Coherent trapping of atomic populations

Abstract

It is often desirable in laser spectroscopy and isotope separation to extract as much as possible of an atomic or molecular population that is distributed among a number of ground-state sublevels and low-lying metastable levels.We describe a form of coherent trapping that occurs when multiple resonant laser beams are used to couple the various ground states to a common upper level. This effect prevents the extraction of the entire population. We then study the effect with two dye lasers and an atomic beam and suggest possible ways to maximize the pumping efficiency.When two cw lasers are tuned so that they couple two different ground-state sublevels to a common upper level, there is no steady-state population in the upper This effect, which holds even for intense laser fields, might be termed coherent trapping of atomic populations. It is due to optical pumping of the ground-state sublevels into a coherent superposition state that is decoupled from the laser fields. The theory of the effect has been worked out by Arimondo and Orriols' and by Whitley.2 The source of the effect is easily seen by writing the wavefunction in the interaction picture, (1) and substituting it into Schrddinger's equation. Here we have taken the atomic-energy eigenfunctions as Oi(r) and the energy of the various states as Ei = hw 1 , i = 1,2,3. The amplitudes then satisfy the equations of motionwhere we have taken the applied field to beand we have neglected the counterrotating terms. The two dipole matrix elements, which are assumed real for convenience, are denoted by gj, i = 1,2, while the detuning of the two lasers from resonance, b6 and 5,, are defined in Fig 1. Examination of Eqs. (2a) and (2c) shows that there is a constant of the motion when Ba = 6b =_ 6, i.e., when the lasers are tuned to the two-photon resonance. The effect of the constant is most easily seen if we introduce two new amplitudes, r(t) = ai(t)cos 0 -a3(t)sin 0, (4a) s(t) = a,(t)sin 0 + a 3 (t)cos 0,where the angle 0 is defined byThe equations of motion for the amplitudes of the two ground states are then expressible in terms of r(t) andwhere R is the generalized Rabi frequency(5b) (6) One linear combination of the ground states is coupled to the excited state by the applied fields, and the other linear combination is decoupled entirely. The population initially in the linear combination,remains there. If the initial states are not prepared coherently, this means that half of the population remains in the ground state and nothing is gained by the application of two lasers rather than one. We have not included spontaneous or collisional damping in the calculations, but these are included in the calculations of Refs. 1 and 2. The result of including damping is that the population initially in the linear combination of states s is optically pumped in a few lifetimes into the decoupled linear combination r. In the steady state there is no population in level 2 or in the linear combination s. All of it is in the linear combination r. The atom is decoupled from the...

Ground State Laser Cooling Using Electromagnetically Induced Transparency

“…The phenomenon is also called "coherent population trapping" [15] or "dark resonance" and has been demonstrated in many systems [16] including single trapped ions [17]. It belongs to a large class of quantum interference effects in multilevel systems [18] and can be understood as a destructive interference of the two pathways to the excited level [19].…”

Control of rubidium low-lying Rydberg states with trichromatic femtosecond π pulses for ultrafast quantum information processing

“…This previous research showed the potential for other interesting phenomena in multilevel systems, such as transfer to higher bound and continuum levels [12], and development of techniques for efficient transfer to unpopulated Rydberg states [19], which is essential for further advancement on spectroscopy, collision dynamics, quantum memories [21] and photon control in quantum information processing [23]. Kuklinski et al [19] showed an extension to the Heisenberg picture which presents a solution of the Liouville equations that allows the computation of the relaxation processes during the evolution of population transfer in multilevel systems.…”

“…Studies on coherent population trapping (CPT) and electromagnetically induced transparency (EIT) set the basis for many coherent control techniques based on combined detuned lasers and adiabatic transfer [10][11][12][13][14][15][16]. The * Electronic address: carles.serrat-jurado@upc.edu concept of CPT was employed to demonstrate pumping of atomic systems in a particular state, and has been theoretically analyzed by Arimondo and Orriols [11] and Gray et al [12] based on the solution of the Bloch-like equations of motion for a 3-level system with applications in Sodium atoms.…”

“…The * Electronic address: carles.serrat-jurado@upc.edu concept of CPT was employed to demonstrate pumping of atomic systems in a particular state, and has been theoretically analyzed by Arimondo and Orriols [11] and Gray et al [12] based on the solution of the Bloch-like equations of motion for a 3-level system with applications in Sodium atoms. This concept was further experimentally demonstrated by Whitley and Stroud [14].…”

An optical soliton pair among absorbing three-level atoms

“…An optically thin ensemble of three-level atoms in the lambda configuration becomes perfectly transparent when driven by two independent laser fields in two-photon resonance [23][24][25][26]. This is of especial importance in spectroscopic applications since, under these conditions, spontaneous emission from the upper level is completely absent.…”