Lower limit on the achievable temperature in resonator-based sideband cooling

Physical Review B - Condensed Matter and Materials Physics

Volumn 78, Issue 3, 2008, Pages

  Grajcar, M ^a,b   Ashhab, S ^a,c   Johansson, J R ^a   Nori, Franco ^a,c,d  

^a INST OF PHYS AND CHEMICAL RESEARCH   (Japan)

^b Physics and Informatics   (Slovakia)

^c UNIVERSITY OF MICHIGAN   (United States)

^d JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 46749124664     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.78.035406     Document Type: Article

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30. It should be emphasized here that the presence of a nonlinearity in the Hamiltonian is crucial for the cooling mechanism. In other words, a completely linear system [i.e., a system composed of two linear oscillators that are coupled linearly to each other, to the environment, and to the driving force (Ref.)] will not experience any thermal change in the presence or absence of an ideal driving force. The nonlinearity can therefore be seen as a mixer between the resonator frequency and the driving frequency that allows the "upconversion" of vibrational quanta and therefore cooling.
31. In this paper we use the convention where linear coupling between two harmonic oscillators means a coupling term of the form g (α ar + α ar†) (β am + β am†) and linear coupling to the driving force means a term of the form (ζ ar + ζ ar† +η am + η am†) cos (ωp t+θ), where α, β, ζ, η, ωp, and θ are constants. Under this convention parametric driving, i.e., when the coupling strength g in Eq. 24 is modulated by an externally applied signal, corresponds to a nonlinear driving term. Although such parametric driving can be used to implement the sideband cooling mechanism, in this paper we are only considering the case where the externally applied driving signal couples to the charge on the resonator, i.e., a linear driving term according to the convention that we follow. Since we further assume a linear mechanical oscillator and linear coupling to the environment (in the case of linear oscillators), a nonlinearity is needed either in the coolant Hamiltonian or the coupling term.
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