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Physical Review A

Dark state in ruby: Analysis of the feasibility

R. N. Shakhmuratov, Arthur G. Szabo, Gregory Kozyreff, Romain Coussement, J. Odeurs, Paul Mandel

Published Sep 15, 2000• 5 citations
Publisher

Abstract

Bichromatic excitation of the ${R}_{1}$ line in ruby at liquid-helium temperature is considered. The frequency difference of the spectral components of the driving field is resonant with the energy gap between the anticrossed spin sublevels $+1/2$ and $+3/2$ in the ground state ${}^{4}{A}_{2}.$ The condition of the spin coherence trapping in the nonabsorbing state is analyzed. Population trapping is revealed in the reduced spontaneous emission from the excited state and in large spin magnetization of the ground state ${\mathrm{Cr}}^{3+}$ precessing with the frequency difference of the spectral components of the driving field. This magnetization can be detected by a pickup coil. The lifetime of the induced magnetization is strongly dependent on the ratio of the lifetime of the excited state $\ifmmode \bar{E}\else \={E}\fi{}$ and the spin coherence decay time ${(T}_{2}{)}_{\mathrm{spin}}.$

DOI
10.1103/physreva.62.043405

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Physical review. B, Condensed matter•Apr 1, 1991•10 citations
Bichromatic excitation of the R1{R}_{1}R1​ line in ruby at liquid-helium temperature is considered. The frequency difference of the spectral components of the driving field is resonant with the energy gap between the anticrossed spin sublevels +1/2+1/2+1/2 and +3/2+3/2+3/2 in the ground state 4A2.{}^{4}{A}_{2}.4A2​. The condition of the spin coherence trapping in the nonabsorbing state is analyzed. Population trapping is revealed in the reduced spontaneous emission from the excited state and in large spin magnetization of the ground state Cr3+{\mathrm{Cr}}^{3+}Cr3+ precessing with the frequency difference of the spectral components of the driving field. This magnetization can be detected by a pickup coil. The lifetime of the induced magnetization is strongly dependent on the ratio of the lifetime of the excited state \ifmmodeEˉ\elseEˉ\fi\ifmmode \bar{E}\else \={E}\fi{}\ifmmodeEˉ\elseEˉ\fi and the spin coherence decay time (T2)spin.{(T}_{2}{)}_{\mathrm{spin}}.(T2​)spin​.
Population trapping in the ground state spin sublevels of Cr 3+ in ruby at liquid helium temperature is considered. It is proposed to excite the R 1 -transition by a bichromatic laser beam with an optical frequency difference matching the ground state spin sublevels splitting. If the excitation is strong enough to decouple Cr 3+ from its environment, responsible for dephasing, an appreciable amount of the population is trapped in a particular superposition of the spin sublevels. This superposition state does not interact with the laser beam because of the destructive interference of the quantum paths constituting the transition. Population trapping can be detected by the reduced luminescence from the excited state and by the magnetization ringing originating from the ground state spin coherence.
The magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a QQQ-switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the 4A2^{4}A_{2}4A2​ ground state to the levels of the E‾(2E)\overline{E}(^{2}E)E(2E) excited state. The change in Mz{M}_{z}Mz​ is linearly proportional to HHH except near the anticrossing points of the 4A2^{4}A_{2}4A2​ spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the 4A2^{4}A_{2}4A2​ wave functions. When HHH has a small component perpendicular to the zzz axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of Mz{M}_{z}Mz​ was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.
Using excitation by ultrashort light pulses from a mode-locked ruby laser, we have observed optically induced magnetization precessing at a frequency corresponding to the energy separation near the level anticrossing points of the ground state 4 A 2 in ruby at room temperature. The motion of the magnetization is detected by a pick-up coil. The decay time of the signal is 5∼6 ns. The analysis is made by using the model of fictitious spin 1/2 and the agreement with the experiment is satisfactory.
Sharp resonances in optical excitation of ruby by laser pulses are observed as Zeeman sublevels anticross in an external magnetic field. For the R1{R}_{1}R1​ optical line of ruby (694.3nm)(694.3\phantom{\rule{0.3em}{0ex}}\mathrm{nm})(694.3nm) excitation drops when the external magnetic field strength approaches 4.14kG4.14\phantom{\rule{0.3em}{0ex}}\mathrm{kG}4.14kG while for the R2{R}_{2}R2​ line (692.9nm)(692.9\phantom{\rule{0.3em}{0ex}}\mathrm{nm})(692.9nm) it increases in 4.144.144.14 and 2.07kG2.07\phantom{\rule{0.3em}{0ex}}\mathrm{kG}2.07kG fields. A simple theoretical description of the observed effects on the basis of level mixing explains both situations.
A large number of small but sharp changes (increases and decreases) of the R 1 fluorescence in ruby are observed as a function of applied magnetic field between 2 K and 77 K. At liquid helium temperatures, these signals have linewidths much narrower than the inhomogeneous linewidth (∼0.1 cm -1 ) of the R 1 line. All of these signals appear at the fields where the Zeeman splittings in the excited state \bar E ( 2 E ) and the ground state 4 A 2 satisfy an energy-matching condition for simultaneous transitions of two or more ions. Two distinct mechanisms are found to be responsible for the signals: spin-spin cross-relaxation between \bar E ( 2 E ) and 4 A 2 , and resonant self-trapping of the R 1 line. From the temperature dependence of the linewidths of the signals, thermal broadening of \bar E ( 2 E ) is measured below 77 K. Similar signals are observed in the N lines due to energy transfer from isolated ions to pairs.
Measurements of photon-echo decays in dilute ruby (Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​ concentration of 0.018 at. %) in magnetic fields up to 29.5 kG are reported. Echoes from the 4^{4}4A2{\mathit{A}}_{2}A2​(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) and 4^{4}4A2{\mathit{A}}_{2}A2​(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) transitions have dephasing times (T2{\mathit{T}}_{2}T2​) that are directly proportional to the ratio of the magnetic field (B) to the temperature (T), for the range 2.5B/T20 kG/K. A transition in the decay from exponential to nonexponential behavior for B/T>10 kG/K is observed. Decay times for the 4^{4}4A2{\mathit{A}}_{2}A2​(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E(-1/2) echo are roughly a factor of 3 longer than for the 4^{4}4A2{\mathit{A}}_{2}A2​(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) echo. We attribute the lengthening of T2{\mathit{T}}_{2}T2​ with increasing B/T to the suppression of Cr-Cr spin flip-flops as the population of the upper 4^{4}4A2{\mathit{A}}_{2}A2​ levels decreases.