Path Entanglement of Continuous-Variable Quantum Microwaves

Menzel, E. P.; Candia, Roberto Di; Deppe, Frank; Eder, Peter; Zhong, L.; Ihmig, Matthias; Haeberlein, M.; Baust, A.; Hoffmann, E.; Ballester, D.; Inomata, K.; Yamamoto, Tsuyoshi; Nakamura, Y.; Solano, E.; Marx, Achim; Gross, Rudolf

doi:10.1103/physrevlett.109.250502

Cited by 154 publications

(172 citation statements)

References 39 publications

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“…Using a momentbased reconstruction method, the squeezing level of a flux-pumped JPA is measured [58,59,61]. Fig.…”

Section: B Squeezing Levelmentioning

confidence: 99%

“…Here G c is the gain of the measurement chain between the JPA output and the ADC in the photon number basis [61,75] andĥ is an effective noise mode dominated by the added noise of the HEMT amplifier. Experimentally, the power gain of the measurement chain was measured to be between 100.1 dB and 100.5 dB.…”

Section: Appendix B: Details Of the Displacement Transformationsmentioning

confidence: 99%

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Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

et al. 2017

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Single-mode Josephson junction-based parametric amplifiers are often modeled as perfect amplifiers and squeezers. We show that, in practice, the gain, quantum efficiency, and output field squeezing of these devices are limited by usually neglected higher-order corrections to the idealized model. To arrive at this result, we derive the leading corrections to the lumped-element Josephson parametric amplifier of three common pumping schemes: monochromatic current pump, bichromatic current pump, and monochromatic flux pump. We show that the leading correction for the last two schemes is a single Kerr-type quartic term, while the first scheme contains additional cubic terms. In all cases, we find that the corrections are detrimental to squeezing. In addition, we show that the Kerr correction leads to a strongly phase-dependent reduction of the quantum efficiency of a phase-sensitive measurement. Finally, we quantify the departure from ideal Gaussian character of the filtered output field from numerical calculation of third and fourth order cumulants. Our results show that, while a Gaussian output field is expected for an ideal Josephson parametric amplifier, higher-order corrections lead to non-Gaussian effects which increase with both gain and nonlinearity strength. This theoretical study is complemented by experimental characterization of the output field of a flux-driven Josephson parametric amplifier. In addition to a measurement of the squeezing level of the filtered output field, the Husimi Q-function of the output field is imaged by the use of a deconvolution technique and compared to numerical results. This work establishes nonlinear corrections to the standard degenerate parametric amplifier model as an important contribution to Josephson parametric amplifier's squeezing and noise performance.

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“…Using a momentbased reconstruction method, the squeezing level of a flux-pumped JPA is measured [58,59,61]. Fig.…”

Section: B Squeezing Levelmentioning

confidence: 99%

Section: Appendix B: Details Of the Displacement Transformationsmentioning

confidence: 99%

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

et al. 2017

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“…In this context, an important aspect is the generation of propagating thermal microwaves using thermal emitters [15][16][17]. These emitters can be spatially separated from the setup components used for manipulation and detection [18,19], which allows one to individually control the emitter and the setup temperature. Due to the low energy of microwave photons, the detection of these fields typically requires the use of nearquantum-limited amplifiers [20][21][22][23], cross-correlation detectors [17, 18, 24], or superconducting qubits [25][26][27][28].…”

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confidence: 99%

Photon Statistics of Propagating Thermal Microwaves

et al. 2017

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In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the n 2 + n photon number variance of thermal microwave photons emitted from a black-body radiator for mean photon numbers 0.05 n 1.5. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier.As propagating electromagnetic fields in general [1][2][3], propagating microwaves with photon numbers on the order of unity are essential for quantum computation [4,5], communication [6], and illumination [7][8][9][10] protocols. Because of their omnipresence in experimental setups, the characterization of thermal states is especially relevant for many applications [11][12][13][14]. Specifically in the microwave regime, sophisticated experimental techniques for their generation at cryogenic temperatures, their manipulation, and detection have been developed in recent years. In this context, an important aspect is the generation of propagating thermal microwaves using thermal emitters [15][16][17]. These emitters can be spatially separated from the setup components used for manipulation and detection [18,19], which allows one to individually control the emitter and the setup temperature. Due to the low energy of microwave photons, the detection of these fields typically requires the use of nearquantum-limited amplifiers [20][21][22][23], cross-correlation detectors [17, 18, 24], or superconducting qubits [25][26][27][28].The unique nature of propagating fields is reflected in their photon statistics, which is described by a probability distribution either in terms of the number states or in terms of its moments. The former were studied by coupling the field to an atom or qubit and measuring the coherent dynamics [29][30][31] or by spectroscopic analysis [32]. The moment-based approach requires knowledge on the average photon number n and its variance Var(n) = n 2 − n 2 to distinguish many states of interest. To this end, the second-order correlation function g (2) (τ ) has been measured to analyze the photon statistics of thermal [33][34][35] or quantum [36][37][38] emitters ever since the ground-breaking experiments of Hanbury Brown and Twiss [39,40]. While these experiments use the time delay τ as control parameter, at microwave frequencies the photon number n can be controlled conveniently [15,32,[41][42][43][44]. In the specific case of a thermal field at frequency ω, the Bose-Einstein distribution yields n(T ) = [exp( ω/k B T ) − 1] −1 and Var(n) = n 2 + n, which can be controlled by the temperature T of the emitter. In practice, one wants to distinguish this relation from both the classical limit Var(n) = n 2 and the Poissonian behavior Var(n) = n characteristic for coherent states [41] or shot noise [45,46]. Hence, as shown in Fig. 1, the most relev...

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“…Using the dispersive interaction between qubit and resonator, we tune the emission frequencies of the two sources to an identical value of ν r = 7.2506 GHz. For our experiments, we sequentially create 20 single photons in each source at a rate 1/t r = 1/512 ns ∼ 1.95 MHz in a sequence repeated every 12.5 µs.To probe the photon statistics in the beam-splitter output modesâ andb we use two spatially separated heterodyne detection channels 21,22 (see dashed rectangle in Fig. 1b).…”

mentioning

confidence: 99%

“…To probe the photon statistics in the beam-splitter output modesâ andb we use two spatially separated heterodyne detection channels 21,22 (see dashed rectangle in Fig. 1b).…”

mentioning

confidence: 99%

Correlations, indistinguishability and entanglement in Hong–Ou–Mandel experiments at microwave frequencies

et al. 2013

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When two indistinguishable single photons impinge at the two inputs of a beam splitter they coalesce into a pair of photons appearing in either one of its two outputs. This effect is due to the bosonic nature of photons and was first experimentally observed by Hong, Ou and Mandel 1 . Here, we present the observation of the Hong-Ou-Mandel effect with two independent single-photon sources in the microwave frequency domain. We probe the indistinguishability of single photons, created with a controllable delay, in time-resolved secondorder cross-and auto-correlation function measurements. Using quadrature amplitude detection we are able to resolve different photon numbers and detect coherence in and between the output arms. This scheme allows us to fully characterize the two-mode entanglement of the spatially separated beam-splitter output modes. Our experiments constitute a first step towards using two-photon interference at microwave frequencies for quantum communication and information processing 2-5 .So far, Hong-Ou-Mandel (HOM) two-photon interference has been demonstrated exclusively using photons at optical or telecom wavelengths. Experiments were performed with photons emitted from a single source using parametric downconversion 1 , trapped ions 3 , atoms 6 , quantum dots 7 and single molecules 8 . The HOM effect has also been observed with two independent sources 9-15 realizing indistinguishable single-photon states, which are required as a resource in quantum networks or linear-optics quantum computation. Such experiments have also been performed using donor impurities as sources 16 including nitrogen-vacancy centres in diamond (see ref. 17 and references therein). Furthermore, the HOM effect has been employed to create entanglement between ions 18 in spatially separated traps, and to realize a controlled-NOT gate in a small-scale photonic network 19 . Similar physics is also actively explored with ballistic electrons in solids (see ref. 20 and references therein).Here, we demonstrate the HOM interference of two indistinguishable microwave photons emitted from independent triggered sources realized in superconducting circuits (see Methods). The photons are prepared in two separate microwave resonators A (B) using transmon-type qubits and decay exponentially at rates κ/2π = 4.1 (4.6) MHz through their strongly coupled output ports into the input modesâ andb of the beam splitter (see Fig. 1). The two photons then interfere at the beam splitter and are emitted into the output modesâ andb (see Fig. 1a). Using the dispersive interaction between qubit and resonator, we tune the emission frequencies of the two sources to an identical value of ν r = 7.2506 GHz. For our experiments, we sequentially create 20 single photons in each source at a rate 1/t r = 1/512 ns ∼ 1.95 MHz in a sequence repeated every 12.5 µs.To probe the photon statistics in the beam-splitter output modesâ andb we use two spatially separated heterodyne detection channels 21,22 (see dashed rectangle in Fig. 1b). Each channel consists of a set of...

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Path Entanglement of Continuous-Variable Quantum Microwaves

Cited by 154 publications

References 39 publications

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

Effect of Higher-Order Nonlinearities on Amplification and Squeezing in Josephson Parametric Amplifiers

Photon Statistics of Propagating Thermal Microwaves

Correlations, indistinguishability and entanglement in Hong–Ou–Mandel experiments at microwave frequencies

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