Four-wave mixing in the hyperfine Paschen-Back regime

Daniel J. Whiting, Renju S. Mathew, James Keaveney, Charles S. Adams, Ifan G. Hughes

Published May 4, 2017• 1 citation

Abstract

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.

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Four-wave mixing in the hyperfine Paschen-Back regime

Daniel J. Whiting, Renju S. Mathew, James Keaveney, Charles S. Adams, Ifan G. Hughes

Published May 4, 2017• 1 citation

OpenAlex

Abstract

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.

Related papers

Four-wave mixing in a non-degenerate four-level diamond configuration in the hyperfine Paschen–Back regime

D. 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 5S1/2,5P1/2,5P3/2 and 5D3/2 terms) in a thermal vapour of 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 realize 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.We present an experimental study of seeded four-wave mixing (4WM) using a diamond excitation scheme (with states from the 5S1/2,5P1/2,5P3/2 and 5D3/2 terms) in a thermal vapour of 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 realize 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.

arXiv:1705.01855Journal of Modern OpticsSep 25, 201742 citations

Nonlinear optics in a thermal Rb vapour at high magnetic fields

Daniel J. Whiting

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.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.

Jan 1, 20171 citation

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 .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:1401.1659Journal of Physics B Atomic Molecular and Optical PhysicsMar 26, 201456 citations

Quantitative investigation of the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium 52S1/2→52D5/2 two-photon transition

Masashi Abe, Ryohei Itoyama, Yuta Komiyama +3 more

We precisely investigate the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium $5{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ two-photon transition. Owing to the high sensitivity of the $D$ state of atoms to a magnetic field, the splittings of the spectra of the $D$ state are sufficiently large in a weak magnetic field of $<10$ G. We experimentally observe how in the hyperfine coupling in the $5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ state is disrupted even in weak magnetic fields around 10 G and the energy levels are arranged according to their total angular momentum $J$ and nuclear spin $I$ . The transient of the spectra known as the Paschen-Back effect is observed even in a weak magnetic field with an order of magnitude of several tens of gauss. The results of theoretical calculations for energy shifts and transition intensities under a magnetic field are in quantitative agreement with the experimental results.We precisely investigate the Zeeman and Paschen-Back effects of the hyperfine structure during the rubidium $5{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ two-photon transition. Owing to the high sensitivity of the $D$ state of atoms to a magnetic field, the splittings of the spectra of the $D$ state are sufficiently large in a weak magnetic field of $<10$ G. We experimentally observe how in the hyperfine coupling in the $5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ state is disrupted even in weak magnetic fields around 10 G and the energy levels are arranged according to their total angular momentum $J$ and nuclear spin $I$. The transient of the spectra known as the Paschen-Back effect is observed even in a weak magnetic field with an order of magnitude of several tens of gauss. The results of theoretical calculations for energy shifts and transition intensities under a magnetic field are in quantitative agreement with the experimental results.

Physical Review AMay 28, 20194 citations

The hyperfine Paschen-Back Faraday effect

Zentile, MA, Andrews, R, Weller, L +4 more

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 87Rb is found to be ∼40 kHz °C−1.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 87Rb is found to be ∼40 kHz °C−1.

Apr 14, 201440 citations

Four-wave mixing in the diamond configuration in an atomic vapor

R. T. Willis, F. E. Becerra, Luis A. Orozco +1 more

We present measurements of the resonance structure for nondegenerate four-wave mixing (4WM) in the diamond configuration in a warm atomic vapor of rubidium. We show that a narrow sub-Doppler feature exists and can be understood as a result of velocity-class selection. We measure the efficiency of the 4WM process and show it to be on the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. Our observations are consistent with the results of a theoretical treatment based on the semiclassical Maxwell-Bloch equations for the system with the appropriate coupling values derived from the experimental values in Rb.We present measurements of the resonance structure for nondegenerate four-wave mixing (4WM) in the diamond configuration in a warm atomic vapor of rubidium. We show that a narrow sub-Doppler feature exists and can be understood as a result of velocity-class selection. We measure the efficiency of the 4WM process and show it to be on the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. Our observations are consistent with the results of a theoretical treatment based on the semiclassical Maxwell-Bloch equations for the system with the appropriate coupling values derived from the experimental values in Rb.

Physical Review AMar 12, 200977 citations

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}

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.

D

state of atoms to a magnetic field, the splittings of the spectra of the

D

state are sufficiently large in a weak magnetic field of

<10

G. We experimentally observe how in the hyperfine coupling in the

5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}

state is disrupted even in weak magnetic fields around 10 G and the energy levels are arranged according to their total angular momentum

J

and nuclear spin

I

. The transient of the spectra known as the Paschen-Back effect is observed even in a weak magnetic field with an order of magnitude of several tens of gauss. The results of theoretical calculations for energy shifts and transition intensities under a magnetic field are in quantitative agreement with the experimental results.