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Optics Letters

Robust coupled-waveguide devices using shortcuts to adiabaticity

Shuo‐Yen Tseng

Published Nov 14, 2014• 51 citations
Publisher

Abstract

Shortcuts to adiabaticity, originally developed in the context of quantum control, are powerful tools for the design of high coupling efficiency, robust, and short coupled-waveguide devices. The counterdiabatic protocol cancels the unwanted coupling in system evolution by the addition of a counterdiabatic term. The invariant-based inverse-engineering approach designs system evolution using the decoupled eigenstates of the Lewis-Riesenfeld invariant. The single-shot shaped-pulse technique directly parameterizes the solution of the coupled-mode equation. Starting from the counterdiabatic protocol, we show that these seemingly very different shortcuts to adiabaticity techniques are equivalent in the framework of coupled-waveguide systems. When combined with perturbation treatment of the coupled-mode equation, robust coupled-waveguide devices against errors can be obtained.

DOI
10.1364/ol.39.006600

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Shortcuts to adiabaticity, originally developed in the context of quantum control, are powerful tools for the design of high coupling efficiency, robust, and short coupled-waveguide devices. The counterdiabatic protocol cancels the unwanted coupling in system evolution by the addition of a counterdiabatic term. The invariant-based inverse-engineering approach designs system evolution using the decoupled eigenstates of the Lewis-Riesenfeld invariant. The single-shot shaped-pulse technique directly parameterizes the solution of the coupled-mode equation. Starting from the counterdiabatic protocol, we show that these seemingly very different shortcuts to adiabaticity techniques are equivalent in the framework of coupled-waveguide systems. When combined with perturbation treatment of the coupled-mode equation, robust coupled-waveguide devices against errors can be obtained.
The goal in designing mode-evolution based devices is to realise short and high-fidelity components. The counterdiabatic protocol in coherent quantum state control can be used to cancel unwanted coupling between adiabatic modes in mode evolution but is not directly realisable in the coupled-waveguide system. By finding alternative coupled-mode equations that links to the same interaction picture dynamical equation as the counterdiabatic protocol via unitary transformations, we have derived a universal formalism for the design of short and high-fidelity mode-evolution based coupled-waveguide devices. Starting from a traditional adiabatic device design, the counterdiabatic protocol leads to a high-fidelity device, with its evolution following the adiabatic modes exactly even when the adiabatic condition is violated. Tolerance analysis shows that the countera-diabatic devices combine the advantages of adiabatic and resonant devices. The formalism is used to design asymmetric waveguide couplers.
Shortcut to Adiabatic Passage (SHAPE) technique, in the context of coherent control of atomic systems has gained considerable attention in last few years. It is primarily because of its ability to manipulate population among the quantum states infinitely fast compared to the adiabatic processes. Two methods in this regard have been explored rigorously, namely the transitionless quantum driving and the Lewis-Riesenfeld invariant approach. We have applied these two methods to realize SHAPE in adiabatic waveguide coupler. Waveguide couplers are integral components of photonic circuits, primarily used as switching devices. Our study shows that with appropriate engineering of the coupling coefficient and propagation constants of the coupler it is possible to achieve efficient and complete power switching. We also observed that the coupler length could be reduced significantly without affecting the coupling efficiency of the system.
One of the most fundamental devices for integrated optics is the beam splitter, which is often realized with a directional coupler. However, it is well known that the robustness of such devices against wavelength and/or fabrication parameter variations is limited. Three waveguide couplers based on the quantum-optical analogy of the stimulated Raman Adiabatic Passage (STIRAP) protocol have emerged as a promising solution to the aforementioned issues of device robustness [1, 2]. The tradeoff is that the adiabatic devices are generally longer than their non-adiabatic counterparts. Recently, devices using shortcuts to adiabaticity [3] have been shown to provide alternative robust beam coupling as the adiabatic devices, but at a shorter device length [4]. In this paper, we use the invariant-based inverse engineering [5] to realize a short and robust arbitrary splitting ratio three waveguide beam splitter.
In general, the conventional Lewis-Riesenfeld invariant-based inverse engineering is a nonadiabatic process that results in the adiabatic final states to achieve the shortcut to adiabaticity, which does not provide complete suppression of non-adiabaticity throughout the evolution. We propose a new method to accomplish the shortcut to adiabaticity through an entirely adiabatic path. This new method is developed using the number operator as an invariant of the Hamiltonian. This paper discusses the mathematical framework of the new method in two-level quantum system and analyzes its performance compared to the conventional Lewis-Riesenfeld invariant-based inverse engineering method.
Different methods have been recently put forward and implemented experimentally to inverse engineer the time-dependent Hamiltonian of a quantum system and accelerate slow adiabatic processes via nonadiabatic shortcuts. In the ``transitionless quantum driving'' proposed by Berry, shortcut Hamiltonians are designed so that the system follows exactly, in an arbitrarily short time, the approximate adiabatic path defined by a reference Hamiltonian. A different approach is based on first designing a Lewis-Riesenfeld invariant to carry the eigenstates of a Hamiltonian from specified initial to final configurations, again in an arbitrary time, and then constructing from the invariant the transient Hamiltonian that connects these boundary configurations. We show that the two approaches, apparently quite different in form and so far in results, are, in fact, strongly related and potentially equivalent, so that the inverse-engineering operations in one of them can be reinterpreted and understood in terms of the concepts and operations of the other one. We study, as explicit examples, expansions of time-dependent harmonic traps and the state preparation of two-level systems.
Shortcuts to adiabaticity are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various shortcuts to adiabaticity protocols have been demonstrated in closed systems. However, realizing shortcuts to adiabaticity for open quantum systems has presented a challenge due to the complex controls in existing proposals. Here, we present the experimental demonstration of shortcuts to adiabaticity for open quantum systems, using a superconducting circuit quantum electrodynamics system. By applying a counterdiabatic driving pulse, we reduce the adiabatic evolution time of a single lossy mode from 800 ns to 100 ns. In addition, we propose and implement an optimal control protocol to achieve fast and qubit-unconditional equilibrium of multiple lossy modes. Our results pave the way for precise time-domain control of open quantum systems and have potential applications in designing fast open-system protocols of physical and interdisciplinary interest, such as accelerating bioengineering and chemical reaction dynamics.