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Journal of Shaanxi University of Science & Technology

DYNAMICS OF A TWO-LEVEL SYSTEM BEYOND RWA

Kang Jian-qiang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

With the time-dependent perturbation theory,the dynamics of a two-level system coupled to an Bose field is revisited.In this paper,the dynamics of the Cooper-pair box and a nanomechanical resonator system including the counter-rotating terms is considered.The simplest dynamical behavior is given when the oscillator begins in a displaced Fock state and Cooper-pair box(CPB) in,and to a certain extent,the result is the same to that with adiabatic approximation.

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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.
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Abstract. In this paper we present a scheme for ground state cooling of a flexural mode of a nanomechanical beam incorporated in a loop-shaped Cooper-pair box (CPB) circuit. Via the Lorentz force coupling of the beam motion to circulating CPB-circuit currents, energy is transferred to the CPB qubit which acts as a dissipative two-level system. The cooling process is driven by a detuned gate-voltage drive acting on the CPB. We analyze the cooling force spectrum and present analytical expressions for the cooling rate and final occupation number for a wide parameter regime. In particular, we find that cooling is optimized in a strong drive regime, and we present the necessary conditions for ground-state cooling. PACS numbers: 85.25.-j, 85.85.+j, 37.10.RsGround state cooling of a nanomechanical resonator via a Cooper pair box qubit 2
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