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Journal of Physics B Atomic and Molecular Physics

An experimental study of the (J,K)=(3,3) inversion spectral line of NH3under the influence of a strong resonant pumping field

J L Steward, Ralph W. Parsons

Published Feb 28, 1983• 4 citations
Publisher

Abstract

A microwave bridge is described which permits radiation from two sources to be propagated through a gas and to be detected separately even when the sources are operating at the same frequency. This bridge is used to study the shape of the (J,K)=(3,3) inversion line in N 14 H 3 when the molecules are subjected to a strong resonant or near-resonant pumping field. The shape of the line is studied by measuring the absorption of a much weaker probe field. For sufficiently strong pump fields, power can be removed from the pump and transferred to the probe field, causing the latter to be amplified. The results are in quantitative agreement with theory. However, the development of a theory which satisfactorily includes the consequences of the degeneracy of the molecular energy levels has not yet been accomplished.

DOI
10.1088/0022-3700/16/4/011

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A microwave bridge is described which permits radiation from two sources to be propagated through a gas and to be detected separately even when the sources are operating at the same frequency. This bridge is used to study the shape of the (J,K)=(3,3) inversion line in N 14 H 3 when the molecules are subjected to a strong resonant or near-resonant pumping field. The shape of the line is studied by measuring the absorption of a much weaker probe field. For sufficiently strong pump fields, power can be removed from the pump and transferred to the probe field, causing the latter to be amplified. The results are in quantitative agreement with theory. However, the development of a theory which satisfactorily includes the consequences of the degeneracy of the molecular energy levels has not yet been accomplished.
The quantum mechanical behavior of the three-level maser was experimentally studied using the rotational spectrum of HCOOH molecule at microwave frequencies. By using the 2 11 ←1 10 line at the frequency of 46581 Mc as the pumping, the induced emission of the 2 11 →2 12 line at the frequency of 4916 Mc was obtained. For a strong pumping, the splitting of emission line due to resonant modulation effect was observed. The line-shape of emission signal under off-resonant pumping was studied in detail. The emission spectrum due to simultaneous emission and absorption of two photons corresponding to the signal and the pumping was observed for the condition of far off-resonant pumping. The results were compared with the theory described in the previous paper, and was found to be in good agreement in many respects. Some discrepancies concerning emission intensity are also discussed. An application of the multiple quantum transition to a four-level system of HC·OOH is described.
A general theory of the saturated-absorption phenomenon in a two-level atomic system is developed, in which the phase relationships between the oscillating atomic dipoles as well as the population differences between energy levels are taken into account. The absorbing gaseous medium considered in this theory is subjected to irradiation by a quasi-running-wave composed of a strong pump field and a weak probe field propagating in opposite directions. Some new interesting results, not predicted by the so-called hole-burning or rate-equation model, are obtained. In particular, the probe-field-transmission peak line shape is found to be markedly different from what is expected according to the rate equations. For finite Doppler widths and a strong saturating pump field, absorption of the probe field can even change sign, and amplification of this field can actually occur. All these features are explained by a close inspection of the evolution of each atomic ensemble of given velocity. Detailed comparison with similar phenomena already observed in rf experiments is presented and permits us to clarify the new predicted effects.
Pump-probe interactions underlie the physics of four-wave and other wave-mixing effects. We present analytic formulas for probe response in a special category of pump-probe experiments. We consider a two-level system excited by two distinct fields, the stronger field with fixed frequency and the weaker with a tunable frequency. We focus attention on the spectral regions near the Rabi sidebands of the strong field and its various subharmonics. We consider times sufficiently short that relaxation effects can be ignored, but sufficiently long to encompass many cycles of population oscillation between the ground and excited states. Because there is no damping, both fields are in this sense strong, and we report here the time average of the response. Our results are obtained by making a suitable second-order rotating wave approximation and are shown to involve the initial phase relation between the two fields as well as the initial angles of orientation of the two-level system's Bloch vector. Depending on these initial phase and orientation angles, the absorption line shape may be either positive or negative and either symmetric or antisymmetric.
We experimentally study the absorption spectroscopy from a collection of gaseous 87Rb^87 Rb87Rb atoms at room temperature irradiated with three fields. Two of these fields are in a pump probe saturation absorption configuration. The third field co-propagates with the pump field. The three fields address Zeeman degenerate transitions between hyperfine levels 5S1/2,F=15S_{1/2}, F = 15S1/2​,F=1 and 5P3/2,F=05P_{3/2}, F = 05P3/2​,F=0 and also between 5S1/2,F=15S_{1/2}, F = 15S1/2​,F=1 and 5P3/2,F=15P_{3/2}, F =15P3/2​,F=1 around the D2 line. We find a sub-natural absorption resonance in the counter-propagating probe field. The novel feature of this absorption is its abrupt onset in the vicinity of 5P3/2,F=05P_{3/2}, F = 05P3/2​,F=0, as the laser frequency is scanned from 5P3/2,F=05P_{3/2}, F = 05P3/2​,F=0 to 5P3/2,F=15P_{3/2}, F =15P3/2​,F=1. The experimental results are compared with the theory modeled after a four level system. There is a qualitative agreement between our theory and experiment. We find the threshold absorption to be a result of the off-resonant interaction of the strong field with nearby hyperfine levels.
The paper reports on experimental investigations of absorption and dispersion profiles of a strongly driven hyperfine transition at various pump field intensities and detunings when probed by a weak field. The transition lies at 5.4 MHz and corresponds to the Iz{\mathit{I}}_{\mathit{z}}Iz​=0\ensuremath{\leftrightarrows}-1 nuclear magnetic transition within the electron spin singlet of the 3^{3}3A ground state of the nitrogen-vacancy (NV) center in diamond. The inhomogeneous linewidth of the transition is 8 kHz whereas the homogeneous linewidth is 2.7 kHz, which is a factor of 3 larger than that limited by the population relaxations. The absorption and dispersion are obtained using Raman heterodyne detection, a coherent optically detected magnetic-resonance technique. Measurements are performed in a situation where there is an anticrossing of the ground-state electron-spin levels, as this leads to an enhancement of the hyperfine transition strengths and the optical sensitivity. Weak probe fields with Rabi frequency 0.6 kHz could then be used. The absorption and dispersion profiles were recorded for on-resonance pump fields of various strengths with Rabi frequencies of 0, 2.1, 3.7, 6.6, 11.8, and 21 kHz. In addition, the responses were recorded for an off-resonance field with a Rabi frequency of 55 kHz and detunings between -40 and +40 kHz. The corresponding response of an idealized driven two-level system has been calculated using an established density-matrix equation of motion formalism.When normalized to the profiles with no driving field, the calculated and experimental profiles are in excellent agreement. The nitrogen-vacancy system provides a very clear experimental illustration of a driven two-level system and some aspects are highlighted. For on-resonance pumping, the dispersion profile consists of a positive and a negative absorptionlike peak separated by twice the pump Rabi frequency. The peaks correspond to a significant signal strength (index of refraction) whereas at the frequency of the peaks in dispersion, the absorption is zero. The corresponding absorption profile consists of two dispersionlike features separated by twice the pump Rabi frequency, and between the two features there is negative absorption or gain. For off-resonance pumping, there are again two features. For example, in absorption response, there is an absorption peak and an amplification peak symmetrically displaced from the pump frequency by the generalized Rabi frequency. In this off-resonance pumping situation, it is pointed out that gain occurs where there is inversion in the dressed state whereas gain for the on-resonance pumping situation is achieved without population inversion in either the bare or dressed state.
The rate of absorption of energy from a weak signal field by an atom driven by a strong pump field is evaluated. The pump field and the signal field are assumed to induce transitions between the same pair of states, and their frequencies are both assumed to lie near the atomic resonance frequency for the transition in question. We find that the signal-field absorption line-shape function takes on negative values, representing stimulated emission rather than absorption, even though population inversion does not occur. This amplification of the signal field, which is most pronounced at high pump intensities, is shown to occur primarily at the expense of the pump field, which suffers an increased rate of attenuation. The results are discussed in the context of a theorem which expresses the absorption line-shape function for general atomic systems in terms of a suitable atomic correlation function.