Single photons emitted by nano-crystals optically trapped in a deep parabolic mirror Vsevolod Salakhutdinov,1, 2 Markus Sondermann,1, 2, ∗ Luigi Carbone,3 Elisabeth Giacobino,4, 2 Alberto Bramati,4 and Gerd Leuchs2, 1, 5 1Friedrich-Alexander-Universit¨atErlangen-N¨urnberg (FAU), Department of Physics, Staudtstr. 7/B2, 91058 Erlangen, Germany 2Max Planck Institute for the Science of Light, Staudtstr. 2, 91058 Erlangen, Germany 3CNR NANOTEC-Institute of Nanotechnology c/o Campus Ecotekne, University of Salento, via Monteroni, Lecce 73100, Italy 4Laboratoire Kastler Brossel, Sorbonne Universit´e,CNRS, ENS-PSL, Research University, Coll`egede France, 4 place Jussieu,case 74 F-75005 Paris, France 5Department of Physics, University of Ottawa, Ottawa, Ont. K1N 6N5, Canada We investigate the emission of single photons from CdSe/CdS dot-in-rods 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. a. Introduction Nano-scale light sources are used the c-axis of the rod [5, 8, 9]. Hence, the rod has to in many areas of research and applications. Examples be aligned along the optical axis of the PM for maxi- range from the use of fluorescent nano-beads in mi- mizing the collection efficiency. This should occur in a croscopy to the role of various nanometer-sized solid- natural way in an optical trap that is built by focusing state systems as sources of single photons in future a radially polarized beam as in Ref. [2]: The electric quantum technology applications. One approach to field in the focus of the PM is purely longitudinal, efficiently collect the emitted photons is to place the i.e. parallel to the PM axis. Since the polarizabil- source at the focus of a parabolic mirror (PM) span- ity of a rod is largest along its symmetry axis [10], ning a huge fraction of the full solid angle. Such a the DR should thus be aligned along the optical axis mirror has been used to study a laser cooled atomic of the PM. However, when trapping the particle un- ion held in a radio-frequency trap in vacuum [1]. More der ambient conditions, this alignment is counteracted recently, the optical trapping of CdSe/CdS dot-in- by random collisions with air molecules which exert a rod particles in a deep PM in air has been demon- random torque on the DR (see, e.g. Refs. [11, 12]). strated [2], and lately also the fabrication of a micro- Thus, the torque induced by the trapping laser onto scopic diamond PM around a nitrogen vacancy cen- the rod has to be larger than this random torque in tre [3]. order to achieve a good alignment of the rods. CdSe/CdS dot-in-rod (DR) particles have the re- The purpose of this work is two-fold: One aspect markable properties of being single-photon emitters at is checking the orientation of the DRs with respect to room temperature as well as emitting light with a high the optical axis of the PM. This is done by analyzing degree of linear polarization [4]. The latter property the spatially resolved pattern of the photons emitted stems from the fact that their emission is dominated by CdSe/CdS DR-particles. Since the rods' alignment by a linear-dipole transition [5]. In order to maximize is governed by their geometry and independent of the the collection efficiency when using a PM, the axis small CdSe core, our results should be applicable for of the linear dipole has to be aligned with the mir- many types of rod-shaped quantum emitters. In this ror's optical axis [6, 7]. Once this is achieved, a PM sense, the CdSe/CdS DR-particles can be considered with the geometry used in Refs. [6, 7] as well as here as a proof model. We again emphasize that a favor- arXiv:1905.09108v2 [quant-ph] 14 Jan 2020 collimates 94% of the emission of a linear dipole, ex- able alignment of a rod-shaped quantum-system is a ceeding the capabilities of a realistic lens-based set-up mandatory prerequisite for efficient photon collection by a factor of two. Moreover, the same requirement as well as for efficient excitation. has to be fulfilled when reversing this scenario, i.e. The other aspect treated here is specific to the when focusing a linear-dipole mode with the purpose CdSe/CdS DR-particles. We will show that clusters of exciting a single quantum emitter with high effi- of DRs can act as a source of single photons. As a ciency [6]. Any tilt of the quantization axis off the matter of fact, it will turn out that indeed all single- PM's axis will lead to a reduced field amplitude along photon sources observed in our experiment are consti- the transition dipole moment of the target. tuted by clusters of emitters. The emission of single For CdSe/CdS DR particles, the dipole-moment of photons from clusters of DRs demonstrated here is in the excitonic transition is found to be aligned along good agreement with recent observations of the same phenomenon for CdSe/CdS core-shell dots [13]. b. Experimental procedure The CdS/CdSe DR- particles investigated here consist of a spherical CdSe ∗ [email protected] core with 2:7 nm diameter. The core is embedded in a 2 CdS rod with a nominal length of 35nm and diameter of 7 nm. Fluorescent photons are emitted at wave- lengths about λDR = 605 nm. The DRs are trapped at ambient conditions in air at the focus of a deep parabolic mirror in an optical dipole-trap (see Ref. [2] and Fig. 3 in appendix for details). The electric field at wavelength λtrap = 1064 nm in the focal region is polarized along the optical axis of the PM, which is here defined as the z-direction. At the beginning of each experiment the power of the trapping laser is set to 360mW and the pulsed ex- citation beam is switched off. Successful trapping of DR particles is witnessed by the onset of a fluorescence signal and from scattered trap light. The fluores- cence is detected with a pair of avalanche photo-diodes (APDs). At this stage, fluorescence photons stem from two-photon excitation at λtrap [2]. To determine the intensity auto-correlation function g(2)(t = 0), the power of the trapping laser is reduced such that the count rate of photons on the APDs is hidden in the background noise. Then, more efficient pulsed excita- tion at λexc = 405 nm is switched on and the value of g(2)(t = 0) is measured. (2) In case that g (0) < 0:5 is observed, i.e. the sig- Figure 1. (a) Normalized second-order intensity cor- nature of single-photon emission, the experiment is relation g(2)(0) of fluorescence photons emitted by DRs continued as follows: Images of the spatial intensity against power Pmin at which the particles escaped the distributions of fluorescence photons as found in the trap. Error bars show the Poissonian uncertainty. Green output aperture of the PM (see example in Fig. 2) are circles denote experiments in which the spatial inten- acquired with an electron-multiplying charge-coupled sity pattern revealed azimuthal symmetry and an obvious alignment of the rods to the axis of the PM. A single such device (EMCCD) camera at several trapping beam (2) powers. For each power setting we have averaged over data point with Pmin = 22 mW and g (0) = 0:19 is off scale. Orange squares correspond to cases where the emis- several images, with an exposure time of 2 s per im- sion pattern shows a clear azimuthal asymmetry. Black age. Vertically and horizontally polarized components triangles mark experiments with an inconclusive outcome. are recorded simultaneously on different parts of the The inset shows a magnified view for low power levels. (b) camera chip. Damping rate of axial motion Γz of trapped nano-particles Next, the trapping beam power is set again to against Pmin. Error bars denote the 95% confidence inter- 360 mW and the motional dynamics of the parti- val of the fit from which Γz was obtained. The dashed 0:48±0:03 cles in the trap is analyzed. The light scattered line denotes the function Γz / Pmin , with the power and Doppler-shifted by the particle interferes with scaling obtained from a fit. The inset is a pictorial view of the trapping light [14]. The corresponding interfer- a cluster of rods aligned along the optical axis of the PM ence signal is measured with a balanced detector (cf. (z-axis). The yellow disc with radius rz denotes the effec- Ref. [2]). From the time series of this signal we com- tive area of the cluster relevant for damping the motion along the z-axis. pute the power-spectral density which contains several Lorentzian-shaped features, each of which corresponds to the motion of the particle in the trap along a cer- detector. tain direction. The width Γi (i = x; y; z) of each of c. Single-photon emission from clusters In our these peaks is proportional to the ratio ri=m, where ri experiments, we observed g(2)(0) < 0:5 for 33 differ- is the radius of the trapped object and m its mass [15].