Three-dimensional atom localization by laser fields in a four-level tripod system

Abstract

We present a scheme of the high-precise three-dimensional (3D) localization by the measurement of the atomic-level population. The scheme is applied to a four-level tripod-type atom coupled by three strong standing waves and a probe running wave. As a result, the atom can be localized in volumes that are substantially smaller than a cubic optical wavelength. The upper-level distribution depends crucially on the atom-field coupling and it forms 3D periodic structures composed of spheres, hourglasses, bowls, donuts, or deformed barrels.PACS numbers: 42.50. Gy, 42.50.Nn, 42.50.Wk, 42.50.St The concept of Heisenberg microscope [1] demonstrates that atoms can not be localized using light within the optical half-wavelength unless one takes advantage of the internal structure of atoms. One approach is to obtain spatially changing structures in level populations in a cloud of atoms. Motivated e.g. by possible applications in atomic nanolithography [2], different methods for going beyond this limit have been proposed over the years, including the measurement of the atomic resonance frequency [3][4][5], the phase shift [6][7][8], or the atomic dipole [9]. The highest theoretical localization degrees have been demonstrated in schemes that rely on measuring either spontaneous emission [10][11][12] or a level population [13,14] of an atom moving through a resonant standing wave.In general, as a proof-of-principle, one-dimensional systems have been very popular, see e.g. the recent studies [15][16][17][18][19][20]. Studies of atomic systems in two dimensions have also been numerous recently [21][22][23][24][25][26][27][28][29][30][31][32]. It is important to note that in 2D, one can obtain, in addition to mere subwavelength localization, further spatial structuring of the atomic locations, see e.g. [33]. A key question is whether localization and structuring can be obtained also in 3D, and what kind of structures can appear. Possible applications may include high-precision position-dependent chemistry without a real change in the atomic distribution, combining state-selective localization with state-selective chemical reactions. In addition, 3D structuring produces a wide variety of practical realizations of such chemical reactions, demonstrating the necessity of reliable methods for the prediction of localization structures. For any realistic scheme one needs to carefully consider the atomic structure and to include spontaneous emission. Previously 3D localization has been discussed in a five-level system without taking the geometry of the atomic dipole coupling into account [34]. We show that 3D localization is realistically possible with only four atomic levels in a tripod scheme, and that one obtains interesting structures around points of localization by simple tuning of the parameters of the localizing fields.We consider the 87 Rb D 2 line (the 5 2 S 1/2 → 5 2 P 3/2 transition), which is only thought as a possible example of tripod system with three ground states |F = 1, m F (m F = −1, 0, 1) and upper state |F = 0, m...

Precision localization of single atom via spontaneous emission in three dimensions

“…It is found that the precision and resolution of the 3D atom localization can be significantly improved due to the spacedependent atom-field interaction. More importantly, the 3D atom localization patterns reveal that the maximal probability of finding an atom within the sub-half-wavelength domain of the standing waves can reach 100 %, which is increased by a factor of 4 or 8 compared with the previous proposed schemes [35,36]. As a result, our scheme may be helpful in realizing spatially selective single-qubit phase gate, entangling gates between cold atoms, and error budget for the single-qubit phase gate in three dimensions.…”

“…In order to deal with the above problem, here we put forward a scheme to realize efficient 3D atom localization based on the measurement of spontaneous emission in a three-level atomic system. The work is mainly based on [35,36]; however, our scheme shows more advantages that the two schemes do not have. First, we show that efficient 3D localization is realistically possible with only three atomic levels, and that one obtains interesting patterns around points of localization by a simple tuning of the parameters of the system.…”

“…First, we show that efficient 3D localization is realistically possible with only three atomic levels, and that one obtains interesting patterns around points of localization by a simple tuning of the parameters of the system. Second, owing to the space-dependent atom-field interaction, the atom can be localized at a particular position, and the maximal probability of finding the atom in one period of the standing-wave fields reaches 100 %, which is the main advantage compared with the previous schemes [35,36]. Third, we can improve the localization precision and spatial resolution of the atom under certain conditions, which provide a possibility of making the atom localized at a given position by varying the system parameters in 3D space.…”

“…More recently, two schemes [35,36] have also been discussed about the threedimensional (3D) atom localization in five-level and four-level atomic systems, respectively. However, to the best of our knowledge, the maximum probability of finding an atom at a particular position in a wavelength domain is very low in these schemes; see, e.g., in the recent work [34], the maximum probability of finding an atom at a particular position in a wavelength domain is 1/8.…”

Phase-sensitive atom localization for closed-loop quantum systems

“…A four-level tripod-type atomic system is also proposed to achieve a high-precision two-dimensional atom localization via measurement of the excited state population [40]. Yet the three-dimensional (3D) atom localization has been investigated only in few proposals [43][44][45]. Compared to the 1D and 2D localization, the 3D localization of an atom gives a more specific information about the position of a moving atom.…”