Observation of Two-Mode Squeezing in a Traveling Wave Parametric Amplifier

Martina Esposito, Arpit Ranadive, Luca Planat, Sébastien Leger, Dorian Fraudet, Vincent Jouanny, Olivier Buisson, Wiebke Guichard, Cécile Naud, José Aumentado, Florent Lecocq, and Nicolas Roch

Phys. Rev. Lett. 128, 153603 – Published 15 April 2022

Abstract

Traveling wave parametric amplifiers (TWPAs) have recently emerged as essential tools for broadband near quantum-limited amplification. However, their use to generate microwave quantum states still misses an experimental demonstration. In this Letter, we report operation of a TWPA as a source of two-mode squeezed microwave radiation. We demonstrate broadband entanglement generation between two modes separated by up to 400 MHz by measuring logarithmic negativity between 0.27 and 0.51 and collective quadrature squeezing below the vacuum limit between 1.5 and 2.1 dB. This work opens interesting perspectives for the exploration of novel microwave photonics experiments with possible applications in quantum sensing and continuous variable quantum computing.

Received 9 November 2021
Accepted 18 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.153603

Physics Subject Headings (PhySH)

Entanglement production Squeezing of quantum noise

Josephson junctions Superconducting devices

Dilution refrigerator Four-wave mixing Homodyne & heterodyne detection Microwave techniques

Quantum Information, Science & TechnologyAtomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Martina Esposito ^1,2,*, Arpit Ranadive ^1,*, Luca Planat¹, Sébastien Leger¹, Dorian Fraudet¹, Vincent Jouanny ¹, Olivier Buisson¹, Wiebke Guichard¹, Cécile Naud¹, José Aumentado³, Florent Lecocq ³, and Nicolas Roch ¹

¹Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
²CNR-SPIN Complesso di Monte S. Angelo, via Cintia, Napoli 80126, Italy
³National Institute of Standards and Technology, Boulder, Colorado 80305, USA

^*These authors contributed equally to this work.

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Vol. 128, Iss. 15 — 15 April 2022

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Images

Figure 1
(a) Simplified sketch of the experimental setup for two-mode squeezing generation and detection. The Josephson TWPA device is composed of 250 SNAIL-based unit cells, and it is anchored at the 20 mK stage of a dilution refrigerator. The input pump field is obtained via up conversion with an $I Q$ mixer: The $I$ and $Q$ inputs at an intermediate frequency ( $f_{pump − IF} = 290 MHz$ ) are mixed with a microwave local oscillator (generated with an rf source). The output microwave radiation is amplified, down-converted with a mixer, split in two paths, and finally digitized. The room temperature electronics is composed by an rf system-on-chip (RFSOC) acquisition board with an integrated field programmable gate array (FPGA), two digital to analog converters (DACs), used to generate the pulsed intermediate frequency inputs for the $I Q$ mixer, and two analog to digital converters (ADCs), used for digitizing the down-converted output radiation. (b) Sketch of the frequency spacing between the pump and a pair of signal and idler. (c) Sketch of the control and readout pulse sequence for a single pump on-off generation and measurement; the duration of the readout pulses (acquisition time) is $6 μ s$ .
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Figure 2
(a) Measured quadrature phase space distribution (two-dimensional differential histogram plots: difference between pump on and pump off histograms) for $10^{8}$ on-off acquisitions and detuning $Δ = 200 MHz$ ; the shape of the differential quadrature distributions in the ( $x_{i}$ , $x_{s}$ ) and ( $p_{i}$ , $p_{s}$ ) phase spaces indicates the presence of two-mode correlations. (b) Reconstructed covariance matrix with uncertainty indicated by shaded regions. (c) Entanglement stability over time: histogram of 50 repeated entanglement measurements, each obtained from a set of $2 \times 10^{6}$ repeated on-off quadrature acquisitions. Pump frequency $f_{p} = 4.415 GHz$ .
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Figure 3
Collective quadrature variance (a), squeezing (b), and logarithmic negativity (c) as a function of the input pump phase. Pump frequency $f_{p} = 4.415 GHz$ ; detuning $Δ = 200 MHz$ ; number of repeated measurements for each phase $N_{rep} = 10^{7}$ . Dashed lines indicate the vacuum state reference. Squeezing below the vacuum limit is highlighted with a shadow area in (b). The gray shadow area in (c) indicates the logarithmic negativity predicted by a simple lumped-element model which takes into account the TWPA gain and the estimated losses (see Supplemental Material [48]).
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Figure 4
Two-mode squeezing (a) and logarithmic negativity (b) as a function of detuning $Δ$ . Pump frequency $f_{p} = 4.415 GHz$ ; number of repeated measurements for each $Δ$ , $N_{rep} = 10^{7}$ . Dashed lines indicate the vacuum state reference. The gray shadowed area in (b) indicates the logarithmic negativity predicted by a simple lumped-element model which takes into account the TWPA gain and the estimated loss (see Supplemental Material [48]).
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