## Abstract

Electromagnetically induced transparency (EIT) was observed with transient optical response of exciton correlation in GaAs/AlGaAs quantum well structure. Decoherence of EIT was increased with temperature (12–60 K), which could be simulated by increasing non-radiation decay rate between coherently coupled ground states in Bloch equation for Λ type three level. The non-radiation decay was mainly due to hole spin dephasing in the system for EIT via coulomb correlation. The hole spin dephasing rate was found with increasing lattice temperature and well accorded to the past results of time resolving method with n-doping material.

© 2008 Optical Society of America

## 1. Introduction

EIT effect has attracted much attention since S. Harris showed the possibility of nonlinear control of light [1]. Photon velocity could be slow down to 17m/sec in ultra cold atoms and photon storage was demonstrated to be applicable to quantum information [2]. Large Kerr nonlinearity based on EIT was observed to induce cross phase modulation (XPM) with low light intensity [3–4]. Single photon phase gate using XPM induced by slow photons in M type five-level system was proposed for quantum logic gate [5].

In company with quantum optics with alkali atom, EIT and coherent population trapping was observed with exciton correlation of semiconductor quantum well recently [6–7]. This showed the possibility of coherent photon control and photonic integrated circuit in semiconductor. Many other coherent effects realized in atomic system like as generation of correlated photon pair and photon storage are on the way of the research to be realized in semiconductor [8–9].

Decoherence is one of the most important factor in quantum information science since it needs stable coherent state for data processing. Non-radiation decay of the ground state is critical parameter for decoherence time in Λ type three-level system [10]. In experiment with alkali atom in magneto-optical trap or buffer gas vapor cell, decoherence time was measured to several hundreds microsecond [11]. Recent experiment of EIT via exciton correlation has been reported with helium cryostat temperature, but decoherence of EIT has not been studied enough. We observed decoherence of EIT with increasing temperature from 11 K, which rendered dephasing time by fitting to theory. Λ type three-level system was implemented by exciton correlation via coulomb correlation on GaAs quantum well structure(Fig. 1) [6]. Single exciton spin states were coupled via unbound biexciton state with opposite circular polarized laser light, which implemented Λ type three-level system in Fig. 1. (b). The same laser lights induced the population of the single exciton spin states in Fig. 1. (a).

## 2. Experiment and Calculation

The GaAs QW sample, grown by molecular beam epitaxy, consists of 20 periods of 10 nm thick GaAs wells and 15 nm thick Al_{0.35}Ga_{0.65}As barriers. The absorption peaks corresponding to the heavy hole and the light hole exciton transitions were clearly observed from 11K up to room temperature [12]. The peaks of exciton transition line were both red-shifted together as temperature increased due to the band gap shrinking effect [13]. For transient coherent spectroscopy, we employed tunable 150 fs pulse laser (MIRA, Coherent). To implement three-level EIT system induced by exciton correlation, spectrally filtered coupling laser pulse was overlapped to broad spectrum probe pulse. The linewidth of the pulse shaped coupling laser was 0.1 nm in spectral domain and the center wavelength could be easily tuned with micro-translator carrying 20 µm slit. The duration of coupling pulse in time domain was 6 ps, which could overlap the probe pulse (150 fs). The coupling and probe laser was focused with 75 mm focal length convex lens to increase the coupling Rabi frequency. The coupling laser frequency was tuned to the center of heavy hole exciton transition line at each temperature. The opposite circular polarization was used for both of the coupling (left circular) and probe laser (right circular) to excite opposite spin state. The measured probe absorbance was shown with depending on coupling laser frequency (Fig. 2).

The Rabi frequency of coupling laser was 1.5γ where the absorption linewidth, γ was measured with heavy hole linewidth (2.8 meV). The Rabi frequency of coupling laser was fixed at all of temperatures. EIT dip was disturbed with increasing temperature and we could not see EIT dip more than 60 K with same coupling Rabi frequency (1.5γ). We intended to quantify the disturbance of EIT with decay of non-radiation coherence between the ground states in three-level system. The decoherence rate between ground states (*γ*
_{-+}) could be found by fitting calculation with Bloch equation to the observed EIT signal.

The coupling laser fields *ε _{c}* and probe laser field

*ε*was noted with ${\epsilon}_{c}\left(t\right)=\frac{1}{2}{E}_{c}\left(t\right){e}^{-{\mathit{i\nu}}_{c}t}+c.c.,\phantom{\rule{.9em}{0ex}}{\epsilon}_{p}\left(t\right)=\frac{1}{2}{E}_{p}\left(t\right){e}^{-{\mathrm{i\nu}}_{p}t}+c.c.$, where

_{p}*ε*(

_{c}*ε*) was a strong coupling field (weak probe field) with center frequency

_{p}*ν*(

_{c}*ν*) and pulse envelope

_{p}*E*(

_{c}*E*). Rabi frequencies Ω

_{p}_{c}=

*µ*(

_{c}E_{c}*t*)/ħ and Ω

*=*

_{p}*µ*(

_{p}E_{p}*t*)/ħ were used for interaction picture, where µ is the dipole transition matrix element. The ground state (single exciton spin states), $|+\frac{1}{2}\u3009$ and $|-\frac{1}{2}\u3009$were prepared by each transition of oppositely circular polarized electric field and coupled each other through biexciton transition implementing Λ type three-level system. The population of $|+\frac{1}{2}\u3009$ was zero with strong coupling Rabi frequency, then the population of $|-\frac{1}{2}\u3009$,ρ

_{--}is 1 with total population normalized. With the rotating wave approximation, the Bloch equations of the density matrices are

The element of the density matrices, ρ^{e+} (ρ^{-+}) is the dipole coherence between biexciton and ground state $|+\frac{1}{2}\u3009$ (ground state $|-\frac{1}{2}\u3009$). The detuning of the applied electric fields were noted by *δ _{c}*=

*ν*-

_{c}*ω*

_{-}and

*δ*=

_{p}*ν*-

_{p}*ω*

_{+}, where

*ω*

_{-}(

*ω*

_{+}) was the resonant frequency of exciton $|-\frac{1}{2}\u3009(|+\frac{1}{2}\u3009)$ transition to biexciton state. Because the single exciton linewidth was almost not changed in the temperature up to 60 K, the radiation decay rate,

*γ*was valued same at the temperature range (11~60 K) in our calculation. Meanwhile, the non radiative decoherence between ground states (

*γ*

_{-+}) with increasing temperature would be adjusted to fit the calculation to experimental EIT curve.

The coupled Block equation was solved numerically using a forth-order Runge-Kutta algorithm. The applied coupling and probe electric field were considered to be Gaussian spectral distribution. The calculation was fitted to EIT signals with adjusting the value of decoherence, *γ*
_{-+} at each temperature (Fig. 3). The value of decoherence, *γ*
_{-+} was decaying function with temperature and it was about 4 picoseconds at 11 K (Fig. 4).

## 3. Dephasing time

We measured the recombination time of exciton with TCSPC (Time Correlation Single Photon Counting) method. The second harmonic femtosecond pulse (400 nm wavelength) was used for PL (photoluminescence) and just heavy hole exciton PL was delivered to PMT (Photo Multiply Tube) of TCSPC setup through a monochromator. The recombination time was increased with increasing temperature (Fig. 4), which was same to other’s work in 1990’s [16]. It could be seen in figure 4 that the behavior of the recombination time with temperature was totally different from decoherence of EIT. Therefore, the radiation decay had no relation with decoherence of EIT as we considered before.

There were two non-radiation decay process of exciton, the decay of electron spin coherence [14] and the decay of hole spin coherence [15]. We could attribute the decay of hole spin coherence to decoherence of EIT because coherent process to biexciton state via single exciton state began from hole spin states (Fig. 1) and the decay time of electron spin coherence was measured to several hundreds picoseconds by A. P. Heberle et al. [14], which was much longer than the decoherence time of EIT (Fig. 4).

It has been known that the hole spin dephasing is coming from the strong band mixing with spin-orbit interaction [17–18]. Time-resolved optical pumping experiments provided the direct measurement of the hole spin dephasing time [17]. Negative modulation doped QW have been used to neglect photo-excited electron since it is so small compared to doping level. Such experiments have been performed by T. C. Damen et al. who measured hole spin relaxation to 4 ps at 10 K [17]. Their result accorded to our measurement with EIT on intrinsic QW.

## 4. Conclusion

In conclusion, Calculation with the Bloch equation describing simple Λ type three level system was fitted to experimental EIT signal, which could afford to select the non-radiation decay rate. The main non-radiation decay factor of EIT via coulomb correlation was the decay of hole spin coherence. Conversely, the decay time of hole spin coherence could be measured with EIT signal. It could be measured without negative modulation doping which should be adopted in other method.

## Acknowledgment

This work is supported by Ministry of Knowledge Economy (MKE) of Korea through the Industrial Technology Infrastructure Building Program.

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