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arXiv:2204.08219 · Chinese Physics B

Entanglement properties of superconducting qubits coupled to a semi-infinite transmission line

Yang-Qing Guo, Ping‐Xing Chen, Jian Li

Published Mar 3, 2023• 1 citation
arXivHTMLPDF

Abstract

Quantum entanglement, a key resource in quantum information processing, is reduced by interaction between the quantum system concerned and its unavoidable noisy environment. Therefore it is of particular importance to study the dynamical properties of entanglement in open quantum systems. In this work, we mainly focus on two qubits coupled to an adjustable environment, namely a semi-infinite transmission line. The two qubits’ relaxations, through individual channels or collective channel or both, can be adjusted by the qubits’ transition frequencies. We examine entanglement dynamics in this model system with initial Werner state, and show that the phenomena of entanglement sudden death and revival can be observed. Due to the hardness of preparing the Werner state experimentally, we introduce a new type of entangled state called pseudo-Werner state, which preserves as much entangling property as the Werner state, and more importantly, it is experiment friendly. Furthermore, we provide detailed procedures for generating pseudo-Werner state and studying entanglement dynamics with it, which can be straightforwardly implemented in a superconducting waveguide quantum electrodynamics system.

DOI
10.1088/1674-1056/acc0fa

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•Jan 1, 2021•0 citations
Quantum entanglement, a key resource in quantum information processing, is reduced by interaction between the quantum system concerned and its unavoidable noisy environment. Therefore it is of particular importance to study the dynamical properties of entanglement in open quantum systems. In this work, we mainly focus on two qubits coupled to an adjustable environment, namely a semi-infinite transmission line. The two qubits’ relaxations, through individual channels or collective channel or both, can be adjusted by the qubits’ transition frequencies. We examine entanglement dynamics in this model system with initial Werner state, and show that the phenomena of entanglement sudden death and revival can be observed. Due to the hardness of preparing the Werner state experimentally, we introduce a new type of entangled state called pseudo-Werner state, which preserves as much entangling property as the Werner state, and more importantly, it is experiment friendly. Furthermore, we provide detailed procedures for generating pseudo-Werner state and studying entanglement dynamics with it, which can be straightforwardly implemented in a superconducting waveguide quantum electrodynamics system.
We investigate the sudden birth and sudden death of entanglement of two qubits interacting with un-correlated structured reservoirs. The system is initially prepared in two-qubit extended Werner-like state. We work out the dependence of the entanglement dynamics on both non-Markovian environments and the purity of initial state, and show that non-Markovian environments and the purity can control the time of the two-qubit entanglement sudden death and the reservoirs' entanglement sudden birth. Furthermore, under the conditions of different purity and initial entanglement, the revival of qubits' entanglement can manifest before, simultaneously or even after the disentanglement of their corresponding reservoirs.
In this paper, we study entanglement dynamics of a two-qubit extended Werner-like state locally interacting with independent noisy channels, i.e., amplitude damping, phase damping, and depolarizing channels. We show that the purity of initial entangled state has direct impacts on the entanglement robustness in each noisy channel. That is, if the initial entangled state is prepared in mixed instead of pure form, the state may exhibit entanglement sudden death (ESD) and/or be decreased for the critical probability at which the entanglement disappear.
We investigate the entanglement dynamics of the bipartite quantum system between two qubits with the dissipative environment. We begin with the standard Markovian master equation in the Lindblad form and the initial state which is prepared in the extended Werner-like state: ρ Φ AB (0). We examine the conditions for entanglement sudden death (ESD) and calculate the corresponding ESD time by the Wootters concurrence. We observe that ESD is determined by the parameters such as the mean occupation number of the environment N , amount of initial entanglement α and the purity r . For N = 0, we get the analytical expressions of both ESD condition and ESD time. For N > 0 we give a theoretical analysis that ESD always occurs, and simulate the concurrence as a function of γ 0 t and one of the parameters N , α and r .
In this paper, the dynamical behavior of entanglement of an uncoupled two-qubit system, which interacts with independent identical amplitude damping environments and is initially prepared in the extended Werner-like (EWL) states, is investigated. The results show that whether entanglement sudden death (ESD) of an EWL state will occur or not depends on initial purity and concurrence. The boundaries between ESD states and ESD-free states for two kinds of EWL states are found to be different. Furthermore, some regions are shown where ESD states can be transformed into ESD-free states by local unitary operations.
In this paper, we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state. The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process. We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth. Furthermore, the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure. In particular, a critical purity of the initial mixed entangled state exists, above which entanglement sudden birth vanishes while entanglement sudden death appears. It is also noticed that stable entanglement, which is independent of different initial states of the qubits (pure or mixed state), occurs even in the presence of decoherence. These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth, death and revival.
Waveguide circuit quantum electrodynamics (waveguide circuit QED) studies light-matter interaction with superconducting circuits in one dimension. In circuit QED, natural atoms are replaced by superconducting qubits consisting of a non-linear Josephson junction, resulting in an anharmonic energy spectrum just like real atoms. With superconducting qubits, it is possible to study quantum optical phenomena and reach new regimes hard to achieve with real atoms due to weak coupling to the electromagnetic field. The reduction to one dimension in waveguide QED increases the electromagnetic field's directionality, which results in reduced losses. In this thesis, we first introduce circuit quantisation, giving the basis for the next part, where we investigate a transmon, a charge-insensitive artificial atom, coupled to a semi-infinite transmission line. An atom coupled to a semi-infinite waveguide is referred to as an atom in front of a mirror and is the subject of all appended papers. We proceed by summarising Paper I and III's main results: in Paper I, we investigate the spontaneous emission of a transmon coupled to a semi-infinite transmission line, where we take time-delay effects into account. We find that the system dynamics strongly depend on the coupling strength to the transmission line and the atom's position with respect to the electromagnetic field, leading to the Purcell effect or the convergence to a dark state with finite excitation probability. In the high-impedance regime, which we investigate in Paper III, the properties of the transmon coupled to the high-impedance transmission line change drastically. It becomes highly reflective and creates its own cavity with the mirror, resulting in the emergence of cavity modes and vacuum Rabi oscillations in the spontaneous emission dynamics. In the next chapter of the thesis, we demonstrate how to quantise an electromagnetic field and derive a light-matter interaction Hamiltonian within dipole approximation. We then give an introduction to open quantum systems and derive the quantum-optical master equation in Lindblad form. Furthermore, we introduce the dressed state picture, where the interaction of light and matter is so strong that the individual energy levels of light and matter are no longer separable. Both the quantum optical master equation and the dressed state picture are relevant in Paper II and IV. In Paper II, an experimental collaboration, we perform several experiments to characterise and discriminate different decay rates of a superconducting qubit coupled to the end of a transmission line. One experiment measured the atomic fluorescence spectral density, which shows an asymmetry for off-resonant driving, resulting from pure dephasing: an effect that we explain in more detail in this thesis and Paper II. In Paper IV, we theoretically investigate amplification mechanisms realised by different set-ups of an atom coupled to a semi-infinite waveguide. In the considered systems, the amplification of a probe field happens either due to population inversion between the pure states or dressed states or multi-photon processes. We find that compared to an open waveguide, we can achieve a higher gain in the amplification with a semi-infinite waveguide.