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arXiv:1011.2862 · Physical Review Letters

Deterministic Entanglement of Photons in Two Superconducting Microwave Resonators

H. Wang, M. Mariantoni, Radoslaw C. Bialczak, M. Lenander, Erik A. Lucero, M. Neeley, A. D. O’Connell, D. Sank, Martin P. Weides, J. Wenner, Tsuyoshi Yamamoto, Yi Yin, Jie Zhao, John M. Martinis, Andrew N. Cleland

Published Feb 7, 2011• 202 citations
arXivHTMLPDF

Abstract

Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spinlike systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states (entangled states |N0> + |0N>) as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two resonators, and we completely characterize the entangled states with bipartite Wigner tomography. These results demonstrate a significant advance in the quantum control of linear resonators in superconducting circuits.

DOI
10.1103/physrevlett.106.060401

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Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spinlike systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states (entangled states |N0> + |0N>) as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two resonators, and we completely characterize the entangled states with bipartite Wigner tomography. These results demonstrate a significant advance in the quantum control of linear resonators in superconducting circuits.
Recent advances in fabricating superconducting circuits have allowed large numbers of microwave resonators and superconducting qubits to be employed in such circuits, but shared quantum entanglement among the photonics states of the resonators has not been attempted. Theorists now present a proposal that uses superconducting circuits to simulate a particular many-body quantum model that until now has been experimentally inaccessible and to create a type of shared quantum entanglement with the simulation.
Entanglement is an extraordinary feature of quantum mechanics. Sources of entangled optical photons were essential to test the foundations of quantum physics through violations of Bell’s inequalities. More recently, entangled many-body states have been realized via strong nonlinear interactions in microwave circuits with superconducting qubits. Here, we demonstrate a chip-scale source of entangled optical and microwave photonic qubits. Our device platform integrates a piezo-optomechanical transducer with a superconducting resonator which is robust under optical illumination. We drive a photon-pair generation process and employ a dual-rail encoding intrinsic to our system to prepare entangled states of microwave and optical photons. We place a lower bound on the fidelity of the entangled state by measuring microwave and optical photons in two orthogonal bases. This entanglement source can directly interface telecom wavelength time-bin qubits and gigahertz frequency superconducting qubits, two well-established platforms for quantum communication and computation, respectively. Published by the American Physical Society 2024
Two-level systems, or qubits, afford complete quantum control using only classical electrical signals. Achieving the same degree of control over harmonic resonators and photons has remained elusive, due to their infinite number of equally spaced energy levels. We exploit our complete qubit control by using a superconducting phase qubit to pump microwave photons into a high-Q coplanar wave guide resonator and, subsequently, use the qubit to read out the resonator state. This scheme has previously allowed us to prepare and detect photon number states (Fock states [1]) in the resonator and to measure their decay. Using a generalization of a scheme developed by Law and Eberly [2], we can now create arbitrary quantum states of the photon field with up to approximately 10 photons [3]. We analyze the prepared states by directly mapping out the corresponding Wigner function, which is the phase-space equivalent of the density matrix, and provides a complete description of the quantum state. Movies of the decay of a variety of non-classical states show a loss of quantum coherence over the energy decay time of the resonator.
Entangled states are self-evidently important to a wide range of applications in quantum communication and quantum information processing. We propose an efficient and convenient two-step protocol for generating Bell states and NOON states of two microwave resonators from merely coherent states. In particular, we derive an effective Hamiltonian for resonators coupled to a superconducting $\mathrm{\ensuremath{\Lambda}}$-type qutrit in the dispersive regime. By the excitation-number-dependent Stark shifts of the qutrit transition frequencies, we are able to individually control the amplitudes of specified Fock states of the resonators associated with relevant qutrit transition, using carefully tailored microwave drive signals. Thereby an arbitrary bipartite entangled state in Fock space can be generated by a typical evolution-and-measurement procedure. We analyze the undesired state transitions and the robustness of our protocol against the systematic errors from the microwave driving intensity and frequency, the quantum decoherence of all components, and the crosstalk of two resonators. In addition, we demonstrate that our protocol can be extended to a similar scenario with a $\mathrm{\ensuremath{\Xi}}$-type qutrit.
Using modern micro and nano-fabrication techniques combined with superconducting materials we realize quantum electronic circuits in which we create, store, and manipulate individual microwave photons. The strong interaction of photons with superconducting quantum two-level systems allows us to probe fundamental quantum effects of microwave radiation and also to develop components for applications in quantum technology. Previously we have realized on-demand single photon sources which we have characterized using correlation function measurements [1] and full quantum state tomography [2]. For this purpose we have developed efficient methods to separate the quantum signals of interest from the noise added by the linear amplifiers used for quadrature amplitude detection [3]. We now regularly employ superconducting parametric amplifiers [4] to perform nearly quantum limited detection of propagating electromagnetic fields. These enable us to probe the entanglement which we generate on demand between stationary qubits and microwave photons freely propagating down a transmission line [5]. Using two independent microwave single photon sources, we have recently performed Hong-Ou-Mandel experiments at microwave frequencies [6] and have probed the coherence of two-mode multi-photon states at the out-put of a beam-splitter. The non-local nature of such states may prove to be useful for distributing entanglement in future small-scale quantum networks.
We present an efficient method to generate Einstein–Podolsky–Rosen (EPR) entanglement of two microwave photons with different frequencies in two superconducting resonators. Our scheme is based on the sideband couplings of two resonators with a single gap-tunable superconducting quantum circuits driven by a controlled field. By the proper choice of the physical parameters, the nonlinear interaction of parametric down-conversion occurs between two resonators while the superconducting qubit remains in the original state, which is responsible for the entanglement generation. The present scheme would provide a promising alternative approach to scalable quantum information processing in solid-state systems.