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Physical Review A

Quantum lithography with classical light

Wenchao Ge, Philip Hemmer, Muhammad Suhail Zubairy

Published Feb 19, 2013• 21 citations
Publisher

Abstract

The concept of performing quantum lithography with classical, instead of entangled, light is of great interest for practical implementation. One recent proposal [Hemmer, Muthukrishnan, Scully, and Zubairy, Phys. Rev. Lett. 96, 163603 (2006)] to accomplish this was based on the use of frequency selective multiphoton transitions in a two-level atom. To analyze this possibility we investigate a four-level system theoretically and show that a high-resolution lithography is possible. We quantitatively identify conditions under which high-contrast lithography can be performed without sacrificing high resolution. The approach is a perturbative density matrix method. This model identifies the tradeoff between resolution and contrast as being due to higher-order terms from intermediate-level Rabi oscillations. We propose using positive and negative one-photon detunings to suppress this effect. Allowing higher Rabi frequencies means that shorter interaction time can be used, and this overcomes the degradation in contrast due to population decay. Finally, we generalize our scheme to $\mathbit{N}$-photon lithography.

DOI
10.1103/physreva.87.023818

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Physical Review A•Nov 11, 2013•15 citations
The concept of performing quantum lithography with classical, instead of entangled, light is of great interest for practical implementation. One recent proposal [Hemmer, Muthukrishnan, Scully, and Zubairy, Phys. Rev. Lett. 96, 163603 (2006)] to accomplish this was based on the use of frequency selective multiphoton transitions in a two-level atom. To analyze this possibility we investigate a four-level system theoretically and show that a high-resolution lithography is possible. We quantitatively identify conditions under which high-contrast lithography can be performed without sacrificing high resolution. The approach is a perturbative density matrix method. This model identifies the tradeoff between resolution and contrast as being due to higher-order terms from intermediate-level Rabi oscillations. We propose using positive and negative one-photon detunings to suppress this effect. Allowing higher Rabi frequencies means that shorter interaction time can be used, and this overcomes the degradation in contrast due to population decay. Finally, we generalize our scheme to \mathbitN\mathbit{N}\mathbitN-photon lithography.
Based on our previous scheme [Hemmer et al., Phys. Rev. Lett. 96, 163603 (2006)] we show the procedures to obtain any one- or two-dimensional pattern by multiple exposures. A key modification to the resonance condition is made to achieve subwavelength pattern resolution. The level separation of the substrate does not pose an upper limit to the frequency summation. So the fundamental frequency can be high and the number of Fourier terms can be large, making our scheme very suitable for subwavelength arbitrary patterns.
The proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)] is studied via a rigorous formalism. It is shown that, contrary to Boto et al.'s heuristic claim, the multiphoton absorption rate of a $(\ensuremath{\mid}N,0⟩+\ensuremath{\mid}0,N⟩)$ quantum state is actually lower than that of a classical state with otherwise identical parameters. The proof-of-concept experiment of quantum lithography [D'Angelo et al., Phys. Rev. Lett. 87, 013602 (2001)] is also analyzed in terms of the proposed formalism, and the experiment is shown to have a reduced multiphoton absorption rate in order to emulate quantum lithography accurately. Finally, quantum lithography by the use of a jointly Gaussian quantum state of light is investigated to illustrate the trade-off between resolution enhancement and multiphoton absorption rate.
At the end of last century, the name of “quantum lithography” has been emerged. This exciting approach was proposed for making a resolution two times higher than that of the conventional optics without changing a wavelength and a numerical aperture. For those who want optical lithography to last long, this has been thought to be a great technology. However, an applicability of the proposed method to the current exposure system i.e., reduced projection exposure system has not yet been examined clearly. We have investigated the proposed quantum lithography to apply into the current exposure system using reticle. For simplicity, coherent illumination i.e. sigma is zero condition is used for calculation. Our quantum lithography compatible to mask exposure system explains probability of one and two photon absorption on the image plane i.e. on wafer. We have shown that the half-wavelength quantum lithography using conventional mask exposure system is impossible because diffraction at the mask makes biphoton into two photon. We have found that there is still super-resolution quantum lithography using mask exposure, however, there is little possibility of quantum lithography practically today because biphoton light source is as dark as stars. To realize quantum lithography practically, further development of not only biphoton light source but also two-photon absorption resist is indispensable.
The resolution of an interferometric optical lithography system is about the half wavelength of the illumination light. We proposed a method based on Doppleron resonance to achieve a resolution beyond half wavelength [Phys. Rev. Lett. 96, 163603 (2006)]. Here, we analyze a possible experimental demonstration of this method in the negatively charged silicon-vacancy (${\mathrm{SiV}}^{\ensuremath{-}}$) system by considering realistic experimental parameters. Our results show that quarter wavelength resolution and beyond can be achieved in this system even in room temperature without using perturbation theory.
The resolution of traditional optical microscope and optical lithography is limited by about half wavelength of the light source, which is well known as the diffraction limit or Abbe limit. The resolution limit is due to the missing of high spatial frequency components in the far-field. One way to achieve high resolution is to move the detector into the near-field region where the evanescent wave can be collected. However, these methods are surface-bound and usually very slow which have limited applications. It has long been an interesting and important question about how to overcome the diffraction limit in the far-field.\n\nFor optical lithography, a number of methods have been proposed to overcome the diffraction limit such as multi-photon scanning, quantum entanglement, quantum inspired process (e.g., dopperlon), and quantum dark state. However, these methods either require multi-photon absorber, quantum entanglement, or multi-energy levels, which restrict them from extending to higher resolution in practice. In this thesis, we showed that sub-diffraction-limited resolution can be generated by the coherent Rabi gradient. This method does not require multi-photon absorber or quantum entanglement but just quantum coherence of the medium. Extension from lower resolution to higher resolution is very straightforward where we just need to increase the pulse intensity or pulse duration. We also proposed two atom lithography experiments based on the Rabi gradient. The first one uses Rubidium Rydberg atom and microwave where we showed that sub-micrometer line spacing is possible. The second one uses Chromium atom and optical field where we showed that sub-10nm line spacing is possible while the wavelength of the light is about 400nm.\n\nFor optical imaging, a number of methods have also been proposed to achieve super-resolution such as multi-photon microscope, stimulated-emission-depletion, structured illumination microscopy, centroid-based techniques and metamaterial-based lens. Here, we will show a new method to achieve resolution beyond the diffraction limit which we called it resonance fluorescence microscopy. Resonance fluorescence has been proposed to localize a single atom with resolution beyond the diffraction limit. The separation between two atoms can also be extracted from the resonance\nfluorescence spectrum. To develop it as microscopy, we need to evaluate the resonance fluorescence spectrum of multiple-atom system. We analytically solved the general feature of the spectrum when the Rabi frequency is much larger than the dipole-dipole interaction and showed how to extract the spatial information of the atoms with resolution far beyond the diffraction limit. This method is entirely based on far-field techniques and it does not require point-by-point scanning.
The resolution of optical lithography and the spacing of atom lithography are limited by about half of the wavelength due to the Rayleigh limit. Here we propose a coherent atom lithography experiment which can print nanometer structures. In this proposal, we show that subwavelength spatial distribution of the atoms in the excited state can be achieved by inducing spatially modulated Rabi oscillations in two-level atoms. We use the internal energy of the atoms to excite the photoresist and it can then print the subwavelength structure into the photoresist. For the peak Rabi frequency of about 2 GHz and the recoil limited collimation, we show that sub-10-nm10\text{-nm}10-nm spacing in both one- and two-dimensional space is possible.