Observation of Two-Mode Squeezing in the Microwave Frequency Domain

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.

Quantum estimation via parametric amplification in circuit-QED arrays

“…We find that the QFI oscillates with θ in such a way that the maximum is reached at θ = π/2, 3π/2 while the minimum is at θ = 0, π. The QFI grows significantly with the value of the squeezing parameter r -as expected-which in the figure is plotted in a realistic range r < 2 [14].…”

Nondegenerate parametric oscillations in a tunable superconducting resonator

“…The linear response of parametric systems to weak external signals exposes many properties of quantum noise. For instance, the presence of an idler in parametric amplification below the parametric instability threshold defines the structure of a squeezed vacuum and twomode entanglement of the output photons [4][5][6]. This is true for both degenerate and nondegenerate parametric resonances, with the only difference being that for the nondegenerate case, the idler has a frequency far detuned from the signal frequency and appears within the bandwidth of the conjugated mode [22], while for the degenerate case, the idler appears within the bandwidth of the signal mode.…”

“…Within cQED, a variety of nonclassical photonic states can be efficiently generated by nonlinear superconducting elements: superpositions of Fock states [3], entangled two-mode photonic states [4][5][6], and multiphoton Schrödinger cat states [7]. Parametric phenomena have played important roles in this development.…”

Higher-order nonlinear effects in a Josephson parametric amplifier

“…Recent experiments confirmed that JPAs [5] and a Josephson traveling-wave parametric amplifier [6] can work near the quantum limit and can be used for a wide range of applications. These include generation of squeezed microwave fields [5,[7][8][9], measurement of a displacement of a nanomechanical oscillator [10,11], implementation of the high-fidelity single-shot measurement [12][13][14][15], quantum feedback [16,17], and feed-forward [18] for superconducting qubits, generation of the two-mode squeezed states of microwave photons [19] as well as read-out of double quantum dots [20,21].…”