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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Understanding laser stabilization using spectral hole burning

Brian Julsgaard, Lars Rippe, Andreas Walther, Stefan Kröll

Published Jun 1, 2007• 3 citations
Publisher

Abstract

The theoretical understanding of such laser stabilization exists for the case of cavities, while it is not very well developed for the case using spectral holes. Our contribution is to provide such a theory in the case of using spectral holes. The main difficulty is the requirement to calculate the coherent response of the atomic reference material to the incoming laser radiation. These calculations are inherently non-linear, but we develop a linearized, analytical theory, which is valid in the frequency stabilized condition.

DOI
10.1109/cleoe-iqec.2007.4386334

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Understanding laser stabilization using spectral hole burning

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The theoretical understanding of such laser stabilization exists for the case of cavities, while it is not very well developed for the case using spectral holes. Our contribution is to provide such a theory in the case of using spectral holes. The main difficulty is the requirement to calculate the coherent response of the atomic reference material to the incoming laser radiation. These calculations are inherently non-linear, but we develop a linearized, analytical theory, which is valid in the frequency stabilized condition.
There have recently been several studies of the performance of laser frequency stabilization using spectral holes in solids, instead of an external cavity, as a frequency reference. Here an analytical theory for Pound-Drever-Hall laser frequency stabilization using spectral hole-burning is developed. The interaction between the atomic medium and the phase modulated light is described using a linearized model of the Maxwell-Bloch equations. The interplay between the carrier and modulation sidebands reveals significant differences from the case of locking to a cavity. These include a different optimum modulation index, an optimum sample absorption, and the possibility to lock the laser in an inherent linear frequency drift mode. Spectral holes in solids can be permanent or transient. For the materials normally used, the dynamics and time scales of transient holes often depend on population relaxation processes between ground state hyperfine levels. These relaxation rates can be very different for different solid state materials. We demonstrate, using radio-frequency pumping, that the hyperfine population dynamics may be controlled and tailored to give optimum frequency stabilization performance. In this way also materials with initially non-optimum performance can be used for stabilization. The theoretical predictions regarding the inherent linear frequency drift is compared to experimental data from a dye laser stabilized to a spectral hole in a Pr(3+)3+:Y(2)SiO(5) crystal.
Summary form only given. The first known demonstration of laser frequency stabilization using a solid-state persistent spectral hole burning material as the frequency reference is reported. Unlike gas phase transitions or Fabry-Perot resonances, spectral holes for frequency references can be prepared at any frequency within a broad inhomogeneous absorption profile (15 GHz in the material demonstrated here). Several lasers may be stabilized to multiple spectral holes, either in the same or separate absorption bands, with arbitrary frequency separations.
We have frequency stabilized a Coherent CR699-21 dye laser to a transient spectral hole on the 606 nm transition in Pr^{+3}:Y_2SiO_5. A frequency stability of 1 kHz has been obtained on the 10 microsecond timescale together with a long-term frequency drift below 1 kHz/s. RF magnetic fields are used to repopulate the hyperfine levels allowing us to control the dynamics of the spectral hole. A detailed theory of the atomic response to laser frequency errors has been developed which allows us to design and optimize the laser stabilization feedback loop, and specifically we give a stability criterion that must be fulfilled in order to obtain very low drift rates. The laser stability is sufficient for performing quantum gate experiments in Pr^{+3}:Y_2SiO_5.
Techniques in frequency stabilization of lasers to fixed-spacer optical cavities have advanced to the point where the ultimate frequency stabilities are limited by thermal noise for standard cavity configurations at room temperature. In early experiments, laser stabilization via spectral-hole burning (SHB) has been shown to be a promising alternative. In this Letter, we explore the thermal-noise limits to frequency stability in spectral holes and compile known material parameters for a typical system used in SHB experiments (Eu3+ doped Y2SiO5) to make numerical estimates for the fundamental thermal-noise induced frequency instability in spectral holes for the liquid-helium temperature and dilution temperature cases. These efforts can guide the design of future SHB experiments and clarify which important material parameters remain to be measured.
We describe a spectroscopic method applicable to inhomogeneously broadened transitions. As a test system we use suitable rare-earth-doped solids in which persistent spectral holes can be burned on weakly allowed electronic transitions. These systems are of interest as frequency references for the stabilization of laser frequencies. In all experiments so far, spectral holes are burned and read out individually. Here we present a demonstration of simultaneous burning and readout of sets of spectral holes, containing up to 1024 individual spectral holes, by a comb of laser frequencies. The simultaneous readout of such a set leads to an effective compound signal that has a higher signal-to-noise ratio. Here, an improvement by a factor of 20 was obtained for a set of 512 spectral holes. We use the method to stabilize the frequency of a laser and characterize its stability.
We demonstrate laser frequency stabilization using a continuously regenerated transient spectral hole in an inhomogeneously broadened resonance of a solid. Regenerative transient holes provide extreme stabilization for time scales appropriate for spectroscopy, signal processing, ranging, and interferometry. Stabilization to 20 Hz on a 10-ms time scale using spectral holes at 793 nm in Tm3+:Y3Al5O12{\mathrm{Tm}}^{3+}{:\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}Tm3+:Y3​Al5​O12​ gives substantial improvement in the reliability of stimulated photon echoes in the same material and enables the observation of a third population storage mechanism for hole burning in Tm3+:Y3Al5O12.{\mathrm{Tm}}^{3+}{:\mathrm{Y}}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}.Tm3+:Y3​Al5​O12​.