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Physical Review A

Phase-modulation laser spectroscopy

Axel Schenzle, Ralph G. DeVoe, Richard G. Brewer

Published May 1, 1982• 88 citations
Publisher

Abstract

A novel phase-modulation technique which permits subkilohertz-laser stability and new levels of precision in laser spectroscopy was reported recently. For spectroscopy, the basic arrangement consists of a combination of an optical pump and a probe field which is phase modulated. The pump prepares the atomic sample by burning a narrow hole within the atom's inhomogeneous line shape, and the probe beam samples the prepared hole when its modulation sidebands are swept into resonance. Off resonance, the probe is balanced as pairs of sidebands produce heterodyne beat signals of opposite phase which just cancel. On resonance, the balance is upset and yields a nonvanishing beat signal with a Lorentzian absorption or dispersion line shape and with residual noise approaching the shot noise limit. Here we investigate the theory of phase-modulation spectroscopy. We treat the nonlinear response of an atomic two-level quantum system subject to an intense pump and a weak copropagating or counterpropagating phase-modulated probe beam. The density-matrix equations of motion are solved by a Laplace-transform method and by the novel use of a translation operator which allows the infinite hierarchy of coupled equations to close. A solution equivalent to the rate-equation result is developed and coherence corrections are found which predict new resonances that have just been detected in this laboratory. The delayed pump-probe technique encountered in solid-state laser spectroscopy is analyzed in this context for two- and three-level quantum systems. The response of a Fabry-Perot cavity to a phase-modulated light wave is examined also and reveals an unexpected absorption feature.

DOI
10.1103/physreva.25.2606

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We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the $3s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}$, $F=2$, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, $F=3$, ${m}_{F}=3$ transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.

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Heterodyne measurements of dispersion in electromagnetically induced absorption

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The dispersive and absorptive features of a closed transition in atomic cesium are investigated by means of a heterodyne interferometer as a function of the powers of probe and pump laser. Coherent population trapping (CPT) phenomena have raised the interest of the community in recent years. Possible applications of such effects are in the field of slow light propagation and, on the other side, superluminal effects. In particular, special interest has been devoted to the investigation of the refractive index of coherently prepared atoms. The goal of this investigation is the design of new optical media which show either negative or positive dispersion without absorption or with increased anomalous absorption. Such media could be useful ui building white light cavities, opto-optical modulators, and in quantum non-demolition (QND) measurements which are crucial to the development of the future generations gravitational wave detectors. Among these coherency processes we have been studying the phenomenon of electromagnetically induced absorption (EIA) (2) in a closed transition in cesiumatoms. The transition under analysis was the 'CS DZ line at 852 nm, in particular the hyperfine transition 6s zS~/2 F=4 + 6p 2P~/2 F'=5. The system was analyzed by means of a three beam heterodyne interferometer (l). This experimental setup shows high sensitivity to phase measurements and strongly reduced sensitivity to acoustical or vibrational noise. Using a third reference laser which does not interact with the mediumone can perform simultaneous measurements of the phase shift and the absorption of either the probe or the pump laser. The dispersion and the absorption of probe and coupling lasers have been measured as a funcion of the power of the coupling and probe lasers themselves. The power of the lasers are changed in the range of several decades. The halfwidth of the EL4 signal shows an increase with respect to the power of the probe laser while the phase shift of the probe laser decreases. The possibility to extend EIA measurements to a closed four level system in cesium is under analysis and is discussed here. Such possible developments of the experimental setup using a fourth laser or modulating the present reference laser enhance the capability to exploit simultaneous measurements of dispersion and absorption even in the four level system. This work was supported by SFB 407 of the Deutsche Forschungsgemeinschaft (German Research Society).

•Jan 1, 2003•0 citations
A novel phase-modulation technique which permits subkilohertz-laser stability and new levels of precision in laser spectroscopy was reported recently. For spectroscopy, the basic arrangement consists of a combination of an optical pump and a probe field which is phase modulated. The pump prepares the atomic sample by burning a narrow hole within the atom's inhomogeneous line shape, and the probe beam samples the prepared hole when its modulation sidebands are swept into resonance. Off resonance, the probe is balanced as pairs of sidebands produce heterodyne beat signals of opposite phase which just cancel. On resonance, the balance is upset and yields a nonvanishing beat signal with a Lorentzian absorption or dispersion line shape and with residual noise approaching the shot noise limit. Here we investigate the theory of phase-modulation spectroscopy. We treat the nonlinear response of an atomic two-level quantum system subject to an intense pump and a weak copropagating or counterpropagating phase-modulated probe beam. The density-matrix equations of motion are solved by a Laplace-transform method and by the novel use of a translation operator which allows the infinite hierarchy of coupled equations to close. A solution equivalent to the rate-equation result is developed and coherence corrections are found which predict new resonances that have just been detected in this laboratory. The delayed pump-probe technique encountered in solid-state laser spectroscopy is analyzed in this context for two- and three-level quantum systems. The response of a Fabry-Perot cavity to a phase-modulated light wave is examined also and reveals an unexpected absorption feature.
The technique of phase-modulation laser spectroscopy is used to detect a coherent four-wave interaction in I2{\mathrm{I}}_{2}I2​ vapor. A phase-modulated probe beam induces in the sample an oscillating population which in turn modulates a counterpropagating pump beam that reveals a characteristic two-resonance spectrum. The observations fully confirm an earlier density-matrix calculation.
The purpose of this work was to investigate coherence effects in the interaction of two counterpropagating electromagnetic waves with the atoms of a gas, in the case in which one of the waves is weak and frequency modulated, while the other is sufficiently intense to cause saturation. Solving the equations for the density matrix in first-order perturbation theory, the authors obtained in analytic form the real part of the susceptibility integrated over the atom's velocity, expressed in terms of the rate equation model (REM) predictions plus the coherence corrections. The relaxation constants of the levels involved in the transition were kept different in order to allow a wider range of applications of the results. Calculated line shapes related either to the frequency-modulated (FM) sideband or to the ordinary dispersion techniques are presented. The REM approximation and the coherence corrections are shown in detail for an optical line which is of interest for frequency standard investigations.
Gain arising from the interaction of intense laser fields and atoms has attracted recent attention because it has been found, for example, that two-photon lasing1 and lasing without inversion2 occurs in these systems. Physical and intuitive models of these interactions can be developed by using the dressed-atom states, which, unfortunately, tend to be difficult to detect directly with high precision. We will report on a new modulation spectroscopy for the quantum limited detection of gain in dressed-atom systems. The spectroscopy involves weak modulation of the dressed-state splitting and lockin detection of the intensity of the probing beam. It differs from classic frequency-modulation spectroscopies in that the probe beam is not modulated before it interacts with the sample of strongly driven atoms and hence does not suffer from the effects of residual amplitude modulation.
We present our experimental investigations of nonlinear ground-state pump-probe spectroscopy in ultracold rubidium 85 produced in a magneto-optical trap (MOT). Nonlinear ground-state pump-probe spectroscopy is a two-photon analog of traditional two-level pump-probe spectroscopy. When a two-level atom is driven with an intense, single frequency near-resonant laser field the absorption spectrum of a weak probe field exhibits absorption and gain features not seen without the pump field. These saturated absorption line shapes, obtained under different pump field conditions, are known as the Mollow spectra. Nonlinear ground-state pump-probe spectroscopy is a three-level process, in which an intense two-photon pump field drives transitions between two components of the ground state coupled through an intermediate excited state. When the frequencies of the pump fields are tuned far from the intermediate state resonance, spontaneous emission is significantly reduced and narrow spectral lines are possible. The absorption/gain spectrum of a weak probe field, tuned in the vicinity of the intermediate state virtual level, resembles the Mollow spectrum except that new interference processes arise due to competition between two-photon pathways involving the probe field and each of the two pump fields. This interference significantly affects the probe absorption spectrum, and new features appear that are not present in the two-level case. We describe our measurements of this process, including the MOT that produces the ultracold collection of atoms, and the system of injection-locked extended cavity diode lasers that produce the phase-coherent laser fields used in our measurements.
We study phase-conjugate degenerate four-wave mixing (DFWM) in an optically pumped, two-level atomic system (the 3s2S1∕23s\phantom{\rule{0.2em}{0ex}}^{2}S_{1∕2}3s2S1∕2​, F=2F=2F=2, ${m}_{F}=2\ensuremath{\rightarrow}3p\phantom{\rule{0.2em}{0ex}}^{2}P_{3∕2}$, F=3F=3F=3, mF=3{m}_{F}=3mF​=3 transition in a diffuse, collision-free, thermal beam of sodium) using phase-modulated laser beams. In this investigation, we study the detailed line shape of the four-wave mixing signal as a function of the temporal delay between the probe field and the pump fields at different intensities of the cw pump waves and modulation frequencies. We show that phase modulation of the pump and probe beams leads to strong amplitude modulation of the phase-conjugate beam and report excellent agreement between our experimental observations of the DFWM spectra and the results of numerical calculations. Our numerical results suggest an enhancement of the ``local'' DFWM signal when the sidebands of the phase-modulated laser are resonant with dressed-state transitions, but that this resonance is less obvious in the total signal generated. We also show that the complex line shapes depend sensitively upon the delay of the probe beam, with the peak DFWM signal occurring when the probe beam is advanced compared to the pump beam.
The dispersive and absorptive features of a closed transition in atomic cesium are investigated by means of a heterodyne interferometer as a function of the powers of probe and pump laser. Coherent population trapping (CPT) phenomena have raised the interest of the community in recent years. Possible applications of such effects are in the field of slow light propagation and, on the other side, superluminal effects. In particular, special interest has been devoted to the investigation of the refractive index of coherently prepared atoms. The goal of this investigation is the design of new optical media which show either negative or positive dispersion without absorption or with increased anomalous absorption. Such media could be useful ui building white light cavities, opto-optical modulators, and in quantum non-demolition (QND) measurements which are crucial to the development of the future generations gravitational wave detectors. Among these coherency processes we have been studying the phenomenon of electromagnetically induced absorption (EIA) (2) in a closed transition in cesiumatoms. The transition under analysis was the 'CS DZ line at 852 nm, in particular the hyperfine transition 6s zS~/2 F=4 + 6p 2P~/2 F'=5. The system was analyzed by means of a three beam heterodyne interferometer (l). This experimental setup shows high sensitivity to phase measurements and strongly reduced sensitivity to acoustical or vibrational noise. Using a third reference laser which does not interact with the mediumone can perform simultaneous measurements of the phase shift and the absorption of either the probe or the pump laser. The dispersion and the absorption of probe and coupling lasers have been measured as a funcion of the power of the coupling and probe lasers themselves. The power of the lasers are changed in the range of several decades. The halfwidth of the EL4 signal shows an increase with respect to the power of the probe laser while the phase shift of the probe laser decreases. The possibility to extend EIA measurements to a closed four level system in cesium is under analysis and is discussed here. Such possible developments of the experimental setup using a fourth laser or modulating the present reference laser enhance the capability to exploit simultaneous measurements of dispersion and absorption even in the four level system. This work was supported by SFB 407 of the Deutsche Forschungsgemeinschaft (German Research Society).