Quantum computation with Kerr-nonlinear photonic crystals
Hiroo Azuma
备注：
20 pages, Latex2e, 4 eps figures; v2: minor corrections; v3: a new section added; v4: Sec. 4 is totally rewritten; v5: one section is removed; v6: minor corrections
In this paper, we consider a method for implementing a quantum logic gate with photons whose wave function propagates in a one-dimensional Kerr-nonlinear photonic crystal. The photonic crystal causes the incident photons to undergo Bragg reflection by its periodic structure of dielectric materials and forms the photonic band structure, namely, the light dispersion relation. This dispersion relation reduces the group velocity of the wave function of the photons, so that it enhances nonlinear interaction of the photons. (Because variation of the group velocity against the wave vector is very steep, we have to tune up the wavelength of injected photons precisely, however.) If the photonic crystal includes layers of a Kerr medium, we can rotate the phase of the wave function of the incident photons by a large angle efficiently. We show that we can construct the nonlinear sign-shift (NS) gate proposed by Knill, Laflamme, and Milburn (KLM) by this method. Thus, we can construct the conditional sign-flip gate for two qubits, which is crucial for quantum computation. Our NS gate works with probability unity in principle while KLM's original one is a nondeterministic gate conditioned on the detection of an auxiliary photon.
Quantum information processing with hybrid protocols making use of discrete- and continuous-variable currently attracts of great interest because of its promising applications in scalable quantum computer and distant quantum network. By inducing a giant cross-Kerr nonlinearity between two cavities, we propose a general protocol for hybrid quantum gate and quantum entanglement with high fidelity between a stationary, discrete photonic qubit and a flying photonic state. Interestingly, our protocol can be used to conduct a controlled-Z quantum gate between a stationary microwave photon stored in …
Kerr nonlinearity in nanophotonic cavities provides a versatile platform to explore fundamental physical sciences and develop novel photonic technologies. This is driven by the precise dispersion control and significant field enhancement with nanoscale structures. Beyond dispersion and pump engineering, the direct control of Kerr nonlinearity can release the ultimate performance and functionality of photonic systems. Here, we report the in situ control of integrated Kerr nonlinearity through its interplay with the cascaded Pockels nonlinear process. Kerr nonlinearity is tuned over 10~dB dynami…
For solid-state spin systems, the collective spin motion in a single crystal embodies multiple magnetostatic modes. Recently, it was found that the cross-Kerr interaction between the higher-order magnetostatic mode and the Kittel mode introduces a new operable degree of freedom. In this work, we propose a scheme to entangle two magnon modes via the cross-Kerr nonlinearity when the bias field is inhomogeneous and the system is driven. Quantum entanglement persists at the steady state, as demonstrated by numerical results using experimentally feasible parameters. Furthermore, we also demonstrate…
Photonic hyper-crystals combine the most interesting features of hyperbolic metamaterials and photonic crystals. Since the dispersion law of extraordinary photons in hyperbolic metamaterials does not exhibit the usual diffraction limit, photonic hyper-crystals exhibit light localization on deep subwavelength scales, leading to considerable enhancement of nonlinear photon-photon interaction. Therefore, similar to their conventional photonic crystal counterparts, nonlinear photonic hyper-crystals appear to be very promising in optical limiting and optical computing applications. Nonlinear optics…
We present a heuristic mathematical model of the relation between the geometry of a photonic crystal waveguide and the Purcell enhancement factor at a particular wavelength of interest. We use this model to propose approaches to the design of a photonic crystal waveguide maximizing the Purcell enhancement at a target wavelength. Numerical simulations indicate that the proposed structures exhibit robustness to fabrication defects introduced into photonic crystal geometry.
Quantum photonic neural networks are variational photonic circuits that can be trained to implement high-fidelity quantum operations. However, work-to-date has assumed idealized components, including a perfect $π$ Kerr nonlinearity. Here, we investigate the limitations of realistic quantum photonic neural networks that suffer from fabrication imperfections leading to photon loss and imperfect routing, and weak nonlinearities, showing that they can learn to overcome most of these errors. Using the example of a Bell-state analyzer, we demonstrate that there is an optimal network size, which bala…
We present a two-dimensional (2D) photonic crystal system for interacting with cold cesium (Cs) atoms. The band structures of the 2D photonic crystals are predicted to produce unconventional atom-light interaction behaviors, including anisotropic emission, suppressed spontaneous decay and photon mediated atom-atom interactions controlled by the position of the atomic array relative to the photonic crystal. An optical conveyor technique is presented for continuously loading atoms into the desired trapping positions with optimal coupling to the photonic crystal. The device configuration also ena…
We demonstrate how the dissipative interaction between a superconducting qubit and a microwave photonic crystal can be used for quantum bath engineering. The photonic crystal is created with a step-impedance transmission line which suppresses and enhances the quantum spectral density of states, influencing decay transitions of a transmon circuit. The qubit interacts with the transmission line indirectly via dispersive coupling to a cavity. We characterize the photonic crystal density of states from both the unitary and dissipative dynamics of the qubit. When the qubit is driven, it dissipates …
