Quantum computing – a real gem

It’s a symbol of love, success and wealth, but the colour centers that make a diamond that extra bit special could also hold the key to quantum computing. Here we learn how one group is close to quantum information processing using the nitrogen vacancy centers responsible for that famous sparkle  

A significant contribution to the aesthetic beauty of diamond comes from the hundreds of colour centers – localised point defects in the diamond lattice that fluoresce at visible wavelengths. A few of these colour centers, most notably the nitrogen vacancy (NV) center, also contribute to the fervent interest in diamond research.

While first characterised in the 1960s, it wasn’t until the 1990s that scientists began to intensely study the NV’s utility for nanoscale magnetic field and temperature sensing as well as for quantum information. Indeed, the NV is considered a promising candidate qubit – the fundamental unit of quantum computation. Qubits are two-state quantum mechanical systems; however, unlike their counterpart classical bits (which can only be either 0 or 1), information can be stored in a quantum superposition of the two qubit states. This capability allows for massive parallelisation and the use of quantum algorithms like the Shor factoring algorithm, which can factor large numbers very quickly and, as such, could transform the field of encryption and digital security.

Before NVs can become a large-scale platform for quantum information however, several challenges must still be addressed, including the ability to controllably enhance the NV’s light output by placing it inside a resonant optical cavity. In this article, we describe recent contributions our research group has made to this endeavor.

Diamond is an extremely hard and chemically resistant substance that can operate at room temperature, making it well suited to solid-state applications. Diamond is composed of a tetrahedral framework of carbon atoms. However, no diamond is 100% pure carbon, and there are many structural defects that can exist within the diamond lattice, leading to unique optical and magnetic properties.

[caption id="attachment_42818" align="aligncenter" width="450"] Figure 1: Image of NV- defect in a diamond lattice. Credit: Nepomo (Eigene Zeichnung.) [Public domain], via Wikimedia Commons[/caption]

Specifically, the NV center in diamond is a substitutional point defect – where one nitrogen atom replaces a carbon atom and an adjacent carbon site is empty, known as a vacancy (Figure 1). The NV center primarily exists in one of two states, neutral NV⁰ or negatively charged NV^-. In its electronic ground state, the NV^- (to which we now limit our discussion) has three energy sublevels – making it a “triplet state” (Figure 2), whose energies are affected by interactions of the electron spins with each other and with the nuclear spins of the defect. The energy splitting between these sublevels is such that microwave radiation can be used to drive transitions between them. We can therefore designate two of these levels as the “0” and “1” states of a qubit and use microwaves to perform quantum operations.

In addition to being able to manipulate the qubit, we need to know which sublevel the NV is in. To find out, we can use a technique known as optical readout. When probed with 532 nm green light, the NV will be excited to another triplet state. The excited state lifetime is approximately 12 ns in bulk diamond, after which the NV center re-emits red light at 637 nm with an intensity that depends on the sublevel the NV^- was in before it was excited. If the NV started in the lowest sublevel, called m_s = 0, then the defect will always decay directly to the ground state, emitting a photon. However, if the NV starts in one of the excited sub-levels, m_s = +/-1, then there is a chance (~30%) that the excited state will decay first to a “dark” singlet state (see Figure 2) and then to the ground state without emitting any visible photons. Therefore, after this detection sequence is repeated thousands of times to get a statistically significant signal, the emission intensity can be used to determine what state the NV center is in. For example, when the signal drops ~30% relative to the m_s = 0 reference intensity, we know that the NV is in the m_s = +/-1 state.

The 637 nm emission signal discussed above, called the zero-phonon line (ZPL), appears as a narrow peak and is generated by direct radiative emission between the excited and ground triplet states. However, the diamond itself is composed of oscillating carbon atoms, which have their own discrete energy levels. When the electron decays from the excited triplet state, some of the energy can generate collective oscillations of carbon atoms, called phonons, while the remaining energy will be emitted as light. Because some energy is transferred to these phonons, the energy emitted as light will be less, resulting in a longer emission wavelength. This phenomenon leads to a broad ‘phonon sideband’ next to the zero phonon line. In a bulk diamond, the phonon sideband dominates the signal, comprising ~97% of total light emission. Unfortunately, for quantum information applications, typically only the ZPL emission is useful. Therefore, we would like to direct more of the emission into the ZPL. One way to accomplish this increase is to embed the NV center inside an optical cavity.

The inherent issues in collecting light from bulk diamond, caused by total internal reflection, as well as the aforementioned problem of low emission into the ZPL have led to efforts to shape diamond to change its emission properties. These efforts include using macro-structures such as solid immersion lenses and nanoscale optical cavities such as photonic crystal structures. These cavities are much smaller than traditional resonators (e.g. Fabry-Perot) and are particularly useful for emission enhancement.

Resonant electromagnetic cavities can increase the spontaneous emission rate of an emitter placed inside them, as pioneered in the 1940s by Edward Purcell. Such cavities confine electromagnetic energy of a particular wavelength both temporally (low losses over time) and spatially. The degree of temporal confinement is given by the quality factor, Q, of the cavity. The higher the Q, the longer the resonant light will remain within the cavity. Similarly, the degree of spatial confinement is given by the modal volume, V, of the cavity. A smaller V means that light is confined within a tighter region.

Cavities with high values of Q/V alter the local density of optical states of the emitter, in such a way that the spontaneous emission rate into the resonant wavelength is increased. The enhanced rate causes an increase in emission intensity at the resonant wavelength as well as a decrease in the excited state lifetime of the emitter. This type of resonant emission enhancement, termed the Purcell effect, can thus be used to increase emission into the NV zero phonon transition. Furthermore, the augmented emission is into a specific cavity mode, which may be engineered for improved out-coupling of light for collection and possible on-chip integration. So, due to the many advantages that can be gained from the use of cavities, our work focuses on integrating NV centers within this type of nanoscale optical cavity.

To achieve maximum enhancement, we pursued Purcell effect improvement on two fronts: the ratio of Q to V and the deterministic placement of the emitter at the location of the cavity’s maximum electric field. First, we were able to improve the Q and V parameters by optimising the design of the cavity that we chose to fabricate. There are many types of photonic cavity structures, including whispering gallery-type microdisk resonators and photonic crystal cavities (PCC). We chose a specific cavity design called a one-dimensional nanobeam PCC because this cavity type generates extremely high Q/V ratios and has one primary resonance with a wavelength that can easily be changed by altering the cavity’s size. The cavity consists of a single line of evenly-spaced holes within a thin beam of the selected material. When the spacing of the middle holes is tapered to less than the spacing of the holes at the ends of the cavity, light can be tightly confined within this middle region; when the cavity is sized correctly, this confinement yields a cavity resonance tuned to the NV ZPL wavelength with very high Q and very low V.

Because the electromagnetic energy is highly localised in the 1D PCC structure, it is also important to position the NV where the field is maximised for optimal enhancement. Therefore, our second means of achieving good Purcell enhancement was placing the NV centers only in a thin diamond layer in the vertical middle of the final cavity (at the electromagnetic field maximum), using a technique known as delta doping. To accomplish this, our collaborators grew a diamond layer on top of a commercially-available bulk diamond sample. Nitrogen was incorporated in the growth chamber for a very short amount of time in the middle of the growth process, so that NV centers would be present only in the middle of the new layer. This 200-nm thick overgrown layer was then used to fabricate our cavities. Through a precisely calibrated process of ion bombardment, reactive ion etching, and electrochemical etching, we removed square membranes, 400 microns to a side, of the overgrown layer and bound them to a sticky polymer on top of silicon (Figure 3a). We then used electron beam lithography and reactive ion etching to pattern the nanobeam cavity design within this membrane (Figure 3b, c).

Once we had fabricated the nanobeam cavities, our final task was to characterise how well they could confine light and enhance the NV ZPL emission. Fabrication imperfections, material defects in the diamond, and other factors combined to depress each cavity’s Q well below the theoretical value, as well as cause cavity-to-cavity variation in the resonant wavelength on the order of tens of nanometers. Using a home-built confocal optical setup at room temperature, we excited the NV centers with a 532-nm laser and collected the emission. Cavity resonances manifest as sharp peaks decorating the standard NV fluorescence signal of ZPL and phonon sideband (Figure 4). By fitting these peaks, we could determine both the Q and the wavelength of the cavity resonance. The best cavities we fabricated showed Q of over 20,000, which was the highest recorded Q for a diamond PCC at visible wavelengths.

To do our final experiments, we chose a cavity with Q of 7,000 and a resonant wavelength just a few nanometers shorter than the NV ZPL. We placed the sample containing this cavity in a cryostat and cooled it to ~4 K with liquid helium. Cooling to such a low temperature allowed us to condense nitrogen gas on the desired cavity, which shifts its resonance to slightly longer wavelengths. We injected the nitrogen in small steps to precisely control the wavelength tuning. As we tuned the cavity resonance through the ZPL of the NVs within the cavity, we monitored the ZPL emission intensity, as well as the NV excited state lifetime. As expected, while on resonance we observed a reduction of the excited state lifetime (Figure 5a.) and an increase in the emission intensity (Figure 5b.), both consistent with a 20-fold Purcell enhancement. Therefore, our experiment had successfully demonstrated that our fabrication approach can be used to create cavities that enhance the NV ZPL, as is necessary for quantum information applications.

Our cavities had the highest measured Q/V ratio to date, but the degree of Purcell enhancement was not as large as theoretically expected by our designs. In order to further improve the enhancement of the NV ZPL, we hope to construct new cavities with single NVs and develop horizontal placement techniques so that the NVs can be created precisely at the field maximum in all 3 dimensions. As these cavities are perfected, we can begin to experiment with control of the magnetic sub-levels of the NV^- within the cavity. Though we cannot expect a quantum computer in every household next year, this continuing work will help develop a possible structure for scalable quantum information processing.

References:

1. Lee, Jonathan C., et al. “Deterministic coupling of delta-doped nitrogen vacancy centers to a nanobeam photonic crystal cavity.” Applied Physics Letters 105.26 (2014): 261101.
2. Doherty, Marcus W., et al. “The nitrogen-vacancy colour centre in diamond.”Physics Reports 528.1 (2013): 1-45.
3. Rondin et al. Magnetometry with nitrogen-vacancy defects in diamond. Rep. Prog Phys. 77 (2014) 056503.
4. Aharonovich, Igor, and Elke Neu. “Diamond nanophotonics.” Advanced Optical Materials 2.10 (2014): 911-928.
5. Ohno, Kenichi, et al. “Three-dimensional localization of spins in diamond using 12C implantation.” Applied Physics Letters 105.5 (2014): 052406.
6. Nielsen, Michael A., and Isaac L. Chuang. Quantum computation and quantum information. Cambridge university press, 2010.