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Optics Express

Understanding laser stabilization using spectral hole burning

Brian Julsgaard, Andreas Walther, Stefan Kröll, Lars Rippe

Published Jan 1, 2007• 49 citations
Publisher

Abstract

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.

DOI
10.1364/oe.15.011444

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Understanding laser stabilization using spectral hole burning

Brian Julsgaard, Lars Rippe, Andreas Walther +1 more

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.

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Laser stabilization using spectral hole burning

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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.

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LASER FREQUENCY STABILIZATION TO SPECTRAL HOLE BURNING FREQUENCY REFERENCES IN ERBIUM-DOPED CRYSTALS: MATERIAL AND DEVICE OPTIMIZATION

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Narrow spectral holes in the absorption lines of Er doped crystals have been explored as references for frequency stabilizing external cavity diode lasers at the important 1.5 μm optical communication wavelength. Allan deviations of the beat signal between two independent stabilized lasers as low as 200 Hz over 10 ms integration time have been achieved using regenerative spectral holes in Er:Y2SiO5 and Er:KTP, while drift was reduced to ~ 7 kHz/min by incorporating the inhomogeneous absorption line as a fixed reference. During active stabilization, the transient spectral hole was continuously regenerated as hole burning balanced relaxation. In contrast, persistent spectral holes in Er:D:CaF2, with lifetimes of several weeks, provided programmable and transportable secondary frequency references that maintained sub-kilohertz stability over several seconds and enabled 6 kHz stability over 3 1.6 10 s × . The error signal was derived from the spectral hole transmission using frequency modulation spectroscopy. A servo amplifier applied fast frequency corrections to the injection current of the laser diode and slower adjustments to the piezo-driven feedback prism plate. These stabilized lasers provide ideal sources for spectral hole burning applications based on optical coherent transients, where laser stability is required over the storage time of the material. Since the lifetime of the frequency reference is exactly the material storage time, this requirement is automatically met by using our technique. This was demonstrated in Er:Y2SiO5 and successfully transferred to high-bandwidth signal processing applications. The material Er:Y2SiO5 was optimized for these applications. The I15/2 and I13/2 crystal field levels were site-selectively determined by absorption and fluorescence spectroscopy. The excited state lifetime was measured to be 11.4 ms for site 1 and 9.2 ms for site 2. Zeeman experiments and two-pulse photon echo spectroscopy as a function of magnetic field orientation were used to determine the anisotropic electronic g-values for both Er sites and established a preferred magnetic field orientation for minimizing homogeneous line broadening by spectral diffusion. The spectral diffusion was characterized by stimulated photon echo spectroscopy and successfully described with established theories. In a 0.02 atomic percent Er:Y2SiO5 crystal at B = 0.8 T and T = 1.6 K, line broadening became significant after 10 μs, increasing the homogeneous linewidth from 7.5 kHz to 75 kHz after 120 μs. Spectral diffusion, primarily caused by direct phonon driven Er spin-flips in the ground state, can be controlled to negligible levels with proper magnetic field strength and orientation, temperature, and erbium concentration. In optimizing Er:Y2SiO5, the narrowest optical resonance in any solid-state material of 73 Hz was measured.

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Programmable frequency reference for subkilohertz laser stabilization by use of persistent spectral hole burning

Peter B. Sellin, Nick Strickland, John L. Carlsten +1 more

We report what is believed to be the first demonstration of laser frequency stabilization directly to persistent spectral holes in a solid-state material. The frequency reference material was deuterated CaF(2): Tm(3+) prepared with 25-MHz-wide persistent spectral holes on the H(6)(3)?H(4)(3) transition at 798 nm. The beat frequency between two lasers that were independently locked to persistent spectral holes in separate crystal samples showed typical root Allan variances of 780+/-120Hz for 20-50-ms integration times.

Optics Letters•Aug 1, 1999•52 citations
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.
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.
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.
Narrow spectral holes in the absorption lines of Er doped crystals have been explored as references for frequency stabilizing external cavity diode lasers at the important 1.5 μm optical communication wavelength. Allan deviations of the beat signal between two independent stabilized lasers as low as 200 Hz over 10 ms integration time have been achieved using regenerative spectral holes in Er:Y2SiO5 and Er:KTP, while drift was reduced to ~ 7 kHz/min by incorporating the inhomogeneous absorption line as a fixed reference. During active stabilization, the transient spectral hole was continuously regenerated as hole burning balanced relaxation. In contrast, persistent spectral holes in Er:D:CaF2, with lifetimes of several weeks, provided programmable and transportable secondary frequency references that maintained sub-kilohertz stability over several seconds and enabled 6 kHz stability over 3 1.6 10 s × . The error signal was derived from the spectral hole transmission using frequency modulation spectroscopy. A servo amplifier applied fast frequency corrections to the injection current of the laser diode and slower adjustments to the piezo-driven feedback prism plate. These stabilized lasers provide ideal sources for spectral hole burning applications based on optical coherent transients, where laser stability is required over the storage time of the material. Since the lifetime of the frequency reference is exactly the material storage time, this requirement is automatically met by using our technique. This was demonstrated in Er:Y2SiO5 and successfully transferred to high-bandwidth signal processing applications. The material Er:Y2SiO5 was optimized for these applications. The I15/2 and I13/2 crystal field levels were site-selectively determined by absorption and fluorescence spectroscopy. The excited state lifetime was measured to be 11.4 ms for site 1 and 9.2 ms for site 2. Zeeman experiments and two-pulse photon echo spectroscopy as a function of magnetic field orientation were used to determine the anisotropic electronic g-values for both Er sites and established a preferred magnetic field orientation for minimizing homogeneous line broadening by spectral diffusion. The spectral diffusion was characterized by stimulated photon echo spectroscopy and successfully described with established theories. In a 0.02 atomic percent Er:Y2SiO5 crystal at B = 0.8 T and T = 1.6 K, line broadening became significant after 10 μs, increasing the homogeneous linewidth from 7.5 kHz to 75 kHz after 120 μs. Spectral diffusion, primarily caused by direct phonon driven Er spin-flips in the ground state, can be controlled to negligible levels with proper magnetic field strength and orientation, temperature, and erbium concentration. In optimizing Er:Y2SiO5, the narrowest optical resonance in any solid-state material of 73 Hz was measured.
We present and analyze a method of laser-frequency stabilization via steady-state patterns of spectral holes in Eu(3+)∶Y(2)SiO(5). Three regions of spectral holes are created, spaced in frequency by the ground-state hyperfine splittings of (151)Eu(3+). The absorption pattern is shown not to degrade after days of laser-frequency stabilization. An optical frequency comparison of a laser locked to such a steady-state spectral-hole pattern with an independent cavity-stabilized laser and a Yb optical lattice clock demonstrates a spectral-hole fractional frequency instability of 1.0×10(-15)τ(-1/2) that averages to 8.5(-1.8)(+4.8)×10(-17) at τ=73 s. Residual amplitude modulation at the frequency of the rf drive applied to the fiber-coupled electro-optic modulator is reduced to less than 1×10(-6) fractional amplitude modulation at τ>1 s by an active servo. The contribution of residual amplitude modulation to the laser-frequency instability is further reduced by digital division of the transmission and incident photodetector signals to less than 1×10(-16) at τ>1 s.
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​.
We report what is believed to be the first demonstration of laser frequency stabilization directly to persistent spectral holes in a solid-state material. The frequency reference material was deuterated CaF(2): Tm(3+) prepared with 25-MHz-wide persistent spectral holes on the H(6)(3)?H(4)(3) transition at 798 nm. The beat frequency between two lasers that were independently locked to persistent spectral holes in separate crystal samples showed typical root Allan variances of 780+/-120Hz for 20-50-ms integration times.