We investigate the diffraction of a three-level atom from a "walking" light wave composed of counterpropagating traveling waves of different frequencies. The coupling of the two nondegenerate internal ground states by means of an off-resonant Raman transition resonantly couples the initial external momentum state to only one other momentum state. This happens even in the Raman-Nath regime, where the interaction time is short enough that momentum transfer is not constrained by phase-matching conditions. The final momentum state depends on the initial internal state of the atom and the relative directions of the two traveling waves. By using multiple diffraction regions, this process can be used to coherently split a beam of atoms into two beams that are widely separated in momentum space. This type of beam splitter would be useful in the building an atom interferometer.
We investigate the diffraction of a three-level atom from a "walking" light wave composed of counterpropagating traveling waves of different frequencies. The coupling of the two nondegenerate internal ground states by means of an off-resonant Raman transition resonantly couples the initial external momentum state to only one other momentum state. This happens even in the Raman-Nath regime, where the interaction time is short enough that momentum transfer is not constrained by phase-matching conditions. The final momentum state depends on the initial internal state of the atom and the relative directions of the two traveling waves. By using multiple diffraction regions, this process can be used to coherently split a beam of atoms into two beams that are widely separated in momentum space. This type of beam splitter would be useful in the building an atom interferometer.
This chapter discusses the basic physics of atom diffraction. Starting with a short review on the diffraction of light, we describe the absorption of photons by an atom and its subsequent emission, where the atom to changes its momentum and internal state. Assuming a two-level atom, we describe the coherent interactions of atoms with light, showing its effect on the ground state of the atoms. We further illustrate how the light impacts forces on the atom that can be used for trapping it in the light field. Next, we discuss Bragg diffraction of atoms, where the internal state of an atom is unchanged after diffraction. Here the external motional state of the atom is put in a linear superposition of its movement. Finally, we describe the diffraction of atoms by Raman pulses, where the internal state of the atom is changed after diffraction, while achieving directed motion.
In a recent experiment (Wang et al., e-print cond-mat/0407689), it was observed that a sequence of two standing-wave square pulses can split a Bose-Einstein Condensate at rest into $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\hbar}\mathbf{k}$ diffraction orders with almost 100% efficiency. By truncating the Raman-Nath equations to a two-state model, we provide an intuitive picture that explains this double-square-pulse beam-splitter scheme. We further show it is possible to optimize a standing-wave multiple-square-pulse sequence to efficiently diffract an atom at rest to a symmetric superposition of $\ifmmode\pm\else\textpm\fi{}2n\ensuremath{\hbar}\mathbf{k}$ diffraction orders with n>1. The approach is considered to be qualitatively different from the traditional light-pulse schemes in the Bragg or the Raman-Nath region, and can be extended to more complex atomic optical elements that produce various tailored output momentum states from a cold atom source.
The diffraction of the wave packet of a three-level atom in a multifrequency optical radiation field is studied. A new type of coherent beam splitter for atoms that employs the scattering of a wave packet in the field of four standing light waves with different spatial shifts is proposed on this basis. It is shown that this interaction scheme makes it possible to obtain large splittings (>100ℏ k ) of the wave packet of a three-level Λ atom in momentum space into only two coherent components. In addition, the atoms in these coherent components are in long-lived atomic states, which substantially simplifies the experimental implementation of such a splitter.
We study the deflection of an atomic system with a resonant multilevel energy structure in classical and quantized wave light fields. We obtain that the shape of the momentum distribution is very sensitive to the energy level structure, whereas its moments are not. Comparison with a two-level case is made. PACS: 32.80, 33.80, 42.50 During the last two decades a remarkable development in mechanically manipulating atomary particles with resonant laser light has taken place (for a review, see for example [1, 2] and references therein). In addition to trapping and cooling of particles, the deflection of particles by a laser beam offers interesting possibilities, for example, to construct atomic interferometers or beam splitters [2-4]. This problem has been studied extensively both theoretically [2, 5, 8] and experimentally [9-12]. The fact that the momentum distribution caused by the scattering is connected to the quantum statistical properties of the scattered light has been known for some time [13]. Recently, one has also realized that the quantum statistics of the light causing the scattering can be important [14]. At low photon numbers, for example, the initial field state strongly influences the resulting momentum distribution. A related effect is that a standing wave and two counterpropagating traveling plane waves of equal emplitudes cause a different diffraction pattern when fields are treated quantum mechanically [15]. Most previous work on the deflection of particles by light fields used two-level atoms. In this paper we study how resonant multilevel systems scatter when they traverse a plane wave. In practical applications, molecules or highly excited atoms have similar energy structures as the models we use in this work. In most cases, we assume that the Raman-Nath regime is valid, i.e., the kinetic energy of the particle can be neglected. However, the field coupling is assumed to be sufficiently strong to make multiple scattering events possible. Our results show that the final momentum distribution of a multi-level system can strongly deviate from that of a two-level atom. It is of interest that the momentum distributions for resonant ladder systems are in general superpositions of few or several distributions similar to that of a two-level system. We also study the expectation values related to the momentum distribution and show that the spread in momentum is remarkably independent of the system considered. The absorption and reabsorption of photons during the scattering process causes the photon distribution to be smoothed out, and for long times a steady state is reached. The cases we studied did not show a creation of sub-Poissonian light. Our model and assumptions are described and discussed in Sect. 1. Some of the general properties of the momentum distribution are discussed in Sect. 2. In Sect. 3 we derive the generating function of the moments of momentum change in Raman-Nath regime. The main part of the paper is contained in Sects. 4 and 5, in which the momentum distribution itself is discussed for several model systems. In Sect. 4 a semiclassical field is assumed and in Sect. 5 a quantum field is used. The effects of the scattering on the field photon statistics are studied in Sect. 6. The final discussion of the results is given in Sect. 7.
A new type of atomic interferometer is discussed, in which atoms with two ground-state Zeeman sub-levels m = ± 1, and an excited state with m = 0, pass through three laser interaction zones—each comprising two counter-propagating waves of opposite circular polarization with a large detuning from resonance. By means of Raman-type transitions between the two ground-state levels, which convey a recoil of two photon momenta, the atomic wave function is split up into two coherent spatially separated branches, and subsequently recombined. In this system, conservation of energy and momentum leads to a strong correlation between the external centre of mass motion and internal magnetic degrees of freedom. As a consequence, the paths within the interferometer are tagged by the internal quantum number m. As an example, we calculate the position and momentum distribution function of a helium atom on its way through the interferometer.
The Bloch-state approach to atomic translational states is extended out of adiabatic following and Raman–Nath approximations, taking into account the possible transfer of population from the initially populated internal energy level. The presented theory suggests a notion of potential energy corresponding to the initially populated internal state, and makes a generalization in the treatment of energy spectrum band-gap structure. Applying the theory to off-resonant Kapitza–Dirac diffraction and two-pulse standing wave atom interferometer (for the study of non-coherent processes in the cold atomic gases) we discuss the ability of the present approach for large-angle split multipath atom interferometry.