1. 2. 3. 4. 5. 6. 7. LITERATURE CITED V. A. Bobyrev, V. I. Boiko, F. V. Bunin, B. S. Luk'yanchuk, and E. V. Tsarev, Izv. AN SSSR, Ser. Fiz., 51, No. 6, 1180-1192 (1987). J. R. Manning, Diffusion Kinetics for Atoms in Crystals, Van Nostrand, New York (1968). L. D. Landau and E. M. Lifshits, Theory of Elasticity [in Russian], Nauka, Moscow (1988). M. A. Alieva, V. I. Emel'yanov, F. Kh. Mirzoev, and L. A. Shelepin, Kratk. Soobshch. Fiz. FIAN, No. i0, 43-55 (1988). A. M. Kosevich, Physical Mechanics of Real Crystals [in Russian], Naukova Dumka, Kiev (1981). V. I. Emel'yanov, P. K. Kashkarov, N. G. Chechenin, and T. Dietrich, Fiz. Tverd. Tela (Leningrad),30, No. 8, 2259-2263 (1988). V. N. Bagratashvili, A. F. Banishev, S. A. Gnedoi, et al., Preprint No. 32, NITs TL AN SSSR [in Russian], Troitsk (1987). CORRELATED STATES IN QUANTUM ELECTRONICS (RESONANT CIRCUIT) V. V. Dodonov,* V. I. Man'ko, and O. V. Man'ko% Coherent and correlated states of a Josephson junction are constructed. Quantum current and voltage noises are calculated. The influence of an external current and of parametric buildup on the Josephson junction is discussed. The feasi- bility in principle of exciting correlated and coherent states in a Josephson junction is suggested. The feasibility of using a Josephson junction (simulated by a quantum resonant circuit) to generate squeezed electromagnetic radiation was considered in [I]. Our purpose here is, by using the analogy between a Josephson junction and a quantum resonant circuit, to demonstrate the possible existence of a new Josephson-junction state - a correlated state - and to suggest the theoretical feasibility of exciting a correlated state by a parametric action that can lead effectively to a temporal variation of, say, the critical current of the junction. We carry out the analysis within the context of the Hamiltonian [2] I~ Q2 hi C h ^ = -- + -- (1-cos~o)- -- l(t)~o. (i) 2C 2e 2e Here C is the capacitance and IC the critica5 current of the junction, e the electron charge, h Planck's constant, Q the charge operator, ~ the phase operator, and I(t) the external cur- rent fed to the junction. The problem is investigated here in the region of small values of the phase ~ , when the term(l-cqs~) in the Hamiltonian (i) can be replaced by the quad- ratic expression ~__2 ; conditions for this have been discussed in [3]. The Hamiltonian (i) is thus reduced to2the Hamiltonian of a quantum resonant circuit 1~I c ~2 h 2C 2e 2 2e I (t)~. (2) *Moscow Physicotechnical Institute, Dolgoprudnyi. tNuclear Research Institute, Academy of Sciences of the USSR, Moscow. High-Energy Electron Laboratory. Translated from Preprint No. 89 of the Lebedev Physics Institute, Academy of Sciences of the USSR, Moscow, 1989. 0270-2010/89/1005-0413512.50 1989 Plenum Pub%ishing Corporation 413