  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.
