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arXiv:1208.1879 · Journal of Physics B Atomic Molecular and Optical Physics

Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen–Back regime

Lee Weller, Kathrin S Kleinbach, Mark A. Zentile, Svenja Knappe, Charles S. Adams, Ifan G. Hughes

Published Oct 4, 2012• 45 citations
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Abstract

Here we report on measurements of the absolute absorption and dispersion properties of an isotopically pure 87 Rb vapour for magnetic fields up to and including 0.6 T. We discuss the various regimes that arise when the hyperfine and Zeeman interactions have different magnitudes, and show that we enter the hyperfine Paschen–Back regime for fields greater than 0.33 T on the Rb D 2 line. The experiment uses a compact 1 mm 3 microfabricated vapour cell that makes it easy to maintain a uniform and large magnetic field with a small and inexpensive magnet. We find excellent agreement between the experimental results and numerical calculations of the weak probe susceptibility where the line positions and strengths are calculated by matrix diagonalization.

DOI
10.1088/0953-4075/45/21/215005

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Absolute absorption and dispersion of a rubidium vapour in the hyperfine Paschen-Back regime

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Here we report on measurements of the absolute absorption and dispersion properties of an isotopically pure 87Rb vapour for magnetic fields up to and including 0.6 T. We discuss the various regimes that arise when the hyperfine and Zeeman interactions have different magnitudes, and show that we enter the hyperfine Paschen–Back regime for fields greater than 0.33 T on the Rb D2 line. The experiment uses a compact 1 mm3 microfabricated vapour cell that makes it easy to maintain a uniform and large magnetic field with a small and inexpensive magnet. We find excellent agreement between the experimental results and numerical calculations of the weak probe susceptibility where the line positions and strengths are calculated by matrix diagonalization.

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An investigation into the temperature evolution of transmission and absorption coefficient spectra of Rubidium atoms in the hyperfine Paschen-Back regime was successfully undertaken for a continuous laser detuning of approximately 150 GHz. All experiments were undertaken using a 1 mm long cell of isotopically enhanced 87Rb. The magnet used had a peak field of 1.54 T. The forms of both the S0 and S1 Stokes Parameters showed excellent agreement with the theory from ElecSus at temperatures ranging from 56◦C to 160◦C, with the S0 parameter also agreeing in narrow-band spectra of up to 20 GHz.The absorption coefficient ratio of strong transitions, expected to be equal to 3.00, was measured to be within their uncertainty of this value when a possible temperature fluctuation of <1 K was taken into account. Both the strong and weak transitions were measured and compared to the theory from ElecSus, which was found to successfully predict the behaviour of 87Rb atoms in the hyperfine Paschen-Back regime. Areas of expansion and improvement of the ElecSus program were identified.The power evolution of the D2 line of Rubidium was also investigated for a narrow beam of w < 0.4 mm in both no external magnetic field and the hyperfine Paschen-Back regime. The inhomogeneous shape of the power evolution was found to not fit the data, while the χ2 analysis showed that the homogeneous shape was better. The Weak Probe regime was found to be reached at values of I/Isat up to 2 orders of magnitude higher than the 1e−3 found previously. This provides possibilities for applications such that the SNR can be increased when measuring transmission or absorption coefficients. It is unclear whether the use of a magnetic field significantly changes the intensity required to reach the Weak Probe regime. This should be investigated using a wider beam, with a different experimental cell.

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Abstract. We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2 % for the D2 line at 16.5 ◦ C. PACS numbers: 32.70.-n, 32.70.Fw, 42.62.FiAbsolute Rb absorption 2 1.

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The hyperfine Paschen–Back Faraday effect

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We investigate experimentally and theoretically the Faraday effect in an atomic medium in the hyperfine Paschen–Back regime, where the Zeeman interaction is larger than the hyperfine splitting. We use a small permanent magnet and a micro-fabricated vapour cell, giving magnetic fields of the order of a tesla. We show that for low absorption and small rotation angles, the refractive index is well approximated by the Faraday rotation signal, giving a simple way to measure the atomic refractive index. Fitting to the atomic spectra, we achieve magnetic field sensitivity at the 10 −4 level. Finally we note that the Faraday signal shows zero crossings which can be used as temperature insensitive error signals for laser frequency stabilization at large detuning. The theoretical sensitivity for 87 Rb is found to be ∼40 kHz °C −1 .

arXiv:1401.1659•Journal of Physics B Atomic Molecular and Optical Physics•Mar 26, 2014•56 citations
Here we report on measurements of the absolute absorption and dispersion properties of an isotopically pure 87 Rb vapour for magnetic fields up to and including 0.6 T. We discuss the various regimes that arise when the hyperfine and Zeeman interactions have different magnitudes, and show that we enter the hyperfine Paschen–Back regime for fields greater than 0.33 T on the Rb D 2 line. The experiment uses a compact 1 mm 3 microfabricated vapour cell that makes it easy to maintain a uniform and large magnetic field with a small and inexpensive magnet. We find excellent agreement between the experimental results and numerical calculations of the weak probe susceptibility where the line positions and strengths are calculated by matrix diagonalization.
Here we report on measurements of the absolute absorption and dispersion properties of an isotopically pure 87Rb vapour for magnetic fields up to and including 0.6 T. We discuss the various regimes that arise when the hyperfine and Zeeman interactions have different magnitudes, and show that we enter the hyperfine Paschen–Back regime for fields greater than 0.33 T on the Rb D2 line. The experiment uses a compact 1 mm3 microfabricated vapour cell that makes it easy to maintain a uniform and large magnetic field with a small and inexpensive magnet. We find excellent agreement between the experimental results and numerical calculations of the weak probe susceptibility where the line positions and strengths are calculated by matrix diagonalization.
An investigation into the temperature evolution of transmission and absorption coefficient spectra of Rubidium atoms in the hyperfine Paschen-Back regime was successfully undertaken for a continuous laser detuning of approximately 150 GHz. All experiments were undertaken using a 1 mm long cell of isotopically enhanced 87Rb. The magnet used had a peak field of 1.54 T. The forms of both the S0 and S1 Stokes Parameters showed excellent agreement with the theory from ElecSus at temperatures ranging from 56◦C to 160◦C, with the S0 parameter also agreeing in narrow-band spectra of up to 20 GHz.The absorption coefficient ratio of strong transitions, expected to be equal to 3.00, was measured to be within their uncertainty of this value when a possible temperature fluctuation of <1 K was taken into account. Both the strong and weak transitions were measured and compared to the theory from ElecSus, which was found to successfully predict the behaviour of 87Rb atoms in the hyperfine Paschen-Back regime. Areas of expansion and improvement of the ElecSus program were identified.The power evolution of the D2 line of Rubidium was also investigated for a narrow beam of w < 0.4 mm in both no external magnetic field and the hyperfine Paschen-Back regime. The inhomogeneous shape of the power evolution was found to not fit the data, while the χ2 analysis showed that the homogeneous shape was better. The Weak Probe regime was found to be reached at values of I/Isat up to 2 orders of magnitude higher than the 1e−3 found previously. This provides possibilities for applications such that the SNR can be increased when measuring transmission or absorption coefficients. It is unclear whether the use of a magnetic field significantly changes the intensity required to reach the Weak Probe regime. This should be investigated using a wider beam, with a different experimental cell.
This thesis presents a comparative study of the measured and calculated absolute absorption and dispersion properties of the Rb D lines through a dense thermal vapour in the absence and presence of an applied magnetic field. A detailed theoretical model valid in the weak-probe regime is calculated. The model uses a matrix representation of the atomic Hamiltonian including the magnetic field interaction for Rb in the completely uncoupled basis. Numerical diagonalisation allows the frequency detunings and transition strengths to be calculated. The lineshape of each transition is modelled as a Voigt profile, a convolution of the inhomogeneous and homogeneous profiles. The medium’s susceptibility is found by summing over all the electric-dipole-allowed transitions. For dense thermal vapours a modification to the homogeneous linewidth of each transition, which grows linearly with the number density of atoms, arises due to resonant dipole-dipole interactions between identical atoms in superpositions of the ground and excited terms. In the presence of an applied magnetic field we investigate the Stokes parameters of light propagating through a dense thermal vapour. For fields larger than 0.33 T we enter the hyperfine Paschen-Back regime on the Rb D lines. We present a compact optical isolator based on an atomic vapour, exploiting the spectral region of high transmission and large dispersion where we would normally expect absorption on the Rb D lines. Frequency up-conversion is shown in the fluorescence measurements over the visible and near infra-red regions for strong excitation. Low density transfer arises due to the energy-pooling effect between two identical atoms in their first excited terms. At high densities resonant dipole-dipole interactions give rise to a threshold for the energy transfer. We characterise the threshold behaviour with increasing number density.
Abstract. We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2 % for the D2 line at 16.5 ◦ C. PACS numbers: 32.70.-n, 32.70.Fw, 42.62.FiAbsolute Rb absorption 2 1.
We study the Doppler-broadened absorption of a weak monochromatic probe beam in a thermal rubidium vapour cell on the D lines. A detailed model of the susceptibility is developed which takes into account the absolute linestrengths of the allowed electric dipole transitions and the motion of the atoms parallel to the probe beam. All transitions from both hyperfine levels of the ground term of both isotopes are incorporated. The absorption and refractive index as a function of frequency are expressed in terms of the complementary error function. The absolute absorption profiles are compared with experiment, and are found to be in excellent agreement provided a sufficiently weak probe beam with an intensity under one thousandth of the saturation intensity is used. The importance of hyperfine pumping for open transitions is discussed in the context of achieving the weak-probe limit. Theory and experiment show excellent agreement, with an rms error better than 0.2% for the D2 line at 16.5 degrees C.
We investigate experimentally and theoretically the Faraday effect in an atomic medium in the hyperfine Paschen–Back regime, where the Zeeman interaction is larger than the hyperfine splitting. We use a small permanent magnet and a micro-fabricated vapour cell, giving magnetic fields of the order of a tesla. We show that for low absorption and small rotation angles, the refractive index is well approximated by the Faraday rotation signal, giving a simple way to measure the atomic refractive index. Fitting to the atomic spectra, we achieve magnetic field sensitivity at the 10 −4 level. Finally we note that the Faraday signal shows zero crossings which can be used as temperature insensitive error signals for laser frequency stabilization at large detuning. The theoretical sensitivity for 87 Rb is found to be ∼40 kHz °C −1 .