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Physical Review A

Phase noise to amplitude noise conversion between statistically independent optical fields

Arielle Little, Michael C. Y. Huang, James C. Camparo

Published Mar 17, 2023• 5 citations

Abstract

Pump-probe experiments are ubiquitous in atomic, molecular, and optical physics, where a strong pump field induces some change in a quantum system that is probed by a much weaker field. Often, high intensity of the pump field is at a premium with all other characteristics of the strong field subordinate. As a particular example, of relevance to atomic clocks and atomic magnetometers, a strong broad-linewidth laser optically pumps an atomic vapor, which is then probed by a much weaker narrow-linewidth laser. Though the broad-linewidth field suffers laser phase noise (PM) to amplitude noise (AM) conversion, the narrow-linewidth probe by itself produces a much quieter signal. Here, we consider the question of whether the noisy pump field maps its (PM-to-AM) absorption cross-section fluctuations onto the quiet probe field's transmission. Our results show that PM-to-AM noise does not transfer directly: atoms interacting with the pump field are instantaneously distinct from those interacting with the probe field. However, the broad-linewidth laser can influence the quiet field's transmission through the vapor due to optical pumping, resulting in fluctuations in the number density of atoms in the absorbing states. Nevertheless, there is a saving grace for this ``PM-to-AM induced optical pumping'' noise transfer: for very high noisy-field intensities (where optical pumping saturates) this type of noise on the probe field becomes negligible.

DOI: 10.1103/physreva.107.033109

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Pump-probe experiments are ubiquitous in atomic, molecular, and optical physics, where a strong pump field induces some change in a quantum system that is probed by a much weaker field. Often, high intensity of the pump field is at a premium with all other characteristics of the strong field subordinate. As a particular example, of relevance to atomic clocks and atomic magnetometers, a strong broad-linewidth laser optically pumps an atomic vapor, which is then probed by a much weaker narrow-linewidth laser. Though the broad-linewidth field suffers laser phase noise (PM) to amplitude noise (AM) conversion, the narrow-linewidth probe by itself produces a much quieter signal. Here, we consider the question of whether the noisy pump field maps its (PM-to-AM) absorption cross-section fluctuations onto the quiet probe field's transmission. Our results show that PM-to-AM noise does not transfer directly: atoms interacting with the pump field are instantaneously distinct from those interacting with the probe field. However, the broad-linewidth laser can influence the quiet field's transmission through the vapor due to optical pumping, resulting in fluctuations in the number density of atoms in the absorbing states. Nevertheless, there is a saving grace for this ``PM-to-AM induced optical pumping'' noise transfer: for very high noisy-field intensities (where optical pumping saturates) this type of noise on the probe field becomes negligible.

When laser light propagates through a resonant medium, the transmitted beam can exhibit excess intensity noise [amplitude modulation (AM)]. In a semiclassical description of the phenomenon, laser phase noise (PM) induces fluctuations in the medium's electric susceptibility, which in turn cause fluctuations in the transmitted intensity. The process provides an efficient means for PM-to-AM conversion, and intuition suggests that large linewidth lasers should exhibit much greater PM-to-AM conversion than narrow linewidth lasers. Here we measure the relative intensity noise (RIN) for two diode lasers whose linewidths $\ensuremath{\Delta}{\ensuremath{\nu}}_{L}$ differ by more than

{10}^{2},

after the lasers have propagated through a resonant rubidium vapor. Though the RIN of the narrow linewidth laser is only reduced by a factor of about 6 compared to the broad linewidth laser, our results are nonetheless consistent with numerical simulations of the PM-to-AM conversion process. In particular, both computation and analytical theory indicate that RIN is a nonlinear function of $\ensuremath{\Delta}{\ensuremath{\nu}}_{L}.$ For single-mode laser linewidths less than the atomic dephasing rate, RIN increases like $\sqrt{\ensuremath{\Delta}{\ensuremath{\nu}}_{L}},$ while for linewidths greater than the atomic dephasing rate RIN is a decreasing function of $\ensuremath{\Delta}{\ensuremath{\nu}}_{L}.$

As laser light propagates through a resonant vapor, laser phase noise (PM) is converted to laser intensity noise (AM) because of the sensitivity of atomic coherence to laser phase fluctuations. In experiments reported here it is shown that this PM-to-AM conversion process is highly efficient and can cause the relative intensity noise of transmitted diode laser light to be 1 to 2 orders of magnitude larger than the laser’s intrinsic relative intensity noise. By use of a semiclassical description of the phenomenon, including the effect of optical pumping, reasonably good agreement between theory and experiment is obtained. The PM-to-AM conversion process discussed here has important consequences for atomic clock development, in which diode-laser optical pumping in thick alkali vapors holds the promise for orders-of-magnitude improvement in atomic clock performance.

In the weak-field limit, resonant absorption is viewed as a passive process: an optical field impinges on an atom, and within some cross-sectional area the atom has a high probability for absorbing the radiant energy. Absorption, however, is a dynamic process. Consequently, though a singlemode laser is highly monochromatic, the field's phase noise (i.e., quantum noise) generates fluctuations in the atom's absorption cross section. Laser phase noise (PM) thereby gives rise to absorption cross-section noise, and hence fluctuations in the medium's transmitted light intensity (AM). Following a brief overview of the PM-to-AM conversion process, we consider the role of collisions on PM-to-AM conversion efficiency in the weak-field regime. Specifically, the relative-intensity-noise of a diode laser, tuned to the Rb D1 transition, was measured after it passed through a rubidium/nitrogen vapor. Varying the nitrogen pressure, we found that rapid collisional dephasing decreased the efficiency of PM-to-AM conversion. Examining the rubidium hyperfine transition lineshape as a function of nitrogen pressure, we then found that pressure-broadening increased the transition's signal-to-noise ratio when limited by the PM-to-AM conversion process.

The optically thick vapors employed in gas-cell atomic clocks provide for very efficient conversion of laser phase noise (PM) to amplitude noise (AM). Here, we discuss the role of PM to AM conversion in determining gas-cell clock performance. First, a brief overview of the PM to AM conversion process will be given, highlighting the fact that laser phase noise creates fluctuations in the atom's optical absorption cross-section which have an exponential influence on the laser's transmitted intensity. Experimental results will then be presented showing that the PM to AM conversion process can increase the relative intensity noise of transmitted laser light by orders of magnitude, and that this can, under certain conditions, cause laser-pumped clock performance to be poorer than lamp-pumped clock performance.

When a vapor absorbs laser light, the field's intrinsic phase fluctuations (PM) induce variations in the atoms' absorption cross section, which in turn yield fluctuations in the transmitted light intensity. In the Born approximation, the observed amplitude noise (AM) arises from a single scattering of the input field. Here, we show that the Born approximation breaks down for optically thick vapors and that the observed AM is influenced by scatterings of the ``medium-perturbed'' field. With importance for spectroscopy, we find that the multiple field-atom scatterings reduce the PM-to-AM conversion efficiency.

When resonant laser light passes through a vapor, the laser's intrinsic phase fluctuations induce random variations in the atomic coherence, which in turn give rise to fluctuations in the medium's absorption cross section. Hence, laser phase modulation noise (PM) is converted to transmitted laser intensity (i.e., amplitude) modulation noise (AM). Here, we consider the influence of collisional dephasing on the PM-to-AM conversion process. Specifically, we measure the relative intensity noise of a diode laser beam, resonant with the Rb

{D}_{1}

transition at 794.7 nm, after it has passed through a

{\mathrm{Rb}}^{87}/{\mathrm{N}}_{2}

vapor as a function of nitrogen number density. Our results demonstrate that when collisional dephasing is very rapid, the spectral density of cross-section fluctuations is reduced, so that there is a significant decrease in the efficiency of PM-to-AM conversion at low Fourier frequencies. These results imply that, in general, when laser PM-to-AM conversion is the dominant noise process, pressure broadening can actually increase spectroscopic sensitivity.