Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Coherent signal amplification of refractive index spectrum in rubidium vapor using phase-shifting interferometry

Chih-Yuan Liu, Dian-Jiun Han

Published May 25, 2016• 2 citations
Publisher

Abstract

We have experimentally demonstrated a general method to perform high-precision refractive index spectrum measurement using phase-shifting interferometry in a phase-tunable Mach–Zehnder interferometer. We observed coherent amplification on the refractive spectrum, across the Lamb dips of ground hyperfine states in a Doppler-broadened Rb87 vapor. Most importantly, the spectrum still has a large signal-to-noise ratio when the probe power is in the dark light level under which the method using a single interferogram fails. This experimental scheme is efficient for refractive spectrum measurements and could be extended for 2D phase imaging. It provides many potential applications for optical phase measurements in linear, nonlinear, and quantum optics.

DOI
10.1364/josab.33.001298

Related papers

Observation of large group index enhancement in Doppler-broadened rubidium vapor

Bo-Xun Wang, Chih-Yuan Liu, D. J. Han

We report experimental observation of large group index across the Lamb dips of ground hyperfine states in Doppler-broadened 87Rb vapor. By sweeping the laser frequency through each hyperfine transition we measure the saturated absorption and optical phase shift using a phase-locked Mach-Zehnder interferometer. Our measurements provide a direct demonstration of the theoretical prediction by Agarwal et al. [G. S. Agarwal and T. N. Dey, Phys. Rev. A 68, 063816, (2003)] for the first time. An enhancement factor as large as 1005 in group index was observed for Rb vapor at temperature of 85 °C. The experimental data are in good agreement with the theory.

Optics Express•Jul 13, 2015•5 citations

Phase sensitive measurements in a nonlinear interferometer using four-wave mixing in Rubidium-85

Tabitha Colter

Conventional interferometers make precision measurements by analyzing the position of interference fringes while nonlinear interferometers rely upon a sensitive measurement of phase difference. We detect this phase sensitivity using a correlated probe and conjugate beam that have undergone four-wave mixing inside a hot Rubidium-85 vapor cell. By placing a piece of glass into the path of the probe we observe a phase shift that indicates a successful nonlinear interferometer. We now plan to place into the probe path oils with known indices of refraction on plasmonic media and measure the resulting phase shifts. These results will then allow us to back-calculate an unknown material’s index of refraction simply by observing the phase shift with a level of sensitivity greater than conventional interferometers. Continued research in the field of interferometry utilizing nonlinear processes should provide even greater sensitivity in precision measurements and applications across a range of scientific disciplines.

•Jan 1, 2016•0 citations

Nonlinear refractive index of warm rubidium vapor

L. Kardum, G. Premec, N. Šantić +1 more

The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale MEMS cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing excellent quantitative agreement. A Kerr nonlinear refractive index $n_2$ of up to $10^{-4}$ cm$^2$/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.

physics.atom-phCross-listedarXiv:2606.24676•Jun 24, 2026•0 citations

Nonlinear Refractive Index of Warm Rubidium Vapor

Lovre Kardum, G. Premec, Neven Šantić +1 more

The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale micro-electro-mechanical system (MEMS) cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing very good quantitative agreement. A Kerr nonlinear refractive index n2 of up to −1.2×10−4 cm2/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.

Photonics•Jul 14, 2026•0 citations

Interferometric measurement of the resonant absorption and refractive index in rubidium gas

Kenneth G. Libbrecht, Maxwell W. Libbrecht

We present a laboratory demonstration of the Kramers-Kronig relation between the resonant absorption and refractive index in rubidium gas. Our experiment uses a rubidium vapor cell in one arm of a simple Mach-Zehnder interferometer. As the laser frequency is scanned over an atomic resonance, the interferometer output is affected by variations of both the absorption and refractive index of the gas with frequency, all of which can be calculated in a straightforward manner. Changing the vapor density and interferometer phase produces a family of different output signals. The experiment was performed using a commercially available tunable diode laser system that was designed specifically for the undergraduate physics laboratory. As a teaching tool this experiment is reliable, fun, and instructive, while it also introduces the student to some sophisticated and fundamental physical concepts.

American Journal of Physics•Nov 22, 2006•24 citations

Measurement of the Kerr nonlinear refractive index of the Rb vapor based on an optical frequency comb using the z-scan method

Sandan Wang, Jinpeng Yuan, Lirong Wang +2 more

We report the measurement of the Kerr nonlinear refractive index of the rubidium vapor via the high sensitivity z-scan method by using an optical frequency comb. The novel self-focusing and self-defocusing effects of the vapor are presented with red and blue detunings of the laser frequency. The optical nonlinear characteristics of the rubidium vapor are clearly interpreted under different experimental parameters. Furthermore, the Kerr nonlinear refractive index n2 is obtained from the measured dispersion curve, and it basically occurs on the order of 10−6 cm2/W. The evolutions of the Kerr nonlinear coefficient n2 with the laser power and frequency detuning, respectively, are studied. To the best of our knowledge, the use of pulsed lasers to measure the Kerr nonlinear refractive index n2 of atomic vapor has not been reported yet. The direct measurement of the Kerr nonlinear coefficient will greatly help us understand and optimize nonlinear optical processes and find its more potential applications in quantum optics.

Optics Express•Nov 23, 2020•21 citations
We have experimentally demonstrated a general method to perform high-precision refractive index spectrum measurement using phase-shifting interferometry in a phase-tunable Mach–Zehnder interferometer. We observed coherent amplification on the refractive spectrum, across the Lamb dips of ground hyperfine states in a Doppler-broadened Rb87 vapor. Most importantly, the spectrum still has a large signal-to-noise ratio when the probe power is in the dark light level under which the method using a single interferogram fails. This experimental scheme is efficient for refractive spectrum measurements and could be extended for 2D phase imaging. It provides many potential applications for optical phase measurements in linear, nonlinear, and quantum optics.
We report experimental observation of large group index across the Lamb dips of ground hyperfine states in Doppler-broadened 87Rb vapor. By sweeping the laser frequency through each hyperfine transition we measure the saturated absorption and optical phase shift using a phase-locked Mach-Zehnder interferometer. Our measurements provide a direct demonstration of the theoretical prediction by Agarwal et al. [G. S. Agarwal and T. N. Dey, Phys. Rev. A 68, 063816, (2003)] for the first time. An enhancement factor as large as 1005 in group index was observed for Rb vapor at temperature of 85 °C. The experimental data are in good agreement with the theory.
Conventional interferometers make precision measurements by analyzing the position of interference fringes while nonlinear interferometers rely upon a sensitive measurement of phase difference. We detect this phase sensitivity using a correlated probe and conjugate beam that have undergone four-wave mixing inside a hot Rubidium-85 vapor cell. By placing a piece of glass into the path of the probe we observe a phase shift that indicates a successful nonlinear interferometer. We now plan to place into the probe path oils with known indices of refraction on plasmonic media and measure the resulting phase shifts. These results will then allow us to back-calculate an unknown material’s index of refraction simply by observing the phase shift with a level of sensitivity greater than conventional interferometers. Continued research in the field of interferometry utilizing nonlinear processes should provide even greater sensitivity in precision measurements and applications across a range of scientific disciplines.
The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale MEMS cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing excellent quantitative agreement. A Kerr nonlinear refractive index n2n_2n2​ of up to 10−410^{-4}10−4 cm2^22/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.
The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale micro-electro-mechanical system (MEMS) cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing very good quantitative agreement. A Kerr nonlinear refractive index n2 of up to −1.2×10−4 cm2/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.
We present a laboratory demonstration of the Kramers-Kronig relation between the resonant absorption and refractive index in rubidium gas. Our experiment uses a rubidium vapor cell in one arm of a simple Mach-Zehnder interferometer. As the laser frequency is scanned over an atomic resonance, the interferometer output is affected by variations of both the absorption and refractive index of the gas with frequency, all of which can be calculated in a straightforward manner. Changing the vapor density and interferometer phase produces a family of different output signals. The experiment was performed using a commercially available tunable diode laser system that was designed specifically for the undergraduate physics laboratory. As a teaching tool this experiment is reliable, fun, and instructive, while it also introduces the student to some sophisticated and fundamental physical concepts.
We report the measurement of the Kerr nonlinear refractive index of the rubidium vapor via the high sensitivity z-scan method by using an optical frequency comb. The novel self-focusing and self-defocusing effects of the vapor are presented with red and blue detunings of the laser frequency. The optical nonlinear characteristics of the rubidium vapor are clearly interpreted under different experimental parameters. Furthermore, the Kerr nonlinear refractive index n2 is obtained from the measured dispersion curve, and it basically occurs on the order of 10−6 cm2/W. The evolutions of the Kerr nonlinear coefficient n2 with the laser power and frequency detuning, respectively, are studied. To the best of our knowledge, the use of pulsed lasers to measure the Kerr nonlinear refractive index n2 of atomic vapor has not been reported yet. The direct measurement of the Kerr nonlinear coefficient will greatly help us understand and optimize nonlinear optical processes and find its more potential applications in quantum optics.