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arXiv:1503.02157 · Physical Review A

Quantum state synthesis of superconducting resonators

Roshan Sharma, Frederick W. Strauch

Published Jan 26, 2016• 16 citations
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Abstract

We present a theoretical analysis of different methods to synthesize entangled states of two quantum mechanical resonators. These methods are inspired by experimentally demonstrated interactions of superconducting resonators with artificial atoms, and offer efficient routes to generate nonclassical states. Using a two-mode Jaynes-Cummings model, we analyze the theoretical structure of these algorithms and their average performance for arbitrary states and for deterministically preparing NOON and maximally entangled states. Using a new state synthesis algorithm, we show that NOON and maximally entangled states can be prepared in a time linear in the desired photon number and without any state-selective interactions.

DOI
10.1103/physreva.93.012342

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We present a theoretical analysis of different methods to synthesize entangled states of two quantum mechanical resonators. These methods are inspired by experimentally demonstrated interactions of superconducting resonators with artificial atoms, and offer efficient routes to generate nonclassical states. Using a two-mode Jaynes-Cummings model, we analyze the theoretical structure of these algorithms and their average performance for arbitrary states and for deterministically preparing NOON and maximally entangled states. Using a new state synthesis algorithm, we show that NOON and maximally entangled states can be prepared in a time linear in the desired photon number and without any state-selective interactions.
NOON states, states between two modes of light of the form | N , 0⟩+e iϕ |0, N ⟩, are highly nonclassical entangled states with applications in super-resolution interferometry. We show how NOON states can be efficiently produced in circuit quantum electrodynamics using superconducting phase qubits and resonators. We propose a protocol where only one interaction between the two modes is required, creating all the necessary entanglement at the start of the procedure. This protocol makes active use of the first three states of the phase qubits. Additionally, we show how to efficiently verify the success of such an experiment, even for large NOON states, using randomly sampled measurements and semidefinite programming techniques.
The generation, manipulation and fundamental understanding of entanglement lies at very heart of quantum mechanics. Among various types of entangled states, the NOON states are a kind of special quantum entangled states with two orthogonal component states in maximal superposition, which have a wide range of potential applications in quantum communication and quantum information processing. Here, we propose a fast and simple scheme for generating NOON states of photons in two superconducting resonators by using a single superconducting transmon qutrit. Because only one superconducting qutrit and two resonators are used, the experimental setup for this scheme is much simplified when compared with the previous proposals requiring a setup of two superconducting qutrits and three cavities. In addition, this scheme is easier and faster to implement than the previous proposals, which require using a complex microwave pulse, or a small pulse Rabi frequency in order to avoid nonresonant transitions.
The NOON states play a critical role as physical resources in quantum information processing and quantum metrology, yet their preparation efficiency and applicability are often constrained by complicated operational procedures or the requirement for nonlinear interactions. In this paper, we propose an efficient protocol to generate the NOON states within two microwave cavities embedded in a superconducting system, assisted by an auxiliary five-level qudit. The state preparation is accomplished in three steps for an arbitrary photon number NNN by adjusting only external classical fields, while keeping the qudit-cavity coupling strengths and the qudit level spacings fixed. Based on parameters accessible in superconducting systems, numerical simulations show that the protocol achieves relatively high fidelity for the NOON states preparation even in the presence of parameter fluctuations and decoherence effects. Thus, this protocol may provide a practical approach for preparing the NOON states with current technology. Notably, since nonlinear interactions are not required, the protocol is flexible and has the potential to be applied across various physical systems.