, B. Patton, and S. Pustelny

Phys. Rev. A 90, 042509 – Published 21 October 2014

Abstract

At the most fundamental level, the performance of atomic sensors is limited by quantum decoherence. The problem of decoherence has been addressed at low magnetic fields with atomic samples, where the limiting factor of the coherence lifetime arises from spin-exchange collisions. In this paper, we demonstrate the complex role of the collisions in the relaxation of quantum states of alkali-metal atoms. The detailed understanding of the collision role allows us to reduce the ground-state relaxation in stronger magnetic fields (tens $μ T$ ). Reduction of the relaxation rate enables improvement of the performance of atomic sensors. In particular, enhancement of the sensitivity of optical magnetometers in the detection of stronger magnetic fields may be obtained. Reduced transverse relaxation also enables increasing quantum-information storage time in atomic vapor.

Received 1 July 2014
Revised 14 August 2014

DOI:https://doi.org/10.1103/PhysRevA.90.042509

Authors & Affiliations

W. Chalupczak¹, P. Josephs-Franks¹, B. Patton², and S. Pustelny^2,3

¹National Physical Laboratory, Hampton Road, Teddington TW11 0LW, United Kingdom
²Department of Physics, University of California at Berkeley, Berkeley, California 94720-7300, USA
³Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

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Vol. 90, Iss. 4 — October 2014

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Figure 1
Geometry of the experiment. The Cs vapor is contained within an antirelaxation-coated glass cell. A 200 $μ W$ , circularly polarized laser light (pump) is tuned to the $F = 3 \to F^{'} = 2$ component of the caesium D2 line (852 nm). The pump strongly polarizes the medium (polarization of the $F = 4$ ground state) along the offset magnetic field $B_{off}$ via the so-called indirect optical pumping [14]. $B_{off}$ splits magnetic sublevels that are coupled by the $\hat{y}$ -polarized rf field of the amplitude $B_{rf}$ (double-headed arrows in energy structure scheme). The state of the medium is detected by analyzing the polarization state of the off-resonant probe light that is detuned 1 GHz above the $F = 4 \to F^{'} = 5$ transition (D2 line) propagating along $\hat{y}$ . The whole system is enclosed inside a multilayer magnetic shield (not shown) with a shielding factor of $10^{6}$ . $B_{off}$ is generated by a set of two solenoids situated inside the shield, providing the field with relative inhomogeneity of less than $10^{- 5}$ over the length of the cell [15].
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Figure 2
(a) Observed and (b) simulated widths of the resonances corresponding to the first two components of the rf spectrum as a function of the offset field (expressed in terms of the Larmor frequency). The signals were measured for a pump power of 200 $μ W$ , probe power of 15 $μ W$ , and atomic density of $1.1 \times 10^{11}$ ${cm}^{- 3}$ , and the simulations were performed for corresponding physical conditions. The quadratic dependence (black solid line) shows separation of the lines (quadratic component of Zeeman effect), while the horizontal dashed lines represent measured asymptotic (high-field) values of the highest four peaks linewidths $(Δ ν_{- 4, - 3}^{\infty} = 3.5$ Hz, $Δ ν_{- 3, - 2}^{\infty} = 8.4$ Hz, $Δ ν_{- 2, - 1}^{\infty} = 10.9$ Hz, and $Δ ν_{- 3, - 2}^{\infty} = 11.3$ Hz). The numbers I–IV mark four regimes with different behavior of the relaxation rate on the magnetic field. The two insets show rf spectra measured at high and low magnetic fields, corresponding to split and unsplit rf spectra recorded in regimes I and II, and III and IV, respectively. The peak on the right represents $(- 4, - 3)$ coupling.
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Figure 3
The field dependence of the resonance linewidth $Δ ν_{- 3, - 2}$ recorded at three different atomic densities: $0.4 \times 10^{11}$ ${cm}^{- 3}$ (blue diamonds), $0.6 \times 10^{11}$ ${cm}^{- 3}$ (red dots), $1.1 \times 10^{11}$ ${cm}^{- 3}$ (green squares).
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Figure 4
Average separation of the rf resonances as a function of the offset magnetic field (expressed in terms of the Larmor frequency) recorded at atomic densities $1.1 \times 10^{11}$ atoms/ ${cm}^{3}$ (red squares) and $2.1 \times 10^{11}$ atoms/ ${cm}^{3}$ (blue dots). The results reveal deviations from the magnetic-sublevel splittings predicted by the Breit-Rabi equation (solid black line).
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Figure 5
Width (blue diamonds) of rf spectral profile, $Δ ν_{- 3, - 2}$ , recorded at 165 kHz as a function of power of the laser beam that generates tensor light shift (atomic densities $0.3 \times 10^{11}$ atoms/ ${cm}^{3})$ . Red squares show averaged peak separation (nonlinear splitting of the sublevels). Solid lines are the trend lines to guide the eye.
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