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arXiv:1101.2136 · Physical Review Letters

Observation of Two-Mode Squeezing in the Microwave Frequency Domain

Christopher Eichler, Deniz Bozyigit, Claus Lang, Matthias Baur, L. Steffen, J. M. Fink, Stefan Filipp, Andreas J. Wallraff

Published Sep 6, 2011• 266 citations
arXivHTMLPDF

Abstract

Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. Here we demonstrate experiments that show the entanglement between microwave photons of different energy in a broadband squeezed beam. We use a Josephson parametric amplifier to generate the two-mode correlated state and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix, which is in good agreement with the one expected for a two-mode squeezed state.

DOI
10.1103/physrevlett.107.113601

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Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. Here we demonstrate experiments that show the entanglement between microwave photons of different energy in a broadband squeezed beam. We use a Josephson parametric amplifier to generate the two-mode correlated state and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix, which is in good agreement with the one expected for a two-mode squeezed state.
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.
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This thesis presents the experimental achievements of (1) generating entangled-microwave fields propagating on two physically separate transmission lines and (2) verifying the entangled states with efficient measurements. Shared entanglement between two parties is an essential resource for quantum information processing and quantum communication protocols. Experimentally, entangled pairs of electromagnetic fields can be realized by distributing a squeezed vacuum over two separated modes. As a result, entanglement is revealed by the strong cross-correlations between specific quadratures of the two modes. Although it is possible to verify the presence of entanglement with low-efficiency quadrature measurements, higher detection efficiencies are desired for performing protocols that exploit entanglement with high fidelity.\nIn the microwave regime, Josephson parametric amplifiers (JPAs) fulfill the two major tasks mentioned above: JPAs prepare the required squeezed states to generate entanglement and enable us to perform efficient quadrature measurements. Therefore, for the purposes of entanglement generation and verification, ultralow-noise--frequency-tunable JPAs have been developed. Additionally, to increase the efficiency of entanglement generation, we integrate JPAs with two on-chip microwave passive components, a directional coupler and a quadrature hybrid, to form an entangler circuit. The two-mode entangled states are created at the two output modes of the entangler and are measured with a two-channel measurement apparatus where each of the two channels incorporates a JPA as a single-quadrature preamplifier. By employing this measurement scheme, the two measured quadratures of the two output modes can be chosen independently of each other, enabling a full characterization of the two-mode state. To definitively demonstrate the two-mode entanglement, I prove that the measured quadrature variances satisfy the inseparability criterion.
We demonstrate the experimental realization of two-dimensional, continuous variable (CV) cluster states between 191 microwave frequency modes. This result is obtained by exposing vacuum fluctuations to the input of a Josephson Parametric Amplifier, parametrically pumped by a sum of coherent tones around twice its resonant frequency. By carefully tuning pump frequencies, amplitudes, and phases we engineer the interference between mixing products and realize honeycomb and square lattice CV cluster states with three and four pump tones respectively. We prove the presence of the cluster states with a suitable nullifier test, reaching up to −1.2-1.2−1.2 dB of squeezing of the cluster state's nullifiers. We study hidden entanglement (HE) and show no hidden entanglement up to ∼−1\sim -1∼−1 dB of squeezing and negligible HE at optimal squeezing.
We present the first measurement of squeezed-state entanglement between the twin beams produced in an optical parametric oscillator operating above threshold. In addition to the usual squeezing in the intensity difference between the twin beams, we have measured squeezing in the sum of phase quadratures. Our scheme enables us to measure such phase anticorrelations between fields of different frequencies. In the present measurements, wavelengths differ by approximately 1 nm. Entanglement is demonstrated according to the Duan et al. criterion [Phys. Rev. Lett. 84, 2722 (2000)] Delta2p- + Delta2q+ = 1.41(2) < 2. This experiment opens the way for new potential applications such as the transfer of quantum information between different parts of the electromagnetic spectrum.
Entangled pairs of microwave photons are commonly produced in the narrow frequency band of a resonator, which represents a modified vacuum density of states. We generate and investigate the entanglement of a stream of photon pairs, generated in a semi-infinite broadband transmission line, terminated by a superconducting quantum interference device (SQUID). A weak pump signal modulates the SQUID inductance, resulting in a single time-varying boundary condition, and we detect all four quadratures of the microwave radiation emitted at two different frequencies separated by 0.7 GHz. Power calibration is done in situ, and we find positive logarithmic negativity and two-mode squeezing below the vacuum in the observed radiation, indicating entanglement.