Exact propagators for atom–laser interactions

Abstract

Abstract. A class of exact propagators describing the interaction of an N -level atom with a set of on-resonance δ-lasers is obtained by means of the Laplace transform method. State-selective mirrors are described in the limit of strong lasers. The ladder, V and Λ configurations for a three-level atom are discussed. For the two level case, the transient effects arising as result of the interaction between both a semi-infinite beam and a wavepacket with the on-resonance laser are examined. The spacetime propagator can be considered as one of the most important tools in quantum physics for it governs any dynamical process. However, the knowledge of propagators corresponding to non-quadratic Hamiltonians is severely restricted. In this line, the spacetime propagator for a δ-potential relevant to tunnelling problems has excited much attention [1,2,3,4,5]. Such interactions turn out to be particularly useful to gain physical insight in systems where only integrated quantities are to be considered. A thorough discussion of point interactions as solvable models using a functional approach can be found in [6], and a formalism to incorporate general pointinteractions and dealing with different boundary conditions has been developed by Grosche [7,8]. Even though the method is particularly suitable to calculate the energydependent Green function, a wide class of propagators was derived in such a fashion. The incorporation of time-dependent point-interactions has been possible through different approaches as Duru's method [9] or the use of integrals of motion [10]. However, most of the effort has been focused on the dynamics of structureless particles and to the knowledge of the authors no attention has been paid to problems involving internal levels. Such state of affairs contrasts dramatically with the current surge of activity in atom optics.In this paper we use the method of Laplace transform [4,5] to tackle particles with internal structure. In particular, we shall focus on exact propagators for atom-laser interactions, namely, those of an atom interacting with a set of δ-laser on-resonance with given interatomic transitions. The method is introduced in section 1 to obtain the exact propagator for a two-level atom. Details of the calculations relevant to the following sections are here provided. In section 2 the propagators for a ladder, V, and Λ configuration (see Fig. 1) of lasers interacting with a three-level atom are obtained. The

Comparison between two models of absorption of matter waves by a thin time-dependent barrier

“…In Ref. [22], an exact propagator was obtained describing the motion of an atom interacting with a point-like, δ-potential laser whose frequency was in resonance with a given interatomic transition. (The corresponding problem for a laser with a semi-infinite spatial extent was studied in Ref.…”

“…The wave function Ψ DPM admits analytical evaluation only in very few special cases. One such case is that of a time-independent potential, Ω(τ ) = Ω 0 [22]. Another exactly solvable case corresponds to Ω(τ ) = Ω 1 /τ , with Ω 1 being a constant; here, the exact propagator is obtained by first making the substitution ψ ± = ψ 1 ± ψ 2 to decouple Eq.…”

Quantum transients

“…In addition, the indefinite integral (which arises in tunneling problem through short-range potentials [110,17]) holds…”

“…The effects of an external linear potential (e.g. due to gravity) on the DIT phenomenon have also be taken into account [17]. The basic results on Moshinsky's shutter are reviewed in Section 2.…”

“…(Color online) Free expansion of the n = 1, 2, 4 eigenstates for a87 Rb atom released from a hard-wall trap of 10 µm, see Eq (17)…”