Physical Review Letters

Microwave Light Modulation by an Optically Pumped Rb87 Vapor

B.S. Mathur, Haoqin Tang, R. Bulos, W. Happer

Published Oct 7, 1968• 21 citations

Abstract

We have observed appreciable light modulation at the 6.835-GHz hfs transition frequency of optically pumped ${\mathrm{Rb}}^{87}$ vapor. The frequency separation between the levels involved in the transition exceeded the total spectral width of the initial lamp profile. These observations indicate that persistent doubts as to the feasibility of a transmission-light-modulation experiment under such conditions are groundless.

DOI: 10.1103/physrevlett.21.1035

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Parametric Frequency Conversion of Resonance Radiation in Optically Pumped Rb87 Vapor

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All-optical microwave frequency standard: a proposal

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Pulsed optically pumped Rb87 vapor cell frequency standard: A multilevel approach

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Physical Review Letters

Microwave Light Modulation by an Optically Pumped Rb87 Vapor

B.S. Mathur, Haoqin Tang, R. Bulos, W. Happer

Published Oct 7, 1968• 21 citations

Publisher

Abstract

We have observed appreciable light modulation at the 6.835-GHz hfs transition frequency of optically pumped

{\mathrm{Rb}}^{87}

vapor. The frequency separation between the levels involved in the transition exceeded the total spectral width of the initial lamp profile. These observations indicate that persistent doubts as to the feasibility of a transmission-light-modulation experiment under such conditions are groundless.

DOI: 10.1103/physrevlett.21.1035

Related papers

Parametric Frequency Conversion of Resonance Radiation in Optically Pumped Rb87 Vapor

Henry Tang

This paper reports an investigation of parametric frequency conversion in a vapor of ${\mathrm{Rb}}^{87}$ atoms in which nearly resonant optical waves are coupled with microwaves at the ground-state hyperfine-structure (hfs) frequency of ${\mathrm{Rb}}^{87}$ by the nonlinear susceptibilities of ${\mathrm{Rb}}^{87}$ vapor. These nonlinear susceptibilities are greatly enhanced by optical pumping of the ground-state hfs levels of ${\mathrm{Rb}}^{87}$ and by using nearly resonant light. The frequency-conversion process generates optical sideband waves which are separated in frequency from the carrier light waves by the ground-state hfs frequency of ${\mathrm{Rb}}^{87}$ (6.835 GHz). These sidebands have been directly observed in the spectral profiles of ${\mathrm{Rb}}^{85}$ resonance light which had passed through ${\mathrm{Rb}}^{87}$ vapor. The conversion efficiency of power from the carrier waves to the sideband waves in a 45-cm length of vapor was greater than 1%. The observed behavior of the sidebands is in excellent qualitative agreement with the predictions of a semiclassical theory.This paper reports an investigation of parametric frequency conversion in a vapor of ${\mathrm{Rb}}^{87}$ atoms in which nearly resonant optical waves are coupled with microwaves at the ground-state hyperfine-structure (hfs) frequency of ${\mathrm{Rb}}^{87}$ by the nonlinear susceptibilities of ${\mathrm{Rb}}^{87}$ vapor. These nonlinear susceptibilities are greatly enhanced by optical pumping of the ground-state hfs levels of ${\mathrm{Rb}}^{87}$ and by using nearly resonant light. The frequency-conversion process generates optical sideband waves which are separated in frequency from the carrier light waves by the ground-state hfs frequency of ${\mathrm{Rb}}^{87}$ (6.835 GHz). These sidebands have been directly observed in the spectral profiles of ${\mathrm{Rb}}^{85}$ resonance light which had passed through ${\mathrm{Rb}}^{87}$ vapor. The conversion efficiency of power from the carrier waves to the sideband waves in a 45-cm length of vapor was greater than 1%. The observed behavior of the sidebands is in excellent qualitative agreement with the predictions of a semiclassical theory.

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Orientational frequency shifts of microwave 0-0 superfine resonance in 87Rb vapor with selective optical pumping

A. A. Baranov, Ермак Сергей Викторович, V. V. Semenov

The orientational frequency shift of the UHF radio-optical resonance in the 87 Rb vapor with a selective optical pumping by laser and lamp sources is studied experimentally and theoretically. A leading role of the tensor component of the light shift is noticed for both excitation modes, and a modulation technique of the resonance frequency orientation shift suppression is demonstrated. We show that it is necessary to ensure a constancy of the angle between the pump light direction and the external magnetic field vector when using a rubidium quantum discriminator based on moving and rotating carriers.The orientational frequency shift of the UHF radio-optical resonance in the 87 Rb vapor with a selective optical pumping by laser and lamp sources is studied experimentally and theoretically. A leading role of the tensor component of the light shift is noticed for both excitation modes, and a modulation technique of the resonance frequency orientation shift suppression is demonstrated. We show that it is necessary to ensure a constancy of the angle between the pump light direction and the external magnetic field vector when using a rubidium quantum discriminator based on moving and rotating carriers.

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A simple method to produce a clock transition with purely optical means by modulated pumping is described. The field-independent ground state resonance of /sup 87/Rb atoms using sinusoidal modulation of the injection current of an AlGaAs laser diode emitting at 780 nm (FM modulation) is observed. The 6.835 GHz resonance with a subharmonic modulation frequency of 1.139 GHz is detected. A high-contrast resonance peak is observed and a condition for zero light shift is found. The linewidth is 3 kHz (at 6.835 GHz) in this preliminary experiment, due to the small size of the light beam ( approximately 2 mm diameter) and the low buffer gas pressure (680 Pa) that was used. A theoretical model that explains the main features of the experiment is described.>A simple method to produce a clock transition with purely optical means by modulated pumping is described. The field-independent ground state resonance of /sup 87/Rb atoms using sinusoidal modulation of the injection current of an AlGaAs laser diode emitting at 780 nm (FM modulation) is observed. The 6.835 GHz resonance with a subharmonic modulation frequency of 1.139 GHz is detected. A high-contrast resonance peak is observed and a condition for zero light shift is found. The linewidth is 3 kHz (at 6.835 GHz) in this preliminary experiment, due to the small size of the light beam ( approximately 2 mm diameter) and the low buffer gas pressure (680 Pa) that was used. A theoretical model that explains the main features of the experiment is described.>

IEEE Transactions on Instrumentation and MeasurementApr 1, 1993157 citations

Study on an all-optical microwave frequency standard

Normand Cyr, M. Têtu, Marc Breton

We describe a simple method to produce a clock transition with purely optical means through modulated pumping. We observe the field-independent ground state resonance of 87Rb atoms using sinusoidal modulation of the injection current of an AlGaAs laser diode emitting at 780 nm (FM modulation). We detect the 6.835 GHz resonance with a modulation frequency of 1.139 GHz. A high contrast resonance peak is observed and a condition for zero light shift is found. With a beam radius of approximately 3 mm and a buffer gas (N2) pressure of 680 Pa (5.1 Torr), a minimal linewidth of 290 Hz is observed. A theoretical study of the excitation of hyperfine coherences by a modulated laser beam is given.We describe a simple method to produce a clock transition with purely optical means through modulated pumping. We observe the field-independent ground state resonance of 87Rb atoms using sinusoidal modulation of the injection current of an AlGaAs laser diode emitting at 780 nm (FM modulation). We detect the 6.835 GHz resonance with a modulation frequency of 1.139 GHz. A high contrast resonance peak is observed and a condition for zero light shift is found. With a beam radius of approximately 3 mm and a buffer gas (N2) pressure of 680 Pa (5.1 Torr), a minimal linewidth of 290 Hz is observed. A theoretical study of the excitation of hyperfine coherences by a modulated laser beam is given.

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Modulation of a Fluorescent Light Beam by an Optically Pumped Vapor Undergoing a Double-Quantum Resonance

W. Franzen, P.B. Newell, Dean S. Edmonds

The high-frequency modulation of a light beam scattered by optically-pumped ${\mathrm{Rb}}^{85}$ vapor undergoing a double-quantum resonance in the ground state has been studied both experimentally and theoretically. The vapor cell used in the experiment was an evacuated 3-in.-diam sphere with paraffin-coated walls. It was subjected simultaneously to a ${\ensuremath{\sigma}}^{+}$-polarized ${D}_{1}$ pumping beam and a $\ensuremath{\pi}$-polarized unfiltered monitoring beam at right angles to the pumping beam. The scattered light was detected in a third orthogonal direction after passage through a $\ensuremath{\sigma}$ polarizer and a ${D}_{2}$ filter. A superheterodyne amplifier was used to select the component of the scattered light modulated at twice the frequency of the pulsed rf driving field. A theoretical analysis has been developed which predicts the existence of two pairs of nonvanishing off-diagonal elements of the excited-state density matrix oscillating at twice the applied frequency under these conditions, and also predicts a corresponding modulation of the scattered light. Despite the feebleness of the observed signal caused by heavy damping in the excited state of ${\mathrm{Rb}}^{85}$ , such a modulation has been observed, and its resonant behavior has been found to agree with theory.The high-frequency modulation of a light beam scattered by optically-pumped ${\mathrm{Rb}}^{85}$ vapor undergoing a double-quantum resonance in the ground state has been studied both experimentally and theoretically. The vapor cell used in the experiment was an evacuated 3-in.-diam sphere with paraffin-coated walls. It was subjected simultaneously to a ${\ensuremath{\sigma}}^{+}$-polarized ${D}_{1}$ pumping beam and a $\ensuremath{\pi}$-polarized unfiltered monitoring beam at right angles to the pumping beam. The scattered light was detected in a third orthogonal direction after passage through a $\ensuremath{\sigma}$ polarizer and a ${D}_{2}$ filter. A superheterodyne amplifier was used to select the component of the scattered light modulated at twice the frequency of the pulsed rf driving field. A theoretical analysis has been developed which predicts the existence of two pairs of nonvanishing off-diagonal elements of the excited-state density matrix oscillating at twice the applied frequency under these conditions, and also predicts a corresponding modulation of the scattered light. Despite the feebleness of the observed signal caused by heavy damping in the excited state of ${\mathrm{Rb}}^{85}$, such a modulation has been observed, and its resonant behavior has been found to agree with theory.

Physical ReviewJun 5, 19687 citations

Pulsed optically pumped Rb87 vapor cell frequency standard: A multilevel approach

Salvatore Micalizio, Aldo Godone, Filippo Levi +1 more

We present a multilevel theoretical approach to describe the behavior of a pulsed optically pumped (POP) $^{87}\mathrm{Rb}$ frequency standard based on a microwave cavity-vapor cell arrangement. The full Zeeman manifold of the ground-state hyperfine levels is then considered, and the dynamics induced among them by relaxation processes (buffer gas, spin exchange, and cell-walls collisions) is taken into account. The model includes as well the absorption of the pumping laser along the cell and the cavity feedback on the atoms; the effects related to a nonuniform excitation of the atomic sample are also discussed. Theoretical predictions are proven with a laboratory prototype of POP passive maser in which the clock transition is excited by means of the Ramsey technique. The agreement between theory and experiment is very satisfactory from both a quantitative and qualitative point of view, in terms of the shape of the Ramsey fringes, microwave power delivered by the atoms, and short-term frequency stability. In particular, a frequency stability of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at one second has been measured, in very good agreement with the expected value. On this basis, the model has been extended to predict the short-term frequency stability of a POP frequency standard operating with optical detection. A shot-noise limited frequency stability (Allan deviation) of ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$ is foreseen. This value can be degraded by microwave phase noise and laser fluctuations so that the overall predicted clock stability is ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$.We present a multilevel theoretical approach to describe the behavior of a pulsed optically pumped (POP) $^{87}\mathrm{Rb}$ frequency standard based on a microwave cavity-vapor cell arrangement. The full Zeeman manifold of the ground-state hyperfine levels is then considered, and the dynamics induced among them by relaxation processes (buffer gas, spin exchange, and cell-walls collisions) is taken into account. The model includes as well the absorption of the pumping laser along the cell and the cavity feedback on the atoms; the effects related to a nonuniform excitation of the atomic sample are also discussed. Theoretical predictions are proven with a laboratory prototype of POP passive maser in which the clock transition is excited by means of the Ramsey technique. The agreement between theory and experiment is very satisfactory from both a quantitative and qualitative point of view, in terms of the shape of the Ramsey fringes, microwave power delivered by the atoms, and short-term frequency stability. In particular, a frequency stability of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at one second has been measured, in very good agreement with the expected value. On this basis, the model has been extended to predict the short-term frequency stability of a POP frequency standard operating with optical detection. A shot-noise limited frequency stability (Allan deviation) of ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$ is foreseen. This value can be degraded by microwave phase noise and laser fluctuations so that the overall predicted clock stability is ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$.

Physical Review AJan 6, 200950 citations

We have observed appreciable light modulation at the 6.835-GHz hfs transition frequency of optically pumped

{\mathrm{Rb}}^{87}

This paper reports an investigation of parametric frequency conversion in a vapor of

{\mathrm{Rb}}^{87}

atoms in which nearly resonant optical waves are coupled with microwaves at the ground-state hyperfine-structure (hfs) frequency of

{\mathrm{Rb}}^{87}

by the nonlinear susceptibilities of

{\mathrm{Rb}}^{87}

vapor. These nonlinear susceptibilities are greatly enhanced by optical pumping of the ground-state hfs levels of

{\mathrm{Rb}}^{87}

and by using nearly resonant light. The frequency-conversion process generates optical sideband waves which are separated in frequency from the carrier light waves by the ground-state hfs frequency of

{\mathrm{Rb}}^{87}

(6.835 GHz). These sidebands have been directly observed in the spectral profiles of

{\mathrm{Rb}}^{85}

resonance light which had passed through

{\mathrm{Rb}}^{87}

vapor. The conversion efficiency of power from the carrier waves to the sideband waves in a 45-cm length of vapor was greater than 1%. The observed behavior of the sidebands is in excellent qualitative agreement with the predictions of a semiclassical theory.

The high-frequency modulation of a light beam scattered by optically-pumped

{\mathrm{Rb}}^{85}

vapor undergoing a double-quantum resonance in the ground state has been studied both experimentally and theoretically. The vapor cell used in the experiment was an evacuated 3-in.-diam sphere with paraffin-coated walls. It was subjected simultaneously to a ${\ensuremath{\sigma}}^{+}$-polarized

{D}_{1}

pumping beam and a $\ensuremath{\pi}$-polarized unfiltered monitoring beam at right angles to the pumping beam. The scattered light was detected in a third orthogonal direction after passage through a $\ensuremath{\sigma}$ polarizer and a

{D}_{2}

filter. A superheterodyne amplifier was used to select the component of the scattered light modulated at twice the frequency of the pulsed rf driving field. A theoretical analysis has been developed which predicts the existence of two pairs of nonvanishing off-diagonal elements of the excited-state density matrix oscillating at twice the applied frequency under these conditions, and also predicts a corresponding modulation of the scattered light. Despite the feebleness of the observed signal caused by heavy damping in the excited state of

{\mathrm{Rb}}^{85}

, such a modulation has been observed, and its resonant behavior has been found to agree with theory.

We present a multilevel theoretical approach to describe the behavior of a pulsed optically pumped (POP)

^{87}\mathrm{Rb}

frequency standard based on a microwave cavity-vapor cell arrangement. The full Zeeman manifold of the ground-state hyperfine levels is then considered, and the dynamics induced among them by relaxation processes (buffer gas, spin exchange, and cell-walls collisions) is taken into account. The model includes as well the absorption of the pumping laser along the cell and the cavity feedback on the atoms; the effects related to a nonuniform excitation of the atomic sample are also discussed. Theoretical predictions are proven with a laboratory prototype of POP passive maser in which the clock transition is excited by means of the Ramsey technique. The agreement between theory and experiment is very satisfactory from both a quantitative and qualitative point of view, in terms of the shape of the Ramsey fringes, microwave power delivered by the atoms, and short-term frequency stability. In particular, a frequency stability of $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ at one second has been measured, in very good agreement with the expected value. On this basis, the model has been extended to predict the short-term frequency stability of a POP frequency standard operating with optical detection. A shot-noise limited frequency stability (Allan deviation) of ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$ is foreseen. This value can be degraded by microwave phase noise and laser fluctuations so that the overall predicted clock stability is ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$.