In this chapter I discuss the questions that remain to be answered for this system and point to possible measurements to explore in the future.
8.1 Limitations to zero-field coherence lifetimes
One of the next major goals with this platform is the generation of indistinguish- able photons. However, measurements of the optical coherence lifetimes at this point indicate that we are not yet near the lifetime-limit necessary to show high in- distinguishability. Further studies in the device are warranted to understand if the observed coherence lifetimes so far are actually at the limit of what is achievable.
Along these lines, more statistics on the coherence lifetimes of di↵erent ions within the cavity would be useful to determine whether this is for instance related to the observed strain splitting. Measurements of the coherence in the same bulk crystals as used for the device will be essential for further understanding of the mechanisms of the observed decoherence. After understanding and pushing the limits of the optical coherence, we should be able to further improve this indistinguishability with improved device fabrication and shorter cavity-enhanced lifetimes. If spectral di↵usion (T2⇤) continues to be a problem, one could also imagine implementing a post-selection procedure similar to that used in NV centers to improve coherence in the presence of spectral jumps [137].
While the demonstrated ⇠ 20 ms spin coherence lifetime is promising, it appears we may be approaching the lifetime limit in this sample. Further investigations of this lifetime with magnetic field and temperature should reveal whether this lifetime is limited by spin lattice relaxation or ion-ion interactions. Similar spectroscopy in the bulk material is necessary to verify that this is not intrinsic to ions in the cavity.
If the lifetime is indeed limited by ion-ion interactions, the next step would be to move to samples with lower doping concentrations or larger spin inhomogeneous broadening to reduce such interactions. We are currently investigating a variety of sources for the YVO crystals in attempts to achieve lower doping concentrations.
To achieve larger inhomogeneous broadening, we could investigate samples that are codoped with other ions such as europium or scandium to introduce more static strain within the sample [149, 150].
For further improvements to coherence lifetimes, another route to explore in the context of single ions will be the high-field regime presented in Chapter 3. In this regime, we observed two-pulse spin echo lifetimes of 6.6 ms at a temperature of
⇠ 600 mK and magnetic field of 440 mT along thec-axis of the crystal in a signif- icantly higher doping density sample (100 ppm). We expect this to improve even further at higher fields, lower temperatures, or lower doping concentrations as the contribution to dephasing from Yb-Yb interactions is reduced. These long coher- ence lifetimes could be extended even further with the use of dynamical decoupling sequences. The high-field limit would bring a new set of experimental challenges as discussed in Chapter 7, but there are no fundamental difficulties to moving to this regime in the future.
8.2 Coupling to nearby spins
One exciting aspect of this work is the coupling to nearby nuclear spins observed in the CPMG measurements. Straightforward extensions to the initial measurements presented here should allow for characterization and control over this coupling.
These nuclear spins could then be harnessed as quantum memories to form a few- qubit quantum register [11, 151]. There is a lot to be explored here and this work will benefit greatly from the progress and techniques demonstrated with the NV center in diamond [11, 143, 144, 152, 153].
8.3 Toward generation of entanglement
Ultimately, the goal is to show that this system is a useful technology for quan- tum networks. As mentioned, one of the next major steps toward this goal will be the demonstration of indistinguishable photon emission. After showing improve- ments to the coherence lifetimes, we then want to show a direct measure of the indistinguishability. This can be done initially with photons from the same ion, but ultimately must be shown with two di↵erent ions.
We can directly measure the photon indistinguishability using a Hong-Ou-Mandel (HOM) interferometer [109]. To measure indistinguishability between a pair of photons from the single emitter, we can introduce an additional delay line such that we interfere photons from consecutive excitations of the same emitter. For this, we need the delay line to be significantly longer than the lifetime of the ion. Let’s get an idea of the requirements of this experiment for the current device. As the fastest observed lifetime isT1 = 2.3 µs, a delay time of a few lifetimes (let’s say 4T1) corresponds to a delay line of⇡ 2 km. For single-mode fiber readily available
from Thorlabs 1, the quoted loss at 980 nm is < 2 dB/km. With the additional insertion loss of the necessary beamsplitters and fiber splices (⇡ 1dB total), this would bring the total detection efficiency from 1% to ⇡ 0.3% for a two-photon detection probability of 9 ⇥ 10 6. For the current Yb-171 singles, a reasonably optimistic estimate for the overall rate of photons generated within the device is 25 kHz given the 10µs wait time between pulses, the branching ratio, and time necessary to reinitialize the system (2 ms). This then corresponds to ⇠ 0.2 two- photon coincidences per second. While certainly not impossible, this measurement would be also be made more challenging by the necessity of stabilizing the 2 km fiber interferometer. This particular measurement is then perhaps best suited for faster ions and thus faster experiments.
A more exciting measurement in the future will be to demonstrate indistinguisha- bility between two separate ions. This is significantly more technically challenging overall, but is also a direct step toward entanglement of two ions. The main chal- lenge to interfering single photons from ions in two di↵erent ions in two di↵erent devices will be the requirement of essentially doubling the experimental infrastruc- ture. This is a significant undertaking, but should be accomplished with enough time, energy, and manpower. Of course, such measurements cannot be accom- plished until the remaining questions about the properties of the system are sorted out.
Ultimately, measurements of indistinguishability of photons from separate emitters is the foundation for the demonstration of entanglement of two single rare-earths ions. We can get a sense of the entanglement distribution rates we might be able to achieve within the lab setting with reasonable improvements to the devices. We estimate this based on the well-known Barret-Kok scheme [154]. The success prob- ability in this experiment is simply given byPs = 12p2⌘2d, where pis overall device system efficiency (i.e. probability that photon emitted by ion is coupled into fiber) and⌘dis the detection chain efficiency.
For the current set of devices, we have p⌘d ⇡ 1%. Assuming two such devices could be made and similar efficiencies achieved, the overall success probability would be 5⇥10 5. Assuming a 25 kHz average excitation rate as above gives a corresponding success rate of 1.25 Hz. The main limits on the system efficiency are the fiber-waveguide coupling and the waveguide-cavity coupling. Based on previously demonstrated devices, it is reasonable that we can improve this overall
1e.g. Thorlabs SM980G80
efficiency in the near term by a factor of at least 5. This then corresponds to a success rate of⇠31 Hz for two ions in the same lab. Further investigations of the ultimate limits of the performance and collection efficiencies in these devices is warranted before making any further speculation. While these rates could enable near-term demonstrations in the lab, we ultimately want much higher count rates to account for fiber-loss when moving to larger scale implementations. In the long- term, the integration of 171Yb:YVO4 with fabrication architectures that allow for efficient coupling to fiber [50, 121, 155] will be an essential step in significantly improving these success rates.
8.4 Conclusion
In conclusion, this thesis has presented on recent progress toward building a nanopho- tonic quantum interface with 171Yb:YVO4. We first investigated the properties of this previously unexplored material and found it will be useful for a variety of quantum technologies. Building on this work, we were able to optically detect and initialize single ytterbium ions coupled to a nanophotonic cavity. After ex- ploring the properties of an ion with zero-nuclear spin, we showed that the hybrid electron-nuclear spin states of Yb-171 at zero-field enable strong transitions with reduced magnetic field sensitivity. Through the use of dynamical decoupling, we showed spin coherence lifetimes of up to 18 ms. We then made use of the zero-field level structure of 171Yb:YVO4 to demonstrate high-fidelity single-shot readout of the spin state. These results serve as the foundation for an exciting array of mea- surements to explore in the future and demonstrate that nanophotonic devices with
171Yb:YVO4 are a promising platform for solid-state quantum light-matter inter- faces.