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Physical Review A

Modulation of gauge field for the parity-time phase transition in circuit QED

Genting Dai, Yongcheng He, Kaiyong He, Liangliang Yang, Jianshe Liu, Wei Chen

Published Mar 25, 2024• 1 citation
Publisher

Abstract

In this work, a parity-time $(\mathcal{PT})$-symmetric system is investigated based on superconducting circuits, which allows the tunability of atom-atom coupling using superconducting qubits. The calculation results demonstrate that the interaction between artificial atoms significantly impacts the transmission spectrum and the conditions of the phase transition in the system. When introducing a weak probe signal into the $\mathcal{PT}$-symmetric system, several findings are observed. (1) The symmetry and intensity of both the linear and nonlinear outputs can be fine-tuned by adjusting the coupling strength between artificial atoms or manipulating the gauge-invariant phase in the system. (2) Nonreciprocal transmission can be achieved by driving different cavity modes. (3) The exceptional point (EP) of the $\mathcal{PT}$ phase transition can be adjusted within a certain range by modifying the gauge-invariant phase or adjusting the coupling strength in the system. One feasible experimental setup is also described and analyzed based on existing experimental techniques. These findings may inspire further research into modulating quantum phase transitions based on superconducting circuits.

DOI
10.1103/physreva.109.033723

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In this work, a parity-time (PT)(\mathcal{PT})(PT)-symmetric system is investigated based on superconducting circuits, which allows the tunability of atom-atom coupling using superconducting qubits. The calculation results demonstrate that the interaction between artificial atoms significantly impacts the transmission spectrum and the conditions of the phase transition in the system. When introducing a weak probe signal into the PT\mathcal{PT}PT-symmetric system, several findings are observed. (1) The symmetry and intensity of both the linear and nonlinear outputs can be fine-tuned by adjusting the coupling strength between artificial atoms or manipulating the gauge-invariant phase in the system. (2) Nonreciprocal transmission can be achieved by driving different cavity modes. (3) The exceptional point (EP) of the PT\mathcal{PT}PT phase transition can be adjusted within a certain range by modifying the gauge-invariant phase or adjusting the coupling strength in the system. One feasible experimental setup is also described and analyzed based on existing experimental techniques. These findings may inspire further research into modulating quantum phase transitions based on superconducting circuits.
Artificially engineered atoms, built using superconducting electrical circuits, have had a broad impact on the field of quantum information and quantum computing. Based on the Josephson effect, superconducting qubits have provided a robust platform for engineering light-matter interactions at the single-photon level. The ability to precisely control and manipulate single photons using superconducting qubits and cavities, a field now popularly known as circuit quantum electrodynamics (circuit QED), has enabled new and novel regimes in quantum physics, which previously remained inaccessible. For instance, the coupling between individual photons and artificial atoms have been shown to reach the ultrastrong and deep-strong regimes, a feat which is difficult to achieve with natural atoms. The superconducting circuit platform is now a promising contender for building large-scale quantum processors, attracting large investments from academic, industry and government players. \n \nThis thesis uses superconducting circuits to engineer photon interactions in two separate studies. The first is aimed at studying the physics of ``giant" artificial-atoms. The second study explores the route towards building a quantum heat engine using two parametrically-coupled, superconducting microwave cavities. We review the theoretical ideas and concepts which motivate our work, along with discussions of the design methodology, simulations, fabrication, measurement setup and the experimental findings. \n \nIn the first study, we explore a giant artificial atom, formed from a transmon qubit, which is coupled to propagating microwaves at multiple points along an open transmission line. The multipoint coupling nature of the transmon allows its radiated field to interfere with itself leading to some striking ``giant" atom effects. For instance, we observe strong frequency dependent couplings of the transmon's transition levels to its electromagnetic environment, a feature which is not observed with ordinary artificial atoms. We measure large on/off ratios, as high as 380380380, for the coupling rate of the ket0−ket1\\ket{0}-\\ket{1}ket0−ket1 transition. Furthermore, we show that we can enhance or suppress the coupling rate of the ket1−ket2\\ket{1}-\\ket{2}ket1−ket2 transition relative to the ket0−ket1\\ket{0}-\\ket{1}ket0−ket1 transition, by more than a factor of 200200200. The relative modulation of the coupling rates was exploited to engineer a metastable state in the giant transmon and demonstrate electromagnetically-induced transparency (EIT), a typical signature of a lambda system. Our results show that we can transform the ladder structure of an ordinary transmon into a more interesting lambda system using a giant transmon, thereby paving the way for exploring new possibilities to study three-level physics in a waveguide-QED setting. \n \nExtending giant atom physics to multiple giant atoms, we then explore a device with two giant artificial atoms connected in a braided configuration to a transmission line. The braided topology of the qubits, offers an interesting regime where the qubits can interact with each other in a decoherence-free environment, where the interaction is mediated by virtual photons in the transmission line. We probe the resonant behavior of the qubits at two different frequency bias points, where we observe qualitatively different scattering behavior. Furthermore, when probing for the Autler-Townes Splitting (ATS), multiple resonances are observed for both resonant and off-resonant cases instead of the familiar doublet in the ATS spectroscopy. This comes as a surprise as the frequency-level spacings in both qubits are nominally identical. We believe these features could be an indication of a novel resonant interaction between the qubits facilitated by the braided topology. An effort to understand this theoretically is underway. \n \nFor our second study, we explore a system with two parametrically-coupled superconducting resonators, which implements an optomechanical-like interaction in an all-electrical network. The nonlinear nature of this interaction is mediated by a superconducting quantum interference device (SQUID), where the current in one resonator couples to the photon number in the other resonator. We propose to use this system to build a ``photonic piston" engine in the quantum regime. We motivate the feasibility of the proposal by reviewing key theoretical results which demonstrate an Otto-cycle by appropriately driving the system with noise. Our experimental findings demonstrate the crucial nonlinear coupling that is required for the engine to work. We also show that we can increase the coupling strength between the resonators depending on the chosen flux operating point.
A parity-time (PT )-symmetric system emerging from a quantum dynamics is highly desirable in order to understand the possible implications of PT symmetry in the next generation of quantum technologies.In this work, we address this need by proposing and studying a circuit-QED architecture that consists of two coupled resonators and two qubits (each coupled to one resonator).By means of external driving fields on the qubits, we are able to tune gains and losses in the resonators.Starting with the quantum dynamics of this system, we show the emergence of the PT symmetry via the selection of both driving amplitudes and frequencies.We engineer the system such that a non-number-conserving dipole-dipole interaction emerges, introducing an instability at large coupling strengths.The PT symmetry and its breaking, as well as the predicted instability in this circuit-QED system, can be observed in a transmission experiment.
The photon transport in a pair of parallel waveguides mediated by a parity-time- (PT-) symmetric trimer QED system is investigated. We demonstrate that the transport behaviors of the incident photons transferring between different waveguides can be actively controlled by the PT symmetry. The efficiency of such photon transport can be tuned to be much larger than 100% when the optical gain is introduced, and the transfer intensity is robust against the weak coupling among the atom, the cavity modes, their corresponding coupling mismatch, as well as the atomic dissipation. Furthermore, we demonstrate that when the system is excited by two input fields, the relative phase of the two input signals can serve as a sensitive control parameter for manipulating the photon transport, and controllable directional amplification of the incident signal photons with a fixed frequency can be realized by modulating the relative phase. The obtained results can be useful for designing phase-dependent active nonreciprocal devices, i.e., a phase-sensitive directional amplifier.
By strongly driving a cyclic-transition three-level artificial atom, demonstrated by such as a flux-based superconducting circuit, we show that coherent microwave signals can be excited along a coupled one-dimensional transmission line. Typically, the intensity of the generated microwave is tunable via properly adjusting the Rabi frequencies of the applied strong-driving fields or introducing a probe field with the same frequency. In practice, the system proposed here could work as an on-chip quantum device with controllable atom-photon interaction to implement a total-reflecting mirror or switch for the propagating probe field.
The ultrastrong-coupling regime, where the atom-cavity coupling rate reaches a considerable fraction of the cavity or atom transition frequencies, has been reported in a flux qubit superconducting quantum circuit coupled to an on-chip coplanar resonator. In this regime situations may arise where the resonator field $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{X}=\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}+{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}^{\ifmmode\dagger\else\textdagger\fi{}}$ acquires a nonzero expectation value in the system ground state. We demonstrate that, in this case, the parity symmetry of an additional artificial atom with an even potential is broken by the interaction with the resonator. Such a mechanism is analogous to the Higgs mechanism where the gauge symmetry of the weak force's gauge bosons is broken by the nonzero vacuum expectation value of the Higgs field. The results presented here open the way to controllable experiments on symmetry-breaking mechanisms induced by nonzero vacuum expectation values. Moreover, the mechanism proposed here can be used as a probe of the ground-state macroscopic coherence emerging from quantum phase transitions with vacuum degeneracy.
For some cavity-quantum-electrodynamics systems, such as a single-electron spin coupled to a passive cavity, it is challenging to reach the strong-coupling regime. In such a weak-coupling regime, the conventional dispersive readout technique cannot be used to resolve the quantum states of the spin. Here we propose an improved dispersive readout method to measure the quantum states of a weakly coupled qubit by harnessing either one or two auxiliary cavities linearly coupled to the passive cavity containing the qubit. With appropriate parameters in both cases, the system excluding the qubit can exhibit a parity-time-symmetric phase transition at the exceptional point (EP). Because the EP can amplify the perturbation induced by the qubit and the parity-time symmetry can narrow the linewidths of the peaks in the transmission spectrum of the passive cavity, we can measure the quantum states of the weakly coupled qubit via this transmission spectrum. Owing to the weak coupling between the qubit and the passive cavity, the backaction due to the measurement of the qubit can also be reduced in comparison with the conventional dispersive readout technique in the strong-coupling regime.