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arXiv:physics/0509228 · Journal of Vacuum Science & Technology B Microelectronics and Nanometer Structures Processing Measurement and Phenomena

Pumped quantum systems: Immersion fluids of the future?

Vikas Anant, Magnus Rådmark, Ayman F. Abouraddy, T. C. Killian, Karl K. Berggren

Published Nov 1, 2005• 1 citation
arXivHTMLPDF

Abstract

Quantum optical techniques may yield immersion fluids with high indices of refraction without absorption. We describe one such technique in which a probe field experiences a large index of refraction with amplification rather than absorption, and examine its practicality for an immersion lithography application. Enhanced index can be observed in a three-level system with a tunable near-resonant coherent probe and incoherent pump field that inverts the population of the probe transition. This observation contradicts the common belief that large indices of refraction are impossible without absorption; however, it is well in accord with existing electromagnetic theory and practice. Calculations show that a refractive index ⪢2 is possible with practical experimental parameters. A scheme with an incoherent mixture of pumped and unpumped atoms is also examined, and is seen to have a lower refractive index (∼2) accompanied neither by gain nor loss.

DOI
10.1116/1.2121732

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Quantum optical techniques may yield immersion fluids with high indices of refraction without absorption. We describe one such technique in which a probe field experiences a large index of refraction with amplification rather than absorption, and examine its practicality for an immersion lithography application. Enhanced index can be observed in a three-level system with a tunable near-resonant coherent probe and incoherent pump field that inverts the population of the probe transition. This observation contradicts the common belief that large indices of refraction are impossible without absorption; however, it is well in accord with existing electromagnetic theory and practice. Calculations show that a refractive index ⪢2 is possible with practical experimental parameters. A scheme with an incoherent mixture of pumped and unpumped atoms is also examined, and is seen to have a lower refractive index (∼2) accompanied neither by gain nor loss.
. We investigate the possibility of enhancing the refractive properties in a nonabsorbing medium via two fundamentally different schemes. First there is the coherent preparation of three-level atoms where absorption is cancelled due to destructive interference while the refractivity is not hampered in the same way. There also is the possibility of cancelling absorption via a mixture of absorbing and emitting two-level atoms without the need of a coherent preparation. One drawback here, however, is high sensitivity to Doppler broadening, collisions and number fluctuations which makes this scheme practically infeasible. Introduction The various application of atomic coherence in laser physics and quantum optics has recently attracted considerable interest. It has been shown that atomic coherence can lead to absorption cancellation (Alzetta, et al., 1976; and Gray, et al., 1979) and quenching of spontaneous emission noise (Scully, 1985). More recently, the notion of noninversion lasing has received attention, and it was shown that atomic coherence leading to cancellation of absorption does not necessarily influence emission (Harris, 1989; Scully, et al., 1989; and Kocharovskaya and Khanin, 1988). There has been extensive research on many schemes that involve coherence between an upper or lower level laser doublet due to various means: microwave or Raman coherent coupling and spontaneous and incoherent pumping coupling just to name the most important.
A new scheme for overcoming losses with incoherent optical gain in a quantum-coherent left-handed atomic vapor is suggested. In order to obtain low-loss, lossless or active left-handed media (LHM), a pump fleld, which aims at realizing population inversion of atomic levels, is introduced into a four-level atomic system. Both analytical and numerical results are given to illustrate that such an atomic vapor can exhibit intriguing electric and magnetic responses required for achieving simultaneously negative permittivity and permeability (and hence a gain-assisted quantum-coherent negative refractive index would emerge). The quantum-coherent left-handed atomic vapor presented here could have four fascinating characteristics: i) three-dimensionally isotropic negative refractive index, ii) double- negative atomic medium at visible and infrared wavelengths, iii) high-gain optical ampliflcation, and iv) tunable negative refractive index based on quantum coherent control. Such a three-dimensionally isotropic gain medium with negative refractive index at visible and infrared frequencies would have a potential application in design of new quantum optical and photonic devices, including superlenses for perfect imaging and subwavelength focusing.
Enhancement and control of the index of refraction in a mixture of two three-level atomic species that form a pair of far-detuned $\ensuremath{\Lambda}$ schemes under two-photon resonance has been studied. We employ the density-matrix approach to properly take population relaxation into account and to describe the interaction of each $\ensuremath{\Lambda}$ system with the electromagnetic fields. Both $\ensuremath{\Lambda}$ systems are driven by a corresponding far-detuned coherent field at one atomic transition and are probed by the same weak field. In the dressed-state basis, it represents a superposition of effective two-level subsystems with the positions, widths, and amplitudes of the resonances controlled by the driving fields and allows for efficient control of the susceptibility of the total system; leading to refractive index (RI) enhancement with vanishing absorption in the absence of amplification. We analyze the experimental implementation of such a system in a cell of Rb atoms with a natural abundance of isotopes. An upper limit estimate of the RI enhancement is obtained.
Index of refraction characterizes the linear response of a medium and hence it is strongly enhanced near atomic resonance. However, it is accompanied by either resonant absorption or gain preventing the use of high index. We show that these problems may be overcome using coherent control of excited state absorption (ESA), i.e. absorption from the populated excited electronic state. The idea is to compensate gain at the lower operating transition via partially suppressed ESA at the frequency of the probe field tuned to the maximum refractive index of the ESA transition. It results in resonant enhancement of refractive index without absorption in the absence of any neighboring amplification regions.
We studied a closed three-level V-type system with two near-degenerate excited levels in the presence of an incoherent pumping field. Quantum interferences of the two-decay channels lead to the achievement of the high index of refraction without absorption via spontaneously generated coherence. We use the exact analytical formula of the refractive index derived by us in a recent paper. We found that the high refractive index varies very much with the angle between the two dipole moments and evidently with the detuning of the coupling field.