ARTICLE IN PRESS
Physica E 40 (2008) 2004–2006 www.elsevier.com/locate/physe
p-Shell Rabi-flopping and single photon emission in an InGaAs/GaAs quantum dot P. Estera,, L. Lackmanna, M.C. Hu¨bnera, S. Michaelis de Vasconcellosa, A. Zrennera, M. Bichlerb a Universita¨t Paderborn, Warburger StraX e 100, D-33098 Paderborn, Germany Walter Schottky Institut, TU Mu¨nchen, Am Coulombwall, D-85748 Garching, Germany
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Available online 29 September 2007
Abstract Very clean single photon emission from a single InGaAs/GaAs quantum dot is demonstrated by the use of a coherent optical state preparation. We present a concept for single photon emission, which uses p-shell Rabi-flopping followed by a sequence of relaxation and recombination. The proof of the (clean) single photon emission is performed by photon correlation measurements. r 2007 Published by Elsevier B.V. PACS: 78.67.Hc; 78.55.m Keywords: Antibunching; Single photon emission; Rabi oscillation; Coherent manipulation
The demonstration of a single photon emitters employing single semiconductor QDs was first reported by Michler et al. [1] followed by many other groups. The generally used concept applies a strong, incoherent and non-resonant inter-band excitation. A sequential decay of the excited multi-excitonic state will finally result in a single exciton in the ground state, which generates the desired single photon emission. The spectral selection of the last photon of the decay cascade is possible due to different renormalization energies of the various multi-excitonic states. Thereby strong excitation intensities are necessary to avoid the case of a missing excitation. A defined excitation of a single exciton would be preferable to the non resonant excitation scheme described above. This can be realized by coherent state preparation. The excellent performance of a coherent manipulation of the single exciton ground state has been shown in previous works [2]. Due to the spectral overlap between psexcitation in the s-shell and single photon emission, we have to perform the coherent state preparation in the Corresponding author. Tel.: +49 5251 60 2689; fax: +49 5251 60 2687.
E-mail addresses:
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[email protected] (P. Ester). URL: http://www.nanooptik.upb.de (P. Ester). 1386-9477/$ - see front matter r 2007 Published by Elsevier B.V. doi:10.1016/j.physe.2007.09.129
spectrally separated p-shell with subsequent relaxation to the ground state, followed by single photon emission. The scheme of our approach for the single photon emission is sketched in the inset of Fig. 1. After the coherent excitation of the p-shell ðjX p iÞ via a p-pulse the generated exciton relaxes into the ground state ðjX s iÞ and subsequently decays by spontaneous emission. The used sample was grown by molecular beam epitaxy on a (1 0 0) nþ -GaAs substrate. The QDs are incorporated into a n–i-Schottky diode. The use of a tunable sample structure (n–i-Schottky) allows for a proper selection of the photoluminescence (PL) regime controlled by an internal electrical field. Thereby we can avoid the regimes of charged excitons and tunneling emission (photocurrent, PC). The QDs are embedded in a 360 nm thick intrinsic GaAs-layer. The distance from the QD layer to the ndoped back contact amounts to 40 nm. A 5 nm thick semitransparent titanium layer is used as a Schottky top contact, which also provides a homogeneous electrical field distribution in the QD region. The QDs on the sample can be individual addressed via near field shadow masks with different hole diameters. The QD used here is located under a hole with 300 nm diameter. Due to the integration of the QD into the Schottky diode this sample is capable for PC
ARTICLE IN PRESS P. Ester et al. / Physica E 40 (2008) 2004–2006
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Fig. 1. Characterization of higher excited QD states using PLE technique. The energy is displayed with respect to the QD ground state. The strongest peak at 29 meV is assigned to the p-shell absorption ðjX p iÞ and the resonances around 36.7 meV correspond to (LO) phonon-assisted absorption ðjX LO iÞ. The inset shows the basic excitation/recombination scheme of our experiment (see text).
as well as PL spectroscopy. We are able to control the internal electric field of the sample simply by adjusting a bias voltage ðV b Þ. The possibility of applying a voltage to the sample provides the opportunity of a fine tuning of the resonances via the quantum confined Stark effect. Because our concept needs a controlled p-shell Rabiflopping, we have first characterized the spectral position of the p-shell absorption using photoluminescence excitation (PLE) spectroscopy. For excitation we use a Ti:Sapphire laser, which is tuned in a region from 10 to 50 meV above the 1X state. The excitation intensity of the Ti:Sapphire laser was stabilized by a power control unit. The laser intensity was coarse adjusted by neutral density filters and continuously tuned via a filter wheel. The laser beam was focused on the sample by a NA ¼ 0:75 microscope objective. All measurements have been performed at T ¼ 4:2 K. The luminescence is detected by a LN2 cooled Si-CCD camera or analyzed by a correlation measurement with a Hanbury–Brown and Twiss (HBT) [3] setup. Fig. 1 shows the PLE spectrum of the investigated QD at an excitation intensity of approximately 4 mW. The spectrum shows two main resonances. The largest peak 29 meV above the ground state ðE jX s i ¼ 1:337 eVÞ is assigned to the p-state ðjX p iÞ and the second largest peak (42 meV above ðjX s iÞ) is found to be the second excited state (probably the d-shell). The small peaks around 36.7 meV above the ground state are assigned to phononassisted absorptions ðjX LO iÞ. The phonon-assisted absorption matches very well to the GaAs LO phonon energy. The results of our PLE measurements are comparable to the results reported in Ref. [4]. The behavior of the s-shell emission with increasing pshell excitation intensity is a very important indicator for the two-level character of the p-shell. A clear nonlinear
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power dependence can be observed (data not shown here). At low excitation intensities the s-shell luminescence increases linear to the excitation power. But for higher excitation intensities the s-shell luminescence will approach a saturation value (see Ref. [5] for PC saturation observed in the s-shell). The physical content of the PL saturation value can be derived fairly easily: If the QD is already excited by one exciton, no further absorption can take place due to a renormalization of energy levels. This also holds true if the exciton relaxes into the ground state. Further absorption in the p-shell can only take place after a relaxation and recombination process. With the observed saturation behavior the p-shell transition can be treated as two-level system. In this section we want to compare the coherent behavior of the s- and p-shell of the single QD. The coherent manipulation of the single exciton ground state (1X) [2] was shown in previous work (see also Ref. [6] for two photon biexciton excitation). The first observation of optical Rabi oscillations in the p-shell was reported by Stievater et al. [7]. The occupancy of the upper level of a two-level system under coherent resonant excitation is given by I ¼ sin2 ðOt=2Þ where the Rabi frequency O is proportional to the square root of the laser intensity and t corresponds to the pulse length. A p-pulse thereby results in a complete inversion of the two-level system. We define the pulse area by adjusting the excitation amplitude. We use a pulse length of 2.3 ps and a repetition frequency of f Laser ¼ 80 MHz. The spectrally pulse width is sufficiently low in order to avoid off-resonance excitations. Due to the use of a tunable sample we are able to choose the dominant dephasing process simply via the applied voltage and excitation conditions (p- or s-shell). In the first case the QD is excited resonantly in the p-shell (low voltage). The main dephasing process here is relaxation into the ground state. After the recombination process the projected state can be observed in the ground state PL, which is shown in Fig. 2(a). In the second case we apply a (reverse) bias voltage of about 0.6 V, which switches our main dephasing process to tunneling. Thereby we can perform the coherent manipulation in the ground state and detect the projected state in the PC (see Fig. 2(b)). Fig. 2 shows the comparison between s- and p-shell Rabi oscillations. The PC signal shows more than eight full inversions (only five inversions are plotted here) at high excitation intensities within each laser pulse. The PL intensity (p-shell excitation) shows an enhanced damping compared to the PC signal (s-shell excitation). The p-shell Rabi oscillations have a clear developed p-pulse maximum, followed by a substantial damping at higher pulse areas. Due to the excellent detection efficiency in the PC the maximum value of the signal is determined by the laser repetition frequency, the elementary charge and the occupation probability. At a p-pulse this will result in a maximum value of 12.8 pA. Whereas, the maximum value of the optical detection depends on the collection efficiency of our measurement setup. Hence it is not possible to
ARTICLE IN PRESS P. Ester et al. / Physica E 40 (2008) 2004–2006
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quantitatively declare a maximum value. The original PC measurement is corrected for a background that increases linearly in power, which corresponds to a quadratic increase in the pulse area, see Ref. [2]. Comparing the pshell p-pulse to the ground state p-pulse we find that the Rabi flop needs about the same excitation intensity (about 2 mW at the sample). This means that the associated s- and p-matrix elements are approximately equal for this QD. The damping of the p-shell indicates a fast dephasing process due to the dominant relaxation process. The proof of single photon emission is performed by a time correlation measurement with the HBT setup. The time correlation measurement gives the probability that a photon is detected at a time t and another photon at the time ðt þ tÞ. The normalized second order correlation function gð2Þ ðtÞ is given by gð2Þ ðtÞ ¼ hIðtÞIðt þ tÞi=hIðtÞi hIðt þ tÞi where IðtÞ corresponds to the emission intensity [8]. Under continuous excitation, a single quantum emitter would generate a dip in the histogram at zero delay time ðt ¼ 0Þ. This means that the system must be re-excited after emission before a second photon can be emitted. This effect is known in literature as antibunching. In our experiments the use of pulsed excitation will lead to a recurring pattern of peaks. Each detected photon can be correlated with a photon generated from one of the next laser pulses. The histogram will consist of a repetitive peak structure with the repetition period of the mode locked laser. Due to the fact that there is at most one photon for each laser pulse, there cannot be a correlation at zero delay time. Therefore single photon emission will lead to a missing peak at zero delay time; gð2Þ ðt ¼ 0Þ should vanish. Fig. 3 shows the result of the correlation measurements with an integration time of 10 h and a time resolution of 300 ps. The correlation peaks have a time period of 12.5 ns. The numbers printed above the peaks correspond to the
Fig. 3. Photon correlation measurement under the condition of p-pulse ð2 mWÞ excitation in the p-shell (10 h integration time). The numbers printed above the peaks give the value of the normalized correlation function. The central peak of the periodic pattern ðt ¼ 0Þ is strongly suppressed, which proves clean single photon emission.
normalized second order correlation function gð2Þ ðtÞ, whereby gð2Þ ¼ 1 corresponds to the average peak height. The peak at zero delay time is basically missing, which proves that our system is in fact a very good single photon emitter. The single photon emission of a QD under coherent p-shell appears surprisingly clean ðgð2Þ ðt ¼ 0Þp 0:02Þ. In summary, we have demonstrated coherent p-state preparation followed by single photon emission from a single QD. It was found that the p-shell transition can basically be treated as a two-level system. Our experiments prove the applicability of a coherent control of an excited state for the defined excitation of a single exciton. The pulsed photon correlation experiments show an excellent suppression of the correlation peak at zero time delay and hence demonstrate a remarkably clean single photon emission. We want to acknowledge financial support by the BMBF via Grant No. 01BM466. References [1] P. Michler, A. Kiraz, C. Becher, W.V. Schoenfeld, P.M. Petroff, L. Zhang, E. Hu, A. Imamoglu, Science 290 (2000) 2282. [2] S. Stufler, P. Ester, A. Zrenner, M. Bichler, Phys. Rev. B 72 (2005) 121301. [3] R. Hanbury-Brown, R. Twiss, Nature (London) 177 (1956) 27. [4] F. Findeis, A. Zrenner, G. Bohm, G. Abstreiter, Phys. Rev. B 61 (2000) R10579. [5] S. Stufler, P. Ester, A. Zrenner, M. Bichler, Appl. Phys. Lett. 85 (2004) 4202. [6] S. Stufler, P. Machnikowski, P. Ester, M. Bichler, V.M. Axt, T. Kuhn, A. Zrenner, Phys. Rev. B 73 (2006) 125304. [7] T.H. Stievater, X. Li, D.G. Steel, D. Gammon, D.S. Katzer, D. Park, C. Piermarocchi, L.J. Sham, Phys. Rev. Lett. 87 (2001) 133603. [8] V. Zwiller, H. Blom, P. Jonsson, N. Panev, S. Jeppesen, T. Tsegaye, E. Goobar, M.-E. Pistol, L. Samuelson, G. Bjork, Appl. Phys. Lett. 78 (2001) 2476.