We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the
nP manifold via an optical transition on one of the spectroscopic
D lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.
We present a general formalism for studying the interaction between laser fields and degenerate-Zeeman-sublevel atoms correct up to the first order in the weak probe field. We derive from this theory the equations of motion for a \ensuremath{\Lambda}-type system involving
S1/2, F=2\ensuremath{\leftrightarrows}
P1/2, F\ensuremath{'}=1\ensuremath{\leftrightarrows}
S1/2, F=1 transitions in
87Rb atoms. These equations are used to numerically investigate the coherent population trapping (CPT) schemes in the
S1/2, F=2\ensuremath{\leftrightarrows}
P1/2, F\ensuremath{'}=1 transition induced by a linearly polarized pumping field and the electromagnetically induced transparency exhibited in the weak probe spectrum in the
S1/2, F=1\ensuremath{\leftrightarrows}
P1/2, F\ensuremath{'}=1 transition. We discuss the effects of the CPT on the probe spectrum with and without the Doppler broadenings by comparing the probe spectrum derived from the real system with that derived from an ideal \ensuremath{\Lambda}-type system. We show that the atoms in the CPT states are shielded from interacting with the probe field while those in the absorbent states make contributions to the weak probe by the Raman anti-Stokes process, and the effect of the real system on the probe field becomes equivalent to the ideal \ensuremath{\Lambda} system only in the strong CPT parameter regime. \textcopyright{} 1996 The American Physical Society.
A full quantum treatment of coherent population trapping (CPT) is given for a system of resonantly coupled atoms and electromagnetic field. We develop a regular analytical method of the construction of generalized dark states (GDS). It turns out that GDS do exist for all optical transitions
FgtoFe, including bright transitions
FtoF+1 and
F′′toF′′ with
F′′ a half-integer, for which the CPT effect is absent in a classical field.
Summary form only given. We have performed a series of experiments on coherent population trapping (CPT) in the presence of strong magnetic flux densities up to 1 mT. CPT can be observed in /spl Lambda/-systems where two ground states are coupled to a common excited state by two near-resonant light fields. Effective formation of ground state coherences takes place when the frequency difference of the light fields precisely matches the ground state splitting. This process leads to reduced absorption in the medium and thus reduced fluorescence intensity ("dark resonance") at the optical resonance frequency.
A full quantum treatment of coherent population trapping (CPT) is given for a system of resonantly coupled atoms and electromagnetic field. We develop a regular analytical method of the construction of generalized dark states (GDS). It turns out that GDS do exist for all optical transitions F g → F e , including bright transitions F → F + 1 and F '' → F '' with F '' a half-integer, for which the CPT effect is absent in a classical field. We propose an idea to use an optically thick medium with a transition F '' → F '' with F '' ⩾ 3/2 a half-integer as a "quantum filter", which transmits only a quantum light with limited number of photons. Such a quantum filter can be used as a deterministic source of Fock's state of light.