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arXiv:1709.09588 · Nature Communications

Quantum wave mixing and visualisation of coherent and superposed photonic states in a waveguide

A. Yu. Dmitriev, Rais S. Shaikhaidarov, Vladimir N Antonov, T. Hönigl-Decrinis, O. V. Astafiev

Published Nov 1, 2017• 38 citations
arXivHTMLPDF

Abstract

Superconducting quantum systems (artificial atoms) have been recently successfully used to demonstrate on-chip effects of quantum optics with single atoms in the microwave range. In particular, a well-known effect of four wave mixing could reveal a series of features beyond classical physics, when a non-linear medium is scaled down to a single quantum scatterer. Here we demonstrate the phenomenon of quantum wave mixing (QWM) on a single superconducting artificial atom. In the QWM, the spectrum of elastically scattered radiation is a direct map of the interacting superposed and coherent photonic states. Moreover, the artificial atom visualises photon-state statistics, distinguishing coherent, one- and two-photon superposed states with the finite (quantised) number of peaks in the quantum regime. Our results may give a new insight into nonlinear quantum effects in microwave optics with artificial atoms.

DOI
10.1038/s41467-017-01471-x

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Superconducting quantum systems (artificial atoms) have been recently successfully used to demonstrate on-chip effects of quantum optics with single atoms in the microwave range. In particular, a well-known effect of four wave mixing could reveal a series of features beyond classical physics, when a non-linear medium is scaled down to a single quantum scatterer. Here we demonstrate the phenomenon of quantum wave mixing (QWM) on a single superconducting artificial atom. In the QWM, the spectrum of elastically scattered radiation is a direct map of the interacting superposed and coherent photonic states. Moreover, the artificial atom visualises photon-state statistics, distinguishing coherent, one- and two-photon superposed states with the finite (quantised) number of peaks in the quantum regime. Our results may give a new insight into nonlinear quantum effects in microwave optics with artificial atoms.
Wave mixing in an optical medium is one of the fundamental nonlinear parametric processes. However, it has not yet been thoroughly studied on single atoms. This effect requires a strong coupling of atoms to propagating waves and is hard to demonstrate with natural atoms. Nevertheless, it is possible to investigate the properties of artificial superconducting atoms coupled with coplanar waveguides. We have prepared an experimental setup and developed a topology of a superconducting chip. This setup is to be used to investigate the mixing of superpositions of the vacuum and single-photon states with coherent pulses on single atoms. An on-chip single-photon source is proposed to generate such states.
A superconducting qubit in a waveguide behaves as a point-like nonlinear element. If irradiated with nearly resonant microwave pulses, the qubit undergoes quantum evolution and generates coherent fields at sideband frequencies due to elastic scattering. This effect is called Quantum Wave Mixing (QWM), and the number of emerged side components depends on the number of interacting photons. By driving a superconducting qubit with short pulses with alternating carrier frequencies, we control the maximal number of photons simultaneously interacting with a two-level system by varying the number and duration of applied pulses. Increasing the number of pulses results in consecutive growth of the order of non-linearity, which manifests in additional coherent side peaks appearing in the spectrum of scattered radiation while the whole spectrum maintains its asymmetry.
We address recent advances in microwave quantum optics with artificial atoms in one-dimensional (1D) open space. This field relies on the fact that the coupling between a superconducting artificial atom and propagating microwave photons in a 1D open transmission line can be made strong enough to observe quantum coherent effects, without using any cavity to confine the microwave photons. We investigate the scattering properties in such a system with resonant coherent microwaves. We observe the strong nonlinearity of the artificial atom and under strong driving we observe the Mollow triplet. By applying two resonant tones, we also observe the Autler–Townes splitting. Exploiting these effects, we demonstrate two quantum devices at the single-photon level in the microwave regime: the single-photon router and the photon-number filter. These devices provide important steps toward the realization of an on-chip quantum network.
A cascade of two-level superconducting artificial atoms---a source and a probe---strongly coupled to a semi-infinite waveguide is a promising tool for observing nontrivial phenomena in quantum nonlinear optics. The probe atom can scatter an antibunched radiation emitted from the source, thereby generating a field with specific properties. We experimentally demonstrate wave mixing between nonclassical light from the coherently cw-pumped source and another coherent wave acting on the probe. We observe unique features in the wave mixing stationary spectrum which differs from the mixing spectrum of two classical waves on the probe. These features are well described by adapting the theory of Gardiner et al. [Phys. Rev. A 50, 1792 (1994)] for a strongly coupled cascaded system of two atoms. We further analyze the theory to predict nonclassical mixing spectra for various ratios of atoms' radiative constants. Both experimental and numerical results confirm the domination of the multiphoton scattering process with only a single photon from the source. We evaluate entanglement of atoms in the quasistationary state and illustrate the connection between the expected second-order correlation function of the source field and wave mixing side peaks corresponding to a certain number of scattered photons.
We address recent advances in quantum optics with propagating microwaves\nin superconducting circuits. This research field exploits on the fact that the coupling between a superconducting artificial atom and propagating microwave photons in a one-dimensional (1D) open transmission line can be made strong enough to observe quantum effects, without using any cavity to confine the microwave photons.\nWe embed an artificial atom, a superconducting transmon qubit, in a 1D open\ntransmission line and investigate the scattering properties of coherent microwaves. When an input coherent state, with an average photon number much less than 1, is on resonance with the artificial atom, we observe extinction of up to 99% in the forward propagating field. We observe the strong nonlinearity of the artificial atom and under strong driving we observe the Mollow triplet. We also study the statistics of the reflected and transmitted beams, which are predicted to be nonclassical states. In particular, we demonstrate photon antibunching in the reflected beam by measuring the second-order correlation function. By applying a second control tone, we observe the Autler-Townes splitting and a giant cross-Kerr effect.\nFurthermore, we demonstrate fast operation of a single-photon router using\nthe Autler-Townes splitting. This device provides important steps towards the realization of a quantum network. This thesis describes the motivation, theoretical background, design, implementation and measurement results.
The study of light-matter interaction in superconducting quantum circuits has seen remarkable progress over the last 202020 years. By engineering artificial atoms, novel quantum phenomena have been demonstrated, and old ideas have come into a new light. Beyond their application to basic science, the prospect of implementing large-scale quantum information processing with superconducting circuits has fueled a rapid development of surrounding technologies, with ever-increasing control over their behavior as a result. The field's success stems primarily from the flexible design and strong non-linearity of the artificial atom, whose coherent interaction with both electrical and mechanical degrees of freedom has opened many doors for science. This thesis deals with the interaction between artificial atoms and quantum fields in one-dimensional waveguides. The waveguide represents a one-dimensional environment for the atom, which we use to study the properties of open quantum systems. All quantum systems are, in fact, open, and interactions between the system and its environment lead inevitably to a loss of energy and quantum coherence. A continuous loss of information into the environment is called a Markovian process. The work contained in this thesis indicates that deviations from a Markovian process can be detected in the steady state of driven systems. This could simplify the detection of non-Markovianity in open quantum systems, as no information about the system's transient dynamics would be necessary.Specifically, this thesis considers both electromagnetic fields in microwave transmission lines and acoustic fields in the form of surface acoustic waves (SAWs) traveling on the surface of solids. The recent realization of artificial atoms interacting with acoustic waves has opened up a new research field called quantum acoustics. We have built a model of the interaction between atoms and SAWs that predicts the existence of a new regime where the atom forms its own cavity. Additionally, we have considered synthesizing electromagnetically induced transparency, a quantum optics phenomena in opaque media where the absorption of photons is canceled, in waveguides using multiple closely spaced two-level systems. Some of the work in this thesis represents experimental work done in collaboration. In the first experiment, we studied the routing of acoustic waves at the quantum level. In the other experiment, we demonstrated electromagnetically induced transparency by creating an effective Lambda\\LambdaLambda system using a giant artificial atom. This thesis reviews the numerical techniques used to model these experiments.