Low energy wave packet tunneling from a parabolic potential well through a high potential barrier

The problem of wave packet tunneling in a potential V (x) = (mω2/2) ( x2 − δxν ) with ν > 2 is considered in the case when the barrier height is much greater than h̄ω and the difference between the average energy of the packet and the oscillator ground state energy h̄ω/2 is sufficiently small. The universal Poisson distribution of the partial tunneling rates from the oscillator energy levels is discovered. The explicit expressions for the tunneling rates of different types of packets (coherent, squeezed, even/odd, thermal, etc.) are given in terms of the exponential and modified Bessel functions. The tunneling rates turn out very sensitive to the energy distributions in the packets, and they may exceed significantly the tunneling rate from the energy state with the same average number of quanta.