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Periodic entanglement revivals of asynchronously excited cavity-coupled qubits

Tiantian Huan, Ri‐Gui Zhou, Franco Nori, Hou Ian

Published May 5, 2020• 0 citations
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Abstract

In a multi-partite system, the multipartite concurrence of the entire system differs from the sum of the bipartite concurrences of its components. For a system with an even number of components, the relation between them is described by a monogamy inequality that compares the bipartite concurrences of two subsystems comprising even-number components and those of two subsystems comprising odd-number components. The difference between the even and the odd clusterings is exactly quantified by a polynomial invariant. We study the dynamic evolution of the polynomial invariant on three superconducting qubits inhomogeneously coupled to a circuit cavity. We show that in this quadripartite system, the non-negativity of the degree-4 invariant holds strictly over time and vanishes periodically. The magnitude of the invariant increases monotonically with the absolute coupling strength while the period of the vanishing and revival maximizes when the couplings among the qubits are inhomogeneous, showing the benefit of asynchronous qubit excitations in extending entanglement time.

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•Jun 12, 2013•0 citations
In a multi-partite system, the multipartite concurrence of the entire system differs from the sum of the bipartite concurrences of its components. For a system with an even number of components, the relation between them is described by a monogamy inequality that compares the bipartite concurrences of two subsystems comprising even-number components and those of two subsystems comprising odd-number components. The difference between the even and the odd clusterings is exactly quantified by a polynomial invariant. We study the dynamic evolution of the polynomial invariant on three superconducting qubits inhomogeneously coupled to a circuit cavity. We show that in this quadripartite system, the non-negativity of the degree-4 invariant holds strictly over time and vanishes periodically. The magnitude of the invariant increases monotonically with the absolute coupling strength while the period of the vanishing and revival maximizes when the couplings among the qubits are inhomogeneous, showing the benefit of asynchronous qubit excitations in extending entanglement time.
The generation of GHZ states calls for simultaneous excitation of multiple qubits. The peculiarity of such states is reflected in their nonzero distributed entanglement which is not contained in other entangled states. We study the optimal way to excite three superconducting qubits through a common cavity resonator in a circuit such that the generation of distributed entanglement among them could be obtained at the highest degree in a time-controllable way. A non-negative measure quantifying this entanglement is derived as a time function of the quadripartite system evolution. We find that this measure does not stay static but obtains the same maximum periodically. When the qubit-resonator couplings are allowed to vary, its peak value is enhanced monotonically by increasing the greatest coupling strength to one of the qubits. The period of its peak to peak revival maximizes when the couplings become inhomogeneous, thus qubit excitation becoming asynchronous, at a relative ratio of 0.35. The study demonstrates the role of asynchronous excitations for time-controlling multi-qubit systems, in particular in extending entanglement time.
The mesoscopic scale of superconducting qubits makes their inter-spacings comparable to the scale of wavelength of a circuit cavity field to which they commonly couple. This comparability results in inhomogeneous coupling strengthes for each qubit and hence asynchronous Rabi excitation cycles among the qubits that form a quasi-lattice. We find that such inhomogeneous coupling benefits the formation of multi-photon resonances between the single-mode cavity field and the quasi-lattice. The multi-photon resonances lead, in turn, to the simultaneous generation of inequivalent GHZ and W types of multipartite entanglement states, which are not transformable to each other through local operations with classical communications. Applying the model on the 3-qubit quasi-lattice and using the entanglement measures of both concurrence and 3-tangle, we verify that the inhomogeneous coupling specifically promotes the generation of the totally inseparable GHZ state.
Some nonlinear radiations such as superfluorescence can be understood as cooperative effects between atoms. We regard the cooperative radiation as a manifested effect secondary to the intrinsic cooperativity among the atoms and propose a time-resolved measure of cooperativity on a cavity-coupled dual-qubit system using multi-partite concurrence measures. We find that the cooperativity features a time delay characterisitic to superfluorescent pulses in its evolution, which coincides with the duration for the qubits to synchronize with each other. Thereafter, the cooperativity monotonically increases to a stationary value while the measure of asynchronicity dives to a steady minimum. Furthermore, the asynchronicity experiences a continuous transition to nonzero values when the coupling strength crosses from the weak to the strong coupling regime.
In this paper, we first present a simple measure for multiqubit entanglement based on the strategy of bipartite cuts and the measure of negativity. Then, we establish generalized monogamy inequalities and associated partition-dependent residual entanglement (PRE) accounting for arbitrary partitions of a multiqubit system. By virtue of the defined quantities, we investigate the entanglement dynamics of a system of N qubits, either in the Greenberger–Horne–Zeilinger (GHZ)-type state or in the W state, interacting with N independent reservoirs in both Markovian and non-Markovian regimes. We observe entanglement revivals of qubits at instantaneous points of disappearance or after a finite interval of abrupt vanishing due to the memory effect of non-Markovian reservoirs. We also follow the whole entanglement evolution in terms of the PRE to demonstrate the process of transition between the bipartite entanglement of all possible bipartitions and the multipartite entanglement. In particular, we show that the change in time of entanglement formats differs qualitatively for the GHZ-type and W states.
We investigate the entanglement dynamics of a quantum system consisting of three Superconducting charge qubits (SCQs) interacting with a single-mode cavity field. Considering the Rotating wave approximation (RWA) and the resonance condition, we give the effective Hamiltonian of the system involving cavity decay. The dynamical evolution is studied in terms of the entanglements in the different bipartite partitions of the system, as quantified by the square concurrence. With the choice of the appropriate initial states, a four-qubit W-entangled state can be obtained. We study the effect of cavity decay on various square concurrences in the system, the results show that the peak value of the square concurrence declines with the increase of cavity decay when the other parameters are fixed, but the cavity decay does not change the period of the square concurrence. We also find a natural entanglement transfer and entanglement invariant under evolution of the effective Hamiltonian.
Unlike atoms in a lattice, the spacings between neighboring qubits in a superconducting quantum circuit are mesoscopic and non-uniform. The strength of interaction between this quasi-lattice chain of qubits and a resonator mode in circuit transmission lines is inhomogeneous and geometrically dependent on the circuit layout. We propose a projection-deformation method to give analytically the eigenstates of the quasi-particle excitation that arise in the quasi-lattice. We further show that, during the quasi-particle excitation, the distribution of multi-photon resonances between the resonator photon and the quasi-lattice is determined by the degree the quasi-lattice is deformed from a normal lattice. The multi-photon resonances lead to simultaneous generation of GHZ-type and W-type of multipartite entanglement states of the qubits, which is enhanced by the inhomogeneous interaction. Comparing the concurrence and the 3-tangle generated, we find that the totally non-separable GHZ entanglement is specifically increased, up to two orders of magnitude.