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Physical Review A

Comparison between dressed-atom and bare-atom pictures in laser spectroscopy

P. R. Berman, Rainer Salomaa

Published May 1, 1982• 89 citations
Publisher

Abstract

The theory of the interaction between radiation fields and atoms as applied to laser spectroscopy can be approached using either a bare-atom picture (BAP) or dressed-atom picture (DAP). In the BAP, the basis states are those of the free atoms and free field while, in the DAP, the basis states encompass some part of the atom-field interaction. The theory of saturation spectroscopy in three-level systems is discussed using both approaches. Whereas calculations are usually more easily done using the BAP, one can gain useful insight into the underlying physical processes from the DAP. Moreover, when the radiation field strengths (in frequency units) are larger than the relaxation rates in the problem, the DAP equations simplify considerably and lead to line-shape expressions which may be given a simple interpretation. The DAP is used to obtain resonance conditions for traveling-wave fields interacting with three- and four-level atoms and for a standing-wave saturator and traveling-wave probe interacting with a three-level atom. In addition, the DAP is applied to several problems involving optical coherent transients. A comparison is made between the various advantages of the BAP and DAP and an interesting duality between the two approaches is noted.

DOI
10.1103/physreva.25.2667

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The theory of the interaction between radiation fields and atoms as applied to laser spectroscopy can be approached using either a bare-atom picture (BAP) or dressed-atom picture (DAP). In the BAP, the basis states are those of the free atoms and free field while, in the DAP, the basis states encompass some part of the atom-field interaction. The theory of saturation spectroscopy in three-level systems is discussed using both approaches. Whereas calculations are usually more easily done using the BAP, one can gain useful insight into the underlying physical processes from the DAP. Moreover, when the radiation field strengths (in frequency units) are larger than the relaxation rates in the problem, the DAP equations simplify considerably and lead to line-shape expressions which may be given a simple interpretation. The DAP is used to obtain resonance conditions for traveling-wave fields interacting with three- and four-level atoms and for a standing-wave saturator and traveling-wave probe interacting with a three-level atom. In addition, the DAP is applied to several problems involving optical coherent transients. A comparison is made between the various advantages of the BAP and DAP and an interesting duality between the two approaches is noted.
A generalized dressed-atom approach (GDAA) is developed to study the interaction of two or more strong fields with atomic and molecular systems. In the GDAA, part of the atom-field interaction is incorporated into the free-atom, free-field Hamiltonian and this expanded Hamiltonian is said to characterize a "dressed atom." The remaining atom-field interaction may then be thought to constitute a probe field interaction for this dressed atom. Provided that the dressed atom constitutes a reasonably good approximation to the true interaction, the GDAA should offer a relatively simple means for semiquantitatively predicting the positions of absorption resonances in quite complex atom-field systems. The GDAA is applied to the theory of a high-intensity, single-mode, standing-wave gas laser, the theory of Bloch-Siegert shifts, and the analysis of Autler-Townes or saturation spectroscopy experiments. The agreement between the GDAA and computer-determined values for laser resonance positions and Bloch-Siegert shifts is found to be surprisingly good over the entire range of applied field strengths. Some methods for using the GDAA to study complex spectroscopic systems are discussed.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bichromatic laser field in the ladder configuration is being formulated. The system is allowed to be dressed by both laser-field photons (double dressing). The temporal behavior of the system under consideration is being explored numerically. Although the use of dressed-basis density matrix equations introduces major complexity into the equations, this procedure has crucial importance to the understanding of the atomic spectrum and the underlying physics of the processes involved. The system is found to possess a gain without population inversion, as well as a regular gain with inversion for various transitions, both in the transient and steady-state regimes. Enhancement of the refractive index accompanied by vanishingly small absorption was also found. The frequency response of various transitions is explored via numerical Fourier analysis. Some transitions are found to exhibit a dispersion-like line shape, clear evidence of a quantum-coherent interference effect. The spectrum consists of two distinct quintets centered about the coupling and probe-laser frequencies. The spectral features consisting of each quintet are located symmetrically (at resonance conditions only) around the line center at positions shifted from the center by the generalized Rabi and double Rabi frequencies.
This chapter shows that several non-linear features can be demonstrated and the line shape of sub-natural line width can be obtained by manipulation of the powers of the two interacting laser radiations. The interaction of the laser radiation can produce a coherent superposition of the atomic states such that atoms are trapped in one state so that the atomic system may be transparent even in the presence of radiation frequency that is on resonance. Saturation spectroscopy is more conveniently performed in three level atomic systems interacting with two laser radiations. One of the radiations, called pump beam, has higher intensity and frequency on resonance or close to resonance with the transition frequency across two levels of the atom. The second laser radiation, called probe beam, is weaker and interacts with two other energy levels, one of which is common to the pump transition. A few hyperfine transitions are within the envelope of one Doppler profile.
Abstract : Work is summarized in areas of: Laser Assisted Collisions; Velocity Changing collisions in Atomic Vapors; Coherent Transients; Collision Induced Extra Resonances; Breakdown of the Optical Bloch Equations; Saturation Spectroscopy; Dynamics of Two-and Three-level Atoms Interacting with Radiation Fields; Pulse Propagation. Keywords: Laser spectroscopy, Optical collisions, Radiative collisions, Two-level atom, Atomic coherence, Degenerate four-wave mixing, Saturation spectroscopy, Laser propagation,, Dressed atom, Photon echo, Bloch equations, Collision kernal, Collisions, Optical noise.
Chapter 5 begins the systematic application of the density matrix to describe optical interactions. Stationary two-and three-level atoms interacting with a traveling wave are compared to show that the presence of additional levels changes the saturation behavior of atoms. Then motion of the atoms is introduced and the phenomena of spatial and frequency-domain hole-burning are analyzed. Special effects due to standing waves, such as the light shift, are covered in this section. Next, tri-level coherence is considered, to extend the concept of coherences to two-photon transitions or Zeeman interactions in folded 3- or Λ-systems. Higher order interactions are also analyzed. This includes four-wave mixing and pump–probe techniques which form the basis of common nonlinear laser spectroscopies. Quantum interference is covered as a prelude to the topic of electromagnetically induced transparency. Higher order coherent interactions are also treated using a diagrammatic calculation technique based on Feynman diagrams.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bi-chromatic laser field in the ladder configuration is presented. In our model we allow the atom to be dressed by both of the coupling and probe fields. The system under consideration is explored both analytically and numerically within the steady-state regime. A parameter study is performed in which we explore the influence of the change of control parameters (Rabi frequencies and incoherent pump rates, etc) on the system behaviour. The parameter study also applies to situations where both coherent fields have comparable intensities. Expressions for steady-state populations and coherences are derived, from which the constraints on the system control parameters allowing gain or absorption of various types, are calculated. The system is demonstrated to possess gain without inversion (GWI), as well as regular gain with inversion, for the appropriate choice of system control parameters. Inversion without lasing (IWL) is also found. The dressed-state approach offers a different insight into the system dynamics in which Rabi oscillations and spectral features appear natural. We believe that the dressed-state approach provides a more adequate description of the system dynamics than that provided by the bare state basis.