Letter pubs.acs.org/NanoLett
Spin-Resolved Purcell Effect in a Quantum Dot Microcavity System Qijun Ren,† Jian Lu,*,† H. H. Tan,‡ Shan Wu,§ Liaoxin Sun,† Weihang Zhou,† Wei Xie,† Zheng Sun,† Yongyuan Zhu,§ C. Jagadish,‡ S. C. Shen,† and Zhanghai Chen*,† †
State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), and Department of Physics, Fudan University, Shanghai 200433, China ‡ Department of Electronic Materials Engineering, Research School of Physics and Engineering, The Australian National University, Canberra ACT 0200, Australia § National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China ABSTRACT: We demonstrate the spin selective coupling of the exciton state with cavity mode in a single quantum dot (QD)−micropillar cavity system. By tuning an external magnetic field, each spin polarized exciton state can be selectively coupled with the cavity mode due to the Zeeman effect. A significant enhancement of spontaneous emission rate of each spin state is achieved, giving rise to a tunable circular polarization degree from −90% to 93%. A four-level rate equation model is developed, and it agrees well with our experimental data. In addition, the coupling between photon mode and each exciton spin state is also achieved by varying temperature, demonstrating the full manipulation over the spin states in the QD-cavity system. Our results pave the way for the realization of future quantum light sources and the quantum information processing applications. KEYWORDS: Quantum dots, Purcell effect, spin polarization, cavity quantum electrodynamics, photonic structures
C
straightforward approach is to introduce an external magnetic field. A field-induced Zeeman effect lifts the degeneracy of the exciton spin states and brings the exciton energy into resonance with the cavity mode, which would give rise to the spin selective coupling of exciton to cavity mode. Recent work on the spinrelated exciton−photon interaction was demonstrated in strong coupling regime for both micropillar21,22 and photonic crystal cavity systems.23 However, in the weak coupling regime of spinrelated CQED, the experimental investigation has yet to be explored. In particular, CQED effects in a weak coupling regime, for example, the Purcell effect, is desirable for the realization of numerous quantum information processing schemes such as quantum CNOT gate and Bell-state analyzer with spin selectivity.1−3 Moreover, in recent years, the spinpolarized light source has attracted much attention for its important applications in spin-optoelectronics, quantum information transport, and so forth. So far, the main mechanisms for circularly polarized light emission are based on the electrical injection of spin-polarized carriers into the active region24 or the fabrication of time-reversal symmetry breaking structures.25 However, the relatively low circular polarization degrees are insufficient for further applications. By utilizing the spin-resolved Purcell effect in QD-microcavity system, one can efficiently control the spontaneous emission
avity quantum electrodynamics (CQED) effects, themed on the coupling between a single quantum emitter and an optical cavity, promise great opportunities in a broad range of applications such as quantum computation, quantum information processing,1−4 and novel quantum light sources.5−9 Over the past decade, considerable efforts have been devoted to the realization of fundamental CQED effects in a solid state system, including the Purcell effect,10−15 vacuum Rabi splitting,16,17 and the Jaynes−Cummings ladder18 of a single quantum dot (QD) coupling with a variety of microcavities.10−13,16−18 Two distinct regimes can be reached for the coupled QD−microcavity system, depending on the coupling strength between the QD and the optical cavity mode. In the weak coupling regime, the light−matter coupling strength is smaller than the combined exciton decay rate and cavity photon decay rate. The Purcell effect, that is, the modification of spontaneous emission (SE) rate of the QD due to the exciton−photon coupling, can be observed.10,18 In the strong coupling regime, the exciton− photon interaction is stronger than the bare exciton and photon decay rate, resulting in periodic energy exchange between the exciton and the photon, giving rise to the Rabi oscillations.19 So far, most of manipulations on the QD−microcavity interaction were performed by conventional temperature6,16,17 or electric field tuning.20 However, both tuning approaches have no control over the spin degree of freedom of excitons, leaving the underlying physics in spin-related CQED regime relatively unexplored. For the study of the exciton spin states interacting with the cavity mode and the control of these interactions, a © XXXX American Chemical Society
Received: February 27, 2012 Revised: June 1, 2012
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configuration. A typical micro-PL spectrum of a micropillar with the diameter of 2.5 μm under magnetic field of 2 T at 37.5 K and the corresponding peaks fitting are presented in Figure 1b. A single exciton transition from one QD is observed. It splits into two circularly polarized PL peaks in the presence of a magnetic field due to the Zeeman effect. Here, we denote the exciton spin state formed by an electron of spin 1/2 (−1/2) and a hole of spin −3/2 (3/2) as X↑ (X↓).23,27 A broader peak located at the higher energy side of the spectrum is identified as the cavity mode (labeled as C). The line width of this peak for this microcavity is about 265 μeV, corresponding to a Q factor of 4950. The crossing behavior observed in the magnetic field dependent second derivative PL mapping at 37.5 K in Figure 2a, shows that the cavity-QD system (labeled as QD1) operates in the weak coupling regime. In such a case, an enhancement of the SE rate of the X↑ transition at zero detuning (Purcell effect) can be expected.10−12 For the excitons in single QD, both spinpolarized exciton energies show quadratic behavior as a function of the magnetic field B due to the exciton diamagnetic shift. However, the cavity mode energy is almost unaffected, indicating the negligible variation of the refractive index of the GaAs and AlAs under magnetic field. The spin-polarized exciton emission energies under magnetic fields can be fitted with the function Ex± = E0 ± (1/2)gexcμBB + κB2, where E0 is the exciton emission energy without magnetic field, κ denotes the diamagnetic coefficient, gexc denotes the effective exciton g factor, and μB is the Bohr magneton.27,28 The magnetic field dependence of the exciton emissions from QD1 shown in Figure 2a was fitted, and the effective g factor and diamagnetic coefficient were extracted to be 1.66 and 12.3 μeV·T−2, respectively. This corresponds to total energy shift of 550 μeV and 76 μeV for X↑ and X↓ from 0 to 5 T, respectively, as shown in Figure 3a. The different energy shifts of the excitons and cavity mode under magnetic field give rise to the crossing of the X↑ transition and mode resonances at around 4 T, while the energy detunings between X↓ and the cavity mode do not change significantly over the range of magnetic field investigated. Figure 3c shows the intensities of both the X↑ and the X↓ transitions as a function of magnetic field for QD1. With the increase of B, the intensity of the X↑ transition also increases due to the decrease of X↑-C detuning (Δ↑). At 4 T (Δ↑ = 0), the intensity of the X↑ transition reaches a peak, which is by a factor of 75 higher compared to its value at low magnetic field, strongly indicating the Purcell enhanced X↑ emission rate at the spectral resonance with the cavity mode.20,29,30 On the other hand, since the detuning between X↓ and C mode is large at 0 T (Δ↓ = 388 μeV) and changes very little (76 μeV for B increasing from 0 to 5 T) due to the competitive driving of Zeeman effect and diamagnetic shift. The intensity of X↓ transition is small and fairly constant over this magnetic field range. The different behaviors of the X↑ and X↓ emissions under magnetic field make it possible to control the coupling of the X↑ and X↓ states with the cavity mode by an external magnetic field. Similarly, as shown in Figure 2b, the coupling of the X↓ transition with the cavity mode and hence the enhancement of the X↓ emission was also demonstrated with another suitable micropillar (d = 2.44 μm, labeled as QD2) at 39 K. In this sample, the exciton emission energy is higher than that of the cavity mode at 0 T, and the resonant coupling of X↓ and the cavity mode occurs at about 2.6 T. A strong enhancement of the X↓ emission was also found at the mode resonance, while
rate of exciton spin states. A dramatic enhancement of SE rate for one preferred exciton spin state relative to the other would be expected, and thus, controllable spin-polarized photon sources with a high circular polarization degree can be realized. Results and Discussion. In this letter, we present the magneto-optical investigation of the coupling between an exciton spin state of a single InGaAs QD and a high-quality micropillar cavity. Through a spin-resolved Purcell effect, we achieve selective enhancement of the SE rate of an exciton state with a specific spin configuration. This gives rise to the continuous tunability of the circular polarization degree of light emitted from the QDs and the enhanced circular polarization degree up to 93% in our experiments. The QD−microcavity samples were grown by metal organic chemical vapor deposition on a semi-insulating GaAs substrate. A λ thickness GaAs cavity is inserted between a 24 stack (top) and a 30 stack (bottom) of highly reflective GaAs/AlAs distributed Bragg reflectors (DBRs). Self-assembled In0.5Ga0.5As QDs were grown in the center of the cavity. The wafer was then processed by focused ion beam etching using a dual beam FEI Helios 600 NanoLab system to form the micropillar structures with circular cross section and diameters ranging from 1.5 to 3.5 μm. To fabricate high quality micropillar structures with smooth surfaces and vertical sidewalls, a successive four etching steps with different ion beam currents were employed. The beam current in fact determines the beam size for the local etching and redeposition rates.26 In the first etching step, a large beam current of 3.3 nA was chosen, and 8 μm conical pillar structures with rough sidewalls were formed; then the beam current was reduced to 470 pA and 130 pA in the following etching steps. To fine polish the sidewalls, at the final step, a beam current of 45 pA was used to further improve the structure qualities and obtain the micropillars with targeted diameters. Figure 1a shows the
Figure 1. (a) Scanning electron microscopy (SEM) image of a micropillar cavity with a diameter of 2.5 μm. (b) Typical PL spectrum was obtained at 37.5 K under a magnetic field of 2 T. The splitting of single exciton transition of a single QD to X↑ and X↓, as well as the fundamental mode C of the micropillar cavity are identified. Solid curves show the results of a multi-Lorentzian fitting.
SEM image of a typical micropillar with a diameter of 2.5 μm. It shows a smooth surface and sidewall with a negligible conicity of the micropillar. Magneto-photoluminescence (PL) studies were carried out using a confocal micro-PL setup with the 632.8 nm line of a He−Ne laser as the excitation source. Both the excitation and the collection are in the normal direction through the same objective with the laser spot size of about 2 μm. A magnetic field from 0 to 5 T is applied in the Faraday B
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Figure 2. Magnetic field dependent second derivative PL mapping spectra for X↑, X↓, and C emission of (a) QD1 at 37.5 K and (b) QD2 at 39 K. (c) PL mapping spectra for QD2-cavity emission as a function of temperature under a magnetic field of 3 T.
Figure 3. (a, b) Detunings of X↑ and X↓ emissions of QD1 and QD2 with respect to the cavity mode as functions of the applied magnetic field. Here we set the energy of the mode as invariant under a magnetic field. Solid curves are fitting curves. (c, d) Integrated intensities of X↑ (red) and X↓ (blue) emissions for QD1 and QD2 obtained from Lorentzian fittings of the PL spectra under different magnetic fields. (e, f) Linewidths of X↑ (red) and X↓ (blue) emissions of QD1 and QD2 as functions of the magnetic field. Solid curves are guides to the eye.
the X↑ transition was not effectively coupled to the cavity mode as it was monotonously far detuned from the cavity mode with increasing B. Figure 3d shows the intensities of the exciton emission extracted from Figure 2b. One can see that, under the magnetic field for resonant coupling, the X↓ emission intensity was about 4 times stronger than that at low field, showing the strong Purcell effect for X↓ state. Therefore, our experimental results demonstrate that one can achieve selective enhancement of the emission rate for any of the spin-polarized exciton emissions (X↑ or X↓ state) by applying an external magnetic field and hence change the relative intensities of X↑ and X↓ transitions. It should be noted that our measurements have been done by using a nonpolarized and nonresonant optical excitation. Besides the magnetic field tuning, temperature is also an effective parameter to tune the coupling of each exciton spin state with the cavity mode in a controlled way. Figure 2c shows the enhancement of X↑ or X↓ emissions of QD2 by varying
temperature at a fixed magnetic field of 3 T. We set the field at 3 T because the energy separation between X↑ and X↓ is 300 μeV at this field; this splitting is larger than the line width of the cavity mode and allows the study of individual coupling of each spin state with the cavity mode. When the temperature increased from 29 to 47 K, both spin polarized exciton emissions redshift faster than the cavity mode, and each of them shifts through resonance with the mode individually at different temperatures. The enhancement of the X↓ emission is observed at 38 K, while the X↑ state is off-resonant with the mode. For the X↑ exciton, the resonant coupling and thus the enhancement of emission are observed at higher temperature (42 K). These results clearly demonstrate the complete control of the coupled single exciton−cavity mode in the spin-resolved CQED regime. To quantify the QD−cavity coupling and determine the effective Purcell factor experienced by the QD, we modeled the system with four-level rate equations which include the C
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Figure 4. (a) Diagram of the transition between single exciton states under a magnetic field, from which the four-level rate equations are developed. (b, c) Circular polarization degree of QD1 and QD2 as functions of the magnetic field. The solid curves are the theoretical calculations based on four-level rate equations.
are shown in Figure 3c as solid curves. They agree well with our experimental results. A similar procedure was taken to fit the QD2 emissions, and good fitting was also obtained as shown in Figure 3d. Note that the enhancement of the intensity for X↓ in Figure 3d is not as large as that for X↑ in Figure 3c. This is due to the much smaller Δ↓ range for QD2 compared to the Δ↑ range for QD1. To minimize the experimentally induced error, we study the intensity ratio of the IX↑ and IX↓ emissions. We define the circular polarization degree as Pc = (IX↑ − IX↓)/(IX↑ + IX↓). The experimental polarization degree Pc (dots) and the rate equation simulation (solid curve) for QD1 (QD2) as functions of the magnetic field are presented in Figure 4b (Figure 4c). Remarkably, the magnetic field dependence of the polarization degree demonstrates a pronounced peak corresponding to the resonance between X↑ (X↓) state and the cavity mode. The decrease of the circular polarization degree with a further increase of the magnetic field is a direct manifestation of the spin-resolved Purcell effect. One can see from the figures that the rate equation simulations agree quantitatively with the experimental results. The best fitting yields an effective Purcell factor of 5.9 ± 2.0 for QD1 (4.6 ± 1.5 for QD2) and a circular polarization degree up to 93% at a magnetic field of 4 T for QD1 and −90% at 2.6 T for QD2. We found the time constant for the spin flip-flop process is about tens of times longer than τX, and this result is consistent with the existing measurement.31 Across the magnetic field range studied here, the intensity ratio between IX↑ and IX↓ as well as the circular polarization degree can be continuously tuned, enabling the control on polarization selectivity of a single QD spin state emission. To further explore the properties of coupling between the exciton spin states and the cavity, the magnetic field dependence of the PL linewidths of the X↑ and X↓ emissions for QD1 and QD2 with respect to the magnetic field are plotted in Figure 3e and f, respectively. It is obvious that the magnetic field dependence of the linewidths is similar to that of the intensity plots, and basically the two spin states behave in the same way when they are approaching the cavity resonance. In Figure 3e, the line width of the X↑ transition increases from 80 μeV (with Δ↑ = −388 μeV at 0 T) to about 250 μeV at 4 T (with Δ↑ = 0) and then decreases to 105 μeV at a magnetic field of about 5 T. For nonresonant excitation, the homogeneous broadening of single QD exciton transition can −1 be expressed as T−1 + (T*2)−1, where T1 is the 2 = (2T1) exciton radiative lifetime and T*2 is the pure dephasing time without recombination.32,33 The exciton radiative lifetime is modulated by the coupling with the cavity mode due to the Purcell effect. In addition, the radiative lifetime can be expressed as a Lorentzian function of the detuning between
biexciton state. The use of semiclassical rate equations for describing the emission from a single QD is justified in our case, as the data were obtained from cw optical excitations. Figure 4a illustrates the energy level diagram of a single QD in an external magnetic field. In our system, the QD is nonresonantly pumped with rates P↑ (P↓) for spin state X↑ (X↓) and decays by emitting photons into cavity mode with the emission rates Fp,Δ/τX. Fp,Δ is defined as Fp,Δ = Fp/(1 + 4Δ2/ γ2c ), where Fp is the effective Purcell factor and γc is the line width of the cavity mode.20,30 We consider the weak excitation limit and neglect the higher energy exciton state, which do not manifest themselves in our experiment. The rate equations for exciton and biexciton transitions with decay lifetimes τX and τXX in a QD can be described as:20,28,30 dPg dt
= −P↑Pg − P ↓Pg +
γ + Fp, Δ↑ τX
P X↑ +
γ + Fp, Δ↓ τX
P X↓
γ + Fp, Δ↑ dP X↑ γ 1 = P↑Pg − P X↑ − P ↓P X↓ + PXX − P X↑ τX τXX τflip dt +
1 τflop
P X↓
γ + Fp, Δ↓ dP X↓ γ P X↓ − P ↓P X↓ + PXX = P ↓Pg − τX τXX dt 1 1 P X↑ − P X↓ + τflip τflop
dPXX γ = 2P ↓P X↓ − 2 PXX τXX dt
where Pg is the occupation probability for the exciton ground state (empty dot) and PX↑ and PX↓ are the probabilities of having a single exciton with −1 spin (spin-up) and +1 spin (spin-down) configuration, respectively. τflip and τflop are the spin flip−flop transition time. We assume the PL measurement at saturation has pumping rates of P↑ ∝ (γ + Fp,Δ↑)1/2 and P↓ ∝ (γ + Fp,Δ↓)1/2.29,30 We note that in our case the measured cavity mode line width γc is actually larger than the value of a bare cavity by a factor of ((γ + Fp/)γ)1/2, due to the low pumping power.29,30 We modeled the cavity−QD system shown in Figure 2a using these rate equations. In the calculation, we take the experimentally measured cavity line width γc = 265 μeV, and the estimated values of γ ≈ 1, τX = 2τXX ≈ 1 ns according to refs 20 and 30.20,30 The calculated emission intensities IX↑ (IX↓) which are proportional to FP,Δ↑/((γ + Fp,Δ↑)1/2 + τX/τflop) (FP,Δ↓/((γ + Fp,Δ↓)1/2 + τX/τflip)) for each applied magnetic field D
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the cavity mode and the emitter. Therefore, we attribute the variation of the emission line width to the modification of the radiative lifetimes of spin-polarized excitons by the Purcell effect in a weak coupling regime. With the increase of magnetic field, the decay rate of the X↑ emission for QD1 is enhanced and the corresponding line width, which is inversely proportional to the decay rate, is broadened due to the decrease of Δ↑. After the X↑ energy crosses the cavity mode, the line width is narrowed again, showing the revival of its decay rate at large detuning.34,35 For the X↓ emission from QD1, the evolution of its line width is not as obvious as that of X↑ due to its small energy change with the applied magnetic field. We notice the line width of X↓ also increases slightly from 80 μeV to 89 μeV as the X↑ energy crosses with the cavity mode, then decreases to 82 μeV at 5 T. Again, for QD2, Figure 3f shows that the Purcell effect governs the line width change of X↓ and X↑ in the same manner as that for QD1. The comparison between linewidths of both X↑ and X↓ emissions clearly demonstrates the coupling between the two exciton spin states and the cavity mode and shows how the emission intensities of these states can be manipulated by an external magnetic field. In summary, we have observed the coupling of single QD exciton spin states with a micropillar cavity controlled by a magnetic field and temperature tuning of their spectral energies. The spin-resolved Purcell effect for both of spin-polarized exciton emissions was observed and analyzed with a four-level scheme. The experimental results as well as the theoretical simulations demonstrate that excitons with specific spin configuration can be selectively coupled to light, and their decay rates can be controlled by magnetic manipulation. Our results demonstrate the feasibility of controlling the polarization of single QD emission, and we achieve photon emission with a circular polarization degree up to 93%, which paves the way for the realization of future quantum light sources and quantum information applications.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected];
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
The work is funded by 973 projects of China (No. 2011CB925600), NSFC (No. 91121007), and ISTCP (No. 2010DFA02600). The authors are grateful to the ARC and ANFF for sample fabrication and Alexey Kavokin for stimulating discussion.
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