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Physica Scripta

Coherent Population Trapping in Multi-Level Atomic Systems

Laurentius Windholz

Published Jan 1, 2001• 13 citations
Publisher

Abstract

Coherent population trapping (CPT) is treated in multi–level systems, excited by two– or four–frequency laser light. The dynamics of filling non–absorbing (dark) states is investigated. In cases where all transitions involved are excited (closed systems), the effect becomes dependent on the relative phase of the light waves. Further electromagnetically induced transparency (EIT) is described in three– and four–level systems and used for effective side band generation.

DOI
10.1238/physica.topical.095a00081

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Coherent population trapping (CPT) is treated in multi–level systems, excited by two– or four–frequency laser light. The dynamics of filling non–absorbing (dark) states is investigated. In cases where all transitions involved are excited (closed systems), the effect becomes dependent on the relative phase of the light waves. Further electromagnetically induced transparency (EIT) is described in three– and four–level systems and used for effective side band generation.
Atomic coherence and interference manifested by electromagentically induced transparency (EIT) and coherent population trapping (CPT) plays an important role in the current studies of atom-photon interactions and has found numerous applications in optical physics. EIT is created in a three-level atomic system by a coupling field and results in destructive interference between two excitation paths of a weak probe laser interacting with the atomic medium. This leads to suppressed linear absorption and rapidly varying atomic dispersion for the probe laser near the atomic resonance, which provides the platform for a variety of applications such as nonlinear optics at low light levels, slow light manipulation, and quantum state engineering for photons and atoms. Here we extend the simple three-level EIT system to more complicated and versatile configurations in a multi-level atomic system coupled by multiple laser fields. We show that with multiple excitation paths provided by different laser fields, phase-dependent quantum interference is induced: either constructive or destructive interference can be realized by varying the relative phases among the laser fields. Two specific examples are discussed. One is a three-level system coupled by bichromatic coupling and probe fields, in which the phase dependent interference between the resonant two-photon Raman transitions can be initiated and controlled. Another is a four-level system coupled by two coupling fields and two probe fields, in which a double-EIT configuration is created by the phase-dependent interference between three-photon and one-photon excitation processes. We analyze the coherently coupled multi-level atomic system and discuss the control parameters for the onset of constructive or destructive quantum interference. We describe two experiments performed with cold Rb atoms that can be approximately treated as the coherently coupled three-level and four-level atomic systems respectively. The experimental results show the phase-dependent quantum coherence and interference in the multi-level Rb atomic system, and agree with the theoretical calculations based on the coherently coupled three-level or four-level model system.
There presented basic information on coherent population trapping (CPT) and related phenomenon of electromagnetically induced transparence, ‘dark’ and ‘bright’ (anomalous absorption) states is presented. Spectrum transformation is considered in probe field spectroscopy for Λ-scheme in various settings. The close relation is revealed between the effect of CPT in the manifold of magnetic sublevels and the phenomenon of optical pumping (optical orientation and optical alignment). CPT is shown to be generalized to the case of several transitions with a common upper level and with the corresponding number of light fields each being in quasiresonance with its ‘own’ transition.
The atomic coherence effect can be used in enhancing the efficiencies of nonlinear optical processes. Particularly, nondegenerate four-wave mixing (NDFWM) in multilevel systems has recently gained attention in connection with the advantage of using coherent population trapping (CPT) or electromagnetically induced transparency (EIT) to enhance the efficiency of generated signals. Generally speaking, linear absorption competes with the nonlinear signal generation at the exact one-photon resonance condition. However, the linear absorption can, in principle, be reduced or even eliminated by preparing the system in the CPT or EIT state. We report experimental demonstrations of NDFWM in several multi-level configurations in rubidium atomic vapor. In one of the double-/spl Lambda/ systems an unusual behavior of signal output power as a function of pump power, i.e. a maximum in the generated signal power is reached as the pump power increases, is experimentally observed. By comparing with several related /spl Lambda/ and double-/spl Lambda/ systems, we have concluded that CPT is the mechanism for this interesting effect.
In the atomic frequency standard, the light shift inevitably affects the long-term stability of the atomic clock. In this work, we accurately calculated the light shifts of electromagnetically induced transparency (EIT) and coherent population trapping (CPT) clocks operating under continuum and pulse sequence regimes by numerically solving the Liouville density matrix equation, including all the relaxation terms of a three-level system. The results show that the light shifts under pulse excitation are smaller than those under continuous excitation and the light shifts of the CPT process are much smaller than those of the EIT process under both excitations. It is also found that the light shifts in the continuous excitation increase and those in the pulse excitation decrease with an increase in the Rabi frequency. The light shifts will increase with an increase of the relaxations of the ground states for both the processes under both regimes. Compared to all process atomic clocks, the light shift of pulse-excited atomic clocks is the smallest, which will be suitable for many applications.
In order to investigate effects of coherent population trapping (CPT) on electromagnetically induced transparency (EIT), we added an external weak magnetic field to identify a quantization axis. The laser beam whose polarization is parallel to the direction of the external magnetic field and the perpendicular laser are coupled to different transitions. CPT generated by two circular polarization components of the strong coupling beam when the polarization was perpendicular to the quantization axis, was competed with (EIT) so that absorption reduction could be larger than the case without CPT. We investigated the mechanism of steady-state light amplification without inversion using an incoherent pumping laser.
The phenomenon of coherent population trapping (CPT) of an atom (or solid state "artificial atom"), and the associated effect of electromagnetically induced transparency (EIT), are clear demonstrations of quantum interference due to coherence in multilevel quantum systems. We report observation of CPT in a superconducting phase qubit by simultaneously driving two coherent transitions in a Lambda-type configuration, utilizing the three lowest lying levels of a local minimum of a phase qubit. We observe 60(+/-7)% suppression of the excited state population under conditions of CPT resonance. We present data and matching theoretical simulations showing the development of CPT in time. Finally, we used the observed time dependence of the excited state population to characterize quantum dephasing times of the system.