Multipartite Entanglement in a Microwave Frequency Comb

Open Access

Multipartite Entanglement in a Microwave Frequency Comb

Shan W. Jolin, Gustav Andersson, J. C. Rivera Hernández, Ingrid Strandberg, Fernando Quijandría, José Aumentado, Riccardo Borgani, Mats O. Tholén, and David B. Haviland

Phys. Rev. Lett. 130, 120601 – Published 23 March 2023

Abstract

Significant progress has been made with multipartite entanglement of discrete qubits, but continuous variable systems may provide a more scalable path toward entanglement of large ensembles. We demonstrate multipartite entanglement in a microwave frequency comb generated by a Josephson parametric amplifier subject to a bichromatic pump. We find 64 correlated modes in the transmission line using a multifrequency digital signal processing platform. Full inseparability is verified in a subset of seven modes. Our method can be expanded to generate even more entangled modes in the near future.

Received 22 December 2021
Accepted 23 February 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.120601

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Quantum entanglement Quantum information processing with continuous variables Squeezing of quantum noise

SQUID Superconducting devices

Microwave techniques

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Shan W. Jolin ^1,*,†, Gustav Andersson ^2,3, J. C. Rivera Hernández ¹, Ingrid Strandberg ³, Fernando Quijandría ^3,‡, José Aumentado ⁴, Riccardo Borgani ^1,5, Mats O. Tholén^1,5, and David B. Haviland¹

¹Department of Applied Physics, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
²Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA
³Department of Microtechnology and Nanoscience MC2, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
⁴National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
⁵Intermodulation Products AB, SE-823 93 Segersta, Sweden

^*shan@meetiqm.com
^†Present address: IQM Finland Oy, Espoo 02150, Finland.
^‡Present address: Quantum Machines Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan.

Article Text

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Issue

Vol. 130, Iss. 12 — 24 March 2023

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Images

Figure 1
(a) The JPA forms a LC circuit with tunable inductance $L_{J}$ due to the SQUID. The inductance, and hence its resonance frequency $ω_{0}$ , is modulated by an external flux field of the monochromatic or bichromatic kind, labeled $b$ and $c$ , respectively. The pump stimulates incoming vacuum noise scattering off the JPA resonance to become entangled (right). The incoming and outgoing noise is separated by a circulator. (b) A monochromatic flux pump is applied at $ω_{p} \approx 2 ω_{0}$ , which correlates modes symmetrically around mode 0. We use a graph to indicate the resulting correlations in the frequency comb. Numbered vertices correspond to labels on the frequency axis and edges indicate classical or quantum correlations. (c) A bichromatic flux pump consists of two different frequencies at roughly $2 ω_{0}$ . We can illustrate the correlations with graphs $K^{0}$ , $K^{- 1}$ , and $K^{1}$ . The superscript indicates the root vertex. In our Letter, $Δ = 2 π \times 9.2 MHz$ and $ω_{0} \approx 2 π \times 4.3 GHz$ .
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Figure 2
(a) Reconstructed covariance matrix generated by a monochromatic pump. The mode at the half-pump frequency is visible at the center where the red diagonal and the red-blue antidiagonal intersect. The red diagonal contains noise, while the red-blue antidiagonal indicates pairwise correlations. For clarity, only the $I$ quadratures are labeled on the $x$ and $y$ axes. The $Q$ quadratures are interleaved between $I$ columns and rows. The subscripts label different modes. The covariance matrix is given in units of twice the photon number $2 \bar{n}$ . (b) Each mode-pair symmetric around the half-pump frequency 4.3 GHz is analyzed for entanglement using the PPT test [69], the Duan criterion [70], and a SvL test [37, 68] using optimization; see Eq. (4). With our convention, non-negative values correspond to separable states. All three tests return negative results. The bottom $x$ axis indicates the detuning between mode $n \in [\pm 1, \pm 2, \pm 3]$ and the half-pump frequency mode. Because of our choice of covariance matrix normalization, the criteria are consequently given in units of twice the photon number. The error bars and values are the weighted mean and uncertainties (1 standard deviation) from an ensemble of six measurements lasting 10 min each.
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Figure 3
Experimental covariance matrix reconstructed from measurement of 64 modes generated by two pumps (left). The presence of off-diagonals indicates at least the presence of classical correlations. To determine whether these are quantum correlations requires further analysis outlined in the main text. Our theory reproduces a qualitatively similar matrix (right). The finite bandwidth of the JPA weakens correlations among modes at the edges of the frequency comb. For clarity, we omit $I$ and $Q$ labels on the $x$ and $y$ axes. Instead they are labeled by the mode index, such that mode 0 lies at exactly half of the average pump frequency, cf. Fig. 1. Each mode is spaced by 2.3 MHz. Covariance matrix elements are given in units of twice the photon number ( $2 \bar{n}$ ), making the identity matrix correspond to the vacuum state.
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Figure 4
Bipartition test for the seven center modes in the $K^{0}$ set and four center modes from $K^{\pm 1}$ . For $K^{0}$ , all tests violate the requirement for separability by at least 2.5 standard deviations, indicating that we have strong evidence for full inseparability. For $K^{1}$ , we have full inseparability with a significance of 2 standard deviations. However evidence for full inseparability for the $K^{- 1}$ set is significantly weaker.
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