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Physical Review A

Temperature-Dependent Phase Memory of Ruby Determined by Self-Induced Transparency

Irvin M. Asher, F. A. Hopf, L. K. Kie

Published Jul 1, 1973• 2 citations
Publisher

Abstract

A computer simulation of recent self-induced-transparency experiments in ruby demonstrates the general appropriateness of a previously derived two-level model for a wide range of attenuator temperatures. The only significant deviation is a sharper rise in the experimental delay curve. The temperature dependence of the homogeneous phase relaxation ${T}_{2}^{\ensuremath{'}}$ was introduced by including a "direct" phonon transition process in our program. The parameters for best fit provide ${{T}^{\ensuremath{'}}}_{2}\ensuremath{\simeq}50$ nsec for $T\ensuremath{\simeq}0$ \ifmmode^\circ\else\textdegree\fi{}K, which emphasizes the importance of phase-memory effects in low-temperature atomic-coherence experiments in ruby.

DOI
10.1103/physreva.8.396

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Journal of Nonlinear Optical Physics & Materials•Oct 1, 1992•1 citation
A computer simulation of recent self-induced-transparency experiments in ruby demonstrates the general appropriateness of a previously derived two-level model for a wide range of attenuator temperatures. The only significant deviation is a sharper rise in the experimental delay curve. The temperature dependence of the homogeneous phase relaxation T2\ensuremath′{T}_{2}^{\ensuremath{'}}T2\ensuremath′​ was introduced by including a "direct" phonon transition process in our program. The parameters for best fit provide T\ensuremath′2\ensuremath≃50{{T}^{\ensuremath{'}}}_{2}\ensuremath{\simeq}50T\ensuremath′2​\ensuremath≃50 nsec for T\ensuremath≃0T\ensuremath{\simeq}0T\ensuremath≃0 \ifmmode^\circ\else\textdegree\fi{}K, which emphasizes the importance of phase-memory effects in low-temperature atomic-coherence experiments in ruby.
We have investigated the self-induced transparency effect in ruby over a range of input energies which range from linear absorption to full transparency. The transmission, pulse delay, and pulse broadening were studied as a function of input energy. The transition region is narrower than that found in similar studies of the CO2{\mathrm{O}}_{2}O2​/SF6{\mathrm{F}}_{6}F6​ system; this is consistent with predictions based on ensembles of two-level systems. Included are the first pulse-delay and pulse-broadening curves to be obtained for the ruby system.
Formation of optical solitons in self-induced transparency (SIT) regime, where light pulses propagate virtually without loss in nominally strongly absorbing medium, is one of the most striking coherent transient phenomena in optics. Here we study experimentally and by numeric simulations how a square shape pulse gradually transforms into a smooth sech shape pulse of well-defined pulse area, depending on the parameters such as the pulse amplitude, duration, propagation distance etc. The SIT experiments for circularly polarized light are performed in the R1−3∕2) line of a 30 ppm ruby (α-Al2O3:Cr3+) at 1.7 K in a magnetic field of BIIc = 4.5 T, which corresponds to effective absorption coefficient, αL =14.5. In such a magnetic field and temperature range, a 30 ppm ruby is in the so-called superhyperfine limit resulting in a very long decoherence (phase memory) time, TM = 50 μs. We show, in good quantitative agreement with the simulations, how SIT soliton is formatted and how this results in extremely slow pulse peak propagation velocity of ∼300 m∕s, which is to date, the slowest pulse propagation ever observed in a SIT experiment. We also show that for accurate quantitative description of the observed SIT and soliton pulse shapes, the simulations need to account for variation of the incident pulse amplitude across the beam spatial profile. Potential implications of the SIT effect on classical- and quantum information storage will be discussed.
The dynamics of self-induced transparency in an inhomogeneously broadened attenuator is investigated with special emphasis on delay times. One finds a strong dependence of delay times on the input value of the area parameter $\ensuremath{\theta}$ with pulses of ${\ensuremath{\theta}}_{\mathrm{in}}\ensuremath{\approx}\ensuremath{\pi}$ exhibiting much larger delay times than for ${\ensuremath{\theta}}_{\mathrm{in}}=2\ensuremath{\pi}$. This investigation is extended to include the effects of an atomic phase memory time T2{T}_{2}T2​ which is of the order of ten times the pulse width (i.e., in accord with current experimental circumstances). The variation of other parameters is considered. A method of measuring $\ensuremath{\theta}$ directly is presented.
Self-induced transparency is reported for circularly polarized light in the R1(−3/2) line of a 30 ppm ruby (α-Al2O3:Cr3+) at 1.7 K in a magnetic field of B‖c=4.5 T. In such a field and temperature, a 30 ppm ruby is in the so-called superhyperfine limit resulting in a long phase memory time, TM=50 μs, and a thousand-fold slower pulse propagation velocity of ∼300 m/s was observed, compared to the ∼300 km/s measured in the first observation of self-induced transparency (SIT) ∼50 years ago, that employed a ruby with a 500 ppm chromium concentration in zero field and at 4.2 K. To date, this is the slowest pulse propagation ever observed in a SIT experiment.
A series of experiments of time-delay four-wave mixing with incoherent light (TDFWM-IL) in absorption bands of ruby and dye molecules at 300 K-20 K are reported, which demonstrate that two-level theory fails in the interpretation of the results, and that our multilevel theory of TDFWM-IL should be applied. The following experimental results are emphasized: the normalized delay-time dependences of the signal intensity IS (τ) are not dependent on the sample temperature from 80 K to 300 K for the pump-beam wavelengths not closed to the zero-phonon line or the absorption edge as the power spectrum S0(ω) of the incoherent light source kept invariable; at low temperature of 20 K, IS(τ) is modulated periodically with a period equal to the interval of two adjacent vibrational transitions in the absorption band 4T2 of ruby, as predicted by the multilevel theory. The experiments performed at the zero-phonon line of ruby and at the absorption edge of Cresyl Violet in PMMA demonstrate that the effective two-level model is suitable to approximately analyze not only the experimental results of TDFWM-IL in the unresolved continuous absorption bands with homogeneous broadening, but also the effects of inhomogeneous broadening on the behavior of TDFWM-IL in these bands. Additionally, some data of the subpicosecond dephasing processes of these materials are also obtained for the first time.