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Entropy

Currents in a Quantum Nanoring Controlled by Non-Classical Electromagnetic Field

Jerzy Dajka

Published May 23, 2021• 2 citations
Publisher

Abstract

Quantum ring accommodating interacting spin-less fermions threaded by magnetic flux with a non-classical component added to a static, inducing persistent current, is considered. It is investigated how current flowing in the ring becomes affected by a state of non-classical flux and how Coulomb interaction between fermions influences entanglement of quantum ring and the driving field. In particular it is shown that in an absence of decoherence and under certain conditions fermion-fermion interaction is necessary for a ring-field entanglement to occur.

DOI
10.3390/e23060652

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Quantum ring accommodating interacting spin-less fermions threaded by magnetic flux with a non-classical component added to a static, inducing persistent current, is considered. It is investigated how current flowing in the ring becomes affected by a state of non-classical flux and how Coulomb interaction between fermions influences entanglement of quantum ring and the driving field. In particular it is shown that in an absence of decoherence and under certain conditions fermion-fermion interaction is necessary for a ring-field entanglement to occur.
We address the issue of whether a system of interacting electrons confined to a one-dimensional ring can sustain a spontaneous persistent current in the absence of an externally applied flux. The current-current coupling between electrons, describing radiative back-action effects, is exactly treated in the formalism of quantum electrodynamics, where the electrons interact via the exchange of virtual photons. In addition, the instantaneous screened Coulomb potential is taken into account using the Luttinger liquid model including finite-size parity effects. The partition function is calculated exactly, with the result that the system does not possess a spontaneous persistent current. We show that, in the presence of an external flux, the amplitude of the (conventional) persistent current is reduced by quantum fluctuations of the internal transverse electromagnetic field. These corrections can be expressed in terms of the self-induction of the ring and are shown to be of first and higher order in the small dimensionless parameter \ensuremath{\alpha}vF∗{\mathit{v}}_{\mathit{F}}^{\mathrm{*}}vF∗​/c, where \ensuremath{\alpha} is the fine-structure constant and vF∗{\mathit{v}}_{\mathit{F}}^{\mathrm{*}}vF∗​ the Fermi velocity renormalized through Coulomb interactions.
Mesoscopic systems and the non-classical electromagnetic fields are of central importance for quantum information processing. Our aim is to present the significant impact of the non-classical radiation on the properties of persistent currents. We study mesoscopic rings or cylinders subject to both classical and non-classical magnetic flux. Our discussion is limited to oneand two-mode fields prepared in a given state. For the monochromatic radiation we study reduction of the current amplitude due to the quantum and classical noise in the field. We also present the change of the sign of the current from parato diamagnetic (and vice versa) controlled by the state of radiation. The effect of temperature will by shortly reviewed. There are two qualitatively distinct classes of two-mode fields: separable and entangled. This is reflected in the properties of the currents which become time-dependent for the fields in an entangled state. We investigate the effect of entanglement for the family of states with various amount of entanglement: from separable to Bell states quantified by the concurrence.
We investigate the ground state persistent spin current and the pair entanglement in one-dimensional antiferromagnetic anisotropic Heisenberg ring with twisted boundary conditions. By solving Bethe ansatz equations numerically, we calculate the dependence of the ground state energy on the total magnetic flux through the ring, and the resulting persistent current. Motivated by the recent development of the quantum entanglement theory, we study the properties of the ground state concurrence under the influence of the flux through the anisotropic Heisenberg ring. We also include an external magnetic field and discuss the properties of the persistent current and the concurrence in the presence of the magnetic field.
We introduce a model for the persistent current carried by spinless fermions moving in a ring with a high-dimensional cross section. The effects of both disorder and electron - electron interaction are considered. It is found that the non-interacting system behaves like previously considered low-dimensional models. The more complicated interacting/disordered case is analysed by means of a functional integral which is evaluated in the limit of infinite dimensionality by expanding in the number of transverse channels. To leading order in this expansion scheme, the Coulomb interaction does not affect the persistent current. It is found that the insensitivity to interaction effects is due to the absence of local contributions to the Coulomb vertex in our model (which in turn is a consequence of the neglect of the electron spin). It is argued that the physical mechanism suppressing the interaction in the high-dimensional spinless model applies to the analogous low-dimensional case as well.
Persistent currents in mesoscopic rings and cylinders threaded by a magnetostatic flux and also by monochromatic nonclassical electromagnetic fields are considered. The results depend on the quantum state of the nonclassical electromagnetic fields. It is shown that quantum and thermal noise in the field reduces the current and can change its character from diamagnetic to paramegnetic, and vice versa. Four different examples of nonclassical electromagnetic fields are considered (number eigenstates, coherent states with randomized phase, coherent states, and thermal states) and the corresponding currents are calculated. Two-mode entangled electromagnetic fields are also considered, and the effect of entanglement on the currents is studied.