Atom localization and center-of-mass wave-function determination via multiple simultaneous quadrature measurements

Abstract

We discuss localization and center-of-mass wave-function measurement of a quantum particle using multiple simultaneous dispersive interactions of the particle with different standing-wave fields. In particular, we consider objects with an internal structure consisting of a single ground state and several excited states. The transitions between ground and the corresponding excited states are coupled to the light fields in the dispersive limit, thus giving rise to a phase shift of the light field during the interaction. We show that multiple simultaneous measurements allow both an increase in the measurement or localization precision in a single direction and the performance of multidimensional measurements or localization. Further, we show that multiple measurements may relax the experimental requirements for each individual measurement.

Subwavelength position measurements with running-wave driving fields

“…Like in standing-wave localization schemes, each ratio R corresponds to several potential positions {z i } [29]. Previous localization schemes concluded that an additional classical measurement is required to determine the true position [18,22,29]. But our running-wave approach allows us to eliminate the need for an additional classical measurement, by choosing the laser field configuration such that |ξ | 1.…”

“…A particular class of subwavelength position measurement schemes is based on the spatial intensity modulation of standing-wave driving fields [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. Note that these schemes consider only single particles, which are well isolated from the environment.…”

“…For example, the atom could be located at a node of the standing-wave field, such that no direct detection is possible. Another disadvantage arises in recent schemes with improved localization that facilitate several position-dependent fields with different frequencies [29][30][31]. The frequency difference leads to a beat, and the relative light field intensities are not periodic in space on the wavelength scale.…”

Quantum atomic lithography via cross-cavity optical Stern–Gerlach setup

“…These OSG strategies differ from other measurement devices in quantum optics, such as quantum nondemolition [5] and homodyne techniques [6], that have been extensively explored from the 1990s until now [7]. More recently, a cross-cavity OSG has been proposed-where a beam of atoms is made to cross two orthogonal cavities-to measure the location and center-of-mass wave function of the atoms [8,9]. Although the cross-cavity OSG has not yet been implemented experimentally, the cross-cavity setup has been built to test Lorentz invariance at the 10 −17 level [10].…”

“…1, where, before entering the cavities, the atoms are confined by a circular pinhole to a small region of space centered around the superimposed nodes of the two cavity modes. Differently from the developments in [8,9], where dispersive atom-field interactions take place, we assume the two-level atoms undergo simultaneous and resonant interactions with two identical modes, one from each cavity, thus being deflected in the plane defined by the two mutually perpendicular cavities' optical axes. An appropriate ansatz on the spatial distribution of the atoms across the pinhole enables us to derive an analytical expression for the atomic momentum distribution after the atom-field interactions.…”