Optical pumping and non-destructive readout of a single magnetic impurity spin in an InAs/GaAs quantum dot

Optical pumping and non-destructive readout of a single magnetic impurity spin in an InAs/GaAs quantum dot

E. Baudin    E. Benjamin    A. Lemaître    O. Krebs CNRS-Laboratoire de Photonique et de Nanostructures, Route de Nozay, 91460 Marcoussis, France
July 18, 2019
Abstract

We report on the resonant optical pumping of the spin states of a single Mn dopant in an InAs/GaAs quantum dot embedded itself in a charge tuneable device. The experiment relies on a “W” scheme of transitions reached when a suitable longitudinal magnetic field is applied. The optical pumping is achieved via the resonant excitation of the central system at the neutral exciton energy. For a specific gate voltage, the red-shifted photoluminescence of the charged exciton is observed, which allows non-destructive readout of the spin polarization. An arbitrary spin preparation in the or state characterized by a polarization near or above 50% is evidenced.

pacs:
78.67.Hc,75.50.Pp,78.55.Cr,33.80.Be
preprint:

The possibility to precisely prepare and control the quantum state of an individual spin in a quantum dot (QD) is an appealing issue both from a fundamental point of view and for potential applications in the field of quantum information Leuenberger and Loss (2001). Recent works have demonstrated that the spin of a an electron localized in a gate-defined or self-assembled semiconductor QD can be coherently manipulated Hanson et al. (2007); Press et al. (2008); Berezovsky et al. (2008); Kim et al. (2010). However, this system is not really ideal because of its intrinsic coupling to the environment (phonons, nuclear spins or surrounding charges) which restrains its potential for future developments. QDs doped with a single magnetic impurity like a Mn atom offer an interesting alternative in this regards Koenraad and Flatté (2011). Such isolated magnetic spin which is provided by core electrons ( for Mn), is potentially better isolated from the environment than valence or conduction electrons. Besides, thanks to the - exchange which yields spin-dependent sub-levels, selective addressing by optical methods is in principle attainable. A singly Mn-doped QD could reveal itself as particularly suitable for the realization of quantum bits.
Among recent investigations in this direction, the initialization of a Mn spin in II-VI semiconductor QDs has been demonstrated via optical pumping (OP) Le Gall et al. (2009); Goryca et al. (2009). In II-VI host materials, the 5/2 Mn spin which presents 6 distinct states is however not ideal for quantum operations. In III-V QDs the Mn effective spin turns out to be much simpler : a Mn atom forms indeed an acceptor state denoted (a negative center and a tightly bound hole) presenting a total angular momentum reduced to in its ground state Schneider et al. (1987); Bhattacharjee (1999). Furthermore, in a non-spherical self-assembled QD, the state is substantially higher in energy than the two circular states by a few meV Kudelski et al. (2007); Krebs et al. (2009). At low temperature these states define a 2-level system, with whole occupation near unity, which we refer to as the spin in the following. Due to the large QD-induced anisotropy Krebs et al. (2009), spin initialization cannot be achieved following a simple non-resonant approach as used recently for the ionized impurities in bulk GaAs Akimov et al. (2011); Myers et al. (2008) and based on - interaction with spin polarized electrons. An OP scheme dedicated to the case of spin in a self-assembled QD is required.
In this Letter, we present an OP experiment in which the spin in an InAs/GaAs QD is pumped arbitrarily into one of its states by using a resonant laser excitation. Its principle relies on a “W” energy level scheme which arises at a specific longitudinal magnetic field, similarly as quantum dot molecules in an electric field Kim et al. (2008); Vamivakas et al. (2010). Besides, the spin initialization and its readout are spectrally dissociated by using a technique recently introduced by Kloeffel et al. (2011) which enables to monitor the spin population by using a standard micro-photoluminescence (-PL) setup. Efficient OP is demonstrated through the vanishing (resp. enhancement) of transitions associated to the pumped (resp. populated) level.
The sample used in this work consists of a Mn-doped QD layer embedded in between an electron reservoir and a Schottky gate allowing the control of the QD charge. The Mn doping is very dilute and less than 1% of the QDs are effectively doped by a single Mn impurity, see Ref. Kudelski et al. (2007) for details. The -PL spectroscopy of such individual QDs is carried out with a 2 mm focal length aspheric lens (N.A. ) actuated by piezo-stages and mounted in a split-coil magneto-optical cryostat. The collected PL is dispersed by a 0.6 m-focal length double spectrometer and detected by a Nitrogen-cooled CCD array camera providing a eV spectral resolution. All measurements presented in this Letter were performed at low temperature ( K) with a magnetic field applied parallel to the optical axis (Fig. 1(a) insert).

Figure 1: (a) Density plot of -PL intensity under non-resonant excitation (HeNe at 633 nm) for a Mn-doped QD in magnetic field. Detection is or polarized as indicated and centered around  eV. (b) Level diagram corresponding to the main transitions in (a) for a field below 1 T. (c) Crossed-sections of and spectra in (a) at 0.7 T. (d) “W” transition scheme at the field where FM and AFM levels anticross in (b). It is valid both for - and -, hence only the selections rules ( or ) and states are indicated.

The QD studied in this work contains a Mn impurity in the configuration Schneider et al. (1987); Bhattacharjee (1999); Govorov (2004). This acceptor is characterized by an antiferromagnetic (AFM) - exchange between the Mn spin and the spin of the bound hole which gives rise to 4 levels as a function of the total angular momentum . At low temperature ( K) only the ground state is significantly occupied so that higher states () can be neglected. Moreover, the lens shape and biaxial strain of InAs self-assembled QDs shift the state of the triplet to a higher energy by about 2 meV Krebs et al. (2009). Consequently, this level is also negligibly occupied at 2 K and one can describe the impurity as an effective 2-level system associated to the spin projections . A natural basis to describe the -QD states in presence of additional (photo-created) carriers in the QD S-shell reads , where denotes the -projection of their total spin.
Figure 1(a) shows for the investigated QD the typical signature of in PL spectroscopy as a function of a positive longitudinal magnetic field. For the gate voltage used here ( V) the QD is charged by an extra electron yielding under optical excitation a negative trion (a hole () with 2 electrons ()). Since both conduction are paired in a singlet configuration in the QD S-shell, its spin is determined by the spin only and hence reads ( or ). A detailed discussion of the spectral signature of Fig. 1(a), i.e. two intense lines denoted FM and AFM which anticross with two weaker lines forming a cross, can be found in Ref.’s Kudelski et al. (2007); van Bree et al. (2008). In brief, the FM and AFM lines correspond respectively to the ferromagnetic and anti-ferromagnetic spin configurations of -. They are split by the exchange energy eV, see Fig. 1(b), mostly due to the - ferromagnetic interaction while the - exchange taking place in the final state of optical recombination can be neglected Kudelski et al. (2007). A second very essential feature is the anisotropic coupling within the states . It gives rise to a level splitting eV at zero field both for or -, and at finite magnetic fields for - or - states when a FM and a AFM level are brought in coincidence by Zeeman effect (Fig. 1(b)). Here, denotes the effective -factor of spin and is the Bohr magneton. For these specific fields we identify a “W” transition scheme (Fig. 1(d)) which, interestingly, reproduces the same scheme as used in Ref.’s Kim et al. (2008); Vamivakas et al. (2010) to initialize and readout non-destructively an electron spin in a QD molecule. It is composed of a central system allowing to induce spin flip transitions ( or ) through resonant excitation followed by spontaneous emission (i.e. OP), and two outer transitions allowing non-destructive readout of the spin as they do not change the state while being cycled 111The crossed transitions are slightly permitted due to the -induced coupling. However, their oscillator strengths are notably reduced by in comparison to the direct ones..
Let’s first examine more closely the - PL spectrum under cw non-resonant and unpolarized excitation at the anticrossing field  T (Fig. 1(c)). The -resolved PL spectrum shows mainly two lines which correspond to the W outer transitions and therefore reflect the population probability of the states. The low energy state is indeed found more populated than the state, yielding a spin polarization of 20%. However, the associated effective temperature determined from the PL intensity ratio amounts to 10 K which is substantially higher than the lattice temperature 222This is also confirmed by the noticeable central line in Fig. 1(a),(c) corresponding to the level which becomes more populated than expected at 2 K.. This effective heating is partially due to the energy relaxation of the photo-carriers under non-resonant excitation. Yet, another key contribution comes from the optical recombination of polarized trions through the transitions which tend to equilibrate the and populations. This mechanism is evidenced by the -resolved PL spectrum in Fig. 1(c) which shows two doublets of roughly equivalent intensity corresponding to both branches. Eventually, and PL spectra under non-resonant excitation are both encouraging indications to achieve OP and spin readout using this W system.

Figure 2: (a) Schematics of the charge tuneable structure and of the - cycle used for selective resonant excitation of a specific - spin configuration ( T). (b) PL intensity density plot of the Mn-doped QD against detection energy and gate voltage. The excitation is quasi-resonant around  meV. (c) Similar density plot of PL observed through the resonant excitation of either the FM or AFM level in a narrow voltage range around the - frontier.

Obviously, non energy-selective excitation of the QD cannot lead to OP. Even with a polarized excitation creating only -polarized trions the conversion via the transitions would be as probable as the conversion. To favor one of them, an energy selective excitation is necessary, but in that case measuring the PL signal at almost the same energy turns out somewhat problematic. To circumvent this issue we used a solution based on a singular excitation-emission cycle that takes place in a narrow range of applied gate voltages at the frontier between and Kloeffel et al. (2011); Simon et al. (2011). In this range, a resonantly created exciton is energetically unstable. It attracts in a time  ps much shorter than the radiative lifetime an electron which tunnels in the QD from the n-GaAs reservoir. This leads to the formation of an trion which recombines optically producing a PL signal red-shifted by 7 meV with respect to the excitation energy, after which the left in the QD escapes back to the reservoir as depicted in Fig. 2(a). This cycle allows to resonantly excite with a laser energy outside of the spectrometer field of view and to collect the red-shifted PL signal in order to probe the spin. In practice, the internal diffusion of the laser inside the spectrometer can still blind the detector. Using crossed polarizers ( or /) between excitation and detection is necessary to reduce this stray light by a factor of a few 10, while the remaining average background can be easily removed by taking a reference spectrum (with no PL signal) at a lower bias. The range of applied gate voltages for which this cycle occurs can be estimated by looking for the coexistence of and spectral lines under quasi-resonant excitation (Fig. 2(b)). However, a significant voltage offset (up to +0.2 V) has to be applied when the excitation goes to resonance, to account for the reduction of the photocarrier-induced electric field screening.
As shown in Fig. 2(c), by resonantly exciting the upper (lower) doublet around  V we are able to detect the PL signal of the corresponding upper (lower) doublet. The good preservation around 70% of the selected FM or AFM configuration validates our approach for selectively addressing and reading out spin states via the - cycle. The unwished “cross-talking” is due to the large broadening of resonance of about eV333The resonance broadening, observed also for undoped QDs in this sample, results both from the lifetime shortening and from a saturating excitation power necessary to deal with a significative QD spectral wandering. We have checked this is not due to Overhauser effect as observed in Ref. Kloeffel et al. (2011). rather than a hole or spin-flip associated to the electron tunnelling in the dot. In this regards we benefit from the fact that all exchange interactions are essentially longitudinal (Ising type) because of the heavy character of the QD and hole, and therefore work together to conserve a given spin orientation during the capture process Krebs et al. (2009). Similarly, when the electron tunnels out of the dot after recombination, one can reasonably expect that the weak - interaction (eV) which is also mainly longitudinal, will not imply any transitions between and states. In practice, the resonant excitation of appears to be equivalent to that of with respect to spin, as it could be anticipated from their very similar PL spectra against magnetic field Kudelski et al. (2007).
Thanks to its broad spectral resonance the - cycle can be driven with a laser line at a fixed wavelength while sweeping the magnetic field from 0 to 1.5 T. Figures 3(b),(c) show the resulting PL density plots for a linearly polarized laser line respectively centered on the upper (AFM) or lower (FM) doublet of - in zero field. As discussed above, the detection is linearly polarized orthogonally to that of the excitation. For a direct comparison, Fig. 3(a) displays a zoom of Fig.1(a) where both (solid lines) and (dashed lines) measurements are reported. Around 0.7 T the W configuration aimed for OP arises and yields indeed drastic changes of the detected PL spectra : the lines corresponding to the pumped level and exhibiting the anticrossing at 0.7 T almost completely vanish, while the outer lines corresponding to the populated spin state are conserved or even reinforced. As sketched in the insets of Fig. 3(b),(c), the laser energy determines which transition of the is selected and in turn which spin state is pumped. Exciting the upper or lower branch transfers the spin in the state (Fig. 3(b)) or state (Fig. 3(c)). Quantitatively, from the PL intensity ratio of the and lines one can estimate the spin polarization achieved in both cases to about -55% and +60% respectively. This analysis relies on the assumption that the PL line intensities correctly reflect the initial and populations, whereas the laser is slightly blue- or red-detuned from the respective resonances. Such assumption sounds yet quite reasonable because the laser line was centered between the and transitions.

Figure 3: (a) Zoom of Fig. 1(a) showing both (solid lines) and (dashed lines) spectra. (b) and (c) PL density plots under resonant excitation centered on the zero field upper or lower - doublet. The vanishing of the anticrossing line around 0.7 T while the line persists or even increases indicates an efficient OP mechanism as depicted in the respective insets. (d) PL spectra at 0.7 T under quasi-resonant excitation (at  meV), with or without a resonant excitation driving the upper branch. The enhancement (reduction) of the () line with the pump laser demonstrates an efficient OP of -49%.

To better evidence the effect of OP by using both outer branches of the W, as done to estimate the thermal polarization in Fig. 1(c), we performed a different experiment (Fig. 3 (d)) : the resonant pump laser is now circularly polarized and drives only the upper branch, while a second quasi-resonant laser (at  meV) is used for the readout. Note that suppressing the pump laser stray light requires now a detection which in turn implies to use such quasi-resonant excitation for the probe laser. The main drawback of this approach is that the polarization of the photo-created excitons or trions is partially lost during the relaxation to the QD S-shell. This leads to some feeding of the upper state, as illustrated in the inset of Fig. 3(d), which tends to depolarize the spin. Nevertheless, when turning on the pump laser, we clearly observe OP signature through the drastic increase (decrease) of the () line intensity. Under these non-optimal conditions a spin polarization, clearly opposite to the thermal one, of -49% is still reached. Conversely, by pumping the lower branch (not shown) we could increase the thermal polarization from +21% to +55%. The unperfect excitation selectivity associated to the - cycle is likely the main limitation of the uncomplete spin preparation achieved here. Truly resonant techniques should be employed to estimate properly the role of intrinsic spin relaxation.
In this Letter we have presented the efficient optical pumping and non-destructive readout of a single magnetic spin forming a 2-level system and embedded in an InAs/GaAs QD. Our results are stimulating for study further its potential as a qubit in condensed matter. In particular, thanks to the QD-induced anisotropy which provides this system with a nano-magnet character, one may anticipate a long spin relaxation time.
We acknowledge B. Urbaszek for fruitful discussions. This work has been supported by French ANR-P3N contract QUAMOS and the région Ile-de-France.

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  • (23) The resonance broadening, observed also for undoped QDs in this sample, results both from the lifetime shortening and from a saturating excitation power necessary to deal with a significative QD spectral wandering. We have checked this is not due to Overhauser effect as observed in Ref. Kloeffel et al. (2011).
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