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Physical Review Letters

Optical nonlinearities of excitonic self-induced-transparency solitons: Toward ultimate realization of squeezed states and quantum nondemolition measurement

Kimitaka Watanabe, H. Nakano, A. Honold, Y. Yamamoto

Published May 8, 1989• 47 citations
Publisher

Abstract

Self-induced transparency in a resonant two-level system creates a 2\ensuremath{\pi}-soliton pulse, which produces large optical nonlinearities with a very fast response time and an extremely small loss. The self-phase modulation of a 2\ensuremath{\pi} soliton and the mutual-phase modulation by the collision of two 2\ensuremath{\pi} solitons in the excitonic range of the spectrum in CdS can achieve the effective ${\ensuremath{\chi}}^{(3)}$ coefficient of ${10}^{\mathrm{\ensuremath{-}}6}$ to ${10}^{\mathrm{\ensuremath{-}}4.5}$ esu for a pulse duration of 1 to 3 ps. The quantum theory of 2\ensuremath{\pi} solitons predicts this new nonlinear process can realize squeezed states and quantum nondemolition measurement 20 dB below the standard quantum limit.

DOI
10.1103/physrevlett.62.2257

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Journal of Nonlinear Optical Physics & Materials•Jan 1, 1996•1 citation
Self-induced transparency in a resonant two-level system creates a 2\ensuremath{\pi}-soliton pulse, which produces large optical nonlinearities with a very fast response time and an extremely small loss. The self-phase modulation of a 2\ensuremath{\pi} soliton and the mutual-phase modulation by the collision of two 2\ensuremath{\pi} solitons in the excitonic range of the spectrum in CdS can achieve the effective \ensuremathχ(3){\ensuremath{\chi}}^{(3)}\ensuremathχ(3) coefficient of 10\ensuremath−6{10}^{\mathrm{\ensuremath{-}}6}10\ensuremath−6 to 10\ensuremath−4.5{10}^{\mathrm{\ensuremath{-}}4.5}10\ensuremath−4.5 esu for a pulse duration of 1 to 3 ps. The quantum theory of 2\ensuremath{\pi} solitons predicts this new nonlinear process can realize squeezed states and quantum nondemolition measurement 20 dB below the standard quantum limit.
Self-induced transparency in a resonant two-level system creates a 2\ensuremath{\pi}-soliton pulse, which realizes large optical nonlinearities with a small absorption loss \ensuremath{\alpha} for a short pulse duration \ensuremath{\tau}. Quantum-mechanical zero-point field fluctuations introduce an ultimate dissipation loss in such a resonant and coherent process and place fundamental limits on the ${\mathrm{\ensuremath{\chi}}}^{(3)}$/\ensuremath{\alpha}\ensuremath{\tau} value. This value is independent of the dipole moment, atomic density, and pulse duration and is uniquely determined by an optical wavelength, e.g., ${\mathrm{\ensuremath{\chi}}}^{(3)}$/\ensuremath{\alpha}\ensuremath{\tau}\ensuremath{\sim}1.2\ifmmode\times\else\texttimes\fi{}1021{10}^{21}1021${\ensuremath{\lambda}}^{4}$ esu cm/s. The similar limit on ${\mathrm{\ensuremath{\chi}}}^{(3)}$/\ensuremath{\alpha}\ensuremath{\tau} value is obtained in a usual operation mode, when the pulse duration becomes much longer than the atomic decay constants and the real excitation of the atoms occurs instead of the virtual excitation in self-induced transparency. The implication of these limits on optical squeezed-state generation, quantum nondemolition measurement, and reversible logic is discussed.
We report the photon-number squeezing of optical solitons. 2.7 ps pulses were launched as solitons down a 1.5 km optical fiber. For energies slightly above that of fundamental solitons, they broadened spectrally due to self-phase modulation caused by ${\ensuremath{\chi}}^{(3)}$ nonlinearities. Filtering away outlying components of the broadened spectra squeezed the soliton's photon-number fluctuations to 2.3 dB (41%) below the shot-noise limit. Accounting for losses, this corresponds to 3.7 dB (57%) photon-number squeezing. A quantum field-theoretic model shows that the outlying spectral components have large energy fluctuations, so that their removal causes squeezing.
Photonic crystals doped with resonant atoms allow for uniquely advantageous nonlinear modes of optical propagation. The first type of mode is self-induced transparency (SIT) solitons and multidimensional localized “bullets” propagating at photonic-bandgap frequencies. Such modes can exist even at ultraweak intensities (few photons) and therefore differ substantially either from solitons in Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. The second type of mode is cross coupling between pulses exhibiting electromagnetically induced transparency and SIT gap solitons. We show that extremely strong correlations (giant cross-phase modulation) can be formed between the two pulses. These features may find applications in high-fidelity classical and quantum optical communications.
A self-induced transparency (DIT) soliton can coexist with a nonlinear Schr\"odinger (NLS) soliton. This mixed state is called an SIT-NLS soliton. The phase change of the new soliton is governed solely by the NLS component and the pulse delay is determined solely by the SIT component when a detuning from the resonance is zero. It is shown for the first time that a stable 2\ensuremath{\pi}-(N=1) SIT-NLS soliton exists and that high-order SIT/NLS solitons always split into multiple 2\ensuremath{\pi}-(N=1) SIT-NLS solitons.
The form invariant coherent pulse propagation in semiconductors excited at 1s-exciton resonance is studied analytically using the reduced semiconductor Maxwell-Bloch equations. The sech-shaped pulse solution for excitonic self-induced transparency (SIT) is presented, showing significant difference in comparison with the well known SIT solution for non-interacting two-level systems. In contrast to 2π pulses in atomic systems, the phenomenon of SIT of interacting excitons in semiconductors occurs for the pulses of area 1.07π. Possible applications of the SIT solitons in semiconductor all-optical switching devices are discussed.