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arXiv:2206.08695

Time dynamics of multi-photon scattering in a two-level mixer

Andrei Vladimirovich Vasenin, A. Yu. Dmitriev, Shamil Kadyrmetov, Aleksey N. Bolgar, O. V. Astafiev

Published Jun 17, 2022• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2206.08695

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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.
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.
We develop a theoretical description of quantum wave mixing (QWM) in a cascaded waveguide-QED system of two superconducting qubits, where the probe is driven by an external coherent tone and by the resonance fluorescence of a strongly driven source qubit. Starting from the field correlation functions of the source emission, we derive an effective master-equation treatment for the probe and identify the regime in which the incident fluorescence is characterized by anomalous correlations. When the coherent Rayleigh component of the source spectrum is suppressed, the probe equations of motion become equivalent to those for a qubit driven by a coherent tone and broadband squeezed light, although the ligt emitted by the source is non-Gaussian and antibunched. This equivalence implies a selection rule for the peaks of the QWM spectrum, with a strong suppression of sidebands associated with processes involving an odd number of photons taken from the source field. Numerical simulations of the full cascaded two-qubit model for different ratios of radiative decay rates unambiguously confirm the participation of correlated photon pairs in QWM processes. The current research illustrates that the analysis of peak amplitudes can be used to probe photon statistics in the incident nonclassical field.
Quantum wave mixing on a single superconducting qubit produces a hierarchy of coherent side peaks associated with elastic multiphoton scattering pathways. In a cascaded source--probe geometry these pathways become sensitive to the photon statistics of the radiation emitted by the source qubit. We develop an analytical theory of this effect starting from the cascaded master equation in the weak-driving regime. In the coherent-filtering limit when the decay rate of the probe qubit is less than that of the source, the standard coherent--coherent wave-mixing hierarchy is recovered. In the opposite limit, side peaks associated with multiphoton absorption from the antibunched source field are parametrically suppressed. Numerical solutions confirm the analytical scaling laws. The resulting sideband hierarchy provides a frequency-domain fingerprint of antibunched itinerant microwave light.
We theoretically study the few-and many-body dynamics of photons in chiral waveguides.In particular, we examine pulse propagation through an ensemble of N two-level systems chirally coupled to a waveguide.We show that the system supports correlated multiphoton bound states, which have a welldefined photon number n and propagate through the system with a group delay scaling as 1=n 2 .This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system.For sufficiently many photons and sufficiently short systems, we show that linear combinations of n-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency.Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition.Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons.Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters.Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.
An electromagnetic wave propagating through a waveguide with a strongly coupled two-level superconducting artificial atom exhibits an evolving superposition with the atom. The Rabi oscillations in the atom result from a single excitation-relaxation, corresponding to photon absorption and stimulated emission from and to the field. In this study, we experimentally investigated the time-dependent behavior of the field transmitted through a waveguide with a strongly coupled transmon. The scattered fields agree well with the predictions of the input-output theory. We demonstrate that the time evolution of the propagating fields, because of the interaction, encapsulates all information about the atom. Furthermore, we deduced the dynamics of the incoherent radiation component from the first-order correlation function of the measured field.