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arXiv:cond-mat/0411115 · Physical review. B, Condensed matter

Quantum statistics and entanglement of two electromagnetic field modes coupled via a mesoscopic SQUID ring

M. J. Everitt, Terrence D. Clark, P. B. Stiffell, Helen Prance, Robert J. Prance, Apostol Vourdas, Jason F. Ralph

Published Oct 19, 2001• 32 citations
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Abstract

In this paper we investigate the behavior of a fully quantum mechanical system consisting of a mesoscopic SQUID ring coupled to one or two electromagnetic field modes. We show that we can use a static magnetic flux threading the SQUID ring to control the transfer of energy, the entanglement and the statistical properties of the fields coupled to the ring. We also demonstrate that at, and around, certain values of static flux the effective coupling between the components of the system is large. The position of these regions in static flux is dependent on the energy level structure of the ring and the relative field mode frequencies, In these regions we find that the entanglement of states in the coupled system, and the energy transfer between its components, is strong.

DOI
10.1103/physrevb.64.184517

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In this paper we investigate the behavior of a fully quantum mechanical system consisting of a mesoscopic SQUID ring coupled to one or two electromagnetic field modes. We show that we can use a static magnetic flux threading the SQUID ring to control the transfer of energy, the entanglement and the statistical properties of the fields coupled to the ring. We also demonstrate that at, and around, certain values of static flux the effective coupling between the components of the system is large. The position of these regions in static flux is dependent on the energy level structure of the ring and the relative field mode frequencies, In these regions we find that the entanglement of states in the coupled system, and the energy transfer between its components, is strong.
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.
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.
In this paper we investigate the dynamical behavior of a SQUID ring coupled to a quantized single-mode electromagnetic field. We have calculated the eigenstates of the combined fully quantum mechanical SQUID-field system. Interesting phenomena occur when the energy difference between the usual symmetric and anti-symmetric SQUID states equals the field energy ℏωF. We find the low-energy lying entangled stationary states of the system and demonstrate that its dynamics is dominated by coherent Rabi oscillations.
In this paper we study, by analogy with quantum optics, the superconducting quantum interference device (SQUID) ring mediated quantum mechanical interaction of an input electromagnetic field oscillator mode with two or more output oscillator modes at subintegers of the input frequency. We show that through the nonlinearity of the SQUID ring multiphoton downconversion can take place between the input and output modes with the resultant output photons being created in an entangled state. We also demonstrate that the degree of this entanglement can be adjusted by means of a static magnetic flux which controls the strength of the interaction between these modes via the SQUID ring.
A ring made from a Josephson array in the insulating phase is considered. The ring contains a ‘dual Josephson junction’ (Josephson junction for vortices). External non-classical electromagnetic fields are coupled to the device and interact with the vortices that circulate the ring. The time evolution of this two-mode fully quantum mechanical system is studied. The effect of the quantum statistics of the photons on the quantum statistics of the vortices is discussed. The entanglement between the two systems is quantified.
We present solutions of the time dependent Schrodinger equation for a SQUID ring coupled to an electromagnetic field, both treated quantum mechanically. We that show the SQUID ring can be used to create a maximally entangled state with the em field that without dissipation remains constant in time. Using methods familiar in quantum optics, we extend the model to include the effects of coupling this system to a dissipative environment. With this model we show that although such an environment makes a noticeable difference to the time evolution of the system, it need not destroy the the entanglement of this coupled system over time scales required for quantum technologies.