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arXiv:1512.05561 · Nature Communications

Coherence and multimode correlations from vacuum fluctuations in a microwave superconducting cavity

Pasi Lähteenmäki, Gheorghe Sorin Paraoanu, Juha Hassel, Pertti Juhani Hakonen

Published Aug 26, 2016• 52 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/ncomms12548

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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.
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.
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.
In this thesis I present different experiments on superconducting circuits exploring parametric interactions with external signals and the vacuum in the microwave regime. These parametric processes are the result of the periodic modulation of a property of a system which results in different interactions. The systems used in this thesis are circuits where the nonlinear inductance of a superconducting quantum interference device (SQUID) is parametrically driven.I present the first experimental observation of the dynamical Casimir effect (DCE), since it was predicted in 1970. The DCE is an interaction between the vacuum and a periodically modulated boundary condition of the electromagnetic field, here implemented by a flux-tuned SQUID. In essence the modulated boundary will parametrically amplify the vacuum fluctuations which results in the pairwise generation of photons over a broad frequency range. I have characterized the system and measured the statistical properties of the emitted radiation to show that the radiation exhibits two-mode squeezing.Next, I present measurements on a superconducting multimode resonator containing a SQUID. I show that it is possible to get parametric amplification by driving the SQUID at either twice the frequency of one of the modes or by driving it at the sum of two mode frequencies. In both cases I show that it is possible to reach quantum-limited noise performance.In the same system I also demonstrate frequency conversion which occurs when the system is pumped at the difference frequency between two modes. Microwave photons are coherently transferred from one mode to the other. I show that the coupling strength depends linearly on the applied pump amplitude.The thesis also contains a linearized theoretical model to describe and analyze the flux-pumped SQUID. The model describes an equivalent circuit element called the pumpistor, with an impedance which depends on the pump phase. I show that under specific conditions the impedance becomes real and negative allowing pump power to be injected into the circuit, providing gain.Finally I also present a demonstration of an on-chip Mach-Zehnder interferometer. This experiment uses the tunability of the SQUID to provide a controllable phase shift in one of the interferometer arms. The transmission through the device can be modulated with a maximum change of 45 dB.
We study the dynamical Casimir effect in a double superconducting cavity in a circuit quantum electrodynamics architecture. Parameters in the quantum circuit are chosen in such a way the superconducting cavity can mimic a double cavity, formed by two perfectly conducting outer walls and a dielectric wall, with arbitrary permittivity separating both halves. We undertake a spectral analysis of the cavity, showing that the spectrum varies significantly depending on the values of the susceptibility of the dielectric mirror and the relative lengths of both cavities. We study the creation of photons when the walls oscillate harmonically with a small amplitude. Furthermore, we explore the possibility of entangling two uncoupled cavities, starting from a symmetric double cavity and having both of its halves become uncoupled at a later given instant. We consider both cases: (i) when the field is initially in a vacuum state and (ii) the situation in which photon creation via the dynamical Casimir effect has already taken place. We show that the cavities become entangled in both cases but, in the latter, the quantum correlation between individual modes can be greatly increased at the cost of diminishing the entanglement between most pairs of modes.
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.
Analysis of the effects of external pumping on the quantum features of cavity radiation of the two-photon correlated emission laser is presented. It turns out that the pumping process induces the atomic coherence responsible for the entanglement of the cavity radiation as well as the correlation between the photon numbers belonging to different modes, despite the arising vacuum fluctuations. The photon number correlation is found to be very close to 2 where the entanglement is relatively better. Moreover, the mean number of photon pairs decreases with the amplitude of the driving radiation which is one of the practical limitations associated with the pumping mechanism. It is also shown that the mean photon number of the radiation in mode b is less than one-third of that in mode a.