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Nonlinear optics in a thermal Rb vapour at high magnetic fields

Daniel J. Whiting

Published Jan 1, 2017• 1 citation
OpenAlex

Abstract

We present investigations of nonlinear optical phenomena using a $^{87}$Rb thermal vapour in a high magnetic field. The magnetic field (of strength 0.6~T) separates the optical transitions by more than their Doppler-broadened linewidths. This technique provides a high level of control over thermal-vapour systems, which can be used as a simpler alternative to conventional state-preparation methods such as optical pumping. Using this approach, we study electromagnetically induced transparency in a non-degenerate 3-level ladder system. Finding excellent agreement with the numerically modelled transmission spectra, we are able to directly infer the dipole moment of the 5P$_{3/2}\to$5D$_{5/2}$ transition $|\langle5P_{3/2}||er||5D_{5/2}\rangle|= (2.27\pm0.002_{\rm stat}\pm0.04_{\rm syst})~ea_{0}$. Changing the coupling field to a standing-wave geometry, we observe resonant enhanced absorption: an effect that previously had only been observed in systems involving 4 or more atomic states. We also consider four-wave mixing (FWM) in a diamond level-scheme. Compared to the zero magnetic field case, we find good agreement with the FWM spectra using a simple model, even in the regime of strong laser dressing. Finally, we investigate heralded single-photon generation by spontaneous FWM. With strong laser dressing we observe the appearance of collective quantum beats, a single-photon interference effect due to the relative motion of atoms in a collective spin excitation. A violation of the Cauchy-Schwarz inequality by 6.7 standard deviations is reported.

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Stokes polarimetry and magnetometry using a thermal Rb vapour in the Voigt geometry with large magnetic field

F. Ponciano-Ojeda

We present investigations of magneto-optical phenomena using a $^{87}$Rb thermal vapour in large magnetic fields. At this point, in the hyperfine Paschen-Back regime, optical transitions can be separated by more than their Doppler-broadened linewidth, providing a high level of control over the atomic system and a simpler theoretical model for studying atom-light-magnetic field interactions. In this context, we study the spectra of $^{87}$Rb at magnetic fields of $0.4~$T and $1.5~$T in the Voigt geometry. In both cases we find excellent agreement between experimental and theoretical absorption spectra. With the $1.5~$T field we also study polarisation changes induced in the light by the atoms subject to a large magnetic field. Using this approach, we consider the practical applications of our system as a vector magnetometer. We present a scheme that eliminates most sources of systematic errors in the measurement of the field strength by using pairs of transitions that cancel excited-state terms in the energy shifts. Finally, we extend the concepts and ideas investigated to an application in precision thermometry. We discuss how good understanding of the spectra and the magnetic field strength potentially allow detection of small differences in different spectral features, which could then be traced to the effect of the Boltzmann factor, $k_{\\rm{B}}T$, on the atomic populations.

•Jan 1, 2021•2 citations

Four-wave mixing in the hyperfine Paschen-Back regime

Daniel J. Whiting, Renju S. Mathew, James Keaveney +2 more

We present an experimental study of seeded four-wave mixing (4WM) using a diamond excitation scheme (with states from the 5S$_{1/2}$, 5P$_{1/2}$, 5P$_{3/2}$ and 5D$_{1/2}$ terms) in a thermal vapour of $^{87}$Rb atoms. We investigate the 4WM spectra under the application of a strong magnetic field (0.6 T). The Zeeman interaction is strong enough to realise the hyperfine Paschen-Back regime, which has the effect of separating the optical transitions by more than the Doppler width, thereby significantly simplifying the spectral features. We show that this facilitates a quantitative comparison, even in the regime of strong dressing, between experimental data and a simple theoretical model based only on four-level optical Bloch equations.

•May 4, 2017•1 citation

Nonlinear optical effects manifested by electromagnetic induced transparency in cold atoms

Jiepeng Zhang

This dissertation reports experimental studies of nonlinear optical effects manifested by electromagnetically induced transparency (EIT) in cold Rb atoms. The cold Rb atoms are confined in a magneto-optic trap (MOT) obtained with the standard laser cooling and trapping technique. Because of the near zero Doppler shift and a high phase density, the cold Rb sample is well suited for studies of atomic coherence and interference and related applications, and the experiments can be compared quantitatively with theoretical calculations. It is shown that with EIT induced in the multi-level Rb system by laser fields, the linear absorption is suppressed and the nonlinear susceptibility is enhanced, which enables studies of nonlinear optics in the cold atoms with slow photons and at low light intensities. Three independent experiments are described and the experimental results are presented. First, an experimental method that can produce simultaneously co-propagating slow and fast light pulses is discussed and the experimental demonstration is reported. Second, it is shown that in a three-level Rb system coupled by multi-color laser fields, the multi-channel two-photon Raman transitions can be manipulated by the relative phase and frequency of a control laser field. Third, a scheme for all-optical switching near single photon levels is developed. The scheme is based on the phase-dependent multi-photon interference in a coherently coupled four-level system. The phase dependent multi-photon interference is observed and switching of a single light pulse by a control pulse containing ∼20 photons is demonstrated. These experimental studies reveal new phenomena manifested by quantum coherence and interference in cold atoms, contribute to the advancement of fundamental quantum optics and nonlinear optics at ultra-low light intensities, and may lead to the development of new techniques to control quantum states of atoms and photons, which will be useful for applications in quantum measurements and quantum photonic devices.

•Oct 1, 2008•0 citations

Active narrowband filtering, line narrowing and gain using ladder electromagnetically induced transparency in an optically thick atomic vapour

James Keaveney, Armen D. Sargsyan, David G. Sarkisyan +2 more

Electromagnetically induced transparency (EIT) resonances using the 5S 1/2 → 5P 3/2 → 5D 5/2 ladder-system in optically thick Rb atomic vapour are studied. We observe a strong line narrowing effect and gain at the 5S 1/2 → 5P 3/2 transition wavelength due to an energy-pooling assisted frequency conversion with characteristics similar to 4-wave mixing. As a result it is possible to observe tunable and switchable transparency resonances with amplitude close to 100% and a linewidth of 15 MHz. In addition, the large line narrowing effect allows resolution of 85 Rb 5D 5/2 hyperfine structure even in the presence of strong power broadening.

arXiv:1311.7268•Journal of Physics B Atomic Molecular and Optical Physics•Mar 14, 2014•28 citations

Sum frequency mixing and quantum interference in three-level atoms

Richard R. Moseley

This work contains theoretical and experimental studies of the properties of three-level atoms subjected to two single-frequency, continuous-wave laser sources with special emphasis on magnetic-field-induced sum frequency mixing (SFM) and electromagnetically-induced transparency (EIT). In sodium vapour, two resonant-enhancement routes for SFM were experimentally studied. In one route (3S-3P-3D) the output is generated on a quadrupole-allowed transition and on the other (3S-3P-4P), a dipole-allowed transition. Phase matching conditions are studied in detail. On the second route, the two contributions to the phase mismatch can combine to heavily distort the spectroscopic lineshapes observed. Doubly-resonant SFM is considered and two paths for excitation of the output coherence are identified. Control of their relative strength, via the input laser strengths, is predicted, as well as interference between them. These are both experimentally observed on the 3S1/2-3P1/2-3D3/2 transition scheme in sodium. Theory is presented to show how the use of a strong upper laser in resonant SFM can, by EIT, greatly reduce the absorption on the lower transition without similarly reducing the nonlinear process. A significant increase in conversion efficiency is predicted. Theory is also presented on the inclusion of the local field correction, which is relevant for high vapour densities, in the Bloch equations for the three-level atom. Nonlinear coherence cross-coupling terms arise and the generalised equations are then used for two case studies; one concerning EIT, the other SFM. EIT is experimentally studied using continuous-wave lasers in rubidium vapour. Focusing and de-focusing were observed on the probe laser beam as it tunes through the transparency window at close, but separate, detunings. This is attributed to the radial intensity profile of the coupling laser which imposes a spatial refractive index modulation on the medium at the probe laser wavelength.

•Jul 1, 1995•2 citations

Absolute Absorption and Dispersion in a Thermal Rb Vapour at High Densities and High Magnetic Fields.

Lee Weller

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.

•Jan 1, 2013•5 citations
We present investigations of nonlinear optical phenomena using a 87^{87}87Rb thermal vapour in a high magnetic field. The magnetic field (of strength 0.6~T) separates the optical transitions by more than their Doppler-broadened linewidths. This technique provides a high level of control over thermal-vapour systems, which can be used as a simpler alternative to conventional state-preparation methods such as optical pumping. Using this approach, we study electromagnetically induced transparency in a non-degenerate 3-level ladder system. Finding excellent agreement with the numerically modelled transmission spectra, we are able to directly infer the dipole moment of the 5P3/2→_{3/2}\to3/2​→5D5/2_{5/2}5/2​ transition ∣⟨5P3/2∣∣er∣∣5D5/2⟩∣=(2.27±0.002stat±0.04syst) ea0|\langle5P_{3/2}||er||5D_{5/2}\rangle|= (2.27\pm0.002_{\rm stat}\pm0.04_{\rm syst})~ea_{0}∣⟨5P3/2​∣∣er∣∣5D5/2​⟩∣=(2.27±0.002stat​±0.04syst​) ea0​. Changing the coupling field to a standing-wave geometry, we observe resonant enhanced absorption: an effect that previously had only been observed in systems involving 4 or more atomic states. We also consider four-wave mixing (FWM) in a diamond level-scheme. Compared to the zero magnetic field case, we find good agreement with the FWM spectra using a simple model, even in the regime of strong laser dressing. Finally, we investigate heralded single-photon generation by spontaneous FWM. With strong laser dressing we observe the appearance of collective quantum beats, a single-photon interference effect due to the relative motion of atoms in a collective spin excitation. A violation of the Cauchy-Schwarz inequality by 6.7 standard deviations is reported.
We present investigations of magneto-optical phenomena using a 87^{87}87Rb thermal vapour in large magnetic fields. At this point, in the hyperfine Paschen-Back regime, optical transitions can be separated by more than their Doppler-broadened linewidth, providing a high level of control over the atomic system and a simpler theoretical model for studying atom-light-magnetic field interactions. In this context, we study the spectra of 87^{87}87Rb at magnetic fields of 0.4 0.4~0.4 T and 1.5 1.5~1.5 T in the Voigt geometry. In both cases we find excellent agreement between experimental and theoretical absorption spectra. With the 1.5 1.5~1.5 T field we also study polarisation changes induced in the light by the atoms subject to a large magnetic field. Using this approach, we consider the practical applications of our system as a vector magnetometer. We present a scheme that eliminates most sources of systematic errors in the measurement of the field strength by using pairs of transitions that cancel excited-state terms in the energy shifts. Finally, we extend the concepts and ideas investigated to an application in precision thermometry. We discuss how good understanding of the spectra and the magnetic field strength potentially allow detection of small differences in different spectral features, which could then be traced to the effect of the Boltzmann factor, krmBTk_{\\rm{B}}TkrmB​T, on the atomic populations.
We present an experimental study of seeded four-wave mixing (4WM) using a diamond excitation scheme (with states from the 5S1/2_{1/2}1/2​, 5P1/2_{1/2}1/2​, 5P3/2_{3/2}3/2​ and 5D1/2_{1/2}1/2​ terms) in a thermal vapour of 87^{87}87Rb atoms. We investigate the 4WM spectra under the application of a strong magnetic field (0.6 T). The Zeeman interaction is strong enough to realise the hyperfine Paschen-Back regime, which has the effect of separating the optical transitions by more than the Doppler width, thereby significantly simplifying the spectral features. We show that this facilitates a quantitative comparison, even in the regime of strong dressing, between experimental data and a simple theoretical model based only on four-level optical Bloch equations.
This dissertation reports experimental studies of nonlinear optical effects manifested by electromagnetically induced transparency (EIT) in cold Rb atoms. The cold Rb atoms are confined in a magneto-optic trap (MOT) obtained with the standard laser cooling and trapping technique. Because of the near zero Doppler shift and a high phase density, the cold Rb sample is well suited for studies of atomic coherence and interference and related applications, and the experiments can be compared quantitatively with theoretical calculations. It is shown that with EIT induced in the multi-level Rb system by laser fields, the linear absorption is suppressed and the nonlinear susceptibility is enhanced, which enables studies of nonlinear optics in the cold atoms with slow photons and at low light intensities. Three independent experiments are described and the experimental results are presented. First, an experimental method that can produce simultaneously co-propagating slow and fast light pulses is discussed and the experimental demonstration is reported. Second, it is shown that in a three-level Rb system coupled by multi-color laser fields, the multi-channel two-photon Raman transitions can be manipulated by the relative phase and frequency of a control laser field. Third, a scheme for all-optical switching near single photon levels is developed. The scheme is based on the phase-dependent multi-photon interference in a coherently coupled four-level system. The phase dependent multi-photon interference is observed and switching of a single light pulse by a control pulse containing ∼20 photons is demonstrated. These experimental studies reveal new phenomena manifested by quantum coherence and interference in cold atoms, contribute to the advancement of fundamental quantum optics and nonlinear optics at ultra-low light intensities, and may lead to the development of new techniques to control quantum states of atoms and photons, which will be useful for applications in quantum measurements and quantum photonic devices.
Electromagnetically induced transparency (EIT) resonances using the 5S 1/2 → 5P 3/2 → 5D 5/2 ladder-system in optically thick Rb atomic vapour are studied. We observe a strong line narrowing effect and gain at the 5S 1/2 → 5P 3/2 transition wavelength due to an energy-pooling assisted frequency conversion with characteristics similar to 4-wave mixing. As a result it is possible to observe tunable and switchable transparency resonances with amplitude close to 100% and a linewidth of 15 MHz. In addition, the large line narrowing effect allows resolution of 85 Rb 5D 5/2 hyperfine structure even in the presence of strong power broadening.
This work contains theoretical and experimental studies of the properties of three-level atoms subjected to two single-frequency, continuous-wave laser sources with special emphasis on magnetic-field-induced sum frequency mixing (SFM) and electromagnetically-induced transparency (EIT). In sodium vapour, two resonant-enhancement routes for SFM were experimentally studied. In one route (3S-3P-3D) the output is generated on a quadrupole-allowed transition and on the other (3S-3P-4P), a dipole-allowed transition. Phase matching conditions are studied in detail. On the second route, the two contributions to the phase mismatch can combine to heavily distort the spectroscopic lineshapes observed. Doubly-resonant SFM is considered and two paths for excitation of the output coherence are identified. Control of their relative strength, via the input laser strengths, is predicted, as well as interference between them. These are both experimentally observed on the 3S1/2-3P1/2-3D3/2 transition scheme in sodium. Theory is presented to show how the use of a strong upper laser in resonant SFM can, by EIT, greatly reduce the absorption on the lower transition without similarly reducing the nonlinear process. A significant increase in conversion efficiency is predicted. Theory is also presented on the inclusion of the local field correction, which is relevant for high vapour densities, in the Bloch equations for the three-level atom. Nonlinear coherence cross-coupling terms arise and the generalised equations are then used for two case studies; one concerning EIT, the other SFM. EIT is experimentally studied using continuous-wave lasers in rubidium vapour. Focusing and de-focusing were observed on the probe laser beam as it tunes through the transparency window at close, but separate, detunings. This is attributed to the radial intensity profile of the coupling laser which imposes a spatial refractive index modulation on the medium at the probe laser wavelength.
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.