Quantum versus classical phase-locking transition in a frequency-chirped nonlinear oscillator
Quantum versus classical phase-locking transition in a frequency-chirped nonlinear oscillator
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DOI：
10.1103/physreva.84.013837
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发表时间：
2011-04
影响因子：
2.9
通讯作者：
I. Barth;L. Friedland;O. Gat;A. Shagalov
中科院分区：
文献类型：
--
作者：
I. Barth;L. Friedland;O. Gat;A. Shagalov
无噪声参数P1 =“/2 m ~！P2 =（3~ φ）/（4 m φ）（“、”、“和！0是驱动幅度、频率啁啾率、非线性参数和振荡器的线性频率）。结果表明，对于P2 <$1，通过线性共振在足够大的P1产生经典的自共振（AR）的系统中，即使在量子基态开始。相比之下，对于P2 π 1，跃迁涉及量子力学能量阶梯攀登（LC）。计算了在AR和LC极限下的锁相跃迁阈值及其在P1中的宽度。通过求解能量基中的薛定谔方程和相空间中的维格纳函数对理论结果进行了验证。PACS编号：42.50.Hz、42.50.Lc、33.80.Wz、05.45.Xt
sionless parameters P1 = "/ √ 2m~!0� and P2 = (3~�)/(4m √ �) (", �, � and !0 being the driving amplitude, the frequency chirp rate, the nonlinearity parameter and the linear frequency of the oscillator). It is shown that for P2 ≪ 1, the passage through the linear resonance at sufficiently large P1 yields classical autoresonance (AR) in the system, even when starting in a quantum ground state. In contrast, for P2 ≫ 1, the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in P1 in both AR and LC limits are calculated. The theoretical results are tested by solving the Schrodinger equation in the energy basis and illustrated via the Wigner function in phase space. PACS numbers: 42.50.Hz, 42.50.Lc, 33.80.Wz, 05.45.Xt