Abstract
Confined spins in selfassembled semiconductor quantum dots promise to serve both as probes for studying mesoscopic physics in the solid state and as stationary qubits for quantuminformation science^{1,2,3,4,5,6,7}. Moreover, the excitations of selfassembled quantum dots can interact with nearinfrared photons, providing an interface between stationary and ‘flying’ qubits. Here, we report the observation of spinselective photon emission from a resonantly driven quantumdot transition. The Mollow triplet^{8} in the scattered photon spectrum—the hallmark of resonance fluorescence when an optical transition is driven resonantly—is presented as a natural way to spectrally isolate the photons of interest from the original driving field. We also demonstrate that the relative frequencies of the two spintagged photon states can be tuned independent of an applied magnetic field through the spinselective dynamic Stark effect, induced by the same driving laser. This demonstration should be a step towards the realization of challenging tasks such as electronspin readout, heralded singlephoton generation for linearoptics quantum computing and spin–photon entanglement.
Main
In the realm of solidstate emitters generating flying qubits, milestone achievements so far include singlephoton antibunching^{9,10}, entangled photonpair generation^{11} and cavity quantum electrodynamics in the strong coupling regime^{12,13,14}. A common feature in all of these studies is the incoherent pumping of the quantumdot transitions through carrier generation in either the host matrix such as GaAs or the quasicontinuum states above the higherlying confined states of the quantum dot. This excitation method leads to photonemissiontime jitter and spectral wandering of the quantumdot transition larger than the transition’s linewidth. Both effects reduce the usefulness of nonresonantly generated single photons in linearoptics quantum computing algorithms^{15}, even if the quantum dot is coupled to a cavity. In an attempt to both address this previous shortcoming and provide spectrally selective access to the quantumdot electronic transitions, increasing attention has turned to resonant optical excitation. So far, resonant optical addressing of quantum dots has relied predominantly on a remarkably powerful laserbased spectroscopy technique: differential transmission^{16}. Although differential transmission has enabled progress in spinselective excitation of quantum dots, access to the scattered photons correlated with the quantumdot spin has proven elusive. Recently, differential transmission and, independently, cavityassisted temporal correlation measurements have shown clear signatures of dressedstate formation under strong laser light excitation on neutral quantum dots^{17,18,19,20,21}. Noting all successful quantuminformation science (QIS) implementations on welldeveloped qubit candidates, such as trapped ions, have relied on spinselective resonance scattering^{22}, it is clear that an immediate goal for quantum dots is the observation of the full resonance fluorescence spectrum carrying the desired spinqubit information.
Coupling two states of a quantum system by a monochromatic laser results in scattered photons with distinct spectral and coherence properties that may be tuned as the properties of the laser (for example, power, frequency and polarization) are varied. Barring any dephasing mechanisms, when the effective Rabi frequency is much less than the spontaneous emission rate, the interference between the scattered photons and the laser field forms the basis of the abovementioned differentialtransmission technique. When the effective Rabi frequency is larger than the spontaneous emission rate, the electronic states are dressed (see Fig. 1a, inset)^{23}. The spectrum of the photons scattered in this limit exhibits a multiLorentzian structure known as the Mollow triplet^{8}—first observed on atomic sodium in 1975 (ref. 24) and as recent as 2007 on a single molecule^{25}. The central frequencies for these transitions are:
and the linewidth of each detuned sideband is (3/2)γ_{sp}. Here, ν_{0} is the bare quantumdot X^{−1} transition frequency, Δ is the laser frequency detuning from ν_{0} (negative for reddetuning) and (Ω_{b}) is the effective (bare) Rabi frequency.
We start by presenting the observation of the Mollow triplet in the resonance fluorescence spectrum from a singlequantumdot transition and then proceed to link this with the quantumdot spin. Figure 1a shows X^{−1} resonance fluorescence spectra on a linear–log scale for a range of laser powers (no external magnetic field). The laser is resonant with the doubly degenerate bare X^{−1} quantumdot transition frequency. For laser powers above 216 nW, two equalweight sidebands emerge, which, together with the central feature, constitute the Mollow triplet. The sharp peak in the central feature is residual laser background (see Supplementary Information, Fig. S2). Peaktopeak sideband splittings determined from this data are plotted in Fig. 1b against the square root of the laser power. In the strong excitation regime (), the linear fit confirms the dependence of the sideband splitting on the square root of the laser power.
The observation of the Mollow triplet from a quantum dot should not come as a surprise; however, the measured sideband linewidths are intriguing. Figure 1c shows a linear–linear zoomin on the Mollow sidebands for a laser power of 1.852 μW (Ω_{b}≈8γ_{sp}). When fitted with the resonance fluorescence spectrum (see Supplementary Information, Discussion), a transition linewidth of 343 (±39) MHz per sideband is extracted, in close agreement with the pure spontaneous emission rate of 227 (±7) MHz obtained from photoncorrelation measurements at an excitation power well below saturation. The linewidth places an upper bound of 81 MHz on further fast dephasing mechanisms as determined from γ_{total}=γ_{sp}+2γ_{dephasing}. This suggests that emission from the triplet sidebands of the dressed quantumdot transition may be at the transform limit. Further first and secondorder coherence experiments on the individual sidebands are necessary to determine the deviation from the Fouriertransform limit for the sideband photons.
In addition to the laser power, the sideband spectrum may also be tuned by the laser frequency. In Fig. 2a, the measured X^{−1} resonance fluorescence spectra, driven by 1.852 μW laser power (Ω_{b}≈8γ_{sp}), are plotted for a set of laserfrequency detunings (Δ). For comparison, Fig. 2b shows equation (1) as a function of the laser frequency detuning at fixed laser power. Measuring the spectral separation of the red sideband (when the laser is reddetuned by 2.48 GHz) from the blue sideband (when the laser is bluedetuned by 3.32 GHz) it is possible to achieve photon emission across a frequency band of ∼14 GHz. This is 40 times larger than the 356 MHz spontaneous emission rate, and is by no means an upper limit, but can be further increased by laser power and detuning. To relate this range to other tuning mechanisms, we emphasize that 16 GHz is the range obtainable through d.c. Stark shift of the X^{−1} transition throughout the whole singleelectron charging plateau^{5}. Alternatively, this is the same frequency shift that each of the two degenerate X^{−1} transitions experiences under an applied magnetic field of 1 T (ref. 26). The sideband splittings extracted from the data set of Fig. 2a are plotted in Fig. 2c as a function of laser detuning. The red fit curve with the functional form of is used to determine a bare Rabi frequency of 2.76±0.2 GHz. From this value, we determine a dipole moment of 27.8±0.2 Debye, in agreement with our differentialtransmission measurements.
The final part of this letter is on optical access to a quantumdot spin, through resonance fluorescence, where a finite magnetic field splits the electronic spin ground states, lifting the X^{−1} spin degeneracy. A reproduction of Fig. 2b under finite magnetic field and accounting for spin is presented in Fig. 3a. The two dressed Zeemansplit sidebands (the blue and red solid lines) are directly correlated to the spin state of the electron and their frequency splitting is controlled by laser detuning beyond that manifested by the magnetic field. In what follows, all frequencies are referenced to the zeromagneticfield quantumdot X^{−1} resonance. First, a 50 mT external magnetic field is applied in the Faraday configuration. In Fig. 3b, the fluorescence spectrum of the bluedetuned sideband (the blue rectangle in Fig. 3a) is plotted for laser detunings of 1.75, 1.25 and 0 GHz, from left to right. By varying the laser detuning, at constant power, the Zeeman splitting of the transitions induced by the magnetic field can be altered (Fig. 3b, panels 1 and 2) and even cancelled (Fig. 3b, panel 3).
What we have demonstrated is a combined outcome of the Zeeman and dynamic Stark effect^{6,18,27}, which enables us to tune independently the energy splitting of the ground and excited states. For InGaAs quantum dots, the electron and hole gfactors are known to be around −0.6 and 1.4 (ref. 26). Therefore, the ground and excitedstate manifolds respond differently to the external magnetic field. The dynamic Stark effect, however, is independent of either manifold’s Landé factor. Consequently, the two state manifolds in this regime exhibit level splittings corresponding to an effective Landé factor tuned by the properties of the laser. The essence of this effect lies in the imbalance of the effective Rabi frequencies () experienced by the two spin transitions. Here, we use the Δdependence to enforce this imbalance and show the cancellation of the magneticfieldinduced spin splitting. The condition given in panel 3 of Fig. 3b is particularly interesting, because both the ground and the excited states are identically split, resulting in an effective Landé factor of 0.4. The consequence is the generation of photons with full spectral overlap, but welldefined spin tags in their circular polarization state for any applied magnetic field strength. This is a regime that merits a thorough investigation for spin–photon entanglement^{28}.
Finally, laser detuning and magnetic field are used to imprint the spin information onto the resonance fluorescence spectrum in the form of a clear, backgroundfree, spectrally distinguished sideband doublet. Figure 4a shows a linear–log plot of the full emission spectrum of another quantum dot under 100 mT magnetic field, 13.2 μW laser power (Ω_{b}≈17γ_{sp}) and 2.5 GHz red laser detuning. The plot exhibits a distinctive fiveLorentzian structure in the resonance fluorescence spectrum beyond the previously discussed triplet and each sideband transition is now a clear doublet linked with a quantumdot electronic spin state. In total there are six features in the spectrum, but, much like the Mollow triplet, the central line comprises two degenerate transitions locked to the detuned laser frequency yielding a spectral signature for the Mollow quintuplet. A zoomin plot of the bluesideband doublet, indicated by the blue rectangle, is presented in Fig. 4b on a linear–linear scale. The red curve is a fit of two Lorentzians and the open circles represent the recorded signal in identical conditions except the single electron in the quantum dot is unloaded back to the reservoir eliminating the X^{−1} transitions (the closest possible quantumdot transition is detuned 1,290 GHz from the laser frequency). This background signal constitutes less than 2% of the total signal. We note here that for all laser powers above 617 nW, when the two sidebands are clearly separable, the total number of photons collected per sideband remains constant, confirming the absence of significant laser background in the abovequoted photon number.
For photonic QIS applications, collection efficiency is as important a factor as spectral purity, so we present an estimate of the photon number collected from the sideband emission. At 13.2 μW excitation power, more than 98% of the emission is coming from the sidebands. Integrating across the blue sideband within the 4 to 7 GHz window (bookkeeping for the cavity transmission and detector efficiencies), we estimate that 48,000 photons per second per spin sideband reach the input of our twomirror cavity. We note that the emission from the two spin sidebands is anticorrelated, determined by the electron spin. Therefore, by matching the cavity transmission spectrum to a spin sideband, quantumdot spin measurements with aboveunity signaltonoise ratio can be carried out within a time integration of around 1 ms. Although this timescale is already at the threshold of the singleshot spinreadout regime, straightforward technical improvements in the photon collection efficiency^{29} will further better this figure of merit.
Propelled by these results, our immediate research directions include the measurement of electronic spin state based on the split sideband detection and the observation of spin quantum jumps. In parallel, the optical tunability and the observation of emission correlations between the two sideband photons (showing the time ordering of the emission due to the Jaynes–Cummings ladder cascade)^{30} may serve both as a heralded photon source and as a sensitive spectroscopic probe for weakly coupled states near the original quantumdot transitions. This step will also be useful when used in conjunction with tunnelcoupled quantumdot pairs, thus probing more complex ground and excitedstate manifolds. Finally, the modest magnetic field value used in these experiments is chosen to avoid any significant spin pumping and nuclear spin polarization effects, while spectrally resolving the two spinselective transitions. Therefore, how the emission spectrum of the dressed states evolves when one or both of these mechanisms are significant is an interesting topic of research on its own. Each one of these next steps, if achieved, is expected to have a direct impact on both the pursuit of solidstate QIS and our understanding and control of mesoscopic physical systems.
Methods
The InAs/GaAs quantum dots studied were grown by molecular beam epitaxy and embedded in a Schottky diode heterostructure. An applied gate bias enables deterministic loading of individual electrons^{31} from a nearby reservoir (see Supplementary Information, Fig. S1a). The sample is housed in a magnetooptical bath cryostat and cooled to 4.2 K. A cubic zirconia solid immersion lens is used to improve both the lightfocusing and lightgathering power of the fibrebased confocal microscope. The differential transmission spectroscopy technique using a scanable singlemode diode laser with 1.2 MHz frequency and 0.5% power stabilization determines the exact spectral location of the X^{−1} transition(s). When the laser is tuned to the X^{−1} transition, resonant scattering from the quantum dot is collected through the second arm of the fibre confocal microscope. The emission is then sent through a moderatefinesse (∼750) twomirror Fabry–Perot cavity with a 30% throughput at the transmission peak and a 34.5 MHz spectral window of transmission (see Supplementary Information, Figs S2,S3) and subsequently analysed with a liquidnitrogencooled CCD (chargecoupled device). To suppress the background laser light and collect the resonance fluorescence spectrum, we operate the microscope in a darkfield configuration by placing a linear polarizer in the microscope collection arm that is perpendicular to the incoming linearly polarized laser field, providing an extinction of the laser greater than 5×10^{3}. The excitedstate lifetime is obtained from Hanbury–BrownandTwisstype photoncorrelation measurements using two singlephotoncounting avalanche photodiodes and recording a timedelay coincidence histogram.
Change history
01 December 2009
The authors wish to point out that in all versions of this Letter originally published, the pure spontaneous emission rate of 356 (±11) MHz quoted on pages 198 and 199 is overestimated by a factor or four owing to an instrumentationsetting error, and erroneously quoted in units of angular frequency. The correct number should read 227 (±7) MHz in linear frequency. The upper bound for fast dephasing mechanisms is therefore limited to 81 MHz, not 18 MHz. The main arguments of the paper are unaffected by this correction. These changes have been made in both PDF and HTML versions of this Letter.
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Acknowledgements
We thank A. Imamoğlu for his continuing support and guidance, S. Fält and A. Badolato for providing highquality quantumdot samples and G. Burkard, J. M. Taylor, H. Türeci, A. K. Swan, M. S. Ünlü, B. B. Goldberg and J.W. Pan for insightful discussions. This work was supported by the University of Cambridge and EPSRC Science and Innovation Awards. A.N.V. is supported by QIPIRC of EPSRC, Y.Z. is supported by the A. v. H. Foundation and LGFG and C.Y.L. is supported by the University of Cambridge, CSC and CAS.
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Nick Vamivakas, A., Zhao, Y., Lu, CY. et al. Spinresolved quantumdot resonance fluorescence. Nature Phys 5, 198–202 (2009). https://doi.org/10.1038/nphys1182
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DOI: https://doi.org/10.1038/nphys1182
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