arXiv:2604.08139

Photon pairs, squeezed light and the quantum wave mixing effect in a cascaded qubit system

R. D. Ivanovskikh, W. V. Pogosov, A. A. Elistratov, S. V. Remizov, A. Yu. Dmitriev, T. R. Sabirov, A. V. Vasenin, S. A. Gunin, O. V. Astafiev

quant-phphysics.opticsSubmitted Apr 9, 2026• Announced Apr 10, 2026• 0 citations• Revised Oct 12, 2026 (v2)

arXiv HTML PDF

Abstract

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.

Journal reference: Phys. Rev. A 114, 043741 (2026)
Comments: accepted for publication in Phys. Rev. A

Related papers

Direct experimental observation of sub-Poissonian photon statistics by means of multiphoton scattering on a two-level system

A. Yu. Dmitriev, Andrei Vladimirovich Vasenin, S. A. Gunin +4 more

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.

arXiv:2409.10975Physical Review AApr 24, 20254 citations

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

Andrei Vladimirovich Vasenin, A. Yu. Dmitriev, Shamil Kadyrmetov +2 more

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.

arXiv:2206.08695Jun 17, 20220 citations

Effects of photon statistics in wave mixing on a single qubit

W. V. Pogosov, A. Yu. Dmitriev, O. V. Astafiev

We theoretically consider wave mixing under the irradiation of a single qubit by two photon fields. The first signal is a classical monochromatic drive, while the second one is a nonclassical light. Particularly, we address two examples of a nonclassical light: (i) a broadband squeezed light and (ii) a periodically excited quantum superposition of Fock states with 0 and 1 photons. The mixing of classical and nonclassical photon fields gives rise to side peaks due to the elastic multiphoton scattering. We show that a side peaks structure is distinct from the situation when two classical fields are mixed. The most striking feature is that some peaks are absent. The analysis of peak amplitudes can be used to probe photon statistics in the nonclassical mode.

arXiv:2107.10769Physical Review AAug 5, 20218 citations

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

A. Yu. Dmitriev, Rais S. Shaikhaidarov, Vladimir N Antonov +2 more

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.

arXiv:1709.09588Nature CommunicationsNov 1, 201738 citations

Waveguide QED: Power spectra and correlations of two photons scattered off multiple distant qubits and a mirror

Yao-Lung L. Fang, Harold U. Baranger

We study two-level systems (2LS) coupled at different points to a one-dimensional waveguide in which one end is open and the other is either open (infinite waveguide) or closed by a mirror (semi-infinite). Upon injection of two photons (corresponding to weak coherent driving), the resonance fluorescence and photon correlations are shaped by the effective qubit transition frequencies and decay rates, which are substantially modified by interference effects. In contrast to the well-known result in an infinite waveguide, photons reflected by a single 2LS coupled to a semi-infinite waveguide are initially bunched, a result that can be simply explained by stimulated emission. As the number of 2LS increases (up to 10 are considered here), rapid oscillations build up in the correlations that persist for a very long time. For instance, when the incoming photons are slightly detuned, the transmitted photons in the infinite waveguide are highly antibunched. On the other hand, upon resonant driving, incoherently reflected photons are mostly distributed within the photonic band gap and several sharp side peaks. These features can be explained by considering the poles of the single-particle Green function in the Markovian regime combined with the time delay. Our calculation is not restricted to the Markovian regime, and we obtain several fully non-Markovian results. We show that a single 2LS in a semi-infinite waveguide can not be decoupled by placing it at the node of the photonic field, in contrast to recent results in the Markovian regime. Our results illustrate the complexities that ensue when several qubits are strongly coupled to a bus (the waveguide) as might happen in quantum information processing.

arXiv:1502.03803Physical Review AMay 22, 2015129 citations

Waveguide QED: Two Photons, Many Qubits, and a Mirror

Yao-Lung L. Fang, Harold U. Baranger

We study two-level systems (2LS) coupled at different points to a one-dimensional waveguide in which one end is open and the other is either open (infinite waveguide) or closed by a mirror (semi-infinite). Upon injection of two photons (corresponding to weak coherent driving), the resonance fluorescence and photon correlations are shaped by the effective qubit transition frequencies and decay rates, which are substantially modified by interference effects. In contrast to the well-known result in an infinite waveguide, photons reflected by a single 2LS coupled to a semi-infinite waveguide are initially bunched, a result that can be simply explained by stimulated emission. As the number of 2LS increases (up to 10 are considered here), rapid oscillations build up in the correlations that persist for a very long time. For instance, when the incoming photons are slightly detuned, the transmitted photons in the infinite waveguide are highly antibunched. On the other hand, upon resonant driving, incoherently reflected photons are mostly distributed within the photonic band gap and several sharp side peaks. These features can be explained by considering the poles of the single particle Green function in the Markovian regime combined with the time delay. Our calculation is not restricted to the Markovian regime, and we obtain several fully non-Markovian results. We show that a single 2LS in a semi-infinite waveguide can not be decoupled by placing it at the node of the photonic field, in contrast to recent results in the Markovian regime. Our results illustrate the complexities that ensue when several qubits are strongly coupled to a bus (the waveguide) as might happen in quantum information processing.

Feb 12, 20151 citation