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Laser Physics

Population trapping in ruby

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

Published Jan 1, 2000• 0 citations
OpenAlex

Abstract

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.

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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.
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 $\ifmmode \bar{E}\else \={E}\fi{}$ and the spin coherence decay time (T2)spin.{(T}_{2}{)}_{\mathrm{spin}}.(T2​)spin​.
Lasing without population inversion was studied in a three-level solid state medium of ruby. The two closely-spaced lower levels are the Zeeman split sublevels of the ground state 4A2 of ruby, corresponding to M=−3/2 and M=+l/2. The transition between the lower levels is the electric dipole-forbidden. When the angle between the constant magnetic field and C-axis of ruby is 90°, the transition matrix element of the electric dipole-forbidden transition is quite large.1 A strong microwave field which operates at K-band coherently couples the two lower levels.2 Changing the constant magnetic field intensity or adjusting the frequency of the pumping microwave field, the exact resonant excitation can be established. The upper level of the lasing process is the Zeeman split sub-level M=−l/2 of 2E state. The ruby crystal, with about 0.05% chromium concentration, is placed at the center of a cylindrical cavity and cooled by liquid helium. With 500 Gauss magnetic field, the coupling microwave frequency is 13.1 Ghz and the required power is around 100 W/cm2.
We propose a scheme to achieve one-dimensional velocity-selective coherent population trapping in a five-level system under two-frequency laser excitation. It may be applied to either D line of alkali-metal atoms. The trapped state is a time-dependent superposition of three sublevels from two different hyperfine ground states. Stable trapping may be produced by correctly detuning the laser beams to compensate for different hyperfine and kinetic energies of these ground states. We present numerical results for a five-level model, as well as for the complete level systems appropriate for alkali-metal atoms.
Observation of coherent population trapping (CPT) at ground-state Zeeman sublevels of Cr3+{\mathrm{Cr}}^{3+}Cr3+ ion in ruby at room temperature is reported. A mechanism of CPT, not owing to optical pumping, is revealed in a situation when the optical pulse duration is shorter than the population decay time from the excited optical state.
Coherent population trapping (CPT) in a three-level atomic medium pumped by two subsequent short optical pulses is considered under the condition of negligible population decay from the excited optical state. It is shown that the amount of atomic population transferred to the excited state by the combined action of the pulses strongly depends on the phase of the ground-state coherence excited by the first pulse at the arrival time of the second pulse. Oscillatory behavior of optical excitation efficiency on the time delay between the pulses is predicted. It is also shown that saturating optical pulses can produce population inversion in a resonantly pumped quasi-two-level system. A class of solid materials in which the predicted phenomena can be observed at room temperature is found. It includes some rare-earth and transition-metal doped dielectric crystals where Orbach relaxation between ground-state Zeeman states is suppressed: ruby, alexandrite, and several others. On the basis of the theoretical predictions, experimental observation of Ramsey fringes in CPT spectrum of ruby is reported.
A spatially periodic distribution of excited electronic states is produced in ruby which is placed into the interference region of two light beams derived from a pulsed laser (wavelength 530 nm). The spatially modulated population density acts like an optical grating and is detected by diffraction of a quasi-cw laser beam (488 nm). The lifetimes of the population density gratings are measured for ruby crystals with 0.05 to 5% Cr-doping and compared with the fluorescence lifetimes of the R-lines (694 nm). For the 0.05% ruby both lifetimes are nearly equal. At higher Cr-concentrations the grating decay is considerably faster than the fluorescent decay. The grating lifetimes are independent of the grating period A = 1 to 100 μm. From this observation an upper limit of the diffusion constant for energy transfer between excited electronic states in ruby is estimated.