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arXiv:2411.16026

Violation of Cluster Property in Superconducting Qubit

Tomo Munehisa

Published Nov 25, 2024• 0 citations
arXivHTMLPDF

Abstract

Spontaneous symmetry breaking is well known to be a macroscopic phenomenon in quantum physics in many body systems. The essential features of this phenomenon are the energy degeneracy and the existence of the local operator that can modify the degenerate states. Due to these properties the lowest energy state is not stable. In order to obtain the stable ground state we introduce the explicitly breaking interaction, by which it is difficult for the local operator to modify the ground state. In the superconducting qubit there exists the stable eigenstate with the definite charge number. We point out that in this system, the local operator can change this state to another state. As results the cluster property violates, which means that the events in the far distance are not irrelevant. In this paper we examine the cluster property in the superconducting qubit. Then we propose a method by cavity quantum electrodynamics with two cavities in order to observe the violation.

DOI
10.48550/arxiv.2411.16026

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Spontaneous symmetry breaking is well known to be a macroscopic phenomenon in quantum physics in many body systems. The essential features of this phenomenon are the energy degeneracy and the existence of the local operator that can modify the degenerate states. Due to these properties the lowest energy state is not stable. In order to obtain the stable ground state we introduce the explicitly breaking interaction, by which it is difficult for the local operator to modify the ground state. In the superconducting qubit there exists the stable eigenstate with the definite charge number. We point out that in this system, the local operator can change this state to another state. As results the cluster property violates, which means that the events in the far distance are not irrelevant. In this paper we examine the cluster property in the superconducting qubit. Then we propose a method by cavity quantum electrodynamics with two cavities in order to observe the violation.
Spontaneous symmetry breaking (SSB) is crucial to the occurrence of phase transitions. Once a phase transition occurs, a quantum system presents degenerate eigenstates that lack the symmetry of the Hamiltonian. After crossing the critical point, the system is essentially evolved to a quantum superposition of these eigenstates until decoherence sets in. Despite the fundamental importance and potential applications in quantum technologies, such quantum-mechanical SSB phenomena have not been experimentally explored in many-body systems. We here present an experimental demonstration of the SSB process in the Lipkin-Meshkov-Glick model, governed by the competition between the individual driving and intraqubit interaction. The model is realized in a circuit quantum electrodynamics system, where 6 Xmon qubits are coupled in an all-to-all manner through virtual photon exchange mediated by a resonator. The observed nonclassical correlations among these qubits in the symmetry-breaking region go beyond the conventional description of SSB, shedding new light on phase transitions for quantum many-body systems.
Based on superconducting charge qubits (SCCQs) coupled to a single-mode microwave cavity, we propose a scheme for generating charge cluster states. For all SCCQs, the controlled gate voltages are all in their degeneracy points, the quantum information is encoded in two logic states of charge basis. The generation of the multi-qubit cluster state can be achieved step by step on a pair of nearest-neighbor qubits. Considering effective long-rang coupling, we provide an efficient way to one-step generating of a highly entangled cluster state, in which the qubit-qubit coupling is mediated by the cavity mode. Our quantum operations are insensitive to the initial state of the cavity mode by removing the influence of the cavity mode via the periodical evolution of the system. Thus, our operation may be against the decoherence from the cavity.
The cluster property is one of fundamental properties in physics.This property means that there are no relations between two events that are sufficiently separated.Because the cluster property is directly connected with entanglement in quantum field theory and in many-body systems, theoretical and experimental progress on entanglement stimulates us to study this property deeply.In this paper we investigate the cluster property in the spin 1/2 XXZ antiferromagnet on the square lattice with an explicitly symmetry breaking interaction of strength g.In this model spontaneous symmetry breaking occurs when the lattice size N is infinitely large.On the other hand, we have to make g zero in order to obtain quantities in the XXZ model with no symmetry breaking interaction.Since some results depend on the sequence of limit operations -N → ∞ and 0 g → , it is difficult to draw a clear conclusion in these limits.Therefore we study the model with finite g on the finite lattice, whose size N is supposed to be 10 20 , for our quantitative calculations.Then we can obtain the concrete ground state.In order to study the cluster property we calculate the spin correlation function.It is known that the function due to Nambu-Goldstone mode (gapless mode), which is calculated using linear spin wave theory, satisfies this property.In this paper we show that almost degenerate states also induce the spin correlation.We assume that the spin correlation function in measurements is a sum of the function due to Nambu-Goldstone mode and one due to these degenerate states.Then we examine whether the additional correlation function violates the cluster property or not.Our conclusion is that this function is finite at any distance, which means the violation of the cluster property, and it is of order of ( )for the case of extremely small g, this violation is the fine effect.Therefore the correlation function due to the degenerate states can be observed only when it is larger than the spin correlation function due to Nambu-Goldstone mode.We show that g required for this condition depends on the distance between positions of two spin operators.
We show that superconductors have a thin spectrum associated with spontaneous symmetry breaking similar to that of antiferromagnets, while still being in full agreement with Elitzur's theorem, which forbids the spontaneous breaking of local (gauge) symmetries. This thin spectrum in the superconductors consists of in-gap states that are associated with the spontaneous breaking of a global phase symmetry. In qubits based on mesoscopic superconducting devices, the presence of the thin spectrum implies a maximum coherence time which is proportional to the number of Cooper pairs in the device. Here we present the detailed calculations leading up to these results and discuss the relation between spontaneous symmetry breaking in superconductors and the Meissner effect, the Anderson-Higgs mechanism, and the Josephson effect. Whereas for the Meissner effect a symmetry breaking of the phase of the superconductor is not required, it is essential for the Josephson effect.
Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.
The modern physics of superconductivity can be called the physics of unconventional superconductivity. The discovery of the d-wave symmetry of the order parameter in high-temperature superconductors and the triplet superconductivity in compound Sr2RuO4 has caused a huge stream of theoretical and experimental investigations of unconventional superconductors. In this review we discuss some novel aspects of the Josephson effect which are related to the symmetry of the order parameter. The most intriguing of them is spontaneous current generation in an unconventional weak link. The example of a Josephson junction in the form of a grain boundary between two disorientated d-wave or f-wave superconductors is considered in detail. Josephson current–phase relations and the phase dependences of the spontaneous current that flows along the interface are analyzed. The spontaneous current and spontaneous phase difference are manifestations of the time-reversal symmetry (𝒯 ) breaking states in the system. We analyzed the region of appearance of 𝒯-breaking states as function of temperature and mismatch angle. A review of the basics of superconducting qubits with emphasis on specific properties of d-wave qubits is given. Recent results in the problem of decoherence in d-wave qubits, which is the major concern for any qubit realization, are presented.