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arXiv:1609.07353 · Physical Review Letters

Photon Statistics of Propagating Thermal Microwaves

Jan Goetz, Stefan Pogorzalek, Frank Deppe, Kirill G. Fedorov, Peter Eder, Michael Fischer, F. Wulschner, E. Xie, Achim Marx, R. Gross

Published Mar 8, 2017• 43 citations
arXivHTMLPDF

Abstract

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 blackbody 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.

DOI
10.1103/physrevlett.118.103602

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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 blackbody 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.
Abstract Microwave photons are essential carriers of quantum information in several promising platforms for quantum computing. However, measurement of the quantum statistical properties of microwave photons is demanding owing to their low energy relative to thermal fluctuations of any room-temperature detector, and phase-insensitive voltage amplification necessarily adds noise. Here, we overcome this trade-off with a nanobolometer that directly measures the photon statistics at millikelvin. Using a cryogenic temperature-controlled blackbody radiator, we demonstrate the detection of the mean photon number ⟨n^⟩\langle \hat{n}\rangle⟨n^⟩ ⟨ n ̂ ⟩ and reveal the expected photon number variance (Δn)2=⟨n^⟩(⟨n^⟩+1){(\Delta n)}^{2}=\langle \hat{n}\rangle \left(\langle \hat{n}\rangle+1\right)(Δn)2=⟨n^⟩(⟨n^⟩+1) ( Δ n ) 2 = ⟨ n ̂ ⟩ ⟨ n ̂ ⟩ + 1 , following the Bose–Einstein distribution. By engineering the coherent and incoherent proportions of the input field, we observe a transition between super-Poissonian and Poissonian statistics from the bolometric second-order correlation measurements. This technique is poised to serve in fundamental tests of quantum mechanics and function as a scalable readout solution for a quantum information processor.
In this thesis, I demonstrate and evaluate an on-demand source of single propagating microwaves photons. Working in the context of a quantum network, nodes are connected via propagating, nonclassical states of the electromagnetic field. As such, preparing and detecting propagating quantum states is an essential task. I work with one particular node consisting of a microfabricated, effective two level system coupled to a microwave resonator and study its ability to produce propagating nonclassical states, such as single photon states. In principle, states generated by this node could be sent to other such nodes. However, I send them into a Josephson parametric amplifier (JPA) to characterize the source. In particular, I discuss how to design and couple the two components that form my source: a fixed frequency transmon qubit and a 3D superconducting waveguide cavity. I demonstrate the ability to control of the dynamics of this combined system and implement a single photon generation protocol, which utilizes a single microwave control field that is far detuned from the photon emission frequency. To characterize the generation, I perform tomography on the propagating photon state to determine its density matrix ρ. I perform repeated JPA-backed, linear measurements of the propagating state. Based on the histograms of my measurements, I infer a maximum single photon component ρ₁₁ = 0.36 ± 0.01. I characterize the imperfections of the photon generation and detection, including detection inefficiency and measurement backaction. I find that within uncertainty my measurements match my expectation.
Using modern micro and nano-fabrication techniques combined with superconducting materials we realize quantum electronic circuits in which we create, store, and manipulate individual microwave photons. The strong interaction of photons with superconducting quantum two-level systems allows us to probe fundamental quantum effects of microwave radiation and also to develop components for applications in quantum technology. Previously we have realized on-demand single photon sources which we have characterized using correlation function measurements [1] and full quantum state tomography [2]. For this purpose we have developed efficient methods to separate the quantum signals of interest from the noise added by the linear amplifiers used for quadrature amplitude detection [3]. We now regularly employ superconducting parametric amplifiers [4] to perform nearly quantum limited detection of propagating electromagnetic fields. These enable us to probe the entanglement which we generate on demand between stationary qubits and microwave photons freely propagating down a transmission line [5]. Using two independent microwave single photon sources, we have recently performed Hong-Ou-Mandel experiments at microwave frequencies [6] and have probed the coherence of two-mode multi-photon states at the out-put of a beam-splitter. The non-local nature of such states may prove to be useful for distributing entanglement in future small-scale quantum networks.
PhD Thesis: Superconducting circuit quantum electrodynamics (QED) has developed into a powerful platform for studying the interaction between matter and different states of light. In this context, superconducting quantum bits (qubits) act as artificial atoms interacting with quantized modes of the electromagnetic field. The field can be trapped in superconducting microwave resonators or propagating in transmission lines. In this thesis, we particularly study circuit QED systems where microwave fields are coupled with superconducting flux and transmon qubits. We optimize the coherence properties of the resonators, by analyzing loss mechanisms at excitation powers of approximately one photon on average. We find that two-level fluctuators associated with oxide layers at substrate and metal surfaces and metal-metal interfaces represent the predominant loss channel. Furthermore, we show how broadband thermal photon fields influence the relaxation and dephasing properties of a superconducting transmon qubit. To this end, we study several second-order loss channels of the transmon qubit and find that the broadband fields introduce a larger decay rate than expected from the Purcell filter defined by the resonator. Additionally, we show that qubit dephasing at the flux-insensitive point as well as low-frequency parameter fluctuations can be enhanced by thermal fields. Finally, we study how artificial atoms react to changes in inherent properties of the light fields. We perform a detailed analysis of the photon statistics of thermal fields using their relation to the qubits coherence properties. We quantitatively recover the expected n2 + nn^{2}\,{+}\,nn2+n-law for the photon number variance and confirm this result by direct correlation measurements. We then show a novel technique for the in-situ conversion of the interaction parity in light-matter interaction. To this end, we couple spatially controlled microwave fields to a flux qubit with two degrees of freedom.
Quantum microwave photonics aims at generating, routing, and manipulating propagating quantum microwave fields in the spirit of optical photonics.To this end, the strong nonlinearities of superconducting quantum circuits can be used to either improve or move beyond the implementation of concepts from the optical domain.In this context, the design of a well-controlled broadband environment for the superconducting quantum circuits is a central task.In this work, we place a superconducting transmon qubit in one arm of an on-chip Mach-Zehnder interferometer composed of two superconducting microwave beam splitters.By measuring its relaxation and dephasing rates we use the qubit as a sensitive spectrometer at the quantum level to probe the broadband electromagnetic environment.For frequencies near the qubit transition frequency, this environment can be well described by an ensemble of harmonic oscillators coupled to the transmon qubit.At low frequencies 0 w  , we find experimental evidence for colored quasi-static Gaussian noise with a high spectral weight, as it is typical for ensembles of two-level fluctuators.Our work paves the way towards possible applications of propagating microwave photons, such as emulating quantum impurity models or a novel architecture for quantum information processing.
Correlations are important tools in the characterization of quantum fields, as they can be used to describe statistical properties of the fields, such as bunching and antibunching, as well as to perform field state tomography. Here we analyze experiments by Bozyigit et al. [Nat. Phys. (to appear), e-print arXiv:1002.3738] where correlation functions can be observed using the measurement records of linear detectors (i.e., quadrature measurements), instead of relying on intensity or number detectors. We also describe how large amplitude noise introduced by these detectors can be quantified and subtracted from the data. This enables, in particular, the observation of first- and second-order coherence functions of microwave photon fields generated using circuit quantum electrodynamics and propagating in superconducting transmission lines under the condition that noise is sufficiently low.