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Fast cooling in dispersively and dissipatively coupled optomechanics.

Chen T, Wang XB - Sci Rep (2015)

Bottom Line: We show that there is distinct advantage in using the chirp-pulse scheme to cool a resonator rapidly.The cooling behaviors of dispersively and dissipatively coupled system is also explored with different types of incident pulses and different coupling strengths.Our scheme is feasible in cooling the resonator for a wide range of the parameter region.

View Article: PubMed Central - PubMed

Affiliation: 1] State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China [2] Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.

ABSTRACT
The cooling performance of an optomechanical system comprising both dispersive and dissipative coupling is studied. Here, we present a scheme to cool a mechanical resonator to its ground state in finite time using a chirped pulse. We show that there is distinct advantage in using the chirp-pulse scheme to cool a resonator rapidly. The cooling behaviors of dispersively and dissipatively coupled system is also explored with different types of incident pulses and different coupling strengths. Our scheme is feasible in cooling the resonator for a wide range of the parameter region.

No MeSH data available.


The time evolution of the phonon number 〈nosc〉 = 〈δb†δb〉.(a) Blue solid one denotes the chirped pulse form, red dashed one is the no-chirped form. Other parameters: A = 0, B = 2 * 10−4, κ/ωm = 0.01, γ/ωm = 10−5, Nth = 100, 〈a(0)〉 = 200, Δ/ωm = −1. For the chirped pulse form, α/ωm = 0.14, β/ωm = 0.04, , ωmt0 = 40. (b) (chirped pulse form) and (c) (no-chirped pulse form), A = 0, B = 2 * 10−4, γ/ωm = 10−6, Nth = 50, 〈a(0)〉 = 103, Δ/ωm = 0.5; for the chirped pulse form (b), α/ωm = 0.15, β/ωm = 0.05, , ωmt0 = 30.
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f1: The time evolution of the phonon number 〈nosc〉 = 〈δb†δb〉.(a) Blue solid one denotes the chirped pulse form, red dashed one is the no-chirped form. Other parameters: A = 0, B = 2 * 10−4, κ/ωm = 0.01, γ/ωm = 10−5, Nth = 100, 〈a(0)〉 = 200, Δ/ωm = −1. For the chirped pulse form, α/ωm = 0.14, β/ωm = 0.04, , ωmt0 = 40. (b) (chirped pulse form) and (c) (no-chirped pulse form), A = 0, B = 2 * 10−4, γ/ωm = 10−6, Nth = 50, 〈a(0)〉 = 103, Δ/ωm = 0.5; for the chirped pulse form (b), α/ωm = 0.15, β/ωm = 0.05, , ωmt0 = 30.

Mentions: We numerically obtain the residual phonon number of the mechanical resonator (〈δb†δb〉) as a function of time. For comparison, two different schemes are provided: with chirped pulse (chirped pulse scheme) and without the chirped pulse (no-chirped pulse scheme). The different driven frequencies ωd are discussed below. Here, the cavity detuning is Δ = ωd − ωc. From Fig. 1(a), when Δ/ωm = −1, we find that at time ωmt = 80 or longer, the phonon number of the mechanical resonator can be reduced to a relatively low value and kept stable for the chirped pulse cooling scheme. The figure inset shows the amplitude of the laser drive Ω(t) with time. By employing the Fourier transform, we find that the full width at half maximum (FWHM) of such a pulse Ω(t) is about 0.05ωm. So for the case of ωmt0 = 40, the effect of pulse bandwidth is neglectable. While, for the no-chirped pulse scheme, the cooling effect of the resonator is not well-behaved, and the phonon number changes with time drastically. Although the small phonon occupation number of the resonator is achieved in the no-chirped pulse case for some time interval, the phonon occupation quickly raises to a high value at later time. It means that we do not achieve perfect cooling of resonator with the no-chirped pulse scheme. Next, another driven frequency is applied (Δ/ωm = 0.5). In our parameters settings (A = 0, B ≠ 0, a purely dissipative optomechanics), this value of driven frequency is the optimal one for the steady state cooling of resonator333536. The cooling behaviors with different cavity damping strengths are shown in Fig. 1(b) and (c). Compared with the cooling results of the no-chirped pulse scheme, an improved cooling performance of the resonator is acheived with the chirped pulse. Taking the cavity damping strength κ/ωm = 0.5 as an example, in the chirped pulse scheme, at time ωmt = 70, the mechanical resonator number (〈δb†δb〉) reaches the value 1.6, which is much smaller than the case with the no-chirped pulse scheme.


Fast cooling in dispersively and dissipatively coupled optomechanics.

Chen T, Wang XB - Sci Rep (2015)

The time evolution of the phonon number 〈nosc〉 = 〈δb†δb〉.(a) Blue solid one denotes the chirped pulse form, red dashed one is the no-chirped form. Other parameters: A = 0, B = 2 * 10−4, κ/ωm = 0.01, γ/ωm = 10−5, Nth = 100, 〈a(0)〉 = 200, Δ/ωm = −1. For the chirped pulse form, α/ωm = 0.14, β/ωm = 0.04, , ωmt0 = 40. (b) (chirped pulse form) and (c) (no-chirped pulse form), A = 0, B = 2 * 10−4, γ/ωm = 10−6, Nth = 50, 〈a(0)〉 = 103, Δ/ωm = 0.5; for the chirped pulse form (b), α/ωm = 0.15, β/ωm = 0.05, , ωmt0 = 30.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4291557&req=5

f1: The time evolution of the phonon number 〈nosc〉 = 〈δb†δb〉.(a) Blue solid one denotes the chirped pulse form, red dashed one is the no-chirped form. Other parameters: A = 0, B = 2 * 10−4, κ/ωm = 0.01, γ/ωm = 10−5, Nth = 100, 〈a(0)〉 = 200, Δ/ωm = −1. For the chirped pulse form, α/ωm = 0.14, β/ωm = 0.04, , ωmt0 = 40. (b) (chirped pulse form) and (c) (no-chirped pulse form), A = 0, B = 2 * 10−4, γ/ωm = 10−6, Nth = 50, 〈a(0)〉 = 103, Δ/ωm = 0.5; for the chirped pulse form (b), α/ωm = 0.15, β/ωm = 0.05, , ωmt0 = 30.
Mentions: We numerically obtain the residual phonon number of the mechanical resonator (〈δb†δb〉) as a function of time. For comparison, two different schemes are provided: with chirped pulse (chirped pulse scheme) and without the chirped pulse (no-chirped pulse scheme). The different driven frequencies ωd are discussed below. Here, the cavity detuning is Δ = ωd − ωc. From Fig. 1(a), when Δ/ωm = −1, we find that at time ωmt = 80 or longer, the phonon number of the mechanical resonator can be reduced to a relatively low value and kept stable for the chirped pulse cooling scheme. The figure inset shows the amplitude of the laser drive Ω(t) with time. By employing the Fourier transform, we find that the full width at half maximum (FWHM) of such a pulse Ω(t) is about 0.05ωm. So for the case of ωmt0 = 40, the effect of pulse bandwidth is neglectable. While, for the no-chirped pulse scheme, the cooling effect of the resonator is not well-behaved, and the phonon number changes with time drastically. Although the small phonon occupation number of the resonator is achieved in the no-chirped pulse case for some time interval, the phonon occupation quickly raises to a high value at later time. It means that we do not achieve perfect cooling of resonator with the no-chirped pulse scheme. Next, another driven frequency is applied (Δ/ωm = 0.5). In our parameters settings (A = 0, B ≠ 0, a purely dissipative optomechanics), this value of driven frequency is the optimal one for the steady state cooling of resonator333536. The cooling behaviors with different cavity damping strengths are shown in Fig. 1(b) and (c). Compared with the cooling results of the no-chirped pulse scheme, an improved cooling performance of the resonator is acheived with the chirped pulse. Taking the cavity damping strength κ/ωm = 0.5 as an example, in the chirped pulse scheme, at time ωmt = 70, the mechanical resonator number (〈δb†δb〉) reaches the value 1.6, which is much smaller than the case with the no-chirped pulse scheme.

Bottom Line: We show that there is distinct advantage in using the chirp-pulse scheme to cool a resonator rapidly.The cooling behaviors of dispersively and dissipatively coupled system is also explored with different types of incident pulses and different coupling strengths.Our scheme is feasible in cooling the resonator for a wide range of the parameter region.

View Article: PubMed Central - PubMed

Affiliation: 1] State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, People's Republic of China [2] Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China.

ABSTRACT
The cooling performance of an optomechanical system comprising both dispersive and dissipative coupling is studied. Here, we present a scheme to cool a mechanical resonator to its ground state in finite time using a chirped pulse. We show that there is distinct advantage in using the chirp-pulse scheme to cool a resonator rapidly. The cooling behaviors of dispersively and dissipatively coupled system is also explored with different types of incident pulses and different coupling strengths. Our scheme is feasible in cooling the resonator for a wide range of the parameter region.

No MeSH data available.