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arXiv:2003.10638 · Physical Review A

Vortex-Meissner phase transition induced by a two-tone-drive-engineered artificial gauge potential in the fermionic ladder constructed by superconducting qubit circuits

Yan-Jun Zhao, Xun‐Wei Xu, Hui Wang, Yu-xi Liu, Wu‐Ming Liu

Published Nov 24, 2020• 6 citations
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Abstract

The authors are proposing a way to engineer artificial gauge fields in systems of superconducting qubits that is applicable, in principle, to circuits with any nonzero anharmonicity, thereby allowing for the simulation of fermionic systems. As an application, they study the transition between vortex and Meissner phases in a two-leg ladder system induced by varying the interleg coupling strength and effective magnetic flux.

DOI
10.1103/physreva.102.053722

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The authors are proposing a way to engineer artificial gauge fields in systems of superconducting qubits that is applicable, in principle, to circuits with any nonzero anharmonicity, thereby allowing for the simulation of fermionic systems. As an application, they study the transition between vortex and Meissner phases in a two-leg ladder system induced by varying the interleg coupling strength and effective magnetic flux.
We consider a two leg bosonic ladder in a U(1)U(1)U(1) gauge field with both interleg hopping and interleg repulsion. As a function of the flux, the interleg interaction converts the commensurate-incommensurate transition from the Meissner to a Vortex phase, into an Ising-type of transition towards a density wave phase. A disorder point is also found after which the correlation functions develop a damped sinusoid behavior signaling a melting of the vortex phase. We discuss the differences on the phase diagram for attractive and repulsive interleg interaction. In particular, we show how repulsion favors the Meissner phase at low flux and a phase with a second incommensuration in the correlation functions for intermediate flux, leading to a richer phase diagram than in the case of interleg attraction. The effect of the temperature on the chiral current is also discussed.
The gauge field is essential for exploring novel phenomena in modern physics. However, it has not been realized in the recent breakthrough experiment on two-leg superconducting circuits with transmon qubits [Y. Ye et al., Phys. Rev. Lett. 123, 050502 (2019)]. Here we present an experimentally feasible method to achieve the synthetic gauge field by introducing ac microwave driving in each qubit. In particular, the effective magnetic flux per plaquette achieved can be tuned independently by properly choosing the driving phases. Moreover, the ground-state chiral currents for single- and two-qubit excitations are obtained and the Meissner-vortex phase transition is found. In the Meissner phase, the ground-state chiral current increases as the magnetic flux increases, while it decreases in the vortex phase. In addition, chiral dynamics, which depends crucially on the initial state of the system, is also revealed. Finally, the possible experimental observations of the chiral current and dynamics are addressed. Our results provide a new route to explore novel many-body properties induced by the interplay of the gauge field, two-leg hoppings, and interaction of photons on superconducting circuits.
We consider a two-leg boson ladder in an artificial U(1) gauge field and show that, in the presence of interleg attractive interaction, the flux induced vortex state can be melted by dislocations. For increasing flux, instead of the Meissner to vortex transition in the commensurate-incommensurate universality class, first, an Ising transition from the Meissner state to a charge density wave takes place, then, at higher flux, the melted vortex phase is established via a disorder point where incommensuration develops in the rung current correlation function and in momentum distribution. Finally, the quasi-long-range ordered vortex phase is recovered for sufficiently small interaction. Our predictions for the observables, such as the spin current and the static structure factor, could be tested in current experiments with cold atoms in bosonic ladders.
We investigate a square-lattice architecture of superconducting transmon qubits with interqubit interactions mediated by inductive couplers. Via periodically modulating the couplers, the Abelian gauge potential, termed effective magnetic flux, can be synthesized artificially, making the system an excellent platform for simulating two-dimensional topological physics. First, we focus on the three-leg ladder which only has three rows and investigate the chiral dynamics therein for the single-particle ground state when the effective magnetic flux varies. We find what we call the ``staggered vortex-Meissner phase transition,'' where the vortex number can typically stagger a few times between one (defined as ``vortex phase'') and larger integers (defined as ``Meissner phase'') when the effective magnetic flux changes between $\ensuremath{-}\ensuremath{\pi}$ and $\ensuremath{\pi}$. This phenomenon, actually not a phase transition by definition, is quite different from the vortex-Meissner phase transition in the two-leg ladder that, in contrast, possesses only two rows and is usually treated as the quasi-two-dimensional model. Also, we find that the chiral current relies on the effective magnetic flux according to a squeezed sinusoidal function. Both the staggering of the vortex number and squeezing of the chiral current can be controllable by the coupling ratio, which is defined by the coupling-strength ratio between the column direction and row direction. Second, we continue to increase the number of rows beyond three, and the topological band structure to be anticipated at an infinite number of rows begins to occur even for a relatively small number (10 or so for typical parameters) of rows. This heralds a small circuit scale enough to observe the topological band. The behavior of the edge state in the band gap can be interpreted by the topological Chern number, which can be calculated through integrating the Berry curvature with respect to the first Brillouin zone. Last, we present a systematic method on how to measure the topological band structure based on time- and space-domain Fourier transformation of the wave function after properly exciting the qubits, which should be helpful for comprehensively analyzing the topological physics since all the topological properties are mainly contained in the band structure. Our results offer an avenue for simulating two-dimensional topological physics on the state-of-the-art superconducting quantum chips.
We consider interacting bosonic particles on a two-leg triangular ladder in the presence of an artificial gauge field. We employ density matrix renormalization group numerical simulations and analytical bosonization calculations to study the rich phase diagram of this system. We show that the interplay between the frustration induced by the triangular lattice geometry and the interactions gives rise to multiple chiral quantum phases. Phase transitions between superfluid to Mott-insulating states occur, which can have Meissner or vortex character. Furthermore, a state that explicitly breaks the symmetry between the two legs of the ladder, the biased chiral superfluid, is found for values of the flux close to $\ensuremath{\pi}$. In the regime of hard-core bosons, we show that the extension of the bond order insulator beyond the case of the fully frustrated ladder exhibits Meissner-type chiral currents. We discuss the consequences of our findings for experiments in cold atomic systems.