Monitoring the dipole-dipole interaction via quantum jumps of individual atoms

Abstract

The emission characteristics in the fluorescence of two laserdriven dipole-dipole-interacting three level atoms is investigated. When the light from both atoms is detected separately a correlation of the emission processes is observed in dependence of the dipole-dipole interaction. This opens the possibility to investigate the dipole-dipole interaction through the emission behavior. We present Monte-Carlo simulations which are in good agreement with the analytic solutions.PACS numbers: 42.50. Fx, 42.50.Lc, 42.50.Ar The problem of the influence of a neighboring atom on atomic emission behavior [1][2][3][4] has been investigated since a very long time. Especially the problem of the correlation of the emission of two neighboring atoms has found quite some interest [5][6][7]. This is a complex issue and the answer is very much dependent on various system parameters such as the strength of the pumping field, the life times and the wavelengths of the different transitions involved. An early theoretical calculation concluded that the dipole-dipole interaction between adjacent atoms is irrelevant for quantum jumps within a 3-level-system under the usual experimental conditions where the Rabi frequency of the pump field is large compared to all other rates in the problem [8,9]. Those results have been confirmed by quantum Monte-Carlo calculations [10][11][12], [13]. In this paper we reconsider the problem of dipole-dipole interaction and investigate especially the correlations in the emissions of two neighboring atoms which are observed individually. The arrangement is shown schematically in Fig. 1. We consider 2 identical nearby atoms in a trap, each with levels |1 , |2 and |3 . One of the atoms (say atom 1) is initially prepared, e.g. by pulsed excitation [14], in a metastable state |2 . A resonant cw pump interacts with both atoms. The initial state of atom 1 is such that it can start interacting with the pump either due to decay to the state |3 by emission of a photon or via excitation to the state |1 as a result of the dipole-dipole interaction. In the second case atom 2 goes to the state |2 . In our analysis we assume that the level spacing |1 ↔ |2 is close enough, so that the dipole-dipole interaction is effective only on this transition. The transitions |1 ↔ |3 and |2 ↔ |3 are supposed to lie in the optical domain, where the distance between two atoms is assumed to be much larger than the wavelengths of the corresponding transitions. For example in In + the wavelength on the |1 ↔ |2 corresponds to 9.3µm which could be two to three times the distance between two trapped ions [15]. We further assume that the fluorescence from each atom can be resolved individually by two distinct detectors 1 and 2. In what follow let us work in the limitIn our prepared system, detector 1 will not detect any fluorescence while atom 2 is fluorescing on the |1 ↔ |3 transition until the dipole-dipole interaction on the transition |1 ↔ |2 brings atom 1 towards the cycling transition |1 ↔ |3 and atom 2 towards the metastable state |2 ...

Double scattering of intense laser light by two atoms

“…In the case of two distant atoms, corresponding to the experimentally realistic case of a dilute atomic medium, however, the classical modeling is perfectly adequate -at least in order to describe the intensity of the atomic radiation. Whether an appropriately extended pump-probe approach could also be able to reproduce intensity-intensity correlations [26,31] is a subject for future studies.…”

Beating Difraction Limit using Dark States

“…Typically, this scheme will be limited by the difficulties in fixing the positions of the two atoms rather than by constraints of the measurement scheme itself, which in principle allows one to achieve resolution far below the classical Rayleigh limit of optical microscopy technology. In addition to the fluorescence spectrum, also the intensity-intensity correlation function of the light emitted by a collection of two-and three-level atom systems subject to driving fields has been investigated [31,32,37,38,39]. Most of these works, however, focused on nonclassical properties of the emitted field.…”

“…The location of the fringes is given by , or (34) Using kd 1, the position of the first fringe can be given by (35) Minimal distance between molecules can be found at the given accuracy of measurement of fringe position as (36) where ε =δ x p /x p . While the change of distance between molecules can be measured much more accurately, namely (37) where we introduce a function (38) optimizing the Rabi frequency of the drive laser field we obtain (39) for Ω D = π /( 5 −1). Thus optimize driving field we obtain In addition, assume that we can measure the ratio with ε = 1% accuracy (44) Interesting feature of the microscope is that it has high sensitivity to small changing of the distance between molecules.…”

Interference of Spontaneously Emitted Photons

“…For a more detailed discussion of interference criteria see also Refs. [4,6,7] and references therein.…”

“…Since then the interpretation of this experiment has attracted continuous interest (see for instance Ref. [4,5,6,7] and references therein). This is mainly due to its simplicity together with the fundamental quantum mechanical issues it deals with.…”