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arXiv:2203.00414 · Physical Review Letters

Frequency Combs with Parity-Protected Cross-Correlations and Entanglement from Dynamically Modulated Qubit Arrays

Denis Ilin, A. V. Poshakinskiy, Alexander N. Poddubny, Ivan V. Iorsh

Published Jan 9, 2023• 14 citations
arXivHTMLPDF

Abstract

We develop a general theoretical framework to dynamically engineer quantum correlations and entanglement in the frequency-comb emission from an array of superconducting qubits in a waveguide, rigorously accounting for the temporal modulation of the qubit resonance frequencies. We demonstrate that when the resonance frequencies of the two qubits are periodically modulated with a π phase shift, it is possible to realize simultaneous bunching and antibunching in cross-correlations as well as Bell states of the scattered photons from different sidebands. Our approach, based on the dynamical conversion between the quantum excitations with different parity symmetry, is quite universal. It can be used to control multiparticle correlations in generic dynamically modulated dissipative quantum systems.

DOI
10.1103/physrevlett.130.023601

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Abstract The capability to design spectrally controlled photon emission is not only fundamentally interesting for understanding frequency‐encoded light–matter interactions, but also is essential for realizing the preparation and manipulation of quantum states. Here, a dynamically modulated qubit array is considered, and realize frequency‐controlled single‐photon emission focusing on the generation of a frequency comb constituted solely of even‐parity or anti‐Stokes sidebands. This system also offers parity‐dependent bunching and antibunching in frequency‐filtered quantum correlations. In particular, the waveguide quantum electrodynamics (QED) setup is extended to include chiral and non‐local coupling architectures, thereby enhancing its versatility in Floquet engineering. This proposal also supports the predictable generation of high‐dimensional entangled quantum states, where the corresponding effective Hilbert space dimension is well controlled by energy modulation. Moreover, the utilisation of sophisticated numerical tools, such as the matrix product states (MPSs) and the discretization approach, enables the efficient simulation of multi‐photon dynamics, in which the non‐Markovian Floquet steady states emerge. This work fundamentally broadens the fields of collective emission, and has wide applications in implementing frequency‐encoded quantum information processing and many‐body quantum simulation.
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We report a theoretical study of coherent collective quantum dynamic effects in an array of NNN qubits (two-level systems) incorporated into a low-dissipation resonant cavity. Individual qubits are characterized by energy level differences ${\ensuremath{\Delta}}_{i}$ and a spread of ${\ensuremath{\Delta}}_{i}$ is taken into account. Noninteracting qubits display coherent quantum beatings with NNN different frequencies, i.e., ${\ensuremath{\omega}}_{i}={\ensuremath{\Delta}}_{i}/\ensuremath{\hbar}$. Virtual emission and absorption of cavity photons provides a long-range interaction between qubits. In the presence of such interaction we analyze quantum correlation functions of individual qubits Ci(t){C}_{i}(t)Ci​(t) to obtain two collective quantum-mechanical coherent oscillations, characterized by frequencies ${\ensuremath{\omega}}_{1}=\overline{\ensuremath{\Delta}}/\ensuremath{\hbar}$ and ${\ensuremath{\omega}}_{2}={\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{R}$, where ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\omega}}}_{R}$ is the resonant frequency of the cavity renormalized by interaction. The amplitude of these oscillations can be strongly enhanced in the resonant case when ${\ensuremath{\omega}}_{1}\ensuremath{\simeq}{\ensuremath{\omega}}_{2}$. These collective quantum oscillations can be directly observed, e.g., by measurements of frequency dependent transmission coefficient $D(\ensuremath{\omega})$ of electromagnetic field propagating in a transmission line coupled to the system.
We study theoretically the collective quantum dynamics occurring in various interacting superconducting qubit arrays (SQAs) in the presence of a spread of individual qubit frequencies. The interaction is provided by mutual inductive coupling between adjacent qubits (short-range Ising interaction) or inductive coupling to a low-dissipative resonator (long-range exchange interaction). In the absence of interaction, the Fourier transform of the temporal correlation function of the total polarization (zzz projection of the total spin), i.e., the dynamic susceptibility $C(\ensuremath{\omega})$, demonstrates a set of sharp small magnitude resonances corresponding to the transitions of individual superconducting qubits. We show that even a weak interaction between qubits can overcome the disorder with a simultaneous formation of the collective excited states. This collective behavior manifests itself by a single large resonance in $C(\ensuremath{\omega})$. In the presence of a weak nonresonant microwave photon field in the low-dissipative resonator, the positions of dominant resonances depend on the number of photons, i.e., the collective ac Stark effect. Coupling of an SQA to the transmission line allows a straightforward experimental access of the collective states in microwave transmission experiments and, at the same time, to employ SQAs as sensitive single-photon detectors.
Controlling photon statistics is pivotal to many applications in classical and quantum photonics. While steady-state photon statistics have been widely studied, dynamically manipulating these statistical properties in time remains elusive. Herein, we propose a scheme to actively control photon statistics between bunching and antibunching regimes through quantum interference. Our approach relies on a Raman-coupled cavity-atom system with parametric amplification, where time modulating the detuning of the intermediate state allows us to either deepen the photon blockade or enhance photon bunching. Simultaneous modulation of the cavity and intermediate-state detunings produces antibunching that cannot be achieved under static conditions or by modulating either detuning alone. Because the modulation is periodic, the antibunching reappears at regular time intervals, enabling time-gated photon antibunching under continuous-wave operation at a repetition rate determined by the modulation frequency. These results show a versatile mechanism based on Raman-assisted quantum interference for dynamically engineering photon correlations.