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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Analysis of Dicke Narrowing in Wall Coated and Buffer Gas Filled Cells with Application to Gas Cell Atomic Clocks

R. P. Frueholz, C. H. Volk

Published Jan 1, 1984• 0 citations
Publisher

Abstract

Spectral lineshape narrowing of atomic vapor emission in a bufferless, wall-coated absorption cell has been analyzed using the same formalism developed t3 describe sub-Doppler linewidths. Dicke-narrowing, in a buffered cell. Dramatic linewidth reductions in the bufferless cell, compared to the buffered cell, occur because of the high probability that Doppler shifts before and after a particular wall collision will cancel each other. The formalism described allows more physical insight than the classic onedimensional box model previously invoked to explain spectral narrowing in bufferless, wall coated cells. Additionally, this formalism reveals a correlation between post-collision velocities and intercollision times in the buffered cell resulting in modifications of the standard Dicke analysia of these cells. Finally, the computational power of the technique is demonstrated. The effects of varying cell size on Rb and CS hyperfine lineshapes and the results of the presence of an inhomogeneous magnetic field within the cell are analyzed.

DOI
10.1109/freq.1984.200784

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It is well known that when a radiator (or absorber) suffers velocity-changing collisions that do not perturb its internal state, the oscillator's successive Doppler shifts are motionally averaged. This process (Dicke narrowing) gives rise to a homogeneously broadened sub-Doppler resonance, which is often astride a broad, apparently Doppler-width, pedestal. Though it has long been held that this pedestal is an inhomogeneous remnant of Doppler broadening, no evidence has ever been obtained to substantiate this expectation. In the present study we investigate the behavior of Dicke-narrowed line shapes in strong fields in an evacuated wall-coated cell. Our experimental results indicate that the hypothesis of an inhomogeneous Doppler remnant pedestal is invalid. Rather, the pedestal is homogeneously broadened and is best understood in terms of the oscillator's response to the electromagnetic field's power spectral density as observed in its rest frame. This conclusion suggests an intimate relationship between the process of Dicke narrowing and the behavior of quantum systems in the presence of stochastic fields. By envisioning the quantum system as a narrow-band antenna that only absorbs a small portion of the field's energy, we develop a simple intuitive model to account for the interaction of the atom with the nonmonochromatic field; the appeal of this simple theory is that it removes the need for extensive computation. Agreement between this ``atom-as-antenna'' analogy and experiment is very good.

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The Dicke-narrowed line shape of an atom in a wall-coated, bufferless atomic storage cell is composed of two parts, a sharp central spike and a broad underlying pedestal. To understand the pedestal shape we find that it is necessary to account for various atom-surface scattering channels. Conversely, analysis of the pedestal shape yields information concerning these scattering channels. In particular, nearly-Doppler-broadened pedestals, observed for alkali-metal hyperfine transitions in cells with paraffin coatings, indicate that both a trapping-desorption channel and a direct inelastic or quasielastic channel are accessible in the atom-surface scattering process. Alternatively, the appearance of much narrower pedestals, observed in cells with dichlordimethysilane coatings, indicates that the trapping-desorption channel dominates the atom-surface scattering process.

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Spectral lineshape narrowing of atomic vapor emission in a bufferless, wall-coated absorption cell has been analyzed using the same formalism developed t3 describe sub-Doppler linewidths. Dicke-narrowing, in a buffered cell. Dramatic linewidth reductions in the bufferless cell, compared to the buffered cell, occur because of the high probability that Doppler shifts before and after a particular wall collision will cancel each other. The formalism described allows more physical insight than the classic onedimensional box model previously invoked to explain spectral narrowing in bufferless, wall coated cells. Additionally, this formalism reveals a correlation between post-collision velocities and intercollision times in the buffered cell resulting in modifications of the standard Dicke analysia of these cells. Finally, the computational power of the technique is demonstrated. The effects of varying cell size on Rb and CS hyperfine lineshapes and the results of the presence of an inhomogeneous magnetic field within the cell are analyzed.
Spectral lineshape narrowing of atomic vapour emission in a bufferless, wall-coated absorption cell has been analysed using the same formalism developed to describe sub-Doppler linewidths, Dicke narrowing, in a buffered cell. Within this formalism lineshapes are generated using Monte Carlo techniques. Dramatic linewidth reductions in the bufferless cell, compared with the buffered cell, occur because of the high probability that Doppler shifts before and after a particular wall collision will cancel each other. The formalism described allows more physical insight than the classic one-dimensional box model previously invoked to explain spectra narrowing in bufferless, wall-coated cells. Additionally, this formalism reveals a correlation between post-collision velocities and intercollision times in the buffered cell resulting in modifications of the standard Dicke analysis of these cells.
Examination of 87Rb δF = 1, δ‖mF‖ = 1 hyperfine resonances in a 200-cm3 evacuated tetracontane wall-coated Pyrex cell which has been sealed since 1968 shows remarkable Dicke-narrowed sub-Doppler Lorentzian line shapes with less than 11 Hz full width. This linewidth is 70 times narrower than that in buffer gas filled cells used in commercial Rb atomic frequency standards. The phase shift per wall collision is 0.058 radians/collision as derived from an observed wall-induced hyperfine frequency shift of −52 Hz at a wall temperature of 26 °C.
Microwave double resonances were measured in a wall-coated Rb vapor cell as a function of additional buffer-gas pressure. These data were compared with similar measurements in an uncoated cell. It was found that the linewidth in the coated spherical cell of diameter 1.6 cm displays a distinct maximum around 0.2 kPa. This agrees well with theoretical solutions of the diffusion equation, assuming a complex reflection coefficient at the wall. It was also found that at intermediate pressures the lineshapes of the microwave resonances become asymmetric with a low-frequency tail. This agrees with the explanation that where the alkali mean free path is substantially smaller than the average distance between wall collisions at zero pressure, there exist two classes of atoms in the cell. The atoms that get trapped near the walls accumulate much larger phase shifts than those toward the center of the cell. This effect is not seen in the longitudinal relaxation rate, indicating that it is related to a phase-shift effect.
When a radiator (or absorber) suffers velocity-changing collisions that do not perturb its internal state, the oscillator's successive Doppler shifts are motionally averaged. This process (Dicke narrowing) gives rise to a homogeneously broadened sub-Doppler resonance, which is often astride a broad, apparently Doppler width, pedestal. It has long been held that this pedestal is an inhomogeneous remnant of Doppler broadening, but no evidence has ever been obtained to substantiate this expectation. In the present study we investigate the behavior of Dicke-narrowed lineshapes in strong fields in an evacuated wall- coated cell. Our experimental results indicate that the hypothesis of an inhomogeneous Doppler remnant pedestal is invalid. Rather, the pedestal is homogeneously broadened, and is best understood in terms of the oscillator's response to the electromagnetic field's power spectral density as observed in its rest frame. This conclusion suggests an intimate relationship between the process of Dicke narrowing and the behavior of quantum systems in the presence of stochastic fields. By envisioning the quantum system as a narrow-band antenna that only absorbs a small portion of the field's energy, we develop a simple intuitive model to account for the interaction of the atom with the nonmonochromatic field; the appeal of this simple theory is that it removes the need for extensive computation. Agreement between this atom-as-antenna analogy and experiment is very good.
It is well known that when a radiator (or absorber) suffers velocity-changing collisions that do not perturb its internal state, the oscillator's successive Doppler shifts are motionally averaged. This process (Dicke narrowing) gives rise to a homogeneously broadened sub-Doppler resonance, which is often astride a broad, apparently Doppler-width, pedestal. Though it has long been held that this pedestal is an inhomogeneous remnant of Doppler broadening, no evidence has ever been obtained to substantiate this expectation. In the present study we investigate the behavior of Dicke-narrowed line shapes in strong fields in an evacuated wall-coated cell. Our experimental results indicate that the hypothesis of an inhomogeneous Doppler remnant pedestal is invalid. Rather, the pedestal is homogeneously broadened and is best understood in terms of the oscillator's response to the electromagnetic field's power spectral density as observed in its rest frame. This conclusion suggests an intimate relationship between the process of Dicke narrowing and the behavior of quantum systems in the presence of stochastic fields. By envisioning the quantum system as a narrow-band antenna that only absorbs a small portion of the field's energy, we develop a simple intuitive model to account for the interaction of the atom with the nonmonochromatic field; the appeal of this simple theory is that it removes the need for extensive computation. Agreement between this ``atom-as-antenna'' analogy and experiment is very good.
The Dicke-narrowed line shape of an atom in a wall-coated, bufferless atomic storage cell is composed of two parts, a sharp central spike and a broad underlying pedestal. To understand the pedestal shape we find that it is necessary to account for various atom-surface scattering channels. Conversely, analysis of the pedestal shape yields information concerning these scattering channels. In particular, nearly-Doppler-broadened pedestals, observed for alkali-metal hyperfine transitions in cells with paraffin coatings, indicate that both a trapping-desorption channel and a direct inelastic or quasielastic channel are accessible in the atom-surface scattering process. Alternatively, the appearance of much narrower pedestals, observed in cells with dichlordimethysilane coatings, indicates that the trapping-desorption channel dominates the atom-surface scattering process.