Resonant excitation of a single self-assembled quantum dot can be achieved using an excitation mode orthogonal to the fluorescence collection mode. We demonstrate a method using the waveguide and Fabry-Perot modes of a planar microcavity surrounding the quantum dots. The method allows complete freedom in the detection polarization.
The ability to perform simultaneous resonant excitation and fluorescence detection is important for quantum optical measurements of quantum dots (QDs). Resonant excitation without fluorescence detection – for example, a differential transmission measurement – can determine some properties of the emitting system, but does not allow applications or measurements based on the emitted photons. For example, the measurement of photon correlations, observation of the Mollow triplet, and realization of single photon sources all require collection of the fluorescence. Incoherent excitation with fluorescence detection – for example, above band-gap excitation – can be used to create single photon sources, but the disturbance of the environment due to the excitation reduces the indistinguishability of the photons. Single photon sources based on QDs will have to be resonantly excited to have high photon indistinguishability, and simultaneous collection of the photons will be necessary to make use of them. We demonstrate a method to resonantly excite a single QD embedded in a planar cavity by coupling the excitation beam into this cavity from the cleaved face of the sample while collecting the fluorescence along the sample's surface normal direction. By carefully matching the excitation beam to the waveguide mode of the cavity, the excitation light can couple into the cavity and interact with the QD. The scattered photons can couple to the Fabry-Perot mode of the cavity and escape in the surface normal direction. This method allows complete freedom in the detection polarization, but the excitation polarization is restricted by the propagation direction of the excitation beam. The fluorescence from the wetting layer provides a guide to align the collection path with respect to the excitation beam. The orthogonality of the excitation and detection modes enables resonant excitation of a single QD with negligible laser scattering background.
Resonant excitation of a single quantum emitter combined with fluorescence detection was a long-term experimental challenge mainly due to the inability to spectrally discriminate the weak fluorescence from the strong excitation scattering. This difficulty, however, has been successfully overcome in the past decade by two different approaches: dark-field confocal excitation based on polarization discrimination1,2,3,4,5, and orthogonal excitation-detection based on spatial mode discrimination6,7,8,9,10,11,12,13,14. Both approaches demonstrate a strong capability to significantly suppress laser scattering and thus are widely adopted in various experiments, for example, observation of spin-photon entanglement5,15,16, demonstration of dressed states2,7,12,17,18,19,20,21,22,23,24,25,26, and coherent manipulation of confined spins3,27,28,29,30. Neither approach can be universally applied to every situation; each is limited to some specific conditions. The dark-field technique utilizes the polarization degree of freedom of photons to suppress the excitation laser scattering. This technique has several advantages. For example, there is no requirement for a well-defined waveguide mode, which enables confocal-only implementation. The confocal implementation allows for circularly polarized excitation and possibly tighter focus of the excitation beam at the quantum emitter, resulting in higher excitation intensity. However, this polarization-selective method restricts the detection polarization to be orthogonal to the excitation polarization, and thus prevents a complete characterization of the polarization properties of the fluorescence. In comparison, spatial mode discrimination preserves the complete freedom of detection polarization by utilizing the orthogonality between the propagation modes of excitation and detection beams to suppress the laser scattering4. The constraints of this technique are the necessity of a waveguide structure in the sample to provide an excitation mode orthogonal to the detection mode, and the restriction of the excitation polarization to be perpendicular to the propagation direction of the beam.
Here, we demonstrate a protocol for constructing a free-space-based orthogonal excitation-detection setup for resonance fluorescence experiments. Compared to the pioneering work on spatial mode discrimination where an optical fiber was used to couple light into the cavity6, this protocol provides a solution in free space, and does not require kinetic components to mount either the sample or the fiber in cryostat. Fine control of the directions of the excitation beam and the detection path are manipulated by optics external to the cryostat, while aspheric singlet lenses act as focusing objectives inside the cold region of the cryostat. We provide representative images of the key alignment steps in the process of achieving resonant excitation and detection of fluorescence from a single quantum dot.
The sample used for this demonstration is grown by molecular beam epitaxy (MBE). The InGaAs quantum dots (QDs) are embedded in a GaAs spacer that is bounded by two distributed Bragg reflectors (DBRs), as shown in the zoom-in view of the sample in Figure 1. The GaAs spacer between the DBRs acts as a waveguide, where the excitation beam is confined by total internal reflection. The DBRs also act as high-reflectivity mirrors for wavevectors that are nearly normal to the sample plane. This forms a Fabry-Perot mode to which the QDs couple when emitting fluorescence. The Fabry-Perot mode must be resonant with the emission wavelength λ of the QDs, which requires the GaAs spacer to be an integer multiple of λ/n, where n is the index of refraction of GaAs. For this demonstration, the thickness of the GaAs spacer is chosen to be 4λ/n, which is approximately 1 µm, so as to be near the diffraction limited spot size of the incident excitation beam. A narrower spacer would result in a lower coupling efficiency of the excitation beam into the waveguide mode.
The experimental setup is shown in Figure 1. To maximize the coupling efficiency, an aspheric single-lens objective Eobj with numerical aperture NA=0.5 and focal length of 8 mm is chosen to focus the excitation beam onto the cleaved face of the sample. The function of the Keplerian telescope (composed of lens pair E1 and E2) in the excitation path is two-fold: (1) to fill the aperture of the excitation objective Eobj so the excitation beam is tightly focused for better mode-matching to the waveguide (in this realization the collimated beam diameter is 2.5 mm), and (2) to provide three degrees of freedom to maneuver the focal point of the excitation beam at the cleaved face of the sample. Lens E1 is mounted on an X-Y translational mount that provides the two degrees of freedom to shift the excitation spot freely in the plane of the cleaved sample face. Lens E2 is mounted on a non-rotating zoom housing which provides the freedom to choose the depth of the focal point in the sample. These three degrees of freedom allow us to optimize the resonant excitation of a single QD without requiring movement of the sample itself.
In the fluorescence collection path, a similar lens configuration (Lobj, L1, and L2) is used to allow detection of fluorescence from different parts of the sample. The light from the sample is focused by one of two tube lenses onto either an IR-sensitive camera (Lcam) or the entrance slit of the spectrometer (Lspec). Motion of L1 along the z-axis adjusts the focus of the image, and lateral translation of L2 causes the image to scan across the plane of the sample. The focal lengths of L1 and L2 are equal so their magnification is unity. This is done to maximize the range L2 can be translated before vignetting occurs.
To facilitate alignment and location of a QD, a home-built illuminator based on Kohler illumination is incorporated into the setup, as shown in Figure 1. The purpose of Kohler illumination is to provide uniform illumination to the sample and ensure that an image of the illumination light source is not visible in the sample image. The lens configurations of both the illuminator and the collection path are carefully designed to separate the conjugate image planes of the sample and the light source. Every lens in the collection path is separated from its neighbors by the sum of their focal lengths. This ensures that wherever the sample image is in focus – such as at the sensor of the camera – the light source image is completely defocused. Similarly, where the light source image is in focus – such as at the back focal plane of the objective – the sample image is completely defocused. The light source is a commercial light emitting diode (LED) emitting at 940 nm. The aperture diaphragm enables the adjustment of the illumination intensity, and the field diaphragm determines the field of view to be illuminated. The keys to realizing uniform illumination are to set the distance between lens K4 and L2 to be the sum of the focal lengths of the two lenses, and to ensure that the aperture of Lobj is not overfilled by the illumination. In this protocol, the illumination is also used to optimize the distance between Lobj and the sample.
The objective Lobj and either tube lens provides a magnification of 20x on the camera or the spectrometer. The lens pair L3 and L4 between Lobj and Lspec forms another Keplerian telescope that provides an extra 4x magnification to the image on the charge-coupled device (CCD) of the spectrometer. The addition of lenses L3 and L4 results in a total magnification of 80x, which is necessary to spatially distinguish fluorescence from nearby QDs. L3 and L4 are mounted on flipping mounts to facilitate switching of the magnification because 20x magnification provides a larger field of view on the sample.
To overlap the field of view of the collection path with the path of the excitation beam through the waveguide, the emission from the continuum of the quantum dot wetting layer is helpful. One can determine the emission wavelength of the wetting layer by measuring the emission spectrum of the sample under above band-gap excitation. For our sample, wetting layer emission occurs at approximately 880 nm at 4.2 K. By coupling a cw laser beam at 880 nm into the waveguide of the sample, one can observe a streak pattern formed by the PL from the wetting layer, which is shown in the accompanying video. The streak reveals the propagation path of the excitation light that has been coupled into the waveguide. The presence of this streak combined with the ability to image the surface of the sample makes alignment straightforward.
Caution: Please be aware of the possible dangers of laser scattering during the alignment. Wear proper safety goggles for protection. To facilitate the alignment process, an infrared viewer (IR-viewer) is necessary. An IR-sensitive fluorescent card is also helpful but not necessary.
1. Sample Preparation
2. Alignment of Resonant Excitation Path
NOTE: To maximize the coupling efficiency into the waveguide, the profile of the incident excitation beam has to be matched with that of an imaginary backwards propagating beam exiting the waveguide.
3. Alignment of Photoluminescence Collection Path
NOTE: The performance of the imaging system built in the collection path is mostly determined by the precision of the positioning of Lobj because of its short focal length (fobj = 10mm, NA=0.55). Two general steps are involved in the alignment of Lobj: coarse alignment by using a HeNe laser, and fine tweaking by using the illuminator and the bulk exciton emission of GaAs. These alignment steps are performed with the sample at room temperature.
4. Overlap of the PL Collection Path with respect to the Resonant Excitation Path
5. Resonant Excitation of a Single Quantum Dot
NOTE: There are two possible approaches to realize resonant excitation of a single QD: (1) tune the excitation frequency of the laser to match a specific QD resonance; or (2) scan the laser frequency across the resonance energies of the QD ensemble until resonance fluorescence from a single QD is observed.
Figure 1 shows one particular realization of the necessary equipment to accomplish resonant excitation of a single quantum dot. Other realizations are possible, but the critical components are: an excitation path to couple to the waveguide; a collection path to guide fluorescence to detectors; a confocal excitation path to excite along the collection path; and an illumination path to enable imaging of the sample surface.
Two representative RPLE spectra are shown in Figure 2. They are collected from a neutral QD [Figure 2(a) and (b)] and a charged QD [Figure 2(c) and (d)]. The exact charge state of the charged QD cannot be determined by examining the spectrum. To achieve the best signal-to-noise ratio, laser scattering must be kept to a minimum. The rightmost images in Figure 2(a) and (c) show the scattering background when the excitation laser is far-detuned from resonance. The laser scattering is much weaker than the QD fluorescence, but to illustrate the typical patterns of scattering, the images have been enhanced by 284 and 23 times, respectively. If these images are encountered in the alignment, it implies that a strong laser scattering is present. Multiple causes can lead to this result, such as misalignment of coupling into the waveguide, scratches on the cleaved face of the waveguide, a field of view too close to the cleaved edge of the sample, etc. Detailed discussions on each point are provided in the Discussion part of this protocol.
The image of a resonantly excited QD in a planar microcavity will typically have central disk with rings around it as shown in Figure 3. This pattern results from the coupling of the QD to the plane-wave eigenmodes of the cavity, whose propagation directions are wavelength dependent33. Thus, fluorescence of a single wavelength emerges from the cavity in a hollow cone whose apex angle is determined by the wavelength of the emission. When this light is collimated by the objective and focused by the tube lens, the image formed has the ring-like structure evident in Figure 2 and Figure 3. The radii of the rings and disk will be determined by the apex angle and thus the emission wavelength. The smaller the emission wavelength, the larger the apex angle, and the smaller the radii. The smallest possible apex angle is zero, which means there is a long-wavelength cutoff for emission that can escape the cavity. The largest possible apex angle is determined by the NA of the objective lens, which means there is a short-wavelength cutoff for emission that can be collected by the optical system. An objective with a larger NA – or the addition of a solid immersion lens – would extend this low end of the collection band to shorter wavelengths. On the other hand, the long wavelength end of the collection band cannot be modified except by changing the sample structure. Figure 3 shows images of fluorescence from QDs with different emission wavelengths ranging from the minimum up to the cutoff wavelength.
Figure 1. Schematic of the experiment.
Resonant excitation of a single QD is realized by coupling a narrow linewidth (1 MHz) cw laser beam into the waveguide of the sample, as depicted by the orange path. The photoluminescence of the sample is collected from the Fabry-Perot mode, following the red path. A Helium-Neon (HeNe) laser provides the above band-gap excitation confocally, following the green path. A home-built illuminator provides uniform illumination of the sample surface with 940 nm light, as depicted by the yellow path. Note that the schematic is not to scale. FC: fiber coupler; AD: aperture diaphragm; FD: field diaphragm; POL: polarizer; F: long-pass filter; NPBS: non-polarizing beam splitter cube; DBR: distributed Bragg reflector; CCD: charge-coupled device; LED: light-emitting diode. Please click here to view a larger version of this figure.
Figure 2. Resonance fluorescence of a single quantum dot.
(a) Images of fluorescence of a neutral quantum dot at different detunings, indicated in linear frequency on the top of each image. Zero detuning corresponds to 927.8597 nm. (b) RPLE spectrum of the same neutral QD, by integrating the PL intensity in a circular area with a diameter of 8 pixels around the center. (c) Images of fluorescence of a charged QD at different detunings, indicated in linear frequency at the bottom of each image. Zero detuning corresponds to 927.653 nm. (d) RPLE spectrum of the same charged QD, by integrating the PL intensity in a circular area of a diameter of 12 pixels around the center. (e) Second-order correlation measurement of the neutral QD in (a) under resonant excitation at the low-energy peak. The right-most frames in (a) and (c) are the far-detuned excitation images, with the intensity multiplied by 284 and 23, respectively, to show the low laser scattering background. Note that the color scale for (a) and (c) are different but shared among the individual sub-plots. The normalized RPLE intensity in (b) and (d) is depicted by orange dots, while blue squares indicate the data corresponding to the images shown in (a) and (b), respectively. Please click here to view a larger version of this figure.
Figure 3. Resonance fluorescence from eight different dots at different wavelengths in the cavity mode.
The resonance wavelength is indicated on the top of each image. Please click here to view a larger version of this figure.
The critical steps in the protocol are: the mode-matching and alignment of the excitation beam to the waveguide mode; and proper alignment and focusing of the collection optics. The most difficult parts of these steps are the initial alignment; optimizing the coupling of an already aligned setup is relatively straightforward. Overlapping the collection and excitation areas is a step that is simple with the ability to image the sample on the camera, but is very difficult without this capability. In order to have high-quality imaging, proper Kohler illumination is critical. The topic of Kohler illumination is outside the scope of this protocol, but is a well-known concept in microscopy and is comprehensively discussed in the published literature34,35.
The lens focal lengths noted here are typical, but not required. Different cryostats and other factors may impose additional or different requirements on the optics arrangement. In such a case, proper choices of lens focal lengths during design is key to satisfy the requirements of mode-matching in the excitation path and Kohler illumination in the collection path. Kohler illumination will be satisfied if lenses are separated by the sum of their focal lengths. Proper mode-matching into the waveguide requires as high an NA as possible, which means the beam must fill the aperture of Eobj. The objective sits in a homemade dovetail rail XYZ mount that is movable only at room temperature because it is located inside the code space of the cryostat. This close-to-sample position allows the use of a large NA lens while minimizing the thermal variation in the lens mounts, which increases mechanical stability. The objectives in this case are aspherical singlet lenses due to space constraints. If more space is available, commercial multi-lens objectives could be used instead to improve imaging quality, NA, and magnification. The experimental setup could be extended to allow confocal resonant or near-resonant excitation by replacing M3 with a dichroic mirror and directing an excitation beam through both the dichroic and the beam splitter NPBS.
If the laser background is too strong, poor coupling of the excitation beam into the waveguide is a possible cause. The coupling can be reduced by roughness, scratches, or contamination on the cleaved face due to improper handling. The face that will be coupled to must not be touched by anything. It is possible but difficult to clean the cleaved face of contamination, but roughness and scratches are permanent. If surface quality is an issue, a different location on the cleaved face can be tried, but a fresh cleave may be necessary. Strong laser scattering background can also be caused by the uncoupled portion of excitation light scattering from dust on the surface of the sample. Another possibility is that the field of view is too close to the edge of the sample and light scattering from edge is entering the collection path. Finally, it may be that the laser power is just too high. Typically, the excitation laser power is in the range of 0.5 to 10 µW measured at the power meter shown in Figure 1. Aside from reducing sources of laser scattering, the scattering can be filtered out by adding a horizontal polarizer in the collection path. However, to see the QD fluorescence in this situation requires a QD whose dipole moment is not aligned to the vertical direction.
The excitation polarization is limited to only one choice; in this case it is vertical polarization. This is because of three constraints. First, the propagation direction of the excitation beam is constrained to be within the sample plane. Second, the polarization must be perpendicular to the propagation direction. Third, the QD dipole moments lie in the sample plane. If, as in this case, the excitation beam propagates horizontally, then the only choice of polarization that can excite the QDs is vertical. In contrast, the detection polarization has no constraints placed on it because the suppression of laser scattering is mainly accomplished by confinement of the laser within the waveguide mode11. Another limitation is that this excitation scheme requires a waveguide to guide the light to the quantum dot, a structure that may not be feasible for all samples. Compare this to the dark-field confocal excitation technique1, which uses crossed polarizers to suppress the laser scattering. In that case, the excitation can use arbitrary polarization, but the detection polarization must be orthogonal.
Single quantum dots under resonant excitation have been demonstrated to be excellent single photon sources with high brightness, narrow linewidth, and high indistinguishability36. This protocol provides a feasible approach to harness these exceptional properties of the self-assembled QD system for various applications, such as quantum information and linear optical quantum computing. Furthermore, photons entangled with either another photon or an electron spin will require collection without regard to polarization, which is a feature of this method.
The authors have nothing to disclose.
The authors would like to acknowledge Glenn S. Solomon for providing the sample. This work was supported by the National Science Foundation (DMR-1452840).
Tunable external cavity diode laser | Toptica Photonics | DL-Pro | |
Closed-cycle cryostat | Montana Instruments | Cryostation | |
Spectrometer, 750 mm focal length | Princeton Instruments | SpectraPro 2750 | |
Thermoelectrically cooled charge-coupled device | Princeton Instruments | Pixis 100BR-eXcelon | |
HeNe laser | JDSU | 1125P | |
Infrared sensitive camera | Sony | NEX-5TL | IR blocking filter removed |
Power meter and detector | Newport | 1918-C, 918D-IR-OD3 | |
Adjustable aspheric fiber collimator | Thorlabs | CFC-8X-A | |
Air-Spaced Doublet Collimator | Thorlabs | F810APC-842 | |
Protected Silver Mirrors x 5 | Thorlabs | PF10-03-P01 | |
Flip mounts x 2 | Thorlabs | FM90 | |
Aspheric condenser lens, f = 20 mm; K1 | Thorlabs | ACL2520-B | |
Best form spherical lens, f = 50 mm; E2, L1, L2, K2 | Thorlabs | LBF254-050-B | |
Best form spherical lens, f = 100 mm; E1, L4, K3, K4 | Thorlabs | LBF254-100-B | |
Best form spherical lens, f = 200 mm; Lspec, Lcam | Thorlabs | LBF254-200-B | |
Plano-convex lens, f = 400 mm; L3 | Thorlabs | LA1172-B | |
Molded glass aspheric lens, f = 8 mm; Eobj | Thorlabs | C240TME-B | |
Precision asphere, f = 10 mm; Lobj | Thorlabs | AL1210-B | |
Longpass Filters, 800 nm, x2 | Thorlabs | FEL0800 | |
Non-polarizing beam splitter cube (NPBS) | Thorlabs | BS029 | |
Pellicle beam splitter | Thorlabs | BP108 | |
Polarizer | Thorlabs | LPNIRE100-B | |
Light emitting diode, 940 nm | Thorlabs | M940D2 |