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arXiv:quant-ph/0611056

Laser stabilization using spectral hole burning

Lars Rippe, Brian Julsgaard, Andreas Walther, Stefan Kröll

Published Nov 5, 2006• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.quant-ph/0611056

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Summary form only given. Laser frequency stabilization to 200 Hz on a 5 ms time scale and to 1 kHz over 30 minutes has been demonstrated using persistent and transient spectral holes in inhomogeneously broadened resonances of Er/sup 3+/,D/sup -/:CaF/sub 2/, Er/sup 3+/:Y/sub 2/SiO/sub 5/, and Er/sup 3+/:KTiOPO/sub 4/ at cryogenic temperatures. Persistent spectral holes with lifetimes of weeks or longer provide a programmable and transportable secondary frequency reference, and kilohertz wide transient spectral holes provide excellent references at millisecond time scales appropriate for spectroscopy and coherent transient signal processing devices. This locking technique has significant applications to devices beyond the field of spectral hole burning.

Quantum Electronics and Laser Science Conference•Nov 13, 2002•0 citations
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.
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.
Laser frequency stabilization giving a 500-Hz Allan deviation for a 2-ms integration time with drift reduced to 7 kHz/min over several minutes was achieved at 1536 nm in the optical communication band. A continuously regenerated spectral hole in the inhomogeneously broadened 4I15/2(1)4I13/2(1){}^{4}{I}_{15/2}{(1)}^{4}{I}_{13/2}(1)4I15/2​(1)4I13/2​(1) optical absorption of an Er3+:Y2SiO5{\mathrm{Er}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Er3+:Y2​SiO5​ crystal was used as the short-term frequency reference, while a variation on the locking technique allowed simultaneous use of the inhomogeneously broadened absorption line as a long-term reference. The reported frequency stability was achieved without vibration isolation. Spectral hole burning frequency stabilization provides ideal laser sources for high-resolution spectroscopy, real-time optical signal processing, and a range of applications requiring ultra-narrow-band light sources or coherent detection; the time scale for stability and the compatibility with spectral hole burning devices make this technique complementary to other frequency references for laser stabilization.
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.
Using an ultrastable continuous-wave laser at 580 nm we performed spectral hole burning of Eu(3+):Y(2)SiO(5) at a very high spectral resolution. The essential parameters determining the usefulness as a macroscopic frequency reference, linewidth, temperature sensitivity, and long-term stability, were characterized using a H-maser stabilized frequency comb. Spectral holes with a linewidth as low as 6 kHz were observed and the upper limit of the drift of the hole frequency was determined to be 5±3 mHz/s. We discuss the necessary requirements for achieving ultrahigh stability in laser frequency stabilization to these spectral holes.
We perform hole burning with a low-drift stabilized laser within the zero phonon line of the $4f\ensuremath{-}5d$ transition in Ce3+:Y2SiO5{\mathrm{Ce}}^{3+}:{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Ce3+:Y2​SiO5​ at 2 K. The narrowest spectral holes appear for small applied magnetic fields and are $6\ifmmode\pm\else\textpm\fi{}4$ MHz wide (FWHM). This puts an upper bound on the homogeneous linewidth of the transition to $3\ifmmode\pm\else\textpm\fi{}2$ MHz, which is close to lifetime limited. The spin level relaxation time is measured to $72\ifmmode\pm\else\textpm\fi{}21$ ms with a magnetic field of 10 mT. A slow permanent hole burning mechanism is observed. If the excitation frequency is not changed the fluorescence intensity is reduced by more than 5050%50 after a couple of minutes of continuous excitation. The spectral hole created by the permanent hole burning has a width in the tens of MHz range, which indicates that a trapping mechanism occurs via the 5d5d5d state.
Summary form only given. Laser frequency stabilization to 200 Hz on a 5 ms time scale and to 1 kHz over 30 minutes has been demonstrated using persistent and transient spectral holes in inhomogeneously broadened resonances of Er/sup 3+/,D/sup -/:CaF/sub 2/, Er/sup 3+/:Y/sub 2/SiO/sub 5/, and Er/sup 3+/:KTiOPO/sub 4/ at cryogenic temperatures. Persistent spectral holes with lifetimes of weeks or longer provide a programmable and transportable secondary frequency reference, and kilohertz wide transient spectral holes provide excellent references at millisecond time scales appropriate for spectroscopy and coherent transient signal processing devices. This locking technique has significant applications to devices beyond the field of spectral hole burning.