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Physical Review B

Magnetic flux in a mesoscopic SQUID controlled by nonclassical electromagnetic fields

Jerzy Dajka, J. Łuczka

Published Nov 30, 2009• 5 citations
Publisher

Abstract

We analyze SQUID coupled to a nonclassical electromagnetic field (NEM) and show that properties of the SQUID can be manipulated by a choice of a state of NEM. In particular, energy or fluctuations of magnetic flux threading the loop of the SQUID can be resolved into separate lines for each photon number state of one-mode NEM. The impact of two-mode NEM prepared in entangled Bell states is discussed. The findings suggest an experimental method of detection of photon states: the SQUID response is dependent on the number of photons in one-mode NEM and on the Bell states of a two-mode NEM.

DOI
10.1103/physrevb.80.174529

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We analyze SQUID coupled to a nonclassical electromagnetic field (NEM) and show that properties of the SQUID can be manipulated by a choice of a state of NEM. In particular, energy or fluctuations of magnetic flux threading the loop of the SQUID can be resolved into separate lines for each photon number state of one-mode NEM. The impact of two-mode NEM prepared in entangled Bell states is discussed. The findings suggest an experimental method of detection of photon states: the SQUID response is dependent on the number of photons in one-mode NEM and on the Bell states of a two-mode NEM.
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A quantum system comprising of a monochromatic electromagnetic field coupled to a superconducting quantum interference device (SQUID) ring with sinusoidal nonlinearity is studied. A magnetostatic flux ${\ensuremath{\Phi}}_{x}$ is also threading the SQUID ring, and is used to control the coupling between the two systems. It is shown that for special values of ${\ensuremath{\Phi}}_{x}$ the system is strongly coupled. The time evolution of the system is studied. It is shown that exchange of energy takes place between the two modes and that the system becomes entangled. A second quasiclassical model that treats the electromagnetic field classically is also studied. A comparison between the fully quantum-mechanical model with the electromagnetic field initially in a coherent state and the quasiclassical model is made.
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.
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.
The interaction of mesoscopic interference devices with nonclassical electromagnetic fields is studied. The external quantum fields induce a phase factor in 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 partly destroys 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 tunnelling through the Josephson junction depends on the statistics of the photons.