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AIP conference proceedings

Vacuum-induced correlations in superconducting microwave cavity under multiple pump tones

Terro Korkalainen, Ilari Lilja, Michael Romanovich Perelshtein, Kirill Viktorovich Petrovnin, Gheorghe Sorin Paraoanu, Pertti Juhani Hakonen

Published Jan 1, 2021• 2 citations
Publisher

Abstract

Quantum correlations are an essential resource in advanced information processing based on quantum phenomena. Remarkably, the vacuum state of a quantum field may act as a key element for generation of strong quantum correlations. Besides, superconducting microwave cavities offer an excellent platform for experimental studies of such quantum effects. In this work, we numerically investigate vacuum correlations in a flux-tunable superconducting cavity under multiple pump tones. We consider double and triple pumping cases and explore pairwise correlations between three frequency bands specified within a single cavity resonance. Our work shows that three pumps produce more correlations than two pumps; thus, quantum resources facilitated by the triple pump scheme offers enhanced prospects for quantum data processing using parametric microwave cavities.

DOI
10.1063/5.0055253

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Quantum correlations are an essential resource in advanced information processing based on quantum phenomena. Remarkably, the vacuum state of a quantum field may act as a key element for generation of strong quantum correlations. Besides, superconducting microwave cavities offer an excellent platform for experimental studies of such quantum effects. In this work, we numerically investigate vacuum correlations in a flux-tunable superconducting cavity under multiple pump tones. We consider double and triple pumping cases and explore pairwise correlations between three frequency bands specified within a single cavity resonance. Our work shows that three pumps produce more correlations than two pumps; thus, quantum resources facilitated by the triple pump scheme offers enhanced prospects for quantum data processing using parametric microwave cavities.
The existence of vacuum fluctuations is one of the most important predictions of modern quantum field theory. In the vacuum state, fluctuations occurring at different frequencies are uncorrelated. However, if a parameter in the Lagrangian of the field is modulated by an external pump, vacuum fluctuations stimulate spontaneous downconversion processes, creating squeezing between modes symmetric with respect to half of the frequency of the pump. Here we show that by double parametric pumping of a superconducting microwave cavity, it is possible to generate another type of correlation, namely coherence between photons in separate frequency modes. The coherence correlations are tunable by the phases of the pumps and are established by a quantum fluctuation that stimulates the simultaneous creation of two photon pairs. Our analysis indicates that the origin of this vacuum-induced coherence is the absence of which-way information in the frequency space.
The flexible engineering of superconducting circuits, together with the nonlinearity available from Josephson junctions, have made microwave quantum optics a blooming research field in the past decade. Key experiments originally performed in the optical domain have become very accessible on this microwave-frequency, such that strong atom-field interactions and optical parametric interactions in microwave. From the latter, one example is the implementation of spontaneous parametric downconversion (SPDC). This process is particularly interesting as it can act as a nonclassical radiation source which give a number of potential applications in quantum information processing. We will focus on studying SPDC in microwave throughout this thesis. \n \nIn the first half of this thesis, from designs to measurements, we will explore the well-known two-photon parametric processes, SPDC and coherent coupling, which are generated by quadratic Hamiltonians. Using three resonant modes of a SQUID-terminated parametric cavity, we proceeded to combine different two-photon processes in an effort to demonstrate a multipartite nonclassical radiation source. With detailed system gain and noise calibration of our cryogenic microwave network, we confirmed our implementation by experimentally verifying that the generated states contain genuine tripartite entanglement. This multimode entangled radiation source can be an important resource for future experiments on quantum networking. \n \nWhile two-photon parametric processes have found numerous important applications, they have also been the limit of experiments for over three decades, with higher-order parametric processes seemingly out of reach. In the second half of this thesis, we explore the potential of parametric resonators for achieving such higher-order processes. To do this, we first studied the necessary conditions for accessing cubic Hamiltonians through our SQUID-based interactions. We then fabricated a device dedicated to performing three-photon processes through these cubic Hamiltonians. For the first time, we observed a direct generation of photon triplets by a single SPDC process in microwave . The generation rate can exceed a photon flux density of 60 photon per second per Hertz at the device output, far surpassing any record to date for photon triplets. We studied various pump configurations corresponding to different three-photon SPDC processes starting from a cold vacuum state. Pumping at triple the frequency of a single mode, we observed a phase-space distribution with a non-Gaussian profile which shows strong skewness (third moment) in the quadrature amplitude distribution. We reconstruct the Wigner function of the propagating states from the directly measured moment matrix, demonstrating Wigner negativity. Pumping at the sum frequency of three modes, we observed non-zero coskewness between the quadrature amplitudes of the modes. By analysing the output signals and comparing their characteristics to the predicted theoretical signatures, we confirm our implementation of three-photon SPDC processes generated by specific cubic Hamiltonians. These types of non-Gaussian states have been suggested as a resource enabling universal quantum computation with continuous variables. Our results thus open up the realm of three-photon quantum optics, enabling a wealth of novel experimental and theoretical studies.
We recently presented [1] experimental results on multimode correlations obtained from pumped superconducting microwave cavity cooled down to its ground state. These correlations originate from an interaction of the pump field with the quantum fluctuations of vacuum in the cavity which includes a pump-amplitude-dependent reactance. In this paper we discuss the nature of the created multimode correlations with the help of a semiclassical simulation carried out in the time domain. In the simulation based on the Heisenberg-Langevin equation of motion, quantum noise is approximated as white noise over small ranges of frequency.
Cavity electro-(opto-)mechanics allows us to access not only single isolated but also multiple mechanical modes in a massive object. Here we develop a multi-mode electromechanical system in which a several membrane vibrational modes are coupled to a three-dimensional loop-gap superconducting microwave cavity. The tight confinement of the electric field across a mechanically-compliant narrow-gap capacitor brings the system into the quantum strong coupling regime under a red-sideband pump field. We demonstrate strong coupling between two mechanical modes, which is induced by two-tone parametric drives and mediated by a virtual photon in the cavity. The tunable inter-mechanical-mode coupling can be used to generate entanglement between the mechanical modes.
We consider a pair of quantum dot-based spin qubits that interact via microwave photons in a superconducting cavity and that are also parametrically driven by separate external electric fields. For this system, we formulate a model for spin qubit entanglement in the presence of mutually off-resonant qubit and cavity frequencies. We show that the sidebands generated via the driving fields enable highly tunable qubit-qubit entanglement using only ac control and without requiring the qubit and cavity frequencies to be tuned into simultaneous resonance. The model we derive can be mapped to a variety of qubit types, including detuning-driven one-electron spin qubits in double quantum dots and three-electron resonant exchange qubits in triple quantum dots. The high degree of nonlinearity inherent in spin qubits renders these systems particularly favorable for parametric drive-activated entanglement. We determine multiple common resonance conditions for the two driven qubits and the cavity and identify experimentally relevant parameter regimes that enable the implementation of entangling gates with suppressed sensitivity to cavity photon occupation and decay. The parametrically driven sideband resonance approach that we describe provides a promising route toward scalability and modularity in spin-based quantum information processing through drive-enabled tunability that can also be implemented in micromagnet-free electron and hole systems for spin-photon coupling. Published by the American Physical Society 2024
Abstract Quantum correlations are a vital resource in advanced information processing based on quantum phenomena. Remarkably, the vacuum state of a quantum field may act as a key element for the generation of multipartite quantum entanglement. In this work, generation of genuine tripartite entangled state and its control is achieved by the use of the phase difference between two continuous pump tones. Control of the subspaces of the covariance matrix for tripartite bisqueezed state is demonstrated. Furthermore, by optimizing the phase relationships in a three‐tone pumping scheme genuine quadripartite entanglement of a generalized H‐graph state (‐graph) is explored. This scheme provides a comprehensive control toolbox for the entanglement structure and allows to demonstrate, for first time to the authors' knowledge, genuine quadripartite entanglement of microwave modes. All experimental results are verified with numerical simulations of the nonlinear quantum Langevin equation. It is envisioned that quantum resources facilitated by multi‐pump configurations offer enhanced prospects for quantum data processing using parametric microwave cavities.