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

Abstract

Self-induced transparency in a resonant two-level system creates a 2^-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/r soliton and the mutual-phase modulation by the collision of two In solitons in the excitonic range of the spectrum in CdS can achieve an effective % i3) coefficient of 10 ~~6 to 10 ~4 5 esu for a pulse duration of 1 to 3 ps. The quantum theory of In solitons predicts this new nonlinear process can realize squeezed states and quantum nondemolition measurement 20 dB below the standard quantum limit.PACS numbers: 42.50.Qg, 32.90.+a, 42.50.Dv Optical nonlinear processes can be divided into two categories: nonresonant coherent and resonant incoherent. ] If a field frequency is well detuned from the atomic transition frequency, the response time is fast and the absorption loss is negligible, but the # (3) coefficient is usually small. On the other hand, when the field frequency is close to the atomic frequency, the / (3) coefficient is enhanced, but the response time becomes slow and the absorption loss is high. These tradeoffs between the x coefficient and the response time or the absorption loss impose a serious limitation on both nonlinear optical switches in classical optics 2 and squeezed-state generation and quantum nondemolition measurement in quantum optics. 3 This Letter demonstrates the possibility of new optical nonlinearities based on the resonant and coherent coupling between the field and the atoms.j Suppose the pulse duration T is much shorter than the energy and phase decay time constants T\ y T2 and the area A=(p2\/h)jEdt of a secant-hyperbolic shaped pulse is a multiple of 2/r. Here pi\\% the atomic dipole moment and E is the electric field envelope. The pulse propagates without being absorbed irrespective of the pulse frequency detuning from the atomic frequency and the inhomogeneous broadening of the atomic frequen- cies. 4 This is a so-called 2K soliton. The Maxwell-Bloch equations for self-induced transparency (SIT) can be solved by the inverse scattering method formula. 5 The 2/r-soliton solution is uniquely determined by the complex eigenvalue $=a + ip of the inverse scattering (Zakharov-Shabat) equations. 5 The field envelope function for the 2K soliton, except for an exp[/(<y 0 f -JCQZ)] term, is expressed as r 2fe 2pvexp(in 2 az/2v 2 Ko)exp[ -2ia(vt -z)]exp0>p) Pi\ cosh{2pv[t -(z/v)(l + n 2 /4v 2 K { )]}Here Ci 2ss conp2\/2he, e^e^nl is the dielectric constant, n is the atomic density, v =*c/n$ is the nonresonant light velocity, a = (<o -co 0 )/2v represents the nonlinear frequency shift, and ca is a real soliton frequency. The pulse height p is proportional to the photon number N p , i.e., p= s cop2\N p /l6hv 2 €Ap, and determines the pulse duration r = l/2/?f. Here Ap is the cross-section area of the pulse. If the line-shape function of the atomic systems is assumed to be a delta function S(co -a>2\), then the coefficients K: O and K\, the group velocity K, and the ph...

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“…(11) represent an effective group velocity and the evanescent coupling strength between the two waveguides. The field term multiplied by the constant m =k EJ /(2P) introduces a phase which can be easily transformed out and will not be considered further.…”

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