Coherence transition of small Josephson junctions coupled to a single-mode resonant cavity: Connection to the Dicke model

被引:1
作者
Kobayashi, Kohiiro [1 ]
Stroud, David [1 ]
机构
[1] Ohio State Univ, Dept Phys, Columbus, OH 43210 USA
来源
PHYSICA C-SUPERCONDUCTIVITY AND ITS APPLICATIONS | 2009年 / 469卷 / 5-6期
基金
美国国家科学基金会;
关键词
Josephson junctions; Electromagnetic cavity; Phase coherence; Dicke model; Coherent state; FREE-ELECTRON LASER; SPONTANEOUS EMISSION; PHASE-TRANSITION; ARRAYS; QUANTUM; SUPERRADIANCE; RADIATION; LOCKING; ATOMS;
D O I
10.1016/j.physc.2009.01.016
中图分类号
O59 [应用物理学];
学科分类号
摘要
We calculate the thermodynamic properties of a collection of N small Josephson junctions coupled to a single-mode resonant electromagnetic cavity, at finite temperature T, using several approaches. In the first approach, we include all the quantum-mechanical levels of the junction, but treat the junction-cavity interaction using a mean-field approximation developed previously for T = 0. In the other approaches, the junctions are treated including only the two lowest energy levels per junction, but with two different Harniltonians. The first of these maps onto the Dicke model of quantum optics. The second is a modified Dicke model which contains an additional XY-like coupling between the junctions. The modified Dicke model can be treated using a mean-field theory, which in the limit of zero XY coupling gives the solution of the Dicke model in the thermodynamic limit using Glauber coherent states to represent the cavity. In all cases, for an N-independent junction-cavity coupling, there is a critical junction number N above which there is a continuous transition from incoherence to coherence with decreasing T. If the coupling scales with N so as to give a well-behaved thermodynamic limit, there is a critical minimum coupling strength for the onset of coherence. In all three models, the cavity photon occupation numbers have a non-Bose distribution when the system is coherent. (C) 2009 Elsevier B.V. All rights reserved.
引用
收藏
页码:216 / 224
页数:9
相关论文
共 32 条
[11]   EXACT SOLUTION FOR SPONTANEOUS EMISSION IN THE PRESENCE OF N ATOMS [J].
CUMMINGS, FW ;
DORRI, A .
PHYSICAL REVIEW A, 1983, 28 (04) :2282-2285
[12]  
Dicke R.H., 1954, PHYS REV, V170, P379
[13]   Phase-locking in quantum and classical oscillators: polariton condensates, lasers, and arrays of Josephson junctions [J].
Eastham, PR ;
Szymanska, MH ;
Littlewood, PB .
SOLID STATE COMMUNICATIONS, 2003, 127 (02) :117-122
[14]   Model for a Josephson junction array coupled to a resonant cavity [J].
Harbaugh, JK ;
Stroud, D .
PHYSICAL REVIEW B, 2000, 61 (21) :14765-14772
[15]   SUPERRADIANT PHASE-TRANSITION FOR MOLECULES IN A QUANTIZED RADIATION FIELD - DICKE MASER MODEL [J].
HEPP, K ;
LIEB, EH .
ANNALS OF PHYSICS, 1973, 76 (02) :360-404
[16]   PHASE-TRANSITIONS IN SOME GENERALIZED DICKE MODELS OF SUPERRADIANCE [J].
HIOE, FT .
PHYSICAL REVIEW A, 1973, 8 (03) :1440-1445
[17]   MUTUAL PHASE-LOCKING IN JOSEPHSON JUNCTION ARRAYS [J].
JAIN, AK ;
LIKHAREV, KK ;
LUKENS, JE ;
SAUVAGEAU, JE .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 1984, 109 (06) :309-426
[18]  
Jeffreys H., 1966, METHODS MATH PHYS, P503
[19]   EFFECT OF DIPOLE INTERACTION AND PHASE-INTERRUPTING COLLISIONS ON THE COLLAPSE-AND-REVIVAL PHENOMENON IN THE JAYNES-CUMMINGS MODEL [J].
JOSHI, A ;
PURI, RR ;
LAWANDE, SV .
PHYSICAL REVIEW A, 1991, 44 (03) :2135-2140
[20]  
Kobayashi K., UNPUB