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Superconducting Analogues of Quantum Optical Phenomena: Schrodinger Cat States and Squeezing in a SQUID Ring

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

Published Jul 24, 2003• 0 citations
OpenAlex

Abstract

In this paper we explore the quantum behaviour of a SQUID ring which has a very strong Josephson coupling energy. We show that that the eigenfunctions of the Hamiltonian for the ring can be used to create Schrodinger cat states. We also show that the ring potential may be utilised to squeeze coherent states. With the SQUID ring as a strong contender as a device for manipulating quantum information, such properties may be of great utility in the future. However, as with all candidate systems for quantum technologies, decoherence is a fundamental problem. In this paper we apply an open systems approach to model the effect of coupling a quantum mechanical SQUID ring to a thermal bath. We use this model to demonstrate the manner in which decoherence affects the quantum states of the ring.

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In this paper we explore the quantum behaviour of a SQUID ring which has a very strong Josephson coupling energy. We show that that the eigenfunctions of the Hamiltonian for the ring can be used to create Schrodinger cat states. We also show that the ring potential may be utilised to squeeze coherent states. With the SQUID ring as a strong contender as a device for manipulating quantum information, such properties may be of great utility in the future. However, as with all candidate systems for quantum technologies, decoherence is a fundamental problem. In this paper we apply an open systems approach to model the effect of coupling a quantum mechanical SQUID ring to a thermal bath. We use this model to demonstrate the manner in which decoherence affects the quantum states of the ring.
In this paper we explore the quantum behavior of a superconducting quantum-interference device (SQUID) ring which has a significant Josephson coupling energy. We show that the eigenfunctions of the Hamiltonian for the ring can be used to create macroscopic quantum superposition states of the ring. We also show that the ring potential may be utilized to squeeze coherent states. With the SQUID ring as a strong contender as a device for manipulating quantum information, such properties may be of great utility in the future. However, as with all candidate systems for quantum technologies, decoherence is a fundamental problem. In this paper we apply an open systems approach to model the effect of coupling a quantum-mechanical SQUID ring to a thermal bath. We use this model to demonstrate the manner in which decoherence affects the quantum states of the ring.
A cat-state is a superposition of two coherent states with amplitudes α0α_{0}α0​ and −α0-α_{0}−α0​. Recent experiments create cat states in a microwave cavity field using superconducting circuits. As with degenerate parametric oscillation (DPO) in an adiabatic and highly nonlinear limit, the states are formed in a signal cavity mode via a two-photon dissipative process induced by the down conversion of a pump field to generate pairs of signal photons. The damping of the signal and the presence of thermal fluctuations rapidly decoheres the state, and the effect on the dynamics is to either destroy the possibility of a cat state, or else to sharply reduce the lifetime and size of the cat-states that can be formed. In this paper, we study the effect on both the DPO and microwave systems of a squeezed reservoir coupled to the cavity. While the threshold nonlinearity is not altered, we show that the use of squeezed states significantly lengthens the lifetime of the cat states. This improves the feasibility of generating cat states of large amplitude and with a greater degree of quantum macroscopic coherence, which is necessary for many quantum technology applications. Using current experimental parameters for the microwave set-up, which requires a modified Hamiltonian, we further demonstrate how squeezed states enhance the quality of the cat states that could be formed in this regime. Squeezing also combats the significant decoherence due to thermal noise, which is relevant for microwave fields at finite temperature. By modeling a thermal squeezed reservoir, we show that the thermal decoherence of the dynamical cat states can be inhibited by a careful control of the squeezing of the reservoir. To signify the quality of the cat state, we consider different signatures including fringes and negativity, and the Cl1C_{l_{1}}Cl1​​ measure of quantum coherence.
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.
Based on the measurement of charge states, we show that the superpositions of two macroscopically distinguishable coherent states (Schr\\"odinger cat states) of a single-mode cavity field can be generated by a controllable interaction between a cavity field and a SQUID-based charge qubit. After such cat states of the cavity field are created, the interaction can be switched off by the classical magnetic field through the SQUID, and there is no information transfer between the cavity field and the charge qubit. We also discuss the generation of superpositions of two squeezed coherent states.
This chapter analyzes the problem of locating the divide between the quantum and classical worlds. It discusses Schrödinger's cat paradox; and Leggett's SQUID (superconducting quantum interference device), that when operated under certain conditions can bring about quantum effects on a fairly large scale. It suggests that superposition states, which are routinely produced in the microworld, are difficult to manufacture in larger-scale systems due to the effects of the environment, i.e., the part of the world directly surrounding the quantum system. For larger-scale systems, such as for the interfering cat states of SQUID, the environment has the effect of destroying the quantum coherence of the superposition state at short times. Quantum coherence for the state of the supercurrents can be maintained in such experiments only for short times. The destruction of quantum coherence is known as decoherence.
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.