Abstract
Strongly coupled quantum dotcavity systems provide a nonlinear configuration of hybridized lightmatter states with promising quantumoptical applications. Here, we investigate the coherent interaction between strong laser pulses and quantum dotcavity polaritons. Resonant excitation of polaritonic states and their interaction with phonons allow us to observe coherent Rabi oscillations and Ramsey fringes. Furthermore, we demonstrate complete coherent control of a quantum dotphotonic crystal cavity based quantumbit. By controlling the excitation power and phase in a twopulse excitation scheme we achieve access to the full Bloch sphere. Quantumoptical simulations are in good agreement with our experiments and provide insight into the decoherence mechanisms.
Introduction
The rapid technological development of classical computing will soon reach fundamental limitations resulting from device miniaturization. However, the quantum regime and integration of optics on existing computing platforms offer a wide range of possibilities for overcoming the obstacles of Moore’s law or charge carrier mobility.
First approaches to develop quantum technologies were made in atomic physics^{1}, while realworld applications are more likely to be realized in solid state quantum systems^{2,3,4,5}. Selfassembled quantum dots (QDs) are particularly attractive due to their optical addressability, their narrow linewidths and ease of integration into optoelectronic devices. To make use of these promising characteristics, complete coherent control of the quantum device is a necessity. For QDs this has already been widely explored in excitons^{6,7,8}. Yet, the operationalrange and the physical properties of QDs are limited, in particular low emission rates impede their application as nonclassical light sources in photonic devices. Furthermore, the strength of their coupling to light poses challenges for the onchip realization of quantum networks.
In contrast, strongly coupled QDcavity systems offer highly efficient outcoupling allowing for onchip integration^{9,10,11,12}. Moreover, they have proven to be extremely versatile, since the hybridization of electromagnetic waves and matter forms polaritons, yielding rich physical characteristics. In particular, it is possible to control the spontaneous emission of a QD in an optical cavity^{13}, while the interaction of excitons and phonons^{14} allows for applications such as indistinguishable photon generation^{15}. Future applications can profit from the systems’ interesting and especially useful physics far beyond that offered by QDs alone. Examples include highfidelity photonblockade^{16}, nonclassical light generation^{17}, single spinphoton interfaces enabling compact onchip quantum circuits^{18} and dynamic cavity frequency tuning with surface acoustic waves^{19}. One crucial element that is needed for successful onchip integration of strongly coupled systems is coherent control.
As discussed theoretically^{20}, dissipation hindered the complete coherent control of QDcavity systems so far. In this work, we overcome this dissipation obstacle and demonstrate complete coherent control of a QDphotonic crystal cavity system. In experiments supported by simulations, we map out the excitation power and phasedependent emission from a polaritonic system and we demonstrate full access of the Bloch sphere.
Results
Strongly coupled QDphotonic crystal cavity system
A system composed of a single QD strongly coupled to an L3 photonic crystal cavity^{21} is the focus of our investigations. This type of cavity offers very high quality factors as well as low mode volumes^{22}, which allows the lightmatter interaction to reach the strongcoupling regime^{23}. Details on the sample fabrication can be found in the Methods section.
The physics of a strongly coupled system is described by the JaynesCummings (JC) model^{24}, with the Hamiltonian . The contributions are
with the cavity field Hamiltonian , the QD Hamiltonian and the QDcavity interaction Hamiltonian , respectively. The cavity frequency is given by ω_{C}, while a is the cavity mode photon annihilation operator, σ the QD’s lowering operator, Δ the QDcavity detuning and g the coupling strength of the quantum emitter and the cavity.
A full description of the system’s complex eigenenergies is obtained by the addition of dissipation to the system and consists of a series of polariton rungs^{25}:
where represents the energy of the nth rung, while κ and γ are the cavity and the QD energy decay rates, respectively.
The energy level structure resulting from equation 2, called the JC ladder, is shown in Fig. 1a. The polariton rungs are indexed by n and each rung is divided into a lower polariton (LPn) and an upper polariton (UPn). Red dotted lines indicate the energy levels of the uncoupled quantum emitter and blue dashed lines the ones of the cavity. The polariton branches show anticrossings which are known as a convincing signature of strong coupling^{26,27}.
Experimentally, the anticrossing of the lowest energy rung can be measured using crosspolarized reflectivity^{28}. The result of a typical measurement is presented in Fig. 1b. Here, the detuning between QD and cavity is controlled by changing the sample temperature^{23,28,29}. Fitting this data with equation 2 reveals values of GHz and GHz. The value of γ cannot be fitted directly as it is much smaller than the other rates due to the highly dissipative character of solidstate systems. Typical values in literature are GHz^{28,30}. Importantly, compared to QDs in a bulk environment, the QD energy decay rate is further reduced due to Purcell suppression in the photonic bandgap.
Coherent control of JC polaritons
The coherent control of the population of exciton states in selfassembled QDs^{7,31,32} or of quantum wellmicrocavity polaritons^{33} is routinely performed. However, for polaritonic states of JC systems, the situation is more complicated due to the higher rungs of the JC ladder. In particular, for currently achievable system parameters and the QD in resonance with the cavity, a shortpulsed laser in resonance with the first rung would also be resonant with higher rungs of the ladder, preventing coherent control of a specific rung^{16}. Moreover, the presence of the higher rungs results in strong coherent scattering of the excitation laser^{34}, which would dominate over the signal of interest at excitation powers needed for coherent control.
We will now detail how we overcome both of these obstacles. To achieve a coherent interaction with a specific rung, the excitation laser needs to be spectrally narrow enough to prevent overlap with other rungs. At the same time, the pulse length needs to be shorter than the state lifetime to prevent reexcitation. At zero QDcavity detuning all resonances of the JC ladder are very close. However, with increasing detuning between the QD and cavity, the energy difference between the two polariton branches within one rung becomes larger as the polaritons gradually evolve into the bare QD and cavity states^{16}. Importantly, when exciting the QDlike polaritonic branch with increasing detuning, the overlap with higher rungs decreases^{16}. Moreover, when the state becomes more QDlike, then the lifetime increases. This allows for a compromise between laser spectral width and pulse length to resonantly access the individual polariton branches (see Fig. 1a,b).
Note that the polaritons are a superposition of the bare QD eigenstates and the bare cavity eigenstates. During the experiments we will focus on detunings of Δ = 6.75 g and Δ = 8.5 g. At a detuning of 6.75 g we find UP1 to be approximately 97.9% QDlike and 2.1% cavitylike, while it is approximately 98.7% QDlike and 1.3% cavitylike at a detuning of 8.5 g. Although the influence of the cavity seems to be insignificant, the QDlike polariton emits almost only through the cavity mode. This is due to the Purcell suppression of noncavity modes and is true for detunings of up to approximately 60 g^{16}. In fact, the cavity completely determines the system’s dynamics and the strong coupling leads to emission rates and an oscillator strength that is three orders of magnitude stronger than in the weak coupling regime. Thus, it is extremely difficult to observe the emission of a weakly coupled system in standard crosspolarized resonance fluorescence since the coherent scattering of the laser light dominates the signal.
We exploit the efficient excitonphonon coupling to avoid the strong coherent scattering of the excitation laser dominating the resonance fluorescence signal. Investigations of the polaritonphonon interactions have led to a better understanding of the system dynamics^{14,35}. Specifically, it was found that excitonphonon coupling leads to a population transfer between the polariton branches^{17,36}. This allows us to monitor the coherent interaction between a laser and the polariton rung UP1 by monitoring the spectrallyfiltered emission from LP1. Intuitively, one would expect this phononassisted emission to be weak. However, for a positive detuning of the QD, the radiative recombination rate of UP1 is strongly Purcell suppressed (as a result of the photonic bandgap), while the radiative decay rate of LP1 is very fast. Therefore, at detunings of , where the phononassisted population transfer rate from UP1 to LP1 is large compared to , most emission actually occurs from LP1^{17}.
In order to further reduce a leakage of the coherently scattered light into our detection channel, the technique of selfhomodyne suppression (SHS)^{34} is applied, where we carefully adjust polarization and focus to interfere the JC coherently scattered light with light scattered from abovethelightline modes destructively.
Rabi oscillations
Rabi oscillations are a fundamental signature of the coherent interaction between the polaritons and the excitation laser. To this end, we perform powerdependent measurements, where we resonantly excite UP1 while we detect the emission from LP1 as discussed above. Note that we did not subtract a background from the data, since the laser light is spectrally separated from the emission of LP1 and thus is excluded by spectral filtering. A typical measurement for a QDcavity detuning of Δ = 6.75 g with 18 ps long pulses and increasing excitation power is presented in Fig. 1c. Clearly, strongly damped oscillations are observed.
We drive the system resonantly as illustrated with a blue arrow in Fig. 1a. In the Bloch sphere this can be described by an excitation pulse inducing a rotation of the Bloch vector about a rotation axis x. This pulse can generate superpositions of the ground and excited state. With increasing excitation power, the Bloch vector is brought all the way to the excited state and further to the ground state, again. A pulse with the area of (m + 1)π, with results in the excited state yielding maximum emission from the system, while a pulse with the area of 2mπ results in the ground state yielding minimum emission.
In order to get a better understanding of the damping mechanisms, we developed a quantum optical model based on a phenomenological twolevel system using the Quantum Toolbox in PYTHON (QuTiP)^{37}. A fit to the data with this model is shown in Fig. 1c as a red line and produces good overall agreement. This simulation reveals that dephasing originating from phonons^{8} and excitation pulses is causing the strong damping observed in the measurements.
Ramsey fringes
To obtain the system’s coherence properties, we performed twopulse experiments. For that purpose, the excitation path was altered as illustrated in Fig. 2a. A 50:50 beamsplitter divides the excitation pulse, sending one pulse through a linear delay line. This allows for variable pulse delays in the psregime, while fine tuning of the delay in the fsregime is realized with a piezocontrolled retroreflector. Therefore, we are able to excite the system using two pulses with precise control of the interpulse time delay.
From the Rabi oscillations in Fig. 1c, the excitation power for each arm of the delay line is carefully chosen to be . Typical results of such a twopulse experiment are presented in Fig. 2b. Here, the QDcavity detuning is , while the coarse pulse separation is set to be ps and is altered in the range of 0–11 fs. Clear oscillations  Ramsey fringes  are observed. The rotation of the Bloch vector is illustrated in Fig. 2c. Starting in the ground state, the first pulse pivots the Bloch vector about the rotation axis x, resulting in a superposition lying on the equator of the Bloch sphere (illustrated in red in Fig. 2c). In the rotating frame, the Bloch vector does not precess on the equator. Instead, the phase difference of the two excitation pulses introduces a second rotation axis x′ (green dashed line in Fig. 2c). Finally, the second pulse pivots the Bloch vector about x′, which is either towards the ground state (as shown in orange in Fig. 2c) or towards the excited state, depending on the phase difference of the two pulses. Thus, the final state is strongly dependent on the pulse separation. This dependence can be monitored by detecting the emission from the excited state. After the arrival of the second excitation pulse, the system can end up in the excited state corresponding to the maxima in the Ramsey fringes, the ground state corresponding to the minima (as illustrated in Fig. 2c), or states in between.
To simulate this experiment, we take the measured polariton lifetime (65 ± 5 ps at Δ = 6.75 g)^{17}, the damping parameters obtained for the Rabi oscillations (presented above) and the alternated pulse separation into account. Then we calculate the population probability of the excited state. The results are presented in Fig. 2b as a red line and show good agreement with the measured emission from LP1.
In order to experimentally determine the dephasing time of our system, we repeat the Ramsey fringe measurements for coarse pulse separations from 0 ps to >100 ps. The evolution of the fringe amplitudes with increasing pulse separation for QDcavity detunings of Δ = 6.75 g and Δ = 8.5 g are shown in Fig. 2d,e, respectively.
We extract the dephasing times by fitting the data with an exponential decay function, resulting in ps and ps, respectively.
Using the same model as in Fig. 2b and the experimentally obtained polariton lifetimes of 65 ± 5 ps (Δ = 6.75 g) and 71 ± 7 ps (Δ = 8.5 g)^{17}, we can reproduce the measured data in simulations. The results are presented as red solid lines in Fig. 2d,e, showing good agreement. Our simulations reveal that the dephasing time is mainly limited by an excitation powerdependent and a phononinduced dephasing^{38,39}. Only for small delay times, the measured amplitudes are smaller than the simulated ones. The mismatch for small pulse separations between data and simulation may result from the interference of the excitation pulses when they overlap in time. Although the model takes this into account, it is not perfectly consistent with the data, probably due to the experimentally limited stability of the phase, which is extremely sensitive when the pulses overlap.
Complete Coherent Control
We now turn our attention to complete coherent control of the polariton on the Bloch sphere. To this end, we perform experiments in which we vary both, the excitation power and phase difference in a twopulse experiment.
In Fig. 3a we present the measured emission from LP1 under resonant excitation of UP1 with two pulses. The pulse separation in this measurement is set to ≈40 ps and altered by 0–11 fs, while the excitation pulse powers are independently increased.
The data clearly reveals firstorder maxima at an excitation power of per pulse, followed by minima at an excitation power of π per pulse. We note here that resolving the secondorder maxima with sufficient contrast is extremely difficult, since the strong powerdependent damping resulting from the polaritonphonon coupling increases with the laser power. This effect originates from the hybridization of the polariton levels. With increasing excitation power higher rungs start to mix with UP1, opening up channels for more phonon interaction within the system^{17}. Another effect reducing the visibility of the secondorder maxima is a very small sample drift in the He flow cryostat during the long measurement time of 30 min and longer. Due to this drift, the effect of the sensitive technique SHS is reduced. In addition to that, the excitation and the detection efficiency suffer from the drift.
Again, we can explain the experiment in the Bloch sphere picture: Depending on the excitation power, the first pulse will rotate the Bloch vector to a corresponding superposition of ground and excited state. Thus, using the phase difference between the pulses, the second pulse can rotate the Bloch vector across the sphere and we can access any point on the Bloch sphere by varying the excitation power.
For our experimental results this means that complete coherent control is successfully demonstrated. The whole Bloch sphere can be accessed with an excitation power of π per pulse, which corresponds to the firstorder minima in the complete coherent control measurements.
Our simulations with the quantum optical model that already show good agreement for Rabi oscillations and Ramsey fringes support our experimental findings and are presented in Fig. 3b.
Conclusion
In this work, we investigate the possibility to perform coherent optical control of a QD strongly coupled to a photonic crystal cavity. The strong excitonphonon interaction within the system facilitates a population transfer from the upper to the lower polariton, which significantly increases the emission rates and allows for sophisticated excitationdetection schemes. Using a crosspolarized setup combined with spectral filtering and selfhomodyne^{34} suppression allows us to infer the population of the polariton state after the interaction with one or two short optical pulses.
With the observation of Rabi oscillations, we provide fundamental confirmation of the coherent interaction between the laser and a polaritonic state. Moreover, the successful demonstrations of Ramsey fringes and finally complete coherent control provide evidence that onchip integrated photonic crystal cavity polaritonbased quantum optical systems can be controlled. Compared to QDs alone, we can benefit from all advantages of the QDphotonic crystal cavity system, such as the efficient photonic interface^{9,15,23,40,41} and unprecedented fast emission rates in nonclassical light generation^{17}, while retaining full access to the Bloch sphere.
To support, understand and interpret the experimental results, we also developed a phenomenological quantum optical model, which produces good overall agreement with the measurements. We find significant phononinduced dephasing, which comes along with a population transfer from UP1 to LP1, facilitating single photon emission from LP1^{17} and indistinguishable photon generation at elevated temperature and unprecedented fast emission rates from UP1^{15}. This interaction also has a strong influence on the excitation conditions for highfidelity photon blockade^{16,17}. In particular, the phonon interaction shortens the lifetime of the polaritons and shorter excitation pulse lengths are required to reach the lowest second order coherence values. Combining our demonstration of coherent control with efficient coupling to waveguides^{42}, would make strongly coupled QDphotonic crystal cavity systems viable candidates for nonclassical onchip photonic devices.
Methods
Sample fabrication
The MBEgrown structure consists of an ~900 nm thick Al_{0.8}Ga_{0.2}As sacrificial layer followed by a 145 nm thick GaAs layer containing a single layer of InAs QDs. Our growth conditions result in a typical QD density of (60–80) μm^{−2}. Using 100 keV ebeam lithography with ZEP resist, followed by reactive ion etching and HF removal of the sacrificial layer, we define the photonic crystal cavity. The photonic crystal lattice constant was a = 246 nm and the hole radius r ~ 60 nm. The cavity fabricated is a linear threehole defect (L3) cavity. To improve the cavity quality factor, holes adjacent to the cavity were shifted.
Optical spectroscopy
All optical measurements were performed with a liquid helium flow cryostat at temperatures in the range 20–30 K. For excitation and detection, a microscope objective with a numeric aperture of NA = 0.75 was used. Crosspolarized measurements were performed using a polarizing beam splitter. To further enhance the extinction ratio, additional thin film linear polarizers were placed in the excitation/detection pathways and a single mode fibre was used to spatially filter the detection signal. Furthermore, two waveplates were placed between the beamsplitter and microscope objective: a halfwave plate to rotate the polarization relative to the cavity and a quarterwave plate to correct for birefringence of the optics and sample itself. Photons are detected after spectral filtering with a single photon avalanche diode.
The thin film polarizers and polarizing beamsplitters allow us to achieve an extinction ratio of 10^{−7} between excitation and detection path on bulk. This suppression ratio is large enough such that light geometrically rotated by the high NA objective plays little role in the ultimate laser suppression. Instead, the amount of light classically scattered into the detection channel is determined by the fidelity of the selfhomodyne effect. Experimentally, we previously found that this effect was capable of interferometrically cancelling >95% of the light scattered through the L3 cavity’s fundamental mode^{34}. In light of this strong suppression, no background has been subtracted from the experimental data.
Throughout the measurements we use a picosecond pulsed laser with 80.2 MHz repetition rate with 3ps laser pulses. We use a 4f pulse shaper with an 1800 lines/mm grating and a 40 cm lens to create 18 ps long pulses.
Simulations
The simulations in this paper are performed using the Quantum Toolkit in PYTHON (QuTiP)^{37}. The model contains of a two level system described by the Hamiltonian , where
is the unperturbed term in the rotating frame with the ground state frequency ω_{cgs} = 0, the eigenfrequency of the system ω_{0} and the frequency of the excitation laser ω_{L} = ω_{0}. While the driving term is given by
with excitation power Ω. The model includes excitation with either one excitation pulse for Rabi oscillations or with two laser pulses with a pulse separation of Δt, introducing a phase shift, for Ramsey fringes and complete coherent control. For all experiments the evolution of the population of the excited state is calculated with respect to the time. In order to do so, the evolution of the density matrix is calculated in the rotating frame
and we numerically integrated equation 5. Each collapse operator c_{j} is included in the model as a Lindblad superoperator . The collapse operators used are: The radiative decay
with the detuning dependent radiative decay rate γ, the phonon dephasing
with a phonon dephasing rate of and a dephasing term that depends on the excitation power
with the fitting parameter . This sum of population directly corresponds to the photon emission of the system^{43} and produces good agreement to all experiments presented throughout this paper.
Additional Information
How to cite this article: Dory, C. et al. Complete Coherent Control of a Quantum Dot Strongly Coupled to a Nanocavity. Sci. Rep. 6, 25172; doi: 10.1038/srep25172 (2016).
References
Monroe, C. Quantum information processing with atoms and photons. Nature 416, 238–246 (2002).
Vučković, J. & Yamamoto, Y. Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot. Appl. Phys. Lett. 82, 2374 (2003).
Jelezko, F. & Wachtrup, J. Single defect centres in diamond: A review. Phys. Status Solidi (A) 203, 3207–3225 (2006).
Michler, P. Single Semiconductor Quantum Dots. Springer (2009).
MasBalleste, R., GomezNavarro, C., GomezHerrero, J. & Zamora, F. 2D materials: to graphene and beyond. R. Soc. Chem. Adv. 3, 20–30 (2011).
Stievater, T. H. et al. Rabi Oscillations of Excitons in Single Quantum Dots. Phys. Rev. Lett. 87, 133603 (2001).
Zrenner, A. et al. Coherent properties of a twolevel system based on a quantumdot photodiode. Nature 418, 612–614 (2002).
Ramsay, A. J. A review of the coherent optical control of the exciton and spin states of semiconductor quantum dots. Semicond. Sci. Technol. 25, 103001 (2010).
Englund, D. et al. Controlling the Spontaneous Emission Rate of Single Quantum Dots in a 2D Photonic Crystal. Phys. Rev. Lett. 95, 013904 (2005).
Brossard, F. S. F. et al. Strongly coupled single quantum dot in a photonic crystal waveguide cavity. Appl. Phys. Lett. 97, 111101 (2010).
Reinhard, A. et al. Strongly correlated photons on a chip. Nature Photon. 6, 93–96 (2011).
Kim, H., Bose, R., Shen, T., Solomon, G. & Waks, E. A quantum logic gate between a solidstate quantum bit and a photon. Nature Photon. 7, 373–377 (2013).
Lodahl, P. et al. Controlling the dynamics of spontaneous emission from quantum dots by photonic crystals. Nature 430, 654–657 (2004).
WilsonRae, I. & Imamoglu, A. Quantum dot cavityQED in the presence of strong electronphonon interactions. Phys. Rev. B 65, 235311 (2002).
Müller, K. et al. Nanocavityenabled ultrafast generation of highlyindistinguishable photons. arXiv preprint, arXiv:1512.05626 (2015).
Müller, K. et al. Coherent Generation of Nonclassical Light on Chip via Detuned Photon Blockade. Phys. Rev. Lett. 114, 233601 (2015).
Müller, K. et al. Ultrafast PolaritonPhonon Dynamics of Strongly Coupled Quantum DotNanocavity Systems. Phys. Rev. X 5, 031006 (2015).
Sun, S., Kim, H., Solomon, G. S. & Waks, E. A quantum phase switch between a single solidstate spin and a photon. Nat. Nano, doi: 10.1038/nnano.2015.334 (2016).
Blattmann, R., Krenner, H. J., Kohler, S. & Hänggi, P., Entanglement creation in a quantumdotnanocavity system by Fouriersynthesized acoustic pulses. Phys. Rev. A 89, 012327 (2014).
Clark, S. M., Fu, K. M. C., Ladd, T. D. & Yamamoto, Y. Quantum computers based on electron spins controlled by ultrafast offresonant single optical pulses. Phys. Rev. Lett. 99, 040501 (2007).
Akahane, Y., Asano, T., Song, B.S. S. & Noda, S. HighQ photonic nanocavity in a twodimensional photonic crystal. Nature 425, 944–947 (2003).
Arakawa, Y., Iwamoto, S., Nomura, M., Tandaechanurat, A. & Ota, Y. Cavity Quantum Electrodynamics and Lasing Oscillation in Single Quantum DotPhotonic Crystal Nanocavity Coupled Systems. IEEE J. Sel. Top. Quantum Electron. 18, 1818–1829 (2012).
Hennessy, K. et al. Quantum nature of a strongly coupled single quantum dotcavity system. Nature 445, 896–899 (2007).
Jaynes, E. T. & Cummings, F. W. Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE 51, 89–109 (1963).
Laussy, F. P., del Valle, E., Schrapp, M., Laucht, A. & Finley, J. J. Climbing the JaynesCummings ladder by photon counting. J. Nanophotonics 6, 061803 (2012).
Reithmaier, J. P. et al. Strong coupling in a single quantum dotsemiconductor microcavity system. Nature 432, 197–200 (2004).
Peter, E. et al. ExcitonPhoton StrongCoupling Regime for a Single Quantum Dot Embedded in a Microcavity. Phys. Rev. Lett. 95, 067401 (2005).
Englund, D. et al. Controlling cavity reflectivity with a single quantum dot. Nature 450, 857–861 (2007).
Kaniber, M. et al. Tunable single quantum dot nanocavities for cavity QED experiments. J. Phys. Condens. Matter 20, 454209 (2008).
Kaniber, M. et al. Highly efficient singlephoton emission from single quantum dots within a twodimensional photonic bandgap. Phys. Rev. B 77, 073312 (2008).
Gaudreau, L. et al. Coherent control of threespin states in a triple quantum dot. Nat. Phys. 8, 54–58 (2011).
Webster, L. A. et al. Coherent Control to Prepare an InAs Quantum Dot for SpinPhoton Entanglement. Phys. Rev. Lett. 112, 126801 (2014).
Dominici, L. et al. Ultrafast Control and Rabi Oscillations of Polaritons. Phys. Rev. Lett. 113, 226401 (2014).
Fischer, K. A. et al. Selfhomodyne measurement of a dynamic Mollow triplet in the solid state. Nature Photon, doi: 10.1038/nphoton.2015.276 (2016).
Ota, Y., Iwamoto, S., Kumagai, N. & Arakawa, Y. Impact of interactions on quantumdot cavity quantum electrodynamics. arXiv preprint, arXiv:0908.0788 (2009).
Hohenester, U. et al. Phononassisted transitions from quantum dot excitons to cavity photons. Phys. Rev. B 80, 201311 (2009).
Johansson, J. R., Nation, P. D. & Nori, F. QuTiP 2: A Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 184, 1234–1240 (2013).
Ramsay, A. J. et al. Damping of Exciton Rabi Rotations by Acoustic Phonons in Optically Excited InGaAs/GaAs Quantum Dots. Phys. Rev. Lett. 104, 017402 (2010).
Ramsay, A. J. et al. PhononInduced RabiFrequency Renormalization of Optically Driven Single InGaAs/GaAs Quantum Dots. Phys. Rev. Lett. 105, 177402 (2010).
Laurent, S. et al. Indistinguishable single photons from a singlequantum dot in a twodimensional photonic crystal cavity. Appl. Phys. Lett. 87, 163107 (2005).
Majumdar, A., Rundquist, A., Bajcsy, M. & Vučković, J. Cavity quantum electrodynamics with a single quantum dot coupled to a photonic molecule. Phys. Rev. B 86, 045315 (2012).
Faraon, A., Waks, E., Englund, D., Fushman, I. & Vučković, J. Efficient photonic crystal cavitywaveguide couplers. Appl. Phys. Lett. 90, 073102 (2007).
Kaer, P., Nielsen, T. R. R., Lodahl, P., Jauho, A. P. & Mørk, J. Microscopic theory of phononinduced effects on semiconductor quantum dot decay dynamics in cavity QED. Phys. Rev. B 86, 085302 (2012).
Acknowledgements
We gratefully acknowledge financial support from the Air Force Office of Scientific Research, MURI center for multifunctional lightmatter interfaces based on atoms and solids (Grant No. FA95501210025) and support from the Army Research Office (Grant No. W911NF1310309). KAF acknowledges support from the Lu Stanford Graduate Fellowship and the National Defense Science and Engineering Graduate Fellowship. KM acknowledges support from the Alexander von Humboldt Foundation. KGL acknowledges support from the Swiss National Science Foundation. JLZ acknowledges support from the Stanford Graduate Fellowship. YK acknowledges support from the Stanford Graduate Fellowship and the National Defense Science and Engineering Graduate Fellowship.
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Contributions
C.D., K.M. and K.G.L. performed the experiments. T.S. performed the MBE growth of the QD structure. A.R. and T.S. fabricated the photonic crystal device. C.D. and K.A.F. performed the theoretical work and simulations. J.L.Z. and Y.K. provided expertise. J.V. supervised the entire project. All authors contributed to discussions and writing the manuscript.
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Dory, C., Fischer, K., Müller, K. et al. Complete Coherent Control of a Quantum Dot Strongly Coupled to a Nanocavity. Sci Rep 6, 25172 (2016). https://doi.org/10.1038/srep25172
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DOI: https://doi.org/10.1038/srep25172
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