From the literature review presented in this chapter, it can be concluded that fabrica- tion of waveguide devices for quantum memories using rare-earth ion doped crystals is possible. The results of these experiments showed that reasonable coherence times can be achieved in waveguides built using rare-earth ions.
In moving towards waveguide fabrication, host crystals with low intrinsic inho- mogeneities are ideal. Most of the demonstrations reviewed in this chapter had used LiNbO3 as the host crystal for rare-earth ions. It was discussed that the intrinsic disorder of LiNbO3 crystals caused the inhomogeneous linewidth to be very large compared to Y2SiO5 host crystals. Hence, the fabricated waveguide presented in this thesis used Y2SiO5 as the host crystal.
The aim of the work presented in this thesis was to fabricate a gradient echo memory on a waveguide platform. In the next chapter, the material properties of the rare-earth ion doped system used to fabricate the waveguides will be discussed. In
§2.8 Summary 47
addition, the complexities of the design and fabrication of these planar waveguides will be explored.
Chapter 3
Proposed Linear Optics Quantum
Processor Architecture
3.1
Introduction
A successful quantum repeater needs single photon sources, quantum memories with long storage times and detectors at each node. All of these individual components need to be highly efficient for the whole quantum repeater to perform better than direct transmission of quantum information between two links. A practical quan- tum repeater also requires complex operations to be performed at each local node. These operations include entanglement swapping and quantum distillation. Cur- rently, there is no way of performing the required operations including two-qubit gates deterministically, but it is possible to build a quantum processor using non- deterministic gates. It was proposed by Knill, Laflamme and Milburn (KLM), that non-deterministic quantum processors can be built using linear optics [144].
In the KLM scheme, the optical modes of photons, vertical and horizontal polar- izations for example, are used as qubits that are to hold the quantum information and the operations performed using these qubits are called quantum gates. In a quantum repeater node, entanglement swapping (local joint measurements on the entangled states) between two quantum memories has to be performed. Such oper- ations are possible by using two-qubit probabilistic quantum gates between the two memories [6, 145].
To fully operate the KLM proposal using non-deterministic gates, a linear optics quantum information processing unit consists of single photon sources, quantum memories, photon detectors, and passive elements such as beam splitters and phase shifters. To construct these complicated circuits and reduce the loss due to coupling in and out of bulk devices, it would be ideal to build an integrated chip containing all the necessary components on the same platform, rather than free space components.
Figure 3.1: An alternative approach to building an optical quantum information processor unit has been built by Carolan et al.. In this architecture, photon pairs are generated using spontaneous parametric down conversion. Created photons are then transmitted through an array of polarization maintaining fibers to the linear optical processing unit (LPU). The LPU consists of 30 thermo-optical phase shifters controlled by a digital to analog convertor (DAC) unit off the chip. 15 of these phase shifters form 15 Mach-Zehnder interferometers. Photons to be measured are coupled out of the LPU using another array of fibers and transmitted to photon counting detectors off the chip [146].
In this chapter, I am proposing how KLM processing units can be designed using rare-earths to build a quantum repeater.
A state of the art linear optical quantum information processor unit built by Carolan et al. is shown in Figure 3.1 [146]. This passive integrated photonic chip is a silica on silicon waveguide circuit, working as a single mode waveguide at the wavelength of 808 nm. Polarization maintaining fibers are connected to the input and output channels of this waveguide circuit, with coupling losses of about 9% for each fiber. This chip has a maximum of six inputs, and consists of an array of 30 waveguide directional couplers and 30 thermo-optic phase shifters. These thermo-optical phase shifters are controlled by thermo-optical heaters, fabricated on top of the waveguide and controlled by an electrical circuit providing the voltage required for any desired phase shift. 15 of these phase shifters create 15 Mach- Zehnder interferometers on this integrated chip. The fiber to fiber loss in this system is about 42%. This integrated chip is reprogrammable and was programmed to realize heralded quantum logic and entangled quantum gates, among other complex processes [146].
§3.1 Introduction 51 RASE Source RASE Source RASE Source RASE Source Superconducting nano-wire detectors Laser . . . Digital Signals 18 x 10 V 18 x 12 bits . . .
D/A D/A D/A
Beam splitter
Mach-Zehnder interferometer Q.M.
Q.M.
Figure 3.2: Linear optical quantum processor. This integrated chip includes 4 RASE photon sources, 2 quantum memories, 4 beam splitters and 2 Mach-Zehnder inter- ferometers. In this chip, the superconducting nano-wire detectors and the electronic control circuitry are off-chip.
To implement the full KLM scheme, due to the non-deterministic nature of events, quantum memories are essential. This integrated chip doesn’t have a quan- tum memory. It is possible to use delay lines instead of quantum memories on this chip, but that would require fast switches, not available on this integrated circuit. The thermal switching speeds are slow compared to the photon packet size and there is no way of acquiring any feedback to the system in real time. Also, this linear optics processor unit is a hybrid device with on chip and off chip components, with the photon source and the photon counting detectors off the chip, which leads to coupling losses. In this chapter, I outline a proposal for a linear optical quantum processor using a rare-earth ion doped integrated platform. This integrated chip can bring the photon sources and quantum memories together with classical con- trol elements such as modulators and switches, and passive elements such as beam splitters and phase shifters on to one processor chip. This platform uses the long storage times of rare-earth quantum memories. Also, different devices on the chip can be controlled by electrical fields inducing Stark shifts on the ions.
The proposed linear optics quantum processor architecture of this chapter is shown in Figure 3.2. In this system, the single photon sources and quantum memo- ries, as well as passive elements such as beam splitters, are on the same chip. As can be observed, these components are controlled by electronic circuits similar to what was required in the chip of Figure 3.1. These components are briefly introduced in
Glass Thin film
Rare-earth ion doped substrate
Figure 3.3: A simplified illustration of the waveguide. TeO2 glass thin film deposited on a Pr3+:Y
2SiO5 substrate.
later Sections.