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Physical Review A

Coherent population trapping at low light levels

Iyyanki V. Jyotsna, G. S. Agarwal

Published Oct 1, 1995• 43 citations
Publisher

Abstract

A three-level lambda ($\ensuremath{\Lambda}$) system driven by two coherent fields at the Raman resonance condition evolves to a nonabsorbing eigenstate of the Hamiltonian called the coherent population trapping (CPT) state. We study the various factors dictating the dynamical evolution of the coherences and the populations to the CPT state. We demonstrate the formation of the CPT state even at low intensities, though it takes much longer to form such a state. For the case of unequal decay rates we demonstrate an interesting sharp dip in the steady-state response of the medium at the Raman resonance condition.

DOI
10.1103/physreva.52.3147

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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.

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Coherent population trapping (CPT) resonance formation is modeled numerically in a three-level Λ -system with one of the near-resonance fields being frequency-modulated. The model is based on density matrix equations in RW approximation with atomic relaxation properly taken into account. Slow modulation is shown to be equivalent to CW excitation with the frequency changed point by point. As the modulation period approaches the relaxation times, the delayed response of the system is shown to cause the CPT resonance shift and reshaping, as well as the appearance of transient oscillations of the energy level populations.

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Coherent population trapping (CPT) in a three-level system in the Λ configuration interacting with two quantized fields is studied. It is shown that, in addition to the known trapping states of the field involving ordinary coherent states of each mode, SU(2) coherent states associated with the Schwinger realization are also field states that give rise to CPT for this system. In addition it is pointed out that superpositions of such states, and statistical mixtures of them, for different total photon numbers also give rise to CPT. The stability of the CPT states against decay of the cavity field modes is examined. CPT is preserved if the modes decay at the same rate. A possible method for generating statistical mixtures of the SU(2) coherent states is described.

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At the conditions of two-photon resonance the effect of coherent population trapping (CPT) can take place. The CPT may be observed as in absorption so in resonance fluorescence. The CPT is widely applied in high resolution spectroscopy, laser cooling, atomic optics and so on. Earlier the peculiarities of CPT resonances on fine structure levels of an atom have been considered on example of thallium atoms. It was shown that the form and number of resonances are influenced by geometry of experiment and initial conditions (initial level populations). As the investigations of CPT on fine structure levels are the object of interest last years, we have considered the numerical analysis of dependence the form of CPT resonances on fine structure levels of T1 atoms as lower levels of Λ-system on polarization of radiation fields. The cases of elliptical, linear and circular polarization have been considered.

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Steady-state behavior in atomic three-level Λ and ladder systems with incoherent population pumping

M. Blaauboer

We study the steady state in three-level lambda (\ensuremath{\Lambda}) and ladder systems. It is well known that in a \ensuremath{\Lambda} system this steady state is the coherent population trapping state, independent of the presence of spontaneous emission. In contrast, the steady state in a ladder system is in general not stable against radiative decay and exhibits a minimum in the population of the ground state. We show that incoherent population pumping destroys the stability of the coherent population trapping state in the \ensuremath{\Lambda} system and suppresses a previously discovered sharp dip in the steady-state response. In the ladder system the observed minimum disappears in the presence of an incoherent pump on the upper transition.

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Coherent population trapping via quantum interference of incoherent pump processes in three-level systems

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Quantum interference has been predicted to occur in a three-level Λ system with near-degenerate dipole allowed transitions, which are coupled to the same linearly polarized incoherent field. For the Λ system with two degenerate lower levels, we show that (a) quantum interference of incoherent pump processes leads to coherent population trapping (CPT), and (b) when two coherent fields are applied to two transitions on two-photon resonance, CPT appears when the amplitudes and phases of the applied coherent fields and the polarization angle of the incoherent field satisfy certain conditions. Further, the physical mechanism and the above conditions for CPT are presented.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 17, 2003•19 citations
A three-level lambda (\ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ) system driven by two coherent fields at the Raman resonance condition evolves to a nonabsorbing eigenstate of the Hamiltonian called the coherent population trapping (CPT) state. We study the various factors dictating the dynamical evolution of the coherences and the populations to the CPT state. We demonstrate the formation of the CPT state even at low intensities, though it takes much longer to form such a state. For the case of unequal decay rates we demonstrate an interesting sharp dip in the steady-state response of the medium at the Raman resonance condition.
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.
Coherent population trapping (CPT) resonance formation is modeled numerically in a three-level Λ -system with one of the near-resonance fields being frequency-modulated. The model is based on density matrix equations in RW approximation with atomic relaxation properly taken into account. Slow modulation is shown to be equivalent to CW excitation with the frequency changed point by point. As the modulation period approaches the relaxation times, the delayed response of the system is shown to cause the CPT resonance shift and reshaping, as well as the appearance of transient oscillations of the energy level populations.
Coherent population trapping (CPT) in a three-level system in the Λ configuration interacting with two quantized fields is studied. It is shown that, in addition to the known trapping states of the field involving ordinary coherent states of each mode, SU(2) coherent states associated with the Schwinger realization are also field states that give rise to CPT for this system. In addition it is pointed out that superpositions of such states, and statistical mixtures of them, for different total photon numbers also give rise to CPT. The stability of the CPT states against decay of the cavity field modes is examined. CPT is preserved if the modes decay at the same rate. A possible method for generating statistical mixtures of the SU(2) coherent states is described.
At the conditions of two-photon resonance the effect of coherent population trapping (CPT) can take place. The CPT may be observed as in absorption so in resonance fluorescence. The CPT is widely applied in high resolution spectroscopy, laser cooling, atomic optics and so on. Earlier the peculiarities of CPT resonances on fine structure levels of an atom have been considered on example of thallium atoms. It was shown that the form and number of resonances are influenced by geometry of experiment and initial conditions (initial level populations). As the investigations of CPT on fine structure levels are the object of interest last years, we have considered the numerical analysis of dependence the form of CPT resonances on fine structure levels of T1 atoms as lower levels of Λ-system on polarization of radiation fields. The cases of elliptical, linear and circular polarization have been considered.
We study the steady state in three-level lambda (\ensuremath{\Lambda}) and ladder systems. It is well known that in a \ensuremath{\Lambda} system this steady state is the coherent population trapping state, independent of the presence of spontaneous emission. In contrast, the steady state in a ladder system is in general not stable against radiative decay and exhibits a minimum in the population of the ground state. We show that incoherent population pumping destroys the stability of the coherent population trapping state in the \ensuremath{\Lambda} system and suppresses a previously discovered sharp dip in the steady-state response. In the ladder system the observed minimum disappears in the presence of an incoherent pump on the upper transition.
Quantum interference has been predicted to occur in a three-level Λ system with near-degenerate dipole allowed transitions, which are coupled to the same linearly polarized incoherent field. For the Λ system with two degenerate lower levels, we show that (a) quantum interference of incoherent pump processes leads to coherent population trapping (CPT), and (b) when two coherent fields are applied to two transitions on two-photon resonance, CPT appears when the amplitudes and phases of the applied coherent fields and the polarization angle of the incoherent field satisfy certain conditions. Further, the physical mechanism and the above conditions for CPT are presented.