The canonical commutation relation is a cornerstone of quantum theory and underlies the Heisenberg uncertainty principle. Although uncertainty relations have been extensively tested, direct verifications of the underlying commutation relation itself have remained elusive. We report an experimental demonstration of the bosonic commutation relation for optical field operators based on measurements of two distinct intensity correlation functions. From these measurements, we extract the expectation value of the field-operator commutator for both a single-photon state and coherent state. In both cases, the measured values are consistent with unity, in quantitative agreement with quantum theory.

We report on a simple and easy to implement method of feedback cooling trapped ions to temperatures below those achievable using only Doppler cooling. Additionally, the feedback cooling results in significantly shorter cooling times. For selected parameters, we demonstrate cooling to temperatures below h & strns;P/2kB. The motion of a single ion is monitored in real time, allowing for the generation of a feedback signal that is applied to an auxiliary trap electrode. Motion detection is implemented by imaging the fluorescence photons emitted by the ion onto a knife edge and detecting the transmitted light, a method used so far to cool trapped nanoparticles. The intensity modulation of the fluorescence resulting from the ion motion is used to generate and apply the feedback signal and also to determine the ion temperature. While the method benefits from a high rate of detected scattered photons, which can be a challenge, and which we address by using a parabolic mirror for collecting the fluorescence, we expect the method to also be applicable when using lenses with moderate numerical apertures.

We report on the first feedback cooling of a single trapped ion below the Doppler limit of /2 k_B. The motion of a single ion is monitored in real-time and cooled up to 9-times below the Doppler cooling temperature by applying electronic feedback. Real-time motion detection is implemented by imaging the fluorescence photons emitted by the ion onto a knife edge and detecting the transmitted light, a method used so far to cool trapped nanoparticles. The intensity modulation of the fluorescence resulting from the ion motion is used to generate and apply the feedback signal and also to determine the ion temperature. The method benefits from a high rate of detected scattered photons, which can be a challenge, and which we address by using a parabolic mirror for collecting the fluorescence.

Experiments and their interpretation on polarization dynamics and polarization switching in vertical-cavity surface-emitting lasers operated in the fundamental transverse mode regime are reviewed. Important observations are switching events to a mode with the lower unsaturated gain and the existence of elliptically polarized dynamical transition states after the destabilization of the low-frequency polarization mode. The observations demonstrate the need to consider explicitly the phase properties of the optical field as well as nonlinear effects affecting polarization selection above threshold. Good qualitative agreement is found with a model which takes into account the spin degrees of freedom of the light field as well as of the carriers (`spin-flip model'), if the spin-flip rate is taken to be some tens of 10^9 s^-1. This constitutes a strong – though indirect – indication that spin dependent processes are important in polarization selection in the devices investigated.

Concentrating light strongly calls for appropriate polarization patterns of the focused light beam and for up to a full 4π solid angle geometry. Focusing on the extreme requires efficient coupling to nanostructures of one kind or another via cylindrical vector beams having such patterns, the details of which depend on the geometry and property of the respective nanostructure. Cylindrical vector beams can not only be used to study a nanostructure, but also vice versa. Closely related is the discussion of topics such as the ultimate diffraction limit, a resonant field enhancement near nanoscopic absorbers, as well as speculations about nonresonant field enhancement, which, if it exists, might be relevant to pair production in vacuum. These cases do require further rigorous simulations and more decisive experiments. While there is a wide diversity of scenarios, there are also conceptually very different models offering helpful intuitive pictures despite this diversity.

The prospects of employing a deep parabolic mirror as a focusing device for trapping neutral atoms in an optical dipole trap are evaluated. It is predicted that such a dipole trap will result in a deep trapping potential as well as in a small spatial spread of the atom's center of mass wave function already for a Doppler cooled atom. This strong confinement is beneficial for many applications, one of which is the increase of the interaction strength between an atom and a light field focused from full solid angle.

We investigate the emission of single photons from CdSe/CdS dots-in-rod which are optically trapped in the focus of a deep parabolic mirror. Thanks to this mirror, we are able to image almost the full 4π emission pattern of nanometer-sized elementary dipoles and verify the alignment of the rods within the optical trap. From the motional dynamics of the emitters in the trap, we infer that the single-photon emission occurs from clusters comprising several emitters. We demonstrate the optical trapping of rod-shaped quantum emitters in a configuration suitable for efficiently coupling an ensemble of linear dipoles with the electromagnetic field in free space.

The smallest possible focus is achieved when the focused wave front is the time reversed copy of the light wave packet emitted from a point in space (S. Quabis et al., Opt. Commun. 179 (2000) 1-7). The best physical implementation of such a pointlike sub-wavelength emitter is a single atom performing an electric dipole transition. In a former paper (N. Lindlein et al., Laser Phys. 17 (2007) 927-934) we showed how such a dipole-like radiant intensity distribution can be produced with the help of a deep parabolic mirror and appropriate shaping of the intensity of the radially polarized incident plane wave. Such a dipole wave only mimics the far field of a linear dipole and not the near field components. Therefore, in this paper, the electric energy density in the focus of a parabolic mirror is calculated using the Debye integral method. Additionally, a comparison with conventional nearly 4pi illumination using two high numerical aperture objectives is performed. The influence of aberrations due to a misalignment of the incident plane wave is discussed.

We present a technique based on high resolution imaging to measure the absolute temperature and the heating rate of a single ion trapped at the focus of a deep parabolic mirror. We collect the fluorescence light scattered by the ion during laser cooling and image it onto a camera. Accounting for the size of the point-spread function and the magnification of the imaging system, we determine the spatial extent of the ion, from which we infer the mean phonon occupation number in the trap. Repeating such measurements and varying the power or the detuning of the cooling laser, we determine the heating rate induced by any kind of effect other than photon scattering. In contrast to other established schemes for measuring the heating rate, the ion is always maintained in a state of thermal equilibrium at temperatures close to the Doppler limit.

We investigate the nonlinear optical process of third-harmonic generation in the thus far unexplored regime of focusing the pump light from a full solid angle, where the nonlinear process is dominantly driven by a standing dipole-wave.We elucidate the influence of the focal volume and the pump intensity on the number of frequency-tripled photons by varying the solid angle from which the pump light is focused, finding good agreement between the experiments and numerical calculations.As a consequence of focusing the pump light to volumes much smaller than a wavelength cubed the Gouy phase does not limit the yield of frequency-converted photons.This is in stark contrast to the paraxial regime.We believe that our findings are generic to many other nonlinear optical processes when the pump light is focused from a full solid angle.

Direct aluminium surface figuring is succeeded for the first time up to 1 µm in height while preserving surface roughness. Sub-aperture reactively-driven ion beam tools allow ultra-precision figure error-correction of aspherical and freeform mirrors.

Focusing with a 4$π$ parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror's fabrication process and might introduce errors that reduce the focusing quality. To determine these errors, we experimentally examine the focusing properties of a 4$π$ parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single $^{174}$Yb$^{+}$ ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap. We demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface. Our findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4$π$ parabolic mirror.

We discuss and measure the phase shift imposed onto a radially polarized light beam when focusing it onto an \(^{174}\text {Yb}^{+}\) 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).

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text L. Alber, M. Fischer, B. Srivathsan, M. Weber, M. Sondermann, and G. Leuchs, "Quantum controlled phase shift with a single 4π mirror," in Frontiers in Optics 2016, OSA Technical Digest (online) (Optica Publishing Group, 2016), paper FF5D.2. Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article

Optical dipole-traps are used in various scientific fields, including classical optics, quantum optics and biophysics. Here, we propose and implement a dipole-trap for nanoparticles that is based on focusing from the full solid angle with a deep parabolic mirror. The key aspect is the generation of a linear-dipole mode which is predicted to provide a tight trapping potential. We demonstrate the trapping of rod-shaped nanoparticles and validate the trapping frequencies to be on the order of the expected ones. The described realization of an optical trap is applicable for various other kinds of solid-state targets. The obtained results demonstrate the feasibility of optical dipole-traps which simultaneously provide high trap stiffness and allow for efficient interaction of light and matter in free space.

We demonstrate the controlled creation of a Yb-174(2+) ion by photo-ionizing Yb-174(+) with weak continuous-wave lasers at ultraviolet wavelengths. The photo-ionization is performed by resonantly exciting transitions of the Yb-174(+) ion in three steps. Starting from an ion crystal of two laser-cooled Yb-174(+) ions localized in a radio-frequency trap, the verification of the ionization process is performed by characterizing the properties of the resulting mixed-species ion-crystal. The obtained results facilitate fundamental studies of physics involving Yb2+ ions.

Efficient coupling of light to single atomic systems has gained considerable attention over the past decades. This development is driven by the continuous growth of quantum technologies. The efficient coupling of light and matter is an enabling technology for quantum information processing and quantum communication. And indeed, in recent years much progress has been made in this direction. But applications aside, the interaction of photons and atoms is a fundamental physics problem. There are various possibilities for making this interaction more efficient, among them the apparently 'natural' attempt of mode-matching the light field to the free-space emission pattern of the atomic system of interest. Here we will describe the necessary steps of implementing this mode-matching with the ultimate aim of reaching unit coupling efficiency. We describe the use of deep parabolic mirrors as the central optical element of a free-space coupling scheme, covering the preparation of suitable modes of the field incident onto these mirrors as well as the location of an atom at the mirror's focus. Furthermore, we establish a robust method for determining the efficiency of the photon-atom coupling.