Initialization of a spin qubit in a site-controlled nanowire quantum dot

A fault-tolerant quantum repeater or quantum computer using solid-state spin-based quantum bits will likely require a physical implementation with many spins arranged in a grid. Self-assembled quantum dots (QDs) have been established as attractive candidates for building spin-based quantum information processing devices, but such QDs are randomly positioned, which makes them unsuitable for constructing large-scale processors. Recent efforts have shown that QDs embedded in nanowires can be deterministically positioned in regular arrays, can store single charges, and have excellent optical properties, but so far there have been no demonstrations of spin qubit operations using nanowire QDs. Here we demonstrate optical pumping of individual spins trapped in site-controlled nanowire QDs, resulting in high-fidelity spin-qubit initialization. This represents the next step towards establishing spins in nanowire QDs as quantum memories suitable for use in a large-scale, fault-tolerant quantum computer or repeater based on all-optical control of the spin qubits.


Introduction
The development of site-controlled quantum dots (QDs), and demonstration of their suitability for hosting spin-based qubits, is a key objective in the roadmap towards a scalable quantum information processing system implemented with QDs [1][2][3]. There has been considerable recent effort in exploring different techniques for fabricating site-controlled QDs, including lithographic patterning of growth substrates [4,5], stress-induced Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. positioning within micropillars [6], and the growth of QDs within seeded nanowires [7]. QDs within nanowires have been shown to have both high photon-extraction efficiencies [8,9], and good single-photon source characteristics [7][8][9]. Furthermore, magneto-photoluminescence spectroscopy studies [10,11] of InAsP QDs in InP nanowires have shown that QDs in nanowires may be a promising platform for hosting spin qubits, but to our knowledge, thus far there have been no demonstrations of the fundamental spin manipulation operations [12][13][14][15][16][17][18][19][20] on spins trapped in nanowire-hosted QDs, nor in any other site-controlled QD devices. Nanowire QDs are a substantially different platform-with respect to both material and structural characteristics-than selfassembled QDs in a bulk host (the system with which the majority of spin qubit studies using optically active QDs have been performed to date). Nanowire QDs have high brightness due to the waveguiding effect of the needle-like structure in which each QD is embedded. Brightness is an advantage that nanowire QDs share with QDs embedded in micropillars, but they currently offer the additional advantage of being deterministically positionable without compromising optical quality. Here we demonstrate all-optical initialization of spin qubits embedded in several deterministically positioned InP nanowire QDs, which is a first step towards realizing more complex spin experiments with nanowire QDs, including coherent spin control [3] and spin-photon entanglement generation [2].

Methods
We studied a sample with InAsP QDs embedded in InP nanowires that was grown using vapor-liquid-solid epitaxy on a (111)B InP substrate; the growth details can be found in [7]. The substrate was covered with a SiO 2 mask containing a grid of apertures, which were produced using e-beam nanopatterning. The growth of each nanowire was seeded by placing a gold nanoparticle in the center of each aperture [7,22,23] and consisted of a two-step process that involves growth of a core nanowire containing the InAsP QD followed by growth of a shell, which results in the needle-like shape of the nanowires.
Photoluminescence spectra were measured using a custom double-grating spectrometer setup with ∼10 μeV resolution, which is necessary in order to spectrally select just a single emission line from the QD, and measure its signal on a single-photon counter, while rejecting light from a CW laser that is used for the spin initialization and has its center frequency near the QD emission line that is being collected.
For all the experiments that required application of a magnetic field, we used the Voigt geometry, since this is the configuration that is used for spin control with optical pulses [15,16,18], and for generation of spin-photon entanglement [24][25][26][27].

Results
In this article we present results from a typical quantum-dot-nanowire device in our sample; the QD exhibited emission under CW above-band (780 nm) excitation that was both bright and spectrally narrow. Figure 1(a) shows the polarization-resolved spectra from the QD. At saturation the QD exhibited a linewidth of ∼60 μeV full-width-at-half-maximum, and an energy difference of δE=1.6 μeV between the two orthogonal linear polarization components (measured between the fitted peak centers; see figure 1(a). The emission intensity of both H-and V-polarized lines have a linear dependence on the above-band laser power, until saturation is reached at approximately 550 nW ( figure 1(b)). The linear power dependence is consistent with these lines corresponding to single exciton emission, as opposed to biexciton emission (which would exhibit a quadratic power dependence). To determine that the QD was charged, we used magneto-photoluminescence spectroscopy in the Voigt configuration (magnetic field perpendicular to the nanowire growth direction): figure 1(c) shows the photoluminescence signal from the QD as a function of its emission energy and polarization. The photoluminescence spectra clearly show a four-fold splitting, which is consistent with emission from a charged dot [28]. We note that in this figure and the remainder of the paper, we define H as the linear polarization that is θ=50°relative to the magnetic field and V as the linear polarization that is at θ=140°relative to the magnetic field, as shown in the illustration in figure 1(d).
We obtained further evidence that the QD was charged by recording photoluminescence spectra as a function of the applied magnetic field strength. Figure 2(a) shows the photoluminescence spectra of the QD for varying magnetic fields in the range from 0 to 5 T for both the H and V polarizations; the splitting of the emission into four lines is clearly evident. This is expected for a charged dot, for which there are two contributions to the transition energies that depend on the magnetic field: a linear dependence due to the Zeeman effect [28] (figure 2(b)), and a quadratic dependence resulting from the diamagnetic shift [29,30], (figure 2(c)).
The four-fold splitting of the spectral lines, their linear dependence on the B-field (after the diamagnetic shift has been subtracted), their polarization properties, and their approximately equal brightness, indicate that the QD has both the level structure and the selection rules of a charged QD. Figure 2(d) shows the relevant energylevel diagram for a charged QD in a Voigt-configuration magnetic field [28], and the polarization selection rules for the optical transitions. Figure 3 illustrates our spin-pumping experiments, and shows the main results. We performed a set of four different experiments, to demonstrate that we can perform spin pumping into either the ñ | state or the ñ | state, in each case using one of two (per spin state) available optical transitions. The inset of figure 3(a) illustrates the QD optical transitions we used for pumping and detection in one of the four experiments, and we use it here as an example case to describe the experiment in detail. The principle of the experiment is as follows [31,32]. A fixed-wavelength above-band laser is used to randomize the state of the spin; it does this by incoherently exciting states at far higher energies than the QD trion levels, and through a series of decay processes, some of which are non-spin-preserving, the QD trion levels are randomly populated, and these levels in turn decay and randomly populate the QD ground-state spin levels. The action of the spin-randomization laser is depicted as violet upward wavy arrows. A tunable laser is used to resonantly excite one of the trion states via a vertical transition ñ -  ñ (| | ). If the system is initially in the state ñ | , then this laser will cause the trion state   ñ | to be populated. This trion state will then decay to either the ñ | or ñ | state with equal probability (gray downward wavy arrows in the inset of figure 3(a)). If the decay is to the state ñ | , then the tunable laser will re-excite the trion state. If, on the other hand, the decay is to the ñ | state, then the tunable laser will no longer be resonant with any transition and the system will be initialized in the ñ | state, until the spin is randomized again. The emission from the   ñ -ñ | | transition is spectrally filtered and sent to a single-photon counter, providing a measurement of the spin state [3]. Figure 3(a) shows the collected photon counts as a function of the wavelength of the spin-pumping laser, as it was tuned over the ñ -  ñ | | transition. Two traces are shown: one when only the spin-pumping laser was on (in blue), and one when both the randomization laser and the spin-pumping laser were on (in red). When both lasers were on, the data (red points) show a clear resonance, corresponding to spin-pumping-laser photons being absorbed by the ñ -  ñ | | transition, and being emitted by the   ñ -ñ | | transition. The reason that photons can be absorbed by the ñ -  ñ | | transition is that the ñ | state is continually being populated as a result of the randomization laser being on. However, when the randomization laser is turned off, the data (blue points) shows no resonance as the spin-pumping laser passed over the ñ -  ñ | | transition. This serves as strong evidence that the QD spin has in this case been optically initialized in the ñ | state. (The intuitive reasoning behind this claim is that if the spin is initialized in the ñ | state, then no further photons from the spinpumping laser can be absorbed, so in the absence of the randomization laser, there will be no excitation of the QD, and hence no photons emitted. In contrast, if the spin was being imperfectly initialized, or the spin relaxation time was very short, then one should expect to observe photons being emitted when the spinpumping laser is on resonance with the ñ -  ñ | | transition. Our data are therefore consistent with our having successfully initialized the spin.) In an analogous manner, figure 3(b) shows how the QD spin can be optically pumped into the ñ | state via the other vertical optical transition ñ -  ßñ (| | ), and figures 3(c) and (d) show how the QD spin can be optically pumped using the two available diagonal optical transitions.
To demonstrate the robustness and repeatability of this spin qubit initialization technique in nanowire QDs, we performed the same type of optical pumping experiments on several nanowire QDs on the same sample, which yielded essentially identical results to those shown in figure 3 (see supplementary data).
To further characterize the spin pumping process, we also studied the spin-pumping signal as a function of the applied spin-pumping-laser power. Figure 4 shows the dependence of the peak spin-pumping signal on the spin-pumping-laser power in the experiment in figure 3(a) (where the spin is pumped into the ñ | state using the ñ -  ñ | | transition). In particular, the red data points in figure 4(a) show that the peak of the spin-pumping signal initially increases rapidly with applied laser power, and saturates once the spin-pumping-laser power reaches approximately 350 nW. The blue data points are from the same experiment, except the randomization laser had been turned off. We note that even with a power well above the value that is sufficient to saturate the ñ -  ñ | | transition (and hence cause maximal spin pumping), when the randomization laser is off, there is no increase in the counts as a function of power, which is consistent with high-fidelity optical pumping and excellent spectral-filtering-based rejection of the scattered spin-pumping-laser light. We also studied the effect of the applied laser power on the width of the transition resonance. Figure 4(b) shows the full-width-at-halfmaximum linewidth of the resonance when both the randomization laser and the spin-pumping laser were on, as a function of the power of the spin-pumping laser. At lower powers (P spin-pump <0.15 μW), we observed a linewidth of less than 20 μeV, with substantial broadening as the power was increased to be above the saturation limit of the transition. The power-dependence measurements in figures 1(b) (above-band excitation photoluminescence power dependence) and 4(a) (spin-pumping laser power dependence) provide valuable photons as a function of the spin-pumping-laser energy, for the specific experimental protocols illustrated in the respective insets. Red data points show the collected photon counts when both lasers were on, whereas the blue data points show the photon counts when only the spin-pumping laser was on. For all four spin pumping schemes the powers used were P spin-pump =500 nW (spin-pumping laser) and P rand =60 nW (above-band spin randomization laser). The insets are showing the relevant levels of the quantum dot, the applied laser fields, and photon collection. The net effect of the spin randomization laser (above-band excitation that decays randomly into the two trion states; see main text for details) is shown as upward violet wavy arrows. Spontaneous decay is depicted as downward gray wavy arrows. A tunable CW laser ('Pumping'), is scanned across one of the optical resonances. Photons emitted by the yellow shaded transition ('Detection') are collected, and measured by a single-photon counter. . Spin-pumping peak amplitude and width as a function of the power of the spin-pumping laser, in the experiment described in figure 3. The randomization laser power was kept constant at P rand =60 nW. (a) Red: photon counts at the peak of the spinpumping resonance (when both lasers were on), as a function of the spin-pumping laser power. Blue: photon counts measured when the randomization laser was off. (b) The full-width-at-half-maximum linewidth of the resonance shown in figure 3(a), as a function of the spin-pumping laser power. information for quantitatively assessing the efficacy of the spin pumping process, since the saturation values can be used to infer the relative rates of spin pumping and spin randomization.
We have used a rate-equation model (described in detail in the supplementary data) of the spin pumping experiment to analyze our experimental results; it shows that our data is consistent with optical spin pumping causing spin qubit initialization with a fidelity of 99% in less than 10 ns. This is similar to the reported performance of spin pumping in self-assembled InAs QDs [13,16,18]. We used our model to infer a lower bound on the spin lifetime of T 1 >3 μs. These values suggest promise for the use of charges in nanowire QDs as spin qubits.

Conclusion
As is the case with micropillar QDs, the structural characteristics of nanowire QDs render them incompatible with most scalable two-qubit gate proposals for spin qubits, due to the lack of a direct way for the trapped electrons (or holes) to interact. Spin qubits in nanowire QDs (and micropillar QDs) are thus perhaps better suited to quantum computing or repeater architectures in which the stationary qubits are entangled indirectly, by interfering and detecting photons that are entangled with the spins [2], which is also the one of the leading approaches for scaling free-space trapped-ion qubits [21]. Our experiments make a contribution towards the intermediate-term goal of entangling two spatially separate QD spins on a single chip by showing that one of the steps of the entanglement-generation protocol-spin initialization-can be performed with QDs that are deterministically positioned and have high brightness. In this paper we have demonstrated that in the InAsP-QD/InP-nanowire system a charged QD in a Voigt magnetic field does yield two optical Λ-systems that can be manipulated, and we have demonstrated optical spin pumping using independent experiments on both transitions in both Λ-systems. Using several different nanowires, we were able to show that spin measurement as part of the optical pumping process is possible in the InAsP-QD/InP-nanowire system. These experiments were all performed on site-controlled nanowires, making this the first demonstration, to our knowledge, of optical pumping of site-controlled QD spins.

Funding sources
We acknowledge financial support from the Air Force Office of Scientific Research, the MURI Center for Multi-functional Light-Matter Interfaces based on Atoms and Solids, and from the Army Research Office (grant number W911NF1310309). This research was also supported by the Cabinet Office, Government of Japan, and the Japan Society for the Promotion of Science (JSPS) through the Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program). KGL acknowledges support by the Swiss National Science Foundation. PLM was supported by a David Cheriton Stanford Graduate Fellowship.