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arXiv:1703.07933

Speeding up adiabatic state conversion in optomechanical system

Feng‐Yang Zhang, Wenlin Li, Yan Xia

Published Mar 23, 2017• 1 citation
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Abstract

Speeding up adiabatic method has attracted much attention with the wide applications in quantum information processing. In this paper, two kinds of methods, Lewis-Riesenfeld invariant-based inverse engineering and transitionless quantum driving are applied to implement speeding up adiabatic state conversion in optomechanical system. The perfect population transfer can be achieved within a short time. At last, the energetic cost is analysed for the transitionless quantum driving.

DOI
10.48550/arxiv.1703.07933

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Speeding up adiabatic method has attracted much attention with the wide applications in quantum information processing. In this paper, two kinds of methods, Lewis-Riesenfeld invariant-based inverse engineering and transitionless quantum driving are applied to implement speeding up adiabatic state conversion in optomechanical system. The perfect population transfer can be achieved within a short time. At last, the energetic cost is analysed for the transitionless quantum driving.
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.
Abstract Adiabatic state conversion in optomechanical systems requires the evolution process to be very slow, which limits its application in quantum information processing. In this paper, we explicitly show that speeding up adiabatic state conversion in optomechanical systems can be implemented. For the case that each cavity is driven far from the red-detuned mechanical sideband, the high-efficiency population transfer between cavity modes is achieved via an additional Hamiltonian  a ( t ) , whereas the population of the mechanical resonator can be effectively inhibited. In the meanwhile, in the case of each cavity driven near the red-detuned mechanical sideband, the population transfers can be realized by varying the modified optomechanical couplings without an additional Hamiltonian. Numerical simulation demonstrates that the transfer is robust to the system decays.
We apply the inversely-engineered control method based on Lewis-Riesenfeld invariants to control mixed states of a two-level quantum system. We show that the inversely-engineered control passages of mixed states - and pure states as special cases - can be made significantly faster than the conventional adiabatic control passages, which renders the method applicable to quantum computation. We devise a new type of inversely-engineered control passages, to be coined the antedated control passages, which further speed up the control significantly. We also demonstrate that by carefully tuning the control parameters, the inversely-engineered control passages can be optimized in terms of speed and energy cost.
Quantum state transfer between cavities is crucial for quantum information processing and quantum computation in optomechanical systems. Here, we present the first scheme for the transitionless intra-cavity quantum state transfer based on transitionless quantum driving (TQD) algorithm in optomechanical systems. We also present a physically feasible system for the TQD process based on largely detuned optomechanical cavity. With the Gaussian time-dependence coupling strengths, our scheme can achieve the perfect quantum state transfer with no undesired transition and reduce the dependence of accurately controlling evolution time and interval of coupling strengths. Our computational results show that the TQD process can be accomplished with no need of the mechanical oscillator in its ground state and is also robust to the mechanical dissipation.
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.
Abstract In this paper, we introduce a feasible scheme for implementing excitation fluctuation transfer between two membranes in a cavity optomechanical system. The transitionless tracking algorithm allows the system to evolve along a single path, and the process is sped up. Numerical simulations are shown to indicate that, compared with the schemes based on conventional adiabatic passage and Lewis–Riesenfeld invariants, the proposed scheme not only shortens the evolution time but also significantly decreases the negative effects of dissipation arising from membrane damping and cavity decay within specified bounds. This work provides a new idea for quantum state transfer between two membranes.