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arXiv:quant-ph/0410149 · Physical Review Letters

Cooling Mechanism for a Nanomechanical Resonator by Periodic Coupling to a Cooper Pair Box

Peng Zhang, Y. D. Wang, C. P. Sun

Published Aug 26, 2005• 94 citations
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Abstract

We propose and study an active cooling mechanism for the nanomechanical resonator (NAMR) based on periodical coupling to a Cooper pair box (CPB), which is implemented by a designed series of magnetic flux pluses threading through the CPB. When the initial phonon number of the NAMR is not too large, this cooling protocol is efficient in decreasing the phonon number by 2 to 3 orders of magnitude. Our proposal is theoretically universal in cooling various boson systems of a single mode. It can be specifically generalized to prepare the nonclassical state of the NAMR.

DOI
10.1103/physrevlett.95.097204

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Publisher’s Note: Cooling Mechanism for a Nanomechanical Resonator by Periodic Coupling to a Cooper Pair Box [Phys. Rev. Lett.95, 097204 (2005)]

P. Zhang, Y. D. Wang, C. P. Sun

Received 12 September 2005DOI:https://doi.org/10.1103/PhysRevLett.95.129901©2005 American Physical Society

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We propose and study an active cooling mechanism for the nanomechanical resonator (NAMR) based on periodical coupling to a Cooper pair box (CPB), which is implemented by a designed series of magnetic flux pluses threading through the CPB. When the initial phonon number of the NAMR is not too large, this cooling protocol is efficient in decreasing the phonon number by 2 to 3 orders of magnitude. Our proposal is theoretically universal in cooling various boson systems of a single mode. It can be specifically generalized to prepare the nonclassical state of the NAMR.
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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.
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We study phonon statistics in a nanomechanical resonator (NAMR) which is resonantly coupled to a qubit. We find that there are two different mechanisms for phonon blockade in such a resonantly coupled NAMR-qubit system. One is due to the strong anharmonicity of the NAMR-qubit system with large coupling strength; the other one is due to the destructive interference between different paths for two-phonon excitation in the NAMR-qubit system with a moderate coupling strength. We find that the phonon blockade is fragile towards thermal mode occupations and can only be observed for NAMR being at ultracold effective temperature. In order to enlarge the mean phonon number for strong phonon antibunching with a moderate NAMR-qubit coupling strength, we assume that two external driving fields are applied to the NAMR and qubit, respectively. In this case, we find that the phonon blockades under two mechanisms can appear at the same frequency regime by optimizing the strength ratio and phase difference of the two external driving fields.
We calculate the dynamics of a nanomechanical oscillator (NMO) coupled capacitively to a Cooper-pair box (CPB) by solving a stochastic Schr\"odinger equation with two Lindblad operators [Commun. Math. Phys. 48, 119 (1976).]. Both the NMO and the CPB are assumed dissipative, and the coupling is treated within the rotating wave approximation. We show numerically that, if the CPB decay time is smaller than the NMO decay time, the coupled NMO will lose energy faster and the coupled CPB more slowly than the uncoupled NMO and CPB do. The results show that the efficiency of energy loss by an NMO can be substantially increased if the NMO is coupled to a CPB.