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Quantum Computing, Communication, and Simulation

Self-induced transparency and soliton formation in ruby: simulations and experiment (Conference Presentation)

Aleksander K. Rebane, Hans Riesen, Steffen Ganschow, Alex Szabo, W. D. Hutchison, Rajitha Papukutty Rajan

Published Mar 14, 2018• 1 citation
Publisher

Abstract

Formation of optical solitons in self-induced transparency (SIT) regime, where light pulses propagate virtually without loss in nominally strongly absorbing medium, is one of the most striking coherent transient phenomena in optics. Here we study experimentally and by numeric simulations how a square shape pulse gradually transforms into a smooth sech shape pulse of well-defined pulse area, depending on the parameters such as the pulse amplitude, duration, propagation distance etc. The SIT experiments for circularly polarized light are performed in the R1−3∕2) line of a 30 ppm ruby (α-Al2O3:Cr3+) at 1.7 K in a magnetic field of BIIc = 4.5 T, which corresponds to effective absorption coefficient, αL =14.5. In such a magnetic field and temperature range, a 30 ppm ruby is in the so-called superhyperfine limit resulting in a very long decoherence (phase memory) time, TM = 50 μs. We show, in good quantitative agreement with the simulations, how SIT soliton is formatted and how this results in extremely slow pulse peak propagation velocity of ∼300 m∕s, which is to date, the slowest pulse propagation ever observed in a SIT experiment. We also show that for accurate quantitative description of the observed SIT and soliton pulse shapes, the simulations need to account for variation of the incident pulse amplitude across the beam spatial profile. Potential implications of the SIT effect on classical- and quantum information storage will be discussed.

DOI
10.1117/12.2287550

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 5, 1999•0 citations
Formation of optical solitons in self-induced transparency (SIT) regime, where light pulses propagate virtually without loss in nominally strongly absorbing medium, is one of the most striking coherent transient phenomena in optics. Here we study experimentally and by numeric simulations how a square shape pulse gradually transforms into a smooth sech shape pulse of well-defined pulse area, depending on the parameters such as the pulse amplitude, duration, propagation distance etc. The SIT experiments for circularly polarized light are performed in the R1−3∕2) line of a 30 ppm ruby (α-Al2O3:Cr3+) at 1.7 K in a magnetic field of BIIc = 4.5 T, which corresponds to effective absorption coefficient, αL =14.5. In such a magnetic field and temperature range, a 30 ppm ruby is in the so-called superhyperfine limit resulting in a very long decoherence (phase memory) time, TM = 50 μs. We show, in good quantitative agreement with the simulations, how SIT soliton is formatted and how this results in extremely slow pulse peak propagation velocity of ∼300 m∕s, which is to date, the slowest pulse propagation ever observed in a SIT experiment. We also show that for accurate quantitative description of the observed SIT and soliton pulse shapes, the simulations need to account for variation of the incident pulse amplitude across the beam spatial profile. Potential implications of the SIT effect on classical- and quantum information storage will be discussed.
Self-induced transparency is reported for circularly polarized light in the R1(−3/2) line of a 30 ppm ruby (α-Al2O3:Cr3+) at 1.7 K in a magnetic field of B‖c=4.5 T. In such a field and temperature, a 30 ppm ruby is in the so-called superhyperfine limit resulting in a long phase memory time, TM=50 μs, and a thousand-fold slower pulse propagation velocity of ∼300 m/s was observed, compared to the ∼300 km/s measured in the first observation of self-induced transparency (SIT) ∼50 years ago, that employed a ruby with a 500 ppm chromium concentration in zero field and at 4.2 K. To date, this is the slowest pulse propagation ever observed in a SIT experiment.
Self-induced transparency (SIT) is a kind of coherent transient phenomena in two-level atomic system. The optical pulse with an area that is an integer multiple of 2π, which causes SIT in an absorber, is stable and a kind of soliton. Thus SIT is expected to be useful in pulse compression and pulse shaping. In this paper, we discuss some problems in experiments of SIT and surveys the experimental results of SIT. It is also described the recent experimental results of coherent nonlinear pulse propagation in BiI3 crystal using tunable sub-picosecond pulses.
This thesis explores the existence and properties of self-induced transparency (SIT) solitons in nanophotonic waveguides. SIT solitons are shape-preserving solutions of the semi-classical Maxwell-Bloch equations, a system of nonlinearly coupled differential equations. In a first investigation, collisions of counterpropagating simultons (SIT solitons in absorbing three-level systems) are studied numerically in the plane-wave approximation and a polarisation- and group-velocity dependent soliton birth is uncovered. Apart from their fundamental interest, such light-light interaction effects may be of use for optical computing applications if they can be transferred to tightly confined light pulses. Confining light is usually achieved by using dielectric waveguides that exhibit group velocity dispersion leading to chirped pulses, which experience absorption when entering an absorbing medium. If the chirp is strong enough and the pulse intense enough, they can even completely invert an absorber. When investigating chirped pulse propagation through a dense ensemble of two-level system it is found that the chirped pulses dynamically reshape into unchirped pulses experiencing transparency. Furthermore, the conditions on the waveguide geometry to enable SIT are analysed, identifying a nanophotonic slot waveguide with a low-index gap, exhibiting high electric field enhancement and a homogeneous field profile, as the ideal candidate system for guided SIT solitons. This analysis is supported by two-dimensional numerical calculations that show the solitary character is maintained during propagation if the absorber density is high enough to ensure a slow-down of the pulse and to thus counteract the waveguide dispersion. Finally, the soliton birth due to simulton collisions and optical memory schemes proposed for plane-wave SIT are investigated in the two-dimensional slot waveguide and found to also be possible in this geometry.
Two types of nonlinear transmission of light pulses associated with phase modulation are observed in experiments connected with self-induced transparency (SIT) in ruby. Anomalous pulse-power transmission is observed to be an order of magnitude greater than linear transmission during the condition of zero-area pulse propagation, where the inhomogeneous line spectral width is greater than the applied pulse spectral width. For application of a pulse off-resonance by the order of a linewidth, nonlinear transmission occurs in which a type of "precursor" phase-modulated signal appears ahead of a developing SIT pulse. The precursor pulse velocity is greater than the SIT pulse velocity, but less than the background velocity of light in the medium.
We study the effects of dispersion in carrier waves on the properties of soliton self--induced transparency (SIT) in two level media. We found substantial impact of dispersion effects on typical SIT soliton features. For example, the degree of SIT pulse velocity slowing down (acceleration) is determined by the ratio of the incoming pulse frequency over atomic transition frequency - x=ω/ω0x=ω/ω_0x=ω/ω0​. Specifically, an immediate pulse stopping is predicted for absorbing media when pulse duration time exceeds some critical value. In the sharp line limit stopping may emerge only for frequency ratio above unity, while for the inhomogeneously broadened systems it appears irrespective of the value of xxx. Analysis performed on the basis of Mcall\& Hahn \textit{Area theorem} implies that pulse stopping is achieved when Ber's absorption coefficient approaches infinity, that is, pulse energy is fully absorbed in the medium. In the case of amplifying media super-luminal motion is predicted as in the case of resonance. However, there is a lowest value in the frequency ratio below which the pulse velocity tends to the sub-luminal region. These new features of the SIT phenomenon open novel ways on how it may be exploited for the control of electromagnetic wave radiation in two-level media. This may be achieved by varying frequency ratio.
Quantum coherence and interference in atomic systems can lead to interesting optical phenomena such as nonabsorbing resonances, lasing without inversion, generating an ultrahigh index of refraction without absorption, propagation of light pulses without losses. In the last-named is given the title transparency. Up to now it is known some types of transparency in multi-level resonant media. One of them is electromagnetically induced transparency (EIT). The phenomenon of EIT in the propagation of laser radiation through an absorbing medium has been recently investigated and explained in terms of quantum coherence and interference for multi-level atomic system. For instance in the (Lambda) -system, if the atomic medium is prepared in a quantum superposition of states, matched pulses, i.e., a pair of optical pulses whose amplitude and phase have a well defined relation, propagate without absorption. The mechanism of coherent population trapping is responsible for EIT in a (Lambda) -system. There is another, well known mechanism for creating transparency in a two-state atom: self-induced transparency, or SIT. Here, a single pulse whose area (the integral of its Rabi frequency over time) is 2(pi) is applied to the medium. Such a pulse causes the atoms to cycle smoothly from the ground to the excited state and then back again. In principle, such a pulse can propagate over long distances. SIT can be generalized to multi-level systems and multiple quasi-monochromatic fields. Generalization of SIT in a (Lambda) -system was obtained in reference 2. In this report we present a new type of transparency (combined transparency). This type describes propagation of laser pulse through a (Lambda) -type medium where the initial atomic state is prepared in the form of spatially varying coherent superposition of low-energetic states (initial coherency gradient). The common envelope behaves as usual 2(pi) hyperbolic secant pulse, but the ratio between the components of frequencies transitions 1> yields 3> and 2> yields 3> changes due to coherent Raman scattering so (phi) equals atan(E1/E2) equals (pi) /2-Gz, where z is the coordinate, G is the constant determined by both the incident pulse parameters and the initial coherence between the atomic states. Our solution demonstrates a direct connection of EIT in adiabatic regime to the SIT effects. This type of a transparency is given the title screw-type transparency, because for the given form of incident pulse (pitch of screw) medium is transparent, if medium's the initial coherence gradient is correspondingly prepared (thread on a engine nut). Besides a transparency, this phenomenon contains a transformation of the incident pulse frequency during the process of the propagation. This property of the phenomena can be result in a complete conversion of the frequency.