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arXiv:1106.3379 · Chinese Physics Letters

Controlling Excitation Inversion of a Cooper Pair Box Interacting with a Nanomechanical Resonator

Clodoaldo Valverde, Heibbe C. B. de Oliveira, Ardiley Torres Avelar, B. Baseia

Published Aug 1, 2012• 3 citations

Abstract

We investigate the action of time-dependent detunings upon the excitation inversion of a Cooper pair box interacting with a nanomechanical resonator. The method employs the Jaynes-Cummings model with damping, assuming different decay rates of the Cooper pair box and various fixed and time-dependent detunings. It is shown that, when the presence of damping plus constant detunings destroys the collapse/revival effects, convenient choices of time-dependent detunings allow one to reconstruct such events in a perfect way. It is also shown that the mean excitation of the nanomechanical resonator is more robust against damping of the Cooper pair box for convenient values of time-dependent detunings.

DOI: 10.1088/0256-307x/29/8/080303

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•Jan 1, 2012•0 citations

We investigate the action of time-dependent detunings upon the excitation inversion of a Cooper pair box interacting with a nanomechanical resonator. The method employs the Jaynes-Cummings model with damping, assuming different decay rates of the Cooper pair box and various fixed and time-dependent detunings. It is shown that, when the presence of damping plus constant detunings destroys the collapse/revival effects, convenient choices of time-dependent detunings allow one to reconstruct such events in a perfect way. It is also shown that the mean excitation of the nanomechanical resonator is more robust against damping of the Cooper pair box for convenient values of time-dependent detunings.

We show two effects as a result of considering the second-order correction to the spectrum of a nanomechanical resonator electrostatically coupled to a Cooper-pair box. The spectrum of the Cooper-pair box is modified in a way which depends on the Fock state of the resonator. Similarly, the frequency of the resonator becomes dependent upon the state of the Cooper-pair box. We consider whether these frequency shifts could be utilized to prepare the nanomechanical resonator in a Fock state, to perform a quantum non-demolition measurement of the resonator Fock state, and to distinguish the phase states of the Cooper-pair box.

We propose a scheme to demonstrate the electromagnetically induced transparency (EIT) in a system consisting of a superconducting Cooper-pair box (CPB) coupled to a nanomechanical resonator (NR). In this scheme, the NR plays an important role to contribute additional auxiliary energy levels to the CPB so that the EIT phenomenon could be realized in such a system. We call it, in this paper, resonator-assisted induced transparency (RAIT). The RAIT technique provides a detection scheme in a real experiment to measure physical properties, such as the vibration frequency and the decay rate, of the coupled NR.

In this work we used an arrangement consisting of Cooper pairs (Cooper Pair Box, CPB) interacting with a nanomechanical Resonator (NR) for various studies: to produce controlable holes in the statistical distribution of excitations of the NR, for resonant and non-resonant cases; to study the evolution of the entropy and the inversion of excitations, including losses in the CPB; and to study the evolution of the Wigner function under the infuence of a reservoir. We have obtained the exact solution of the master equation describing the non-degenerate parametric amplifier interacting with a generalized model of linear phase sensitive reservoir, having the form of the equation equivalent to that of the Fokker-Planck propagator for the Wigner function. We have calculated the Wigner function describing the temporal evolution of a state initially in a superposition of two coherent states, a kind of "Schr?odinger cat", and finally, we have also studied the temporal evolution of the negativity of this function, one of the indicators of nonclassicality of vibrational states of the NR.