Room temperature superradiance due to coherent coupling between light and extended single quantum state

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Abstract

We have established the newly-developed growth method of high-quality CuCl thin film based on molecular-beam epitaxy. In qualified films, where harmonized coupling between an excitonic polarization wave and a resonant electromagnetic wave over a range of multiple wavelengths is achieved, we have observed an exceptionally high speed nonlinear response of excitons at room temperature, wherein the excitons decay radiatively before its coherence is destroyed by dephasing. A component with extremely large radiative width can be observed in the nonlinear optical spectrum only when the other components with smaller radiative widths disappear by the room-temperature dephasing. The radiative decay time of the excitonic state with the largest radiative width reaches the order of 100 fs, which is much faster than the dephasing process. The mechanism demonstrated by our results contradicts the conventional physical description of light–matter interaction based on the long-wavelength approximation. The shapes of the measured degenerate four-wave mixing spectrum and the radiative decay profile closely reflect those of the calculated induced-polarization spectrum and the radiative decay profile obtained by real-time analysis, respectively.

Highlights

► We have established growth method of high-quality CuCl thin film based on molecular beam epitaxy. ► We have observed an exceptionally high speed nonlinear response of excitons at room temperature. ► The observed radiative decay time reaches the order of 100 fs.

Introduction

The exciton effect is essential for an optical response with a large nonlinearity. However, the application of excitons for the all-optical switching devices, in which the competence to transfer much information in a very short time is required, has been considered to be difficult due to the long radiative decay time more than a few tens of picoseconds. Optical properties of nanocrystals have attracted much attention as one of the promising candidates for uniting a large nonlinearity with an ultrafast response. In nanocrystals, where the center-of-mass motion of excitons is confined, the long wavelength approximation (LWA) is applied. In this regime, the light–matter interaction volume is in proportion to the system size and an enhancement of the radiative decay rate i.e. superradiance appears [1], [2], [3], while linear dependence on the size has been believed to be limited in an unexpected small size region because the internal field has nanoscale spatial structures determined self-consistently with the induced polarization via a nonlocal relationship between them and the LWA breaks down. On the other hand, a remarkably strong coupling between the light wave and n  2 excitonic wave over several wavelengths is formed as long as wave functions of center-of-mass motion of excitons are coherently extended to the whole volume of a system [4]. In thin films with adequately improved crystalline quality, the size-dependent increase in the light–matter interaction volume is no longer limited by the light wavelength, and the radiative decay rate is unlimitedly enhanced in a larger system than nanostructures. Regarding the nonlinear response, the self-consistent interaction between the response field and the induced polarization at non-LWA regime causes an enhancement of the internal field at a particular size and energy. For example, degenerate four-wave mixing (DFWM), which is one of the most important nonlinear optical processes, is greatly enhanced with the transition associated with the nondipole type polarization pattern [5]. This effect was actually observed in the experiment with GaAs thin films [6], [7]. Furthermore, the size dependences of the decay time show nonmonotonical behavior [8], [9], and for a particular film thickness, a large nonlinear response combined with the ultrafast radiative decay is expected [10].

As theoretically demonstrated in Ref. [5], wide-gap semiconductor CuCl is expected to be the material that manifests itself remarkable nonlinear effects in the non-LWA regime, though any experimental demonstrations have not been reported yet. The excitons of CuCl have very strong radiative coupling per unit cell volume and extremely stable at low temperature due to the huge exciton binding energy of about 0.2 eV. The very small Bohr radius (0.7 nm) is suitable for investigating the system where the center-of-mass motion of excitons is confined, while it has never been utilized except for basic research at low temperatures because the radiative decay rate is low around room temperature due to the dephasing of excitons by the interaction with optical phonons. In an exciton–radiation coupled system where the waves of “multinode-type” excitons coherently interact with the light wave, the radiative decay time is expected to be shorter than the excitonic dephasing time (normally on the order of picoseconds) by optimizing the system size [11], [12]. This interchange would lead to an unconventional situation where the coherent optical response is completed before the excitation is affected by the phase decay. That is, in this inverted situation, the efficiency of radiative decay peculiar to CuCl would be maintained even at high temperatures.

In the present work, we have established the growth method of CuCl thin films with thickness above the LWA regime and high crystalline quality, and have experimentally demonstrated the nonlinear optical response associated with the ultrafast radiative decay.

Section snippets

Growth of high-quality CuCl thin film

The growth method of CuCl thin films was based on molecular-beam epitaxy (MBE) [13]. As a substrate, CaF2 was used, of which the lattice constant (0.5463 nm) is almost the same as that of CuCl (0.5406 nm). A block of CaF2 single crystal was cleaved along the (111) plane to the thickness of 1 mm, because interference structure by internal reflection in the substrate appears on measured spectra in films grown on substrates with the thickness below 1 mm due to too high spectral resolution (< 0.08 meV).

Results

Fig. 2(a) shows an atomic force microscope (AFM) image of a CuCl thin film grown by our new technique using electron beam irradiation, and an AFM image of a film grown by the conventional MBE method is shown in Fig. 2(b) for the comparison. The prominent surface roughness in (b) is remarkably reduced in (a).

Fig. 3(a) shows the DFWM spectrum of a high-quality CuCl thin film grown by the new technique with a thickness of 268 nm. The measurement temperature is 5.6 K. The spectrum of the incident

Quality improvement of CuCl thin film

The surface morphology of CuCl film is extremely improved by our growth method using electron beam irradiation as shown in Fig. 2. Furthermore, the optical quality is also found to be improved from the fact that the phase decay constant derived by fitting to the reflection spectrum is reduced to less than 0.5 meV. Such improvements of the quality in CuCl thin films can be explained as follows. The surface of CaF2 buffer layer is composed of fluoride ions, from which core electrons are emitted by

Conclusion

We have successfully established the growth method of high-quality CuCl thin films. The films grown using this technique show peculiar optical properties due to the harmonized long-length coupling between a light wave and the excitonic wave over multiple wavelengths. The anomalous mode structures can be observed in the measurement of DFWM spectrum and the energy at each peak is in good agreement with the calculated eigenenergy including the radiative shift. Several excitonic states show

Acknowledgment

The present work was supported by the Murata Science Foundation and by a Grant-in-Aid for Scientific Research (B) (21340085, 2009) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

References (18)

  • K. Akiyama et al.

    Physica B

    (2002)
  • H. Ishihara et al.

    J. Lumin.

    (2004)
  • A. Kawamori et al.

    J. Cryst. Growth

    (2002)
  • T. Mita et al.

    Solid State Commun.

    (1980)
  • E. Hanamura

    Phys. Rev. B

    (1988)
  • T. Takagahara

    Phys. Rev. B

    (1989)
  • A. Nakamura et al.

    Phys. Rev. B

    (1989)
  • H. Ishihara et al.

    Phys. Rev. B

    (1996)
  • H. Ishihara et al.

    Phys. Rev. B

    (2001)
There are more references available in the full text version of this article.
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