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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Design of single-photon Mach-Zehnder interferometer based devices for quantum information processing

Hubert Pascal Seigneur, Michael Niklaus Leuenberger, Winston Vaughan Schoenfeld

Published Jan 10, 2008• 2 citations
Publisher

Abstract

A comprehensive theoretical analysis of the cavity quantum electrodynamics (QED) in single-photon Mach-Zehnder Interferometer (SMZI) based switches and single quantum gates that are intended for the processing of quantum information encoded in the polarization of single photons inside integrated photonic crystal (PC) quantum networks is presented. These devices rely on manipulating the geometrical phase of single photons by means of the Single-Photon Faraday Effect (SPFE), which can be described in terms of a detuned single mode quantum field strongly interacting with a two-level system or quantum dot (QD) inside nanocavities. The feasibility of such devices depends on the ability for the field in each arm of the interferometer to couple in their respective nanocavities, successfully interact with the quantum dot, and when the appropriate phase is accumulated couple out; all these steps being performed with minimum phase error and losses. Using the Jaynes-Cummings model, the cavity dynamics is studied for various detuning energies and coupling energies, and it is shown that the design of these devices can achieve low phase error and robustness against fabrication errors.

DOI
10.1117/12.761236

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A comprehensive theoretical analysis of the cavity quantum electrodynamics (QED) in single-photon Mach-Zehnder Interferometer (SMZI) based switches and single quantum gates that are intended for the processing of quantum information encoded in the polarization of single photons inside integrated photonic crystal (PC) quantum networks is presented. These devices rely on manipulating the geometrical phase of single photons by means of the Single-Photon Faraday Effect (SPFE), which can be described in terms of a detuned single mode quantum field strongly interacting with a two-level system or quantum dot (QD) inside nanocavities. The feasibility of such devices depends on the ability for the field in each arm of the interferometer to couple in their respective nanocavities, successfully interact with the quantum dot, and when the appropriate phase is accumulated couple out; all these steps being performed with minimum phase error and losses. Using the Jaynes-Cummings model, the cavity dynamics is studied for various detuning energies and coupling energies, and it is shown that the design of these devices can achieve low phase error and robustness against fabrication errors.
Combining the recent progress in semiconductor nanostructures along with the versatility of photonic crystals in confining and manipulating light, quantum networks allow for the prospect of an integrated and low power quantum technology. Within quantum networks, which consist of a system of waveguides and nanocavities with embedded quantum dots, it has been demonstrated in theory that many-qubit states stored in electron spins could be teleported from one quantum dot to another via a single photon using the single-photon Faraday effect. However, in addition to being able to transfer quantum information from one location to another, quantum networks need added functionality such as (1) controlling the flow of the quantum information and (2) performing specific operations on qubits that can be easily integrated. In this paper, we show how a single-photon Mach–Zehnder interferometer (SMZI), that uses the concept of the single-photon Faraday effect to manipulate the polarization of a single photon, can be operated both as a switch to control the flow of quantum information inside the quantum network and as various single-qubit quantum gates to perform operations on a single photon. Given that the X gate, the Z gate, and the XZ gate are essential for the implementation of quantum teleportation, we show explicitly their implementation by means of our proposed SMZI. We also present the implementation of the Hadamard gate and the single-qubit phase gate, which are needed to complete the universal set of quantum gates for integrated quantum computing in a quantum network. Finally, the expected fidelity and robustness of the proposed SMZI are quantitatively explored by considering the phase errors within the SMZI.
A single atom in a cavity is the model system of cavity quantum electrodynamics (CQED). The strong coupling regime between the atom and cavity-confined photon corresponds to the reversible exchange of energy between the two modes, and underpins a wide range of CQED phenomena with applications in quantum information science, including for example as quantum logic gates and as sources of entangled states. An important advance was achieved recently when strong coupling between excitons and cavity photons was reported for the first time for localized quantum dots (QDs) in micron-size solid state cavities. This has significance in terms of scalability and integration with other optical devices, and could lead to the emergence of "quantum optics on a chip" technology. However the results presented so far for quantum dots are in the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi splitting); they are not a true QED effect and can equally well be described by classical physics as the coupling between two oscillators. In this paper, we present evidence for a purely quantum phenomenon for the QD/cavity photon system, namely the increase in splitting of the levels when the mean number of photons in the cavity is increased. This corresponds to non-linearities on the single-photon scale: the presence of a single excitation in the cavity changes the level structure, affecting the emission energies for a second photon. Such results are a first step in demonstrating the promise of quantum dots for CQED applications.
Efficient single-photon routing and switching are crucial for optical quantum computing and communication. For this purpose, all-optical switches are designed for gigahertz bandwidths. The switching mechanism is based on the optical Kerr effect via cross-phase modulation (CPM) of the single-photon signal by a strong 1550-nm pump pulse. For energy-efficient switching, this nonlinear effect is exploited in a microresonator that can either be used directly as an intensity switch in a typical add–drop configuration or as a phase shifter in a Mach–Zehnder interferometer (MZI) structure. To speed up resonance build-up and quenching, a pre-emphasis build and an off-resonance wipe pulse are used. The proposed designs are verified by traveling-wave simulations which demonstrate that 0.1 dB insertion loss and ~1 ns switching windows can be achieved. For a scalable out-of-the-lab transfer, we investigate the feasibility of the proposed switch designs for fabrication in a mature photonic integrated circuit (PIC) platform. In particular, silicon nitride PICs have demonstrated record-low losses which makes them suitable for single-photon applications. By parametric modelling of the microresonator’s directional couplers based on Lumerical EME and 2.5-dimensional varFDTD simulations, the required power transmission coefficients for both signal and pump wavelength can be achieved. This results in an all-optical switch design ready for fabrication in a commercial PIC foundry which can potentially enable scalable architectures for quantum photonic applications.
Generating strong interactions between single quanta of light and matter is central to quantum information science, and a key component of quantum computers and long-distance quantum networks. In quantum information processing, these interactions are required to create elementary logic operations (quantum gates) between stationary matter quantum bits (qubits) and photonic qubits that can be transmitted over long distances. Efficient quantum gates between photonic and matter qubits are a crucial enabler for a broad range of applications that include robust quantum networks, nondestructive quantum measurements, and strong photon-photon interactions. So far these qubit-photon gates have been achieved using single atoms and at microwave frequencies in circuit QED systems. Their implementation with solidstate quantum emitters, however, has remained a difficult challenge. We demonstrate that the qubit state of a photon can be controlled by a single solid-state qubit composed of a quantum dot (QD) strongly coupled to an optical nanocavity. We show that the QD acts as a coherently controllable qubit system that conditionally flips the polarization of a photon reflected from the cavity mode on picosecond timescales. This operation implements a controlled NOT (cNOT) logic gate between the QD and the incident photon, which is a universal quantum operation that can serve as a general light-matter interface for remote entanglements and quantum computations. Our results represent an important step towards an all solid-state implementation of quantum networks and quantum computers, and provide a versatile approach for controlling and probing interactions between a photon and a single quantum emitter on ultra-fast timescales.
We theoretically demonstrate that a photonic crystal microcavity coupled to waveguides works as an optical beam splitter. Numerical simulations illustrate that spatially separated two output modes have a relative phase close to $\ensuremath{\pi}/2$ and tunable transmission coefficients. The general transformation of this beam splitter gives a single-qubit rotation operator about the xxx axis. Using such beam splitters, we show single-photon interference via the Mach-Zehnder interferometer and two-photon entanglement via Hong-Ou-Mandel effect. This system may have great applications in constructing interferometers and integrated circuits for optical quantum information processing with solid-state materials.