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arXiv:1309.3097 · Journal of the Optical Society of America B

Noise reduction and hyperfine level coherence in spontaneous noise spectroscopy of atomic vapor

Takahisa Mitsui, Kenichiro Aoki

Published Jan 2, 2014• 7 citations
arXivHTMLPDF

Abstract

We developed a system for measurements of power spectra of transmitted light intensity fluctuations, in which the extraneous noise, including shot noise, is reduced. In essence, we just apply light, measure the power of the transmitted light, and derive its power spectrum. We use this to observe the spontaneous noise spectra of photon atom interactions. Applying light with frequency modulation, we can also observe the spontaneous noise reflecting the coherence between the hyperfine levels in the excited state. There are two main novel components in the measurement system, the noise reduction scheme and the stabilization of the laser system. The noise reduction mechanism can be used to reduce the shot noise contribution to arbitrarily low levels through averaging, in principle. This is combined with differential detection to keep unwanted noise at low levels. The laser system is stabilized to obtain spectral width below 1 kHz without high frequency (≳10 MHz) noise. These methods are described systematically and the performance of the measurement system is examined through experimental results.

DOI
10.1364/josab.31.000195

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We developed a system for measurements of power spectra of transmitted light intensity fluctuations, in which the extraneous noise, including shot noise, is reduced. In essence, we just apply light, measure the power of the transmitted light, and derive its power spectrum. We use this to observe the spontaneous noise spectra of photon atom interactions. Applying light with frequency modulation, we can also observe the spontaneous noise reflecting the coherence between the hyperfine levels in the excited state. There are two main novel components in the measurement system, the noise reduction scheme and the stabilization of the laser system. The noise reduction mechanism can be used to reduce the shot noise contribution to arbitrarily low levels through averaging, in principle. This is combined with differential detection to keep unwanted noise at low levels. The laser system is stabilized to obtain spectral width below 1 kHz without high frequency (≳10 MHz) noise. These methods are described systematically and the performance of the measurement system is examined through experimental results.
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We have experimentally demonstrated a new type of noise spectroscopy, which requires neither amplitude nor frequency noise of the light source. A highly stabilized diode laser provides low-noise light for the optical magnetic resonance of Rb atoms. The laser light transmitted through the Rb vapor contains significant intensity fluctuations whose power spectrum has a distinct peak at the Larmor frequency. The fluctuations are spontaneously generated by the atoms and are attributed to the stochastic properties of the photon scattering which randomly interrupts the Larmor precession of the atomic magnetic moment.
The frequency noise of an ordinary diode laser, often a nuisance in spectroscopy, can be used to measure atomic coherence. When atoms are prepared in a coherent superposition of two ground states, each random shift in laser frequency changes how much light they absorb, so the transmitted light carries a record of that coherence. Correlating the intensity fluctuations of two fields, each linking one ground state to a shared excited state, reads this record out, a technique known as noise correlation spectroscopy. The correlation signal is narrower than the transparency window the same fields create and switches sign as their frequency difference is tuned. Its width is set by the rate at which the atoms lose coherence and, over a wide range, does not grow with laser power. Over two decades the method has spread from warm vapors to cold atoms, to multi-field schemes, and to diamond and rare-earth-doped crystals. This review, to the author's knowledge the first, brings together its theory, experiments and applications, and examines its limits, the challenges that remain, and the opportunities that could make it a standard spectroscopic tool.
Using resonant light absorption, random-walk motions of rubidium atoms in nitrogen buffer gas are observed directly. The transmitted light intensity through atomic vapor is measured, and its spectrum is obtained, down to orders of magnitude below the shot-noise level to detect fluctuations caused by atomic motions. To understand the measured spectra, the spectrum for atoms performing random walks in a Gaussian light beam is computed, and its analytical form is obtained. The spectrum has 1/f21/{f}^{2}1/f2 (fff is frequency) behavior at higher frequencies, crossing over to a different, but well-defined, behavior at lower frequencies. The properties of this theoretical spectrum agree excellently with the measured spectrum. This understanding also enables us to obtain the diffusion constant, the photon cross section of atoms in buffer gas, and the atomic number density from a single spectral measurement. We further discuss other possible applications of our experimental method and analysis.
We consider the problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field. We consider two models based on an atomic medium, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed. When the atomic lifetimes are comparable, spontaneous emission reduces the amount of noise reduction. For example, for equal atomic lifetimes regular pump excitation will result in a maximum noise reduction in the output field of one-half the shot-noise limit.
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 D1{D}_{1}D1​ transition at 794.7 nm, after it has passed through a Rb87/N2{\mathrm{Rb}}^{87}/{\mathrm{N}}_{2}Rb87/N2​ 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.