Shifting the phase of a coherent beam with a $$^{174}\hbox {Yb}^+$$ 174 Yb + ion: influence of the scattering cross section

Abstract

Birthdays often evoke memories of the one who is celebrating. Sometimes it is a single question they have asked you that has stuck in your mind for a long time. Of the many times I met Ted Hänsch one comes to my mind in particular. It was when I saw him in a corridor at the Max Planck Institute of Quantum Optics, about thirty years ago-the building was quite new at the time. I vividly remember the question he asked me: 'Do you have a good explanation why the cross section of an atom for scattering light is as large as it is?' He was referring to the classical on-resonance cross section of an atom, σ sc = 3 2 /2π, being so much largeri.e. many orders of magnitude-than the cross section of the atomic charge distribution. Naturally, I knew the phenomenon and answered that in scattering processes the larger of the two following values dominates: the cross section of the atom as a massive object or the cross section of the particle you send in to probe the atom, namely a photon in the case under consideration. Obviously, the smallest cross section of an optical beam is limited by diffraction and this, I had thought, should define the cross section of the photon. I was surprised to see that Ted Hänsch did not seem satisfied as he slowly turned away. At the time, this made me think, and throughout the years since then I have returned to this thought every now and then.Ten years later, after I moved to Erlangen, this 'thinking' became more intense when within my group we started to first discuss spontaneous emission and the possibility of observing its time-reversed counterpart. In spontaneous emission, the energy is initially concentrated in a tiny volume, which is orders of magnitude smaller than the wavelength cubed-partially still stored in the atom-and begins to travel outwards. At first, the energy is both in the evanescent and propagating components of the field. Then, Abstract We discuss and measure the phase shift imposed onto a radially polarized light beam when focusing it onto an 174 Yb + ion. In the derivation of the expected phase shifts, we include the properties of the involved atomic levels. Furthermore, we emphasize the importance of the scattering cross section and its relation to the efficiency for coupling the focused light to an atom. The phase shifts found in the experiment are compatible with the expected ones when accounting for known deficiencies of the focusing optics and the motion of the trapped ion at the Doppler limit of laser cooling (Hänsch and Schawlow in Opt Commun 13: [68][69] 1975 This article is dedicated to Theodor W. Hänsch at the occasion of his 75th birthday. We are grateful to him for all he has done for our field and we wish him all the best for the next 25 years.

Polarimetric nonregularity of evanescent waves

“…The rapid progress in nano-optics [1] and ever-growing interest toward complex structured light [2] have witnessed the need for a full three-dimensional (3D) treatment of polarization [3][4][5][6][7][8][9][10]. In particular, whereas for two-dimensional (2D) light, such as directional beams, the polarization ellipse is restricted to a plane, evanescent waves [11,12], optical surface fields [13,14], and tightly focused light [15][16][17] encompass 3D polarization states with the electric field fluctuating in three orthogonal directions. The polarization states of such genuine 3D light fields can be classified into regular and nonregular states according to the nature of their characteristic decomposition [18].…”

Extreme Concentration and Nanoscale Interaction of Light

“…But even with the highest numerical aperture readily available (NA = 0.95), two such lenses together will focus only 69% of the full solid angle. In comparison, just as an example, a deep parabolic mirror (see Figure ) with an opening angle of 46°, as in refs and , covers 82% of the full solid angle. The parabolic mirror serves as a mode converter, for example, converting a paraxial radially polarized cylindrical vector mode into a good approximation of an ingoing electric-dipole wave.…”

“…To this end, Paul and Fischer 86 studied how a single subwavelength dipole antenna (such as an atom) distorts the initially parallel energy flux lines of an incident plane wave. It is remarkable to see how, in the region around the atom, the flux lines are distorted to match an ingoing dipole wave, which also results in a scattering cross section much larger than the physical dimensions of the atom (see also the introduction of ref 80).…”

“…Pictorial view of a radially polarized cylindrical vector beam impinging onto a parabolic mirror. The parabolic mirror shown in the image has the same geometry as the mirrors used in refs and .…”

Memory-assisted long-distance phase-matching quantum key distribution

“…Mostly the entanglement was generated between the internal state of an atom/ion and its motional degree of freedom or with microwave radiation [36][37][38]. A few other experiments with atom-induced phase shifts were realized for electromagnetic radiation in the optical frequency domain [39,40].…”