Electron interference in mesoscopic devices in the presence of nonclassical electromagnetic fields

Abstract

Abstract. The interaction of mesoscopic interference devices with nonclassical electromagnetic fields is studied. The external quantum fields induce a phase factor on the electric charges. This phase factor, which is a generalization of the standard Aharonov-Bohm phase factor, is in the case of nonclassical electromagnetic fields a quantum mechanical operator. Its expectation value depends on the density matrix describing the nonclassical photons and determines the interference. Several examples are discussed, which show that the quantum noise of the nonclassical photons destroys slightly the electron interference fringes. An interesting application arises in the context of distant electron interference devices, irradiated with entangled photons. In this case the interfering electrons in the two devices become entangled. The same ideas are applied in the context of SQUID rings irradiated with nonclassical electromagnetic fields. It is shown that the statistics of the Cooper pairs tunneling through the Josephson junction depend on the statistics of the photons.

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

“…At the same time, however, an effect of interaction is manifested in current time characteristics. This observation which is the main result of our present studies additionally justifies applicability of an external field approximation utilized in previous studies [ 20 , 36 , 37 , 38 , 39 , 40 , 41 , 54 ] for a free-electron model of conduction.…”

“…For a monochromatic non-classical field of frequency operating at low temperature [ 41 , 44 ] a vector potential and an electric field are dual quantum variables [ 44 ]. The corresponding operators of a magnetic flux and an electromotive force are given [ 41 ] by integrals and, respectively, where the integration contour C is small with respect to a size of of the ring.…”

“…For a monochromatic non-classical field of frequency operating at low temperature [ 41 , 44 ] a vector potential and an electric field are dual quantum variables [ 44 ]. The corresponding operators of a magnetic flux and an electromotive force are given [ 41 ] by integrals and, respectively, where the integration contour C is small with respect to a size of of the ring. A non-classical electromagnetic field, as an essentially bosonic system, allows for the Heisenberg–Weyl representation of the field operators or in terms of bosonic annihilation and creation operators satisfying with related to the area of C [ 44 ].…”

“…Here we apply phenomenological modelling an we assume that the particle-field composite Equation ( 6 ) undergoes completely positive [ 45 ] time evolution governed by a master equation where the dissipative part, having a phenomenological amplitude , represents decoherence affecting particles in the nanoring. In a low temperature limit —suitable for non-classical properties of electromagnetic fields [ 41 ] considered here—dissipators containing bosonic operators are omitted. From a physical perspective the master equation Equation ( 12 ) describes completely positive dynamics of the nanoring–field system with a decoherence of the same strength locally affecting each of L lattice sites in the nanoring.…”

“…Carefully prepared non-classical electromagnetic fields applicable in quantum information processing [ 31 , 32 , 33 , 34 , 35 ] are shown to modify properties of currents flowing in nanosystems [ 20 , 36 , 37 , 38 , 39 , 40 ] (and Ref. [ 41 ] for detailed review) under external field approximation [ 36 ] assumed. External field approximation introduced in Ref.…”