Superconducting analogs of quantum optical phenomena: Macroscopic quantum superpositions and squeezing in a superconducting quantum-interference device ring

Abstract

Prance, R J and Prance, H (2004) Superconducting analogs of quantum optical phenomena: Macroscopic quantum superpositions ans squeezing in a superconducting quantum-interference device ring. Physical Review A, 69 (4). p. 43804. ISSN 105043804. ISSN -2947 This version is available from Sussex Research Online: http://sro.sussex.ac.uk/20502/ This document is made available in accordance with publisher policies and may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the URL above for details on accessing the published version. Copyright and reuse:Sussex Research Online is a digital repository of the research output of the University.Copyright and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable, the material made available in SRO has been checked for eligibility before being made available.Copies of full text items generally can be reproduced, displayed or performed and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. 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. INTRODUCTIONIn two recent publications [1,2] we reported on the theoretical description of a quantum-mechanical superconducting quantum-interference device (SQUID) ring (here, a thick superconducting ring enclosing a single Josephson weak link device) coupled to quantized electromagnetic field (em) oscillator modes. In this work we emphasized that the SQUID ring could be used to control various quantum phenomena involving each of the circuit components of the coupled system via the static magnetic bias flux ⌽ x applied to the ring. These included frequency conversion between the em modes and quantum entanglement extending across the system, both with relevance to emerging quantum technologies based on Josephson devices [3][4][5][6][7][8][9]...

Engineering Dissipative Channels for Realizing Schrödinger Cats in SQUIDs

“…We have solved the master equation for the ring in a lossy bath, with a Lindblad of L = √ 0.2a and allowed the system to reach its steady state to obtain Figure 3B. This is the Wigner function of a statistical mixture of two macroscopically distinct states and is in-line with expectations of the effect of a decohering environment on such a device (Everitt et al, 2004). In FIGURE 2 | Effect of decoherence on energy and entropy.…”

“…The even and odd nature of these superpositions is reflected in the Wigner function by the phase of the interference terms between the two Gaussians of the cat. It is known that such states would decohere under the environment of a lossy bath to a statistical mixture (Everitt et al, 2004). The dynamics of the system coupled to an environment comprising a bath of two-photon absorbers are, once more, found by solving the master equation with an L = √ 0.2a 2 , until an approximate steady state is reached.…”

“…These interference terms, indicating quantum www.frontiersin.org and we do not see the interference terms between them that are characteristic of a Schrödinger cat state. We have instead a statistical mixture, the usual and expected result (Everitt et al, 2004). (C) The steady state solution to the master equation for the ring coupled to a bath of two-photon absorbers (with a Lindblad proportional to the square of annihilation operator, L = √ 0.2a 2 ).…”

Energetics of an rf SQUID Coupled to Two Thermal Reservoirs

“…In the limit E J → 0, Eq (4) reduces to the equation of motion for a harmonic oscillator of mass M = C and frequency . By analogy to the harmonic oscillator, we introduce a corresponding Hamiltonian in the form [ 21 ] where the annihilation and creation bosonic operators are defined as [ 21 ] …”

“…Moreover, a similar approach has been used in Ref. [ 21 ] to demonstrate the manner in which decoherence affects the quantum states of the loop. Lately [ 22 ], the same dissipators have been applied with success for analysis of the quantum dynamics of two electromagnetic oscillators coupled in series to a voltage-biased Josephson junction.…”