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arXiv:cond-mat/0011497 · Physical review. B, Condensed matter

Meissner effect in a bosonic ladder

E. Orignac, Thierry Giamarchi

Published Sep 21, 2001• 168 citations
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Abstract

We investigate the effect of a magnetic field on a bosonic ladder. We show that such a system leads to the one-dimensional equivalent of a vortex lattice in a superconductor. We investigate the physical properties of the vortex phase, such as vortex density and vortex correlation functions, and show that magnetization has plateaus for some commensurate values of the magnetic field. The lowest plateau corresponds to a true Meissner to vortex transition at a critical field ${H}_{c1}$ that exists although the system has no long-range superconducting order. Implications for experimental realizations such as Josephson-junction arrays are discussed.

DOI
10.1103/physrevb.64.144515

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We investigate the effect of a magnetic field on a bosonic ladder. We show that such a system leads to the one-dimensional equivalent of a vortex lattice in a superconductor. We investigate the physical properties of the vortex phase, such as vortex density and vortex correlation functions, and show that magnetization has plateaus for some commensurate values of the magnetic field. The lowest plateau corresponds to a true Meissner to vortex transition at a critical field Hc1{H}_{c1}Hc1​ that exists although the system has no long-range superconducting order. Implications for experimental realizations such as Josephson-junction arrays are discussed.
By periodically driving a single bosonic Josephson junction (BJJ) with an impurity, a synthetic gauge field is generated in the Fock space of the system. At a critical synthetic gauge flux the ground state undergoes a quantum phase transition which is analogous to the Meissner-Abrikosov-vortex transition found in type-II superconductors with an applied magnetic field. A second quantum phase transition involving attractive interactions between the bosons of the BJJ is shown to enhance the sensitivity of the system to the Meissner-Abrikosov-vortex transition.
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.
Ultracold bosonic atoms trapped in a two-leg ladder pierced by a magnetic field provide a minimal and quasi-one-dimensional instance to study the interplay between orbital magnetism and interactions.Using time-dependent matrix-product-state simulations, we investigate the properties of the so-called 'Meissner' and 'vortex' phases which appear in such a system, focusing on the experimentally accessible observables.We discuss how to experimentally monitor the phase transition, and show that the response to the modulation of the density imbalance between the two legs of the ladder is qualitatively different in the two phases.We argue that this technique can be used as a tool for many-body spectroscopy, allowing us to quantitatively measure the spin gap in the Meissner phase.We finally discuss its experimental implementation.
A boson two-leg ladder in the presence of a synthetic magnetic flux is investigated by means of bosonization techniques and density matrix renormalization group (DMRG). We follow the quantum phase transition from the commensurate Meissner to the incommensurate vortex phase with increasing flux at different fillings. When the applied flux is ρπ and close to it, where ρ is the filling per rung, we find a second incommensuration in the vortex state that affects physical observables such as the momentum distribution, the rung–rung correlation function and the spin–spin and charge–charge static structure factors.
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 superconductor-to-insulator transition is studied in a self-charging model for a ladder of Josephson junctions in the presence of an external magnetic field. Path integral Monte Carlo simulations of the equivalent (1+1)(1+1)(1+1)-dimensional classical model are used to study the phase diagram and critical behavior. In addition to a superconducting (vortex-free) phase, a vortex phase can also occur for an increasing magnetic field and small charging energy. It is found that an intervening insulating phase separates the superconducting from the vortex phases. Surprisingly, a finite-size scaling analysis shows that the field-induced superconducting-to-insulator transition is in the KT universality class, even though the external field breaks time-reversal symmetry.