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Laser Cooling of Two-Level Atoms by Two-Photon Transition

Aranya B. Bhattacherjee

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

It is shown that nonlinear interaction between two-level atom and the radiation field can profoundly modify the optical force experienced by the atom The dynamic stark shift now provides a cooling force even at zero detuning.Due to two-photon interaction the 'radiation pressure force' experienced by the atom is twice as large as that for one-photon case, consequently temperatures much lower than the one-photon limit can be achieved Keywords Two-photon interaction, laser cooling, optical force

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It is shown that nonlinear interaction between two-level atom and the radiation field can profoundly modify the optical force experienced by the atom The dynamic stark shift now provides a cooling force even at zero detuning.Due to two-photon interaction the 'radiation pressure force' experienced by the atom is twice as large as that for one-photon case, consequently temperatures much lower than the one-photon limit can be achieved Keywords Two-photon interaction, laser cooling, optical force
Radiation pressure and laser cooling of a moving three-level ladder-type atom in bichromatic travelling fields are considered. The dependence of the force on parameters such as detunings, Rabi frequencies and spontaneous decay rates is calculated numerically and shown graphically and analytical expressions for the force are obtained for some special parameter values. It is shown that the radiation pressure shows Doppler-shifted resonance peaks resulting respectively from one-photon and two-photon transitions. Using the present scheme, Doppler cooling of sodium exploiting the 3 2 S 1/2 –3 2 P 3/2 –3 2 D 5/2 cascade transitions is investigated. It is found that temperatures lower than the Doppler limit can be achieved.
The optical forces exerted on a slowly moving two-level atom in a standing wave are profoundly modified when the normal decay rates of the atom are altered. The theory presented in this paper shows that the stimulated emission force becomes dominant at a very low laser intensity. Furthermore, it can change sign to provide an additional cooling force instead of a heating force at laser detunings below the atomic resonance. These phenomena can lead to equilibrium temperatures below the Doppler limit.
A theory of deep laser cooling of atoms by counterpropagating circular polarized laser waves in multilevel interaction schemes is developed. Using a (3+5)-level atom as an example, we show that in multilevel interaction schemes two-photon processes are responsible for creating a narrow structure near zero velocity in the ground-state atomic coherence. This structure is in turn responsible for narrow velocity structures in atomic populations and optical coherences. A Fokker-Planck-type kinetic equation is derived for a model of a (3+5)-level interaction scheme. It is found that two-photon coherent processes considerably enhance the radiation force at low velocities and the friction produced by the force at a negative detuning, and considerably decrease the diffusion coefficient. Two-photon processes in multilevel interaction schemes are identified as the basic physical mechanism responsible for deep laser cooling of atoms. The temperature of laser-cooled atoms is derived for a model (3+5)-level atom, and found to be in good agreement with the experimentally observed temperature for laser-cooled cesium atoms.
The process of laser cooling in a quasi resonant standing laser wave is one of the principal techniques of laser cooling of free atoms. It will be shown that the nonlinear interaction between the counter propagating waves in a standing wave have a profound affect on the mechanical manifestations of the light on the atoms. This can be understood simply by noting that in the Two Wave Mixing (TWM) process, a momentum kick of 2ℏk is transferred to the atom, as a photon is absorbed from one wave and emitted into the counter propagating wave. This process is in fact responsible for the so called "Dipole force" Or "Stimulated Molasses" and has been verified experimentally!. However, since the TWM process requires high laser intensity under normal conditions it does not usually lead to lower equilibrium temperatures. Nevertheless, It has been shown that the TWM process can be modified when the normal decay rates of the atom are altered. This modification can give rise to the appearance of the TWM at lower intensity and can even change its lineshape. This in turn have an important implications on the laser cooling process in a standing wave. Among the important effects: (i) The appearance of the stimulated force at lower intensity when the dipole decay rate is increased by dephasing events.(ii) The appearance of a narrow resonance characterized by the ground state decay in an open system. (iii) The modification of the stimulated force when the quantum fluctuations of the vacuum field are modified by quadrature squeezing3. Processes (ii) and (iii) can change the sign of the stimulated force from a heating force to a cooling force at the red side of the atomic resonance and give additional cooling force much larger than the radiation pressure force.
The study of the motion of neutral atoms under the action of light fields dates back to work of Albert Einstein published as early as 1916. This chapter describes a sample of molecules subjected to a thermal light field. It discusses atoms having only two levels at some optical energy separation. The chapter also discusses radiation pressure in two important examples of light fields, plane travelling and plane standing waves. The two-level atom interacting with a monochromatic laser mode represents one of the most fundamental models in quantum optics and has been extensively studied. The light-shift is an important phenomenon at the basis of many laser cooling mechanisms. In the presence of interaction, the combined system of an ‘atom plus light-field’ is often referred to as the ‘dressed atom’. The steady state temperature in Equation represents the minimum temperature that can be achieved with radiation pressure cooling and can be quite small.
The radiation pressure and laser cooling of a V-type three level atom in coherent fields in a squeezed vacuum are considered. From the Hamiltonian of the atomic system, making use of Born-Markoff approximation, the optical Bloch equations are derived. Using the adiabatic approximation, the expression of the mean dissipative force are acquired. The achievable equilibrium temperature is given by the quantum regression theorem and Einstein relation. The dependence of the spontaneous radiation pressure and ultimate temperature on quantum interference, average photon number and Rabi frequency are analyzed. The result shows that temperatures lower than the Doppler limit can be achieved.