Nanostructured Diamond Metalens For Compact Quantum Technologies

The key to harnessing the potential power of quantum systems is being able to create or find structures that allow electron spin to be reliably manipulated and measured, a difficult task considering the fragility of quantum states.

Bassett’s lab at the University of Pennsylvania approaches this challenge from a number of directions. Recently, the lab developed a quantum platform based on a two-dimensional (2D) material called hexagonal boron nitride which, due to its extremely thin dimensions, allows for easier access to electron spins. In the current study, the team returned to a 3D material that contains natural imperfections with great potential for controlling electron spins: diamonds.

Nature Communications – A monolithic immersion metalens for imaging solid-state quantum emitters

Small defects in diamonds, called nitrogen-vacancy (NV) centers, are known to harbor electron spins that can be manipulated at room temperature, unlike many other quantum systems that demand temperatures approaching absolute zero. Each NV center emits light that provides information about the spin’s quantum state.

Bassett explains why it is important to consider both 2D and 3D avenues in quantum technology:

“The different material platforms are at different levels of development, and they will ultimately be useful for different applications. Defects in 2D materials are ideally suited for proximity sensing on surfaces, and they might eventually be good for other applications, such as integrated quantum photonic devices,” Bassett says. “Right now, however, the diamond NV center is simply the best platform around for room-temperature quantum information processing. It is also a leading candidate for building large-scale quantum communication networks.”

So far, it has only been possible to achieve the combination of desirable quantum properties that are required for these demanding applications using NV centers embedded deep within bulk 3D crystals of diamond.

Unfortunately, those deeply embedded NV centers can be difficult to access since they are not right on the surface of the diamond. Collecting light from those hard-to-reach defects usually requires a bulky optical microscope in a highly controlled laboratory environment. Bassett’s team wanted to find a better way to collect light from NV centers, a goal they were able to accomplish by designing a specialized metalens that circumvents the need for a large, expensive microscope.

“We used the concept of a metasurface to design and fabricate a structure on the surface of diamond that acts like a lens to collect photons from a single qubit in diamond and direct them into an optical fiber, whereas previously this required a large, free-space optical microscope,” Bassett says. “This is a first key step in our larger effort to realize compact quantum devices that do not require a room full of electronics and free-space optical components.”

Metasurfaces consist of intricate, nanoscale patterns that can achieve physical phenomena otherwise impossible at the macroscale. The researchers’ metalens consists of a field of pillars, each 1 micrometer tall and 100–250 nanometers in diameter, arranged in such a way that they focus light like a traditional curved lens. Etched onto the surface of the diamond and aligned with one of the NV centers inside, the metalens guides the light that represents the electron’s spin state directly into an optical fiber, streamlining the data collection process.

“The actual metalens is about 30 microns across, which is about the diameter of a piece of hair. If you look at the piece of diamond that we fabricated it on, you can’t see it. At most, you could see a dark speckle,” says Huang. “We typically think of lenses as focusing or collimating, but, with a metastructure, we have the freedom to design any kind of profile that we want. It affords us the freedom to tailor the emission pattern or the profile of a quantum emitter, like an NV center, which is not possible, or is very difficult, with free-space optics.”

This study is just one of many steps towards the goal of compacting quantum technology into more efficient systems. Bassett’s lab plans to continue exploring how to best harness the quantum potential of 2D and 3D materials.

“The field of quantum engineering is advancing quickly now in large part due to the convergence of ideas and expertise from many disciplines including physics, materials science, photonics and electronics,” Bassett says. “Penn Engineering excels in all these areas, so we are looking forward to many more advances in the future. Ultimately, we want to transition this technology out of the lab and into the real world where it can have an impact on our everyday lives.”

Abstract
Quantum emitters such as the diamond nitrogen-vacancy (NV) center are the basis for a wide range of quantum technologies. However, refraction and reflections at material interfaces impede photon collection, and the emitters’ atomic scale necessitates the use of free space optical measurement setups that prevent packaging of quantum devices. To overcome these limitations, we design and fabricate a metasurface composed of nanoscale diamond pillars that acts as an immersion lens to collect and collimate the emission of an individual NV center. The metalens exhibits a numerical aperture greater than 1.0, enabling efficient fiber-coupling of quantum emitters. This flexible design will lead to the miniaturization of quantum devices in a wide range of host materials and the development of metasurfaces that shape single-photon emission for coupling to optical cavities or route photons based on their quantum state.

Introduction
Solid-state quantum emitters have emerged as robust single-photon sources1 and addressable spins—key components in rapidly developing quantum technologies for nanoscale magnetometry, biological sensing, and quantum-information science. Performance in these applications, be it magnetometer sensitivity or quantum key generation rate, is limited by photon-collection efficiency. However, efficient collection of a quantum emitter’s photoluminescence (PL) is challenging as its atomic scale necessitates diffraction-limited imaging with nanometer-precision alignment, oftentimes at cryogenic temperatures or in other situations incompatible with free-space bulk optics. Beyond their atomic scale, the challenges associated with coupling to solid-state quantum emitters are exacerbated by the high refractive index of their host substrates. Diamond, for example, has a refractive index of nD ~ 2.4 at visible wavelengths, which traps photons in the material by the total internal reflection for propagation vectors oriented beyond θc ~ 25° from the surface normal of a planar air interface. Furthermore, imaging through more than a few microns of diamond with a high-numerical-aperture objective results in spherical aberrations that severely limit collection efficiency. While a number of nanophotonic structures have been investigated for increasing emission from diamond nitrogen-vacancy (NV) centers through Purcell enhancement these devices require NV centers positioned close to diamond surfaces, which degrades their spin and optical properties.

For this reason, a common approach to minimizing optical losses when addressing single NV centers in bulk diamond is to mill or etch a hemispherical surface, known as a solid immersion lens (SIL), around the NV center of interest. By ensuring uniform optical path length and reflectance for rays emanating to all angles, SILs remove the losses caused by the total internal reflection and spherical aberration. SILs have enabled numerous advances in quantum optics using NV centers, including all-optical quantum control and loophole-free violations of Bell’s inequality. However, a high-NA objective lens is still required to image a quantum emitter through a SIL. For quantum-optics experiments, a cryostat that can accommodate a vacuum-compatible objective and associated optomechanics must be used, or the optical losses associated with imaging through a cryostat window must be accepted. Neither option provides a clear route for packaging quantum emitters in a scalable fashion.

Since quantum emitters are point sources with relatively narrow emission spectra, the compound optical system of a microscope objective, designed for broadband imaging with a flat field-of-view, is not actually necessary for efficient photon collection. Flat optics, such as phase Fresnel lenses used to image trapped ions in ultra-high-vacuum cryostats, are an attractive alternative; however, a flat optic on its own cannot compensate for the high refractive index of a solid-state quantum emitter’s host material. The ideal solution is a flat optic fabricated at the air/diamond interface to form a planar immersion lens; such a design can be realized using the concept of a metasurface.

Discussion
The immersion metalens lays the foundation for future advances in controlling light-matter interactions for quantum emitters in high-refractive-index substrates. By integrating the typical objective/SIL combination onto the quantum emitter’s host substrate, the metalens has the potential to enable direct fiber coupling of quantum emitters. In their experiment, two relay lenses and a free-space long-pass filter were used to prevent the pump beam from entering the collection fiber However, the metalens output can be coupled directly into a fiber using a different excitation geometry or a commercially available multilayer-dielectric-coated fiber tip (available from Omega Optical, Inc., for example). Another limitation of our current demonstration is the inability to co-focus the pump beam and collection volume through the metalens due to chromatic aberration inherent to the Fresnel lens phase profile. Going forward, achromatic metalens designs can enable co-focusing of multiple wavelengths, or a second metalens can be incorporated on the backside of the diamond to focus the pump beam, replacing the objective in our experiment.

Unlike previous high-NA metalens demonstrations that relied on diffraction to focus wide angles far from the optical axis the high NA of our metalens is achieved by using diamond as an immersion medium. This implies that optimized design strategies could yield a diamond metalens with a substantially larger NA, potentially with a value approaching the maximum, NAmax = nD = 2.4. Beyond lenses, the expanding body of research on metasurface design can be leveraged to explore phase profiles that shape emission from quantum emitter ensembles, compensate for an emitter’s dipole orientation, control coupling to orbital–angular–momentum modes and enable chiral quantum photonics. An immersion metasurface can also be incorporated with nanophotonic structures for Purcell enhancement, for example to collimate the output of a chirped grating structure or parabolic mirror through the backside of the diamond, or to extend the cavity length of a fiber-based resonator cavity.

The immersion metalens promises major advances in performance and scalability of quantum devices. Its top-down fabrication processes are readily compatible with those used to fabricate on-chip microwave antennas and electric-field gates required for dynamic spin control and Stark shifting in quantum optics applications. Furthermore, the metalens design can be applied directly to other quantum-emitter systems, including spin defects in silicon carbide, quantum dots in III–V compound semiconductors, and rare-earth ions in laser crystals. More generalized metasurface designs can mediate quantum entanglement and interference of quantum emitters. Ultimately, this demonstration has broad implications for nanophotonics, quantum optics, and quantum nanotechnology, as dielectric metasurface design will lead to compact, fiber-coupled single-photon sources, sensors, and quantum memories, with further potential applicability to designing diffractive optics for space and Raman lasers.

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